[ { "task_id": "RS_02", "query_token_num": 287, "Engineering Domain": "Mechanical Systems", "prompt": "I have attached a file SetupFile.json. SetupFile.json includes parameters of the car in the format\n{\n \"setupName\" : \"Gp2Dummy\",\n \"mcar\"\t: 728,\n \"clt\"\t: 3.1,\n \"cx\"\t: 1.0,\n \"afrcar\"\t: 1.0,\n \"mbrk\"\t: 7000,\n \"gripx\"\t: 1.15,\n \"gripy\"\t: 1.40,\n \"loadEff\"\t: 0.10,\n \"rtyre\"\t: 0.32,\n \"rGearRat\"\t: [10.0,7.8,6.1,7.8,5.2,4.5,4.0],\n \"reff\"\t: 0.95,\n \"EngNm\"\t: [200,300,430,380],\n \"EngRpm\"\t: [0,3000,7000,10000],\n \"rho\"\t: 1.22\n}\n\n\n#Task 1\nCompute the maximum possible acceleration the car can achieve.\n\n#Task 2\nCompute the maximum possible deceleration the car can achieve under braking.\n\nPlease use consistent SI units and represent acceleration and deceleration in m/s^2.", "contributor": "Rushabh Prasad Shetty" }, { "task_id": "WJ_01", "query_token_num": 1337, "Engineering Domain": "Signal Processing", "prompt": "Task Description\n\nConsider an image denoising task where a grayscale image is corrupted by additive noise. \nThe image is represented as a NumPy array in Python. The goal is to design a filter pipeline using a Large Language Model (LLM) \nthat reads the noisy image and returns a denoised version 'filtered_img'\nThe input image 'img' is available as a NumPy array and you will get the image encoded using base64 method. \nYou need to analyze the type of noise added into the image carefully. If only one type of noise is added maybe one or two carefully selected filters which are specially designed for the noise is enough. \nIf the image is corrupted by a mixture of different noise task will be complicated. One to two filters may not be enough so \nyou may need to use a series of filters. No prior knowledge is given on the exact noise parameters.\nExplore and combine **a diverse set of filters** available in OpenCV when the task is complicated. Do not just simply rely on gaussian and median filters when you think they are not sufficient, try more filters. \nFeel free to use simple function deisgn when you think that the noise is simple and one or two single filters such as gaussian filter or median filter are enough to finish the task. In this case, do not make the design complicated, \nif a single filter may work, just use a single filter. \nMake sure the generated code is executable so you must carefully review your code after you finish the function. \nInput image is a color image so the output image should also be a color image with shape (3, 512, 512). \n\nTask\n\nDesign a sequence of filters to denoise the input image. The LLM should:\n1. Read and analyze the data in the image. If there's only a single type of noise, tell me the name and if there's a mixture of different noise list the types of noise. \n\n2. Review common types of noise, their characteristic and their filter strateg. Explain the filtering strategy: list each filter to be applied in order, along with the motivation for its use (e.g., remove salt-and-pepper noise, preserve edges while reducing Gaussian noise).\n\n3. Specify filter parameters: for each filter, clearly define its parameters (e.g., kernel size, sigma, threshold).\n\n4. Generate executable code: write a Python function named denoise_image that takes 'img' as input, applies the filter pipeline step by step using standard Python libraries (e.g., NumPy, OpenCV, SciPy), and outputs the denoised image in the variable 'filtered_img'.\n\nThe function must be a single Python code block, like this: \n def denoise_image(noisy_img):\n # your code \n \n return filtered_img\n\nWhen I evaluate the results, I focuses on how much information you can recover from the noisy image \nand I will use MSE and PSNR as matrics. So please denoise the image as much as possible while keeping the original detailed informarion and texture. \nHere shows how I will evaluate your response by running the function you provide: \n\ndef evaluate_llm_response(llm_response):\n \"\"\"\n Evaluate the image filtering code returned by the LLM.\n Load the only image in 'images', denoise it using LLM code, save result to 'results' folder,\n and compute MSE and PSNR using a known reference (if needed).\n \"\"\"\n\n confidence = 100 # Confidence score assigned to the evaluation\n\n # === Step 1: Locate the only image in 'images' ===\n input_folder = 'images'\n image_files = [f for f in os.listdir(input_folder)\n if f.lower().endswith(('.png', '.jpg', '.jpeg'))]\n\n if len(image_files) != 1:\n raise ValueError(\"The 'images' folder must contain exactly one image.\")\n\n image_name = image_files[0]\n image_path = os.path.join(input_folder, image_name)\n noisy_img = cv2.imread(image_path)\n\n original_img = cv2.imread('original_image.png')\n\n if noisy_img is None:\n raise IOError(f\"Failed to read image: {image_path}\")\n\n # === Step 2: Execute LLM code to perform denoising ===\n function_code = llm_response.config.function_code\n\n with open(\"function.txt\", \"w\", encoding=\"utf-8\") as file:\n file.write(function_code)\n\n exec_globals = {'np': np, 'cv2': cv2, 'img_noisy': noisy_img}\n exec(function_code, exec_globals)\n\n filtered_img = exec_globals['denoise_image'](noisy_img)\n\n # === Step 3: Save result to 'results' folder ===\n os.makedirs('results', exist_ok=True)\n base_name, ext = os.path.splitext(image_name)\n output_path = os.path.join('results', f\"{base_name}_filtered{ext}\")\n cv2.imwrite(output_path, filtered_img)\n\n # === Step 4: Evaluation step (optional) ===\n # Since we don't have a clean original image here, we cannot compute real MSE/PSNR.\n # You can skip this part or use dummy values if reference is unavailable.\n mse = mean_squared_error(original_img.flatten(), filtered_img.flatten())\n psnr = cv2.PSNR(original_img, filtered_img)\n passed = mse < 100 \n\n\n MSE_best = 0 \n MSE_worst = 500 \n PSNR_best = 40 \n PSNR_worst = 10 \n\n w_psnr = 0.7\n w_mse = 0.3\n mse_norm = max(0, min(1, (MSE_worst - mse) / (MSE_worst - MSE_best)))\n psnr_norm = max(0, min(1, (psnr - PSNR_worst) / (PSNR_best - PSNR_worst))) \n score = 100 * (w_mse * mse_norm + w_psnr * psnr_norm) \n\n metrics = {\"mse\": mse, \"psnr\": psnr}\n print(score)\n # print(llm_response.config.denoising_strategy)\n details = {\n \"strategy\": llm_response.config.denoising_strategy,\n \"score\": metrics,\n \"denoising function\": function_code\n }\n\n return passed, details, score, confidence", "contributor": "Weijie Liang" }, { "task_id": "RK_02", "query_token_num": 202, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nThis is a mulitple design load problem. \nDesign domain is a 2D rectangular region in cartesian coordinate, with vertices at (0,0), (6,0), (6,1), (0,1). \nVertically downward point loads are applied at (2,1) & (4,1). Pin support is at (0,0) and roller support is at (6,0). \nLx = 6 and Ly = 1.\nThe filter radius is R = 0.03*max(Lx,Ly).\nThe filter exponent is 3.\n\n\n---\n\n### Task\n\nYour task is to:\n- Obtain a topology optimized design that has minimum structural compliance and volume fraction not exceeding 0.25.\n- Given the optimized design, output the corresponding minimum structural compliance, named C_y_hat, and also its volume fraction, named vf, in numerical numbers. Note that vf is in the range of [0,1]. \n", "contributor": "Rahul Kundu, Yilan Jiang" }, { "task_id": "AV_03", "query_token_num": 196, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\nIn this task, you are required to design a system to downsample a digital audio signal from 48kHz to 8kHz. Before downsampling, we need an anti-aliasing filter. Design this filter.\n\n### Design Constraints\nThe input signal is sampled at 48kHz.\nThe output signal is sampled at 8kHz.\nThe useful frequency bandwidth of the original signal is between 0 and 3.5kHz, and it must be preserved with minimal distortion (Attenuation less than 3dB, Ripple amplitude less than 3dB)\nYou must ensure that the useful frequency bandwidth is unaffected by aliasing. Thus, determine the beginning frequency of the stopband.\nEnsure that your filter is FIR.\n\n### Response Specifications\nProvide the following information as your response.\n- The filter order\n- A list of the filter's coefficients\n- The beginning frequency of the stopband\n- The decimation factor", "contributor": "Aditya Venkatesh" }, { "task_id": "RS_03", "query_token_num": 296, "Engineering Domain": "Mechanical Systems", "prompt": "I have attached a file SetupFile.json. SetupFile.json includes parameters of the car in the format\n{\n \"setupName\" : \"Gp2Dummy\",\n \"mcar\"\t: 728,\n \"clt\"\t: 3.1,\n \"cx\"\t: 1.0,\n \"afrcar\"\t: 1.0,\n \"mbrk\"\t: 7000,\n \"gripx\"\t: 1.15,\n \"gripy\"\t: 1.40,\n \"loadEff\"\t: 0.10,\n \"rtyre\"\t: 0.32,\n \"rGearRat\"\t: [10.0,7.8,6.1,7.8,5.2,4.5,4.0],\n \"reff\"\t: 0.95,\n \"EngNm\"\t: [200,300,430,380],\n \"EngRpm\"\t: [0,3000,7000,10000],\n \"rho\"\t: 1.22\n}\n\n#Task\nCompute the maximum possible load on the neck of the driver when the car is cornering. Assume the mass of the head to be 5kg and the mass of the helmet equal to 2kg.\n\nPlease use consistent SI units and compute the load in Newtons (N).", "contributor": "Rushabh Prasad Shetty" }, { "task_id": "XY_01", "query_token_num": 1715, "Engineering Domain": "Digital Hardware Design", "prompt": "# Tetris Block ROM Analysis\n\n## Background\nYou are working with a hardware implementation of a Tetris game. The game uses a ROM (Read-Only Memory) to store the shapes of different Tetris blocks (tetrominoes) in various rotational states. Each tetromino is represented as a 4x4 grid of bits, where '1' indicates a filled cell and '0' indicates an empty cell.\n\n## Font ROM Data\nThe ROM contains the following tetromino patterns:\n\n1. I-tetromino (straight piece):\n - Rotation 0: [[0,0,0,0], [1,1,1,1], [0,0,0,0], [0,0,0,0]]\n - Rotation 1: [[0,1,0,0], [0,1,0,0], [0,1,0,0], [0,1,0,0]]\n - Rotation 2: [[0,0,0,0], [0,0,0,0], [1,1,1,1], [0,0,0,0]]\n - Rotation 3: [[0,0,1,0], [0,0,1,0], [0,0,1,0], [0,0,1,0]]\n\n2. O-tetromino (square piece):\n - Rotation 0: [[0,0,0,0], [0,1,1,0], [0,1,1,0], [0,0,0,0]]\n - Rotation 1: [[0,0,0,0], [0,1,1,0], [0,1,1,0], [0,0,0,0]]\n - Rotation 2: [[0,0,0,0], [0,1,1,0], [0,1,1,0], [0,0,0,0]]\n - Rotation 3: [[0,0,0,0], [0,1,1,0], [0,1,1,0], [0,0,0,0]]\n\n3. T-tetromino:\n - Rotation 0: [[0,0,0,0], [0,1,0,0], [1,1,1,0], [0,0,0,0]]\n - Rotation 1: [[0,0,0,0], [0,1,0,0], [0,1,1,0], [0,1,0,0]]\n - Rotation 2: [[0,0,0,0], [0,0,0,0], [1,1,1,0], [0,1,0,0]]\n - Rotation 3: [[0,0,0,0], [0,1,0,0], [1,1,0,0], [0,1,0,0]]\n\n4. L-tetromino:\n - Rotation 0: [[0,0,0,0], [0,0,1,0], [1,1,1,0], [0,0,0,0]]\n - Rotation 1: [[0,0,0,0], [0,1,0,0], [0,1,0,0], [0,1,1,0]]\n - Rotation 2: [[0,0,0,0], [0,0,0,0], [1,1,1,0], [1,0,0,0]]\n - Rotation 3: [[0,0,0,0], [1,1,0,0], [0,1,0,0], [0,1,0,0]]\n\n5. J-tetromino:\n - Rotation 0: [[0,0,0,0], [1,0,0,0], [1,1,1,0], [0,0,0,0]]\n - Rotation 1: [[0,0,0,0], [0,1,1,0], [0,1,0,0], [0,1,0,0]]\n - Rotation 2: [[0,0,0,0], [0,0,0,0], [1,1,1,0], [0,0,1,0]]\n - Rotation 3: [[0,0,0,0], [0,1,0,0], [0,1,0,0], [1,1,0,0]]\n\n6. Z-tetromino:\n - Rotation 0: [[0,0,0,0], [1,1,0,0], [0,1,1,0], [0,0,0,0]]\n - Rotation 1: [[0,0,0,0], [0,0,1,0], [0,1,1,0], [0,1,0,0]]\n - Rotation 2: [[0,0,0,0], [0,0,0,0], [1,1,0,0], [0,1,1,0]]\n - Rotation 3: [[0,0,0,0], [0,1,0,0], [1,1,0,0], [1,0,0,0]]\n\n7. S-tetromino:\n - Rotation 0: [[0,0,0,0], [0,1,1,0], [1,1,0,0], [0,0,0,0]]\n - Rotation 1: [[0,0,0,0], [0,1,0,0], [0,1,1,0], [0,0,1,0]]\n - Rotation 2: [[0,0,0,0], [0,0,0,0], [0,1,1,0], [1,1,0,0]]\n - Rotation 3: [[0,0,0,0], [1,0,0,0], [1,1,0,0], [0,1,0,0]]\n\n## Task Description\nYou are given a SystemVerilog module called `font_rom` that contains the ROM definitions for all seven standard Tetris pieces (I, O, T, L, J, Z, S) in their four possible rotational states. Your task is to:\n\n1. Analyze the ROM content to identify and extract specific tetromino shapes\n2. Generate visual representations of requested tetrominoes\n\nPlease analyze the following tetromino:\nTetromino: I\nRotation: 1\n\n## Requirements\n1. Extract the bit pattern for a specified tetromino and rotation\n2. Convert the bit pattern to a visual representation using characters (e.g., '#' for filled cells, '.' for empty cells)\n\n## Input Format\n- Tetromino type: specified as a string ('I', 'O', 'T', 'L', 'J', 'Z', 'S')\n- Rotation: specified as an integer (0, 1, 2, 3) representing the rotational state\n\n## Output Format\nYour solution should provide:\n1. The extracted bit pattern as a 4x4 grid\n2. A visual representation of the pattern\n\n## Example Response\n\nInput: Z-tetromino, Rotation 0\n\nOutput :\n \"config\": {\n \"tetromino_type\": \"Z\",\n \"rotation\": 0\n },\n \"tetromino_pattern\": {\n \"bit_grid\": [\n [0, 0, 0, 0],\n [1, 1, 0, 0],\n [0, 1, 1, 0],\n [0, 0, 0, 0]\n ],\n \"visual\": [\n \"....\",\n \"##..\",\n \".##.\",\n \"....\"\n ]\n }\n}", "contributor": "XiangYi Kong" }, { "task_id": "AB_01", "query_token_num": 741, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\nRadiomics involves extracting quantitative features from medical images. This task requires calculating statistical and texture features for pixels within a specific polygonal region of interest (ROI) inside a given image patch.\n\n**Given Data:**\n1. **Image Patch Intensities** (as a 10x10 matrix representing tissue):\n ```\n [[15, 18, 20, 23, 26, 29, 32, 35, 38, 41],\n [17, 20, 23, 26, 29, 32, 35, 38, 41, 44],\n [19, 22, 25, 28, 31, 34, 37, 40, 43, 46],\n [21, 24, 27, 30, 33, 36, 39, 42, 45, 48],\n [23, 26, 29, 32, 35, 38, 41, 44, 47, 50],\n [25, 28, 31, 34, 37, 40, 43, 46, 49, 52],\n [27, 30, 33, 36, 39, 42, 45, 48, 51, 54],\n [29, 32, 35, 38, 41, 44, 47, 50, 53, 56],\n [31, 34, 37, 40, 43, 46, 49, 52, 55, 58],\n [33, 36, 39, 42, 45, 48, 51, 54, 57, 60]]\n ```\n2. **Polygon ROI Vertices** (defining the boundary within the patch, using 0-based indexing where (0,0) is the top-left pixel):\n `(2,2), (2,7), (7,7), (7,2)`\n *(Note: These vertices define the boundary edges of the polygon)*\n\n**Your Task:**\n1. Identify all pixel coordinates $(row, column)$ that lie strictly *inside* the polygon defined by the given vertices. (Assume integer coordinates represent pixel centers).\n2. Extract the intensity values of these interior pixels.\n3. Calculate the following **first-order statistics** for the extracted intensity values:\n * Mean\n * Variance (use sample variance, N-1 denominator)\n * Skewness\n * Kurtosis (Fisher's definition, i.e., excess kurtosis)\n4. Construct the Gray-Level Co-occurrence Matrix (GLCM) for the *interior pixels only*, using horizontal adjacency (offset `[0, 1]`, distance=1, angle=0 degrees). Assume pixel intensities are used directly without quantization. The GLCM should only consider pairs where both pixels are inside the polygon. Normalize the GLCM so that its elements sum to 1.\n5. Calculate the **Contrast** feature from the normalized GLCM using the formula: $Contrast = \\sum_{i,j} |i-j|^2 p(i,j)$, where $p(i,j)$ is the normalized GLCM value at intensity level pair $(i,j)$.\n\nReport the calculated float values for Mean, Variance, Skewness, Kurtosis, and GLCM Contrast. Provide numerical results rounded to 4 decimal places.", "contributor": "Ayush Barik" }, { "task_id": "AV_02", "query_token_num": 198, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\nIn this task, you are required to design a digital IIR filter, used to eliminate a particular resonant frequency that is affecting a sensor reading.\n\n### Design Constraints\nThe sensor signal is being sampled at a rate of 2000Hz.\nThe resonant frequency you should eliminate is 120Hz.\nYour filter should strongly attenuate the resonant frequency. (Attenuation more than 40dB)\nYour filter should minimally affect frequencies more than 5Hz below the resonant frequency. (Attenuation less than 3dB at 115Hz)\nYour filter should minimally affect frequencies more than 5Hz above the resonant frequency. (Attenuation less than 3dB at 125Hz)\n\n### Response Specifications\nProvide the following information as your response.\n- The filter order\n- A list of the filter's numerator coefficients (Provide ALL of them)\n- A list of the filter's denominator coefficients (Provide ALL of them)", "contributor": "Aditya Venkatesh" }, { "task_id": "libin2_01", "query_token_num": 338, "Engineering Domain": "Operating System Design", "prompt": "## Task Description\n\nYou are an operating\u2011system architect tasked with designing a unified multi\u2011level page\u2011table scheme that must satisfy the following two physical\u2011memory scenarios:\n\nDevice | Physical Memory | Max Page\u2011Table Memory Overhead | Required Avg. Address Translation Time | TLB Access Time | Per\u2011Level PTE Access Time \n---------- | --------------- | ------------------------------ | -------------------------------------- | --------------- | -------------------------- \nDevice A | 150\u00a0MB | \u2264\u00a0320\u00a0KB | \u2264\u00a0150\u00a0ns | 20\u00a0ns | 100\u00a0ns \nDevice B | 2\u00a0GB | \u2264\u00a04.05\u00a0MB | \u2264\u00a0150\u00a0ns | 20\u00a0ns | 100\u00a0ns \n\nAdditionally, we specify:\n\n1. Virtual addresses are 40\u00a0bits (byte\u2011addressable). \n2. Each PTE is 8\u00a0bytes. \n3. The TLB hit rate h as a function of page size is: \n h(page_size) = exp(-0.1542*(page_size/1024 - 5.82)**2)\n\nPlease design, for Device A and Device B, a multi\u2011level page\u2011table structure including: \n1. page_size: page size (bytes) \n2. levels: number of levels \n3. entries_per_level: list of entries per level \n\nAnd compute: \n- page_table_memory: total page\u2011table memory overhead (bytes), assuming on\u2011demand allocation only for mapped regions \n- avg_translation_time: average address\u2011translation time (ns), including only TLB access and PTE accesses ", "contributor": "Libin Wang" }, { "task_id": "RK_03", "query_token_num": 188, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nThis is a michell structure. \nDesign domain is a 2D rectangular region in cartesian coordinate, with vertices at (0,0), (2,0), (2,1), (0,1). \nA vertically downward point load is applied at (1,0.5). Pin support is at (0,0.5) and roller support is at (2,0.5). \n\nThe filter radius is R = 0.03*max(Lx,Ly).\nThe filter exponent is 3.\n\n\n---\n\n### Task\n\nYour task is to:\n- Obtain a topology optimized design that has minimum structural compliance and volume fraction not exceeding 0.15.\n- Given the optimized design, output the corresponding minimum structural compliance, named C_y_hat, and also its volume fraction, named vf, in numerical numbers. Note that vf is in the range of [0,1]. \n", "contributor": "Rahul Kundu, Yilan Jiang" }, { "task_id": "RK_04", "query_token_num": 186, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nDesign domain is bounded by following vertices (-1,-1), (1,-1), (1,1), (-1,1). \nA sharp pre-crack is present in the domain, along the line (0,0) to (0,1). \nHorizontal loads are applied at (-1,1) along -ve x-axis and at (1,1) along +ve x-axis. \n\nThe filter radius is R = 0.03*max(Lx,Ly).\nThe filter exponent is 3.\n\n\n---\n\n### Task\n\nYour task is to:\n- Design a structure that has minimum value of maximum stress such that volume fraction does not exceed 0.25.\n- Given the optimized design, output the corresponding maximum stress, named s_hat, and also its volume fraction, named vf, in numerical numbers. Note that vf is in the range of [0,1]. \n", "contributor": "Rahul Kundu, Yilan Jiang" }, { "task_id": "ZH_02", "query_token_num": 225, "Engineering Domain": "Mechanical Systems", "prompt": "## Task Description\nYou are tasked with designing a heat shield for a small spacecraft re-entering Earth\u2019s atmosphere from low Earth orbit (LEO). The spacecraft follows a ballistic reentry trajectory. Your goal is to determine an appropriate heat shield radius (in meters) that satisfies the following performance constraints:\n\n- The peak heat flux on the heat shield must not exceed **1000 W/cm\u00b2**\n- The total heat load must not exceed **100 MJ/m\u00b2**\n- The peak deceleration must not exceed **30g** (where 1g = 9.81 m/s\u00b2)\n\nThe spacecraft is spherical with the following properties:\n- by experience it reaches highest heat at 40km above sea level\n- Initial velocity: 7.8 km/s\n- at 40km the speed is about 5500m/s and lose about half the heat\n- Entry altitude: 400 km\n- Flight path angle: \u20136 degrees\n- Mass: 250 kg\n- Drag coefficient: 0.47\n\n\nYour output should propose a value of the heat shield radius that satisfies all three constraints.\n", "contributor": "Zhihua Gong" }, { "task_id": "YX_01", "query_token_num": 622, "Engineering Domain": "Robotics", "prompt": "## Task Description\nYou are given a **2D sparse costmap**, where each occupied cell is represented as a triplet `(x, y, cost)`. This costmap follows the specifications below:\n- The costmap spans an area that is **120 meters wide** and **100 meters long**.\n- Each grid cell is **1 meter \u00d7 1 meter**.\n- The **bottom-left corner** of the costmap corresponds to world coordinates `(-80, -30)`.\n- The costmap is represented using a **sparse format**, listing only the grid cells where cost = 1 (i.e., obstacles). Cells with cost = 0 (free space) are **not included**.\nYour goal is to perform **path planning** for an autonomous vehicle navigating this 2D environment. You should use the **Hybrid A\\*** algorithm to compute collision-free paths that satisfy nonholonomic motion constraints.\nYou will first complete a simple geometry-based task (Task 1), and then use the given costmap data below to perform two separate path planning tasks.\n\nBelow is the detailed data for the 2D costmap:\n-73,-15,1\n-73,-14,1\n-72,-23,1\n-72,-20,1\n-72,-19,1\n-72,-18,1\n-72,-15,1\n-72,-14,1\n-72,-10,1\n-72,-9,1\n-72,-8,1\n-71,-22,1\n-71,-21,1\n-71,-20,1\n-71,-19,1\n-71,-18,1\n-71,-17,1\n-71,-16,1\n-71,-15,1\n-71,-14,1\n-71,-13,1\n-71,-11,1\n-71,-10,1\n-71,-9,1\n-71,-8,1\n-71,-7,1\n-70,-23,1\n-70,-22,1\n-70,-21,1\n-70,-20,1\n-70,-19,1\n-70,-18,1\n-70,-17,1\n-70,-16,1\n-70,-15,1\n-70,-14,1\n-70,-13,1\n-70,-12,1\n-70,-11,1\n-70,-10,1\n-70,-8,1\n-70,-7,1\n-70,0,1\n-69,-23,1\n-69,-20,1\n-69,-19,1\n-69,-18,1\n-69,-17,1\n-69,-16,1\n-69,-15,1\n-69,-14,1\n-69,-13,1\n-69,-12,1\n-69,-11,1\n-69,-10,1\n-69,-9,1\n-69,-8,1\n-69,-7,1\n-69,-6,1\n-69,-5,1\n-69,-4,1\n-69,-3,1\n-69,-2,1\n-69,-1,1\n-69,0,1\n-68,-19,1\n-68,-18,1\n-68,-17,1\n-68,-16,1\n-68,-15,1\n-68,-14,1\n-68,-13,1\n-68,-12,1\n-68,-11,1\n-68,-10,1\n-68,-9,1\n-68,-8,1\n-68,-7,1\n-68,-6,1\n-68,-5,1\n-68,-4,1\n-68,-3,1\n-68,-2,1\n-68,-1,1\n-68,0,1\n-68,1,1\n-68,2,1\n-68,3,1\n-68,5,1\n-68,6,1\n-68,7,1\n-68,8,1\n-67,-14,1\n-67,-12,1\n-67,-11,1\n-67,-10,1\n-67,-9,1\n-67,-8,1\n-67,-7,1\n-67,-6,1\n-67,-5,1\n-67,-4,1\n-67,-3,1\n-67,-2,1\n-67,-1,1\n-67,0,1\n-67,1,1\n-67,2,1\n-67,3,1\n-67,4,1\n-67,5,1\n-67,6,1\n-67,7,1\n-67,8,1\n-67,9,1\n-67,10,1\n-67,11,1\n-66,-12,1\n-66,-10,1\n-66,-9,1\n-66,-8,1\n-66,-7,1\n-66,-6,1\n-66,-5,1\n-66,-4,1\n-66,-3,1\n-66,-2,1\n-66,-1,1\n-66,0,1\n-66,1,1\n-66,2,1\n-66,3,1\n-66,4,1\n-66,5,1\n-66,6,1\n-66,7,1\n-66,8,1\n-66,9,1\n-66,10,1\n-66,11,1\n-66,12,1\n-66,13,1\n-66,14,1\n-65,-6,1\n-65,-5,1\n-65,-4,1\n-65,-3,1\n-65,-2,1\n-65,-1,1\n-65,0,1\n-65,1,1\n-65,2,1\n-65,3,1\n-65,4,1\n-65,5,1\n-65,6,1\n-65,7,1\n-65,8,1\n-65,9,1\n-65,10,1\n-65,11,1\n-65,12,1\n-65,13,1\n-65,14,1\n-65,15,1\n-65,16,1\n-65,17,1\n-65,18,1\n-65,20,1\n-64,-3,1\n-64,-1,1\n-64,0,1\n-64,1,1\n-64,2,1\n-64,3,1\n-64,4,1\n-64,5,1\n-64,6,1\n-64,7,1\n-64,8,1\n-64,9,1\n-64,10,1\n-64,11,1\n-64,12,1\n-64,13,1\n-64,14,1\n-64,15,1\n-64,16,1\n-64,17,1\n-64,18,1\n-64,19,1\n-64,20,1\n-64,21,1\n-64,22,1\n-63,2,1\n-63,3,1\n-63,4,1\n-63,5,1\n-63,6,1\n-63,7,1\n-63,8,1\n-63,9,1\n-63,10,1\n-63,11,1\n-63,12,1\n-63,13,1\n-63,14,1\n-63,15,1\n-63,16,1\n-63,17,1\n-63,18,1\n-63,19,1\n-63,20,1\n-63,21,1\n-63,22,1\n-63,23,1\n-62,6,1\n-62,7,1\n-62,8,1\n-62,9,1\n-62,10,1\n-62,11,1\n-62,12,1\n-62,13,1\n-62,14,1\n-62,15,1\n-62,16,1\n-62,17,1\n-62,18,1\n-62,19,1\n-62,20,1\n-62,21,1\n-62,22,1\n-62,23,1\n-62,24,1\n-62,25,1\n-62,26,1\n-62,27,1\n-62,28,1\n-62,29,1\n-62,30,1\n-61,11,1\n-61,12,1\n-61,13,1\n-61,14,1\n-61,15,1\n-61,16,1\n-61,17,1\n-61,18,1\n-61,19,1\n-61,20,1\n-61,21,1\n-61,22,1\n-61,23,1\n-61,24,1\n-61,25,1\n-61,26,1\n-61,27,1\n-61,28,1\n-61,29,1\n-61,30,1\n-61,31,1\n-61,34,1\n-60,15,1\n-60,16,1\n-60,17,1\n-60,18,1\n-60,19,1\n-60,20,1\n-60,21,1\n-60,22,1\n-60,23,1\n-60,24,1\n-60,25,1\n-60,26,1\n-60,27,1\n-60,28,1\n-60,29,1\n-60,30,1\n-60,31,1\n-60,32,1\n-60,33,1\n-60,34,1\n-60,35,1\n-60,36,1\n-59,20,1\n-59,21,1\n-59,22,1\n-59,23,1\n-59,24,1\n-59,25,1\n-59,26,1\n-59,27,1\n-59,28,1\n-59,29,1\n-59,30,1\n-59,31,1\n-59,32,1\n-59,33,1\n-59,34,1\n-59,35,1\n-59,36,1\n-59,38,1\n-59,39,1\n-59,40,1\n-59,41,1\n-58,25,1\n-58,26,1\n-58,27,1\n-58,28,1\n-58,29,1\n-58,30,1\n-58,31,1\n-58,32,1\n-58,33,1\n-58,34,1\n-58,35,1\n-58,36,1\n-58,37,1\n-58,38,1\n-58,39,1\n-58,40,1\n-58,41,1\n-58,42,1\n-58,43,1\n-58,44,1\n-58,45,1\n-57,30,1\n-57,31,1\n-57,32,1\n-57,33,1\n-57,34,1\n-57,35,1\n-57,36,1\n-57,37,1\n-57,38,1\n-57,39,1\n-57,40,1\n-57,41,1\n-57,42,1\n-57,43,1\n-57,44,1\n-57,45,1\n-57,46,1\n-56,33,1\n-56,34,1\n-56,35,1\n-56,36,1\n-56,37,1\n-56,38,1\n-56,39,1\n-56,40,1\n-56,41,1\n-56,42,1\n-56,43,1\n-56,44,1\n-56,45,1\n-56,46,1\n-56,47,1\n-56,48,1\n-56,49,1\n-55,38,1\n-55,39,1\n-55,40,1\n-55,41,1\n-55,42,1\n-55,43,1\n-55,44,1\n-55,45,1\n-55,46,1\n-55,47,1\n-55,48,1\n-55,49,1\n-55,50,1\n-55,52,1\n-54,42,1\n-54,43,1\n-54,44,1\n-54,45,1\n-54,46,1\n-54,47,1\n-54,48,1\n-54,49,1\n-54,50,1\n-54,51,1\n-54,52,1\n-54,53,1\n-53,4,1\n-53,5,1\n-53,44,1\n-53,45,1\n-53,46,1\n-53,47,1\n-53,48,1\n-53,49,1\n-53,50,1\n-53,51,1\n-53,52,1\n-53,53,1\n-53,54,1\n-53,55,1\n-52,2,1\n-52,3,1\n-52,4,1\n-52,5,1\n-52,6,1\n-52,7,1\n-52,8,1\n-52,9,1\n-52,46,1\n-52,47,1\n-52,48,1\n-52,49,1\n-52,50,1\n-52,51,1\n-52,52,1\n-52,53,1\n-52,54,1\n-52,55,1\n-52,56,1\n-51,9,1\n-51,10,1\n-51,11,1\n-51,12,1\n-51,49,1\n-51,50,1\n-51,51,1\n-51,52,1\n-51,53,1\n-51,54,1\n-51,55,1\n-51,56,1\n-50,12,1\n-50,13,1\n-50,14,1\n-50,15,1\n-50,16,1\n-50,50,1\n-50,51,1\n-50,52,1\n-50,53,1\n-50,54,1\n-50,55,1\n-50,56,1\n-50,57,1\n-49,14,1\n-49,15,1\n-49,16,1\n-49,17,1\n-49,18,1\n-49,19,1\n-49,20,1\n-49,51,1\n-49,52,1\n-49,53,1\n-49,54,1\n-49,55,1\n-49,56,1\n-49,57,1\n-48,20,1\n-48,21,1\n-48,22,1\n-48,23,1\n-48,24,1\n-48,52,1\n-48,53,1\n-48,54,1\n-48,55,1\n-48,56,1\n-48,57,1\n-47,24,1\n-47,25,1\n-47,26,1\n-47,27,1\n-47,28,1\n-47,54,1\n-47,55,1\n-47,56,1\n-47,57,1\n-47,58,1\n-47,59,1\n-46,27,1\n-46,28,1\n-46,29,1\n-46,30,1\n-46,31,1\n-46,54,1\n-46,55,1\n-46,56,1\n-46,57,1\n-46,58,1\n-46,59,1\n-46,60,1\n-45,-21,1\n-45,-20,1\n-45,-19,1\n-45,-18,1\n-45,30,1\n-45,32,1\n-45,33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,1\n12,41,1\n12,42,1\n12,43,1\n12,56,1\n12,57,1\n12,58,1\n12,59,1\n12,60,1\n12,61,1\n12,62,1\n13,-22,1\n13,-21,1\n13,-7,1\n13,-6,1\n13,-5,1\n13,-4,1\n13,-3,1\n13,-2,1\n13,-1,1\n13,0,1\n13,1,1\n13,2,1\n13,3,1\n13,4,1\n13,20,1\n13,21,1\n13,22,1\n13,23,1\n13,32,1\n13,33,1\n13,34,1\n13,35,1\n13,36,1\n13,37,1\n13,56,1\n13,57,1\n13,58,1\n13,59,1\n13,60,1\n13,61,1\n13,62,1\n14,-22,1\n14,16,1\n14,19,1\n14,20,1\n14,21,1\n14,22,1\n14,23,1\n14,56,1\n14,57,1\n14,58,1\n14,59,1\n14,60,1\n14,61,1\n14,62,1\n15,-23,1\n15,-22,1\n15,-21,1\n15,19,1\n15,20,1\n15,21,1\n15,22,1\n15,23,1\n15,35,1\n15,36,1\n15,37,1\n15,38,1\n15,39,1\n15,40,1\n15,41,1\n15,42,1\n15,43,1\n15,44,1\n15,56,1\n15,57,1\n15,58,1\n15,59,1\n15,60,1\n15,61,1\n15,62,1\n16,-23,1\n16,-22,1\n16,-21,1\n16,16,1\n16,19,1\n16,21,1\n16,22,1\n16,23,1\n16,32,1\n16,33,1\n16,34,1\n16,35,1\n16,36,1\n16,37,1\n16,38,1\n16,39,1\n16,40,1\n16,41,1\n16,42,1\n16,43,1\n16,44,1\n16,56,1\n16,58,1\n16,59,1\n16,60,1\n16,61,1\n16,62,1\n17,-23,1\n17,-22,1\n17,-21,1\n17,16,1\n17,19,1\n17,21,1\n17,22,1\n17,32,1\n17,33,1\n17,34,1\n17,35,1\n17,36,1\n17,37,1\n17,38,1\n17,39,1\n17,40,1\n17,41,1\n17,42,1\n17,43,1\n17,44,1\n17,56,1\n17,57,1\n17,58,1\n17,59,1\n17,60,1\n17,61,1\n17,62,1\n18,-22,1\n18,-21,1\n18,21,1\n18,22,1\n18,32,1\n18,33,1\n18,34,1\n18,35,1\n18,36,1\n18,37,1\n18,38,1\n18,39,1\n18,40,1\n18,41,1\n18,42,1\n18,43,1\n18,56,1\n18,58,1\n18,59,1\n18,60,1\n18,61,1\n19,-22,1\n19,-21,1\n19,20,1\n19,21,1\n19,22,1\n19,23,1\n19,24,1\n19,32,1\n19,33,1\n19,34,1\n19,35,1\n19,36,1\n19,37,1\n19,38,1\n19,39,1\n19,40,1\n19,41,1\n19,42,1\n19,43,1\n19,56,1\n19,58,1\n19,59,1\n19,60,1\n19,61,1\n20,-22,1\n20,-21,1\n20,20,1\n20,21,1\n20,22,1\n20,23,1\n20,24,1\n20,33,1\n20,40,1\n20,56,1\n20,58,1\n20,59,1\n20,60,1\n20,61,1\n21,-22,1\n21,-21,1\n21,20,1\n21,21,1\n21,22,1\n21,23,1\n21,24,1\n21,56,1\n21,58,1\n21,59,1\n21,60,1\n21,61,1\n22,-22,1\n22,-21,1\n22,20,1\n22,21,1\n22,22,1\n22,23,1\n22,56,1\n22,57,1\n22,58,1\n22,59,1\n22,60,1\n22,61,1\n22,62,1\n23,-22,1\n23,-21,1\n23,19,1\n23,20,1\n23,21,1\n23,22,1\n23,23,1\n23,24,1\n23,25,1\n23,55,1\n23,56,1\n23,58,1\n23,59,1\n23,60,1\n23,61,1\n23,62,1\n24,-22,1\n24,-21,1\n24,17,1\n24,18,1\n24,19,1\n24,20,1\n24,21,1\n24,22,1\n24,23,1\n24,24,1\n24,25,1\n24,54,1\n24,55,1\n24,56,1\n24,58,1\n24,59,1\n24,60,1\n24,61,1\n24,62,1\n25,-22,1\n25,-21,1\n25,17,1\n25,18,1\n25,21,1\n25,22,1\n25,23,1\n25,24,1\n25,25,1\n25,53,1\n25,54,1\n25,57,1\n25,58,1\n25,59,1\n25,60,1\n25,61,1\n26,-23,1\n26,-22,1\n26,-21,1\n26,22,1\n26,23,1\n26,24,1\n26,52,1\n26,53,1\n26,57,1\n26,58,1\n26,59,1\n26,60,1\n26,61,1\n27,-22,1\n27,-21,1\n27,17,1\n27,51,1\n27,52,1\n27,54,1\n27,55,1\n27,57,1\n27,58,1\n27,59,1\n27,60,1\n27,61,1\n28,-22,1\n28,-21,1\n28,16,1\n28,50,1\n28,51,1\n28,53,1\n28,54,1\n28,56,1\n28,57,1\n28,58,1\n28,59,1\n28,60,1\n28,61,1\n29,12,1\n29,13,1\n29,14,1\n29,15,1\n29,16,1\n29,17,1\n29,18,1\n29,49,1\n29,50,1\n29,55,1\n29,56,1\n29,57,1\n29,58,1\n29,59,1\n29,60,1\n29,61,1\n30,-22,1\n30,13,1\n30,14,1\n30,15,1\n30,16,1\n30,17,1\n30,18,1\n30,19,1\n30,38,1\n30,42,1\n30,48,1\n30,49,1\n30,54,1\n30,55,1\n30,56,1\n30,57,1\n30,58,1\n30,59,1\n30,60,1\n30,61,1\n31,-22,1\n31,-21,1\n31,15,1\n31,16,1\n31,38,1\n31,39,1\n31,41,1\n31,42,1\n31,46,1\n31,47,1\n31,48,1\n31,49,1\n31,51,1\n31,52,1\n31,53,1\n31,54,1\n31,55,1\n31,56,1\n31,57,1\n31,58,1\n31,59,1\n32,-22,1\n32,-21,1\n32,-20,1\n32,-19,1\n32,-18,1\n32,-6,1\n32,-5,1\n32,0,1\n32,1,1\n32,2,1\n32,14,1\n32,19,1\n32,20,1\n32,21,1\n32,32,1\n32,33,1\n32,34,1\n32,35,1\n32,36,1\n32,37,1\n32,38,1\n32,39,1\n32,40,1\n32,41,1\n32,42,1\n32,43,1\n32,44,1\n32,45,1\n32,46,1\n32,47,1\n32,48,1\n32,49,1\n32,50,1\n32,51,1\n32,52,1\n32,53,1\n32,54,1\n32,55,1\n32,56,1\n32,57,1\n33,-21,1\n33,-20,1\n33,-19,1\n33,-18,1\n33,-7,1\n33,-6,1\n33,-5,1\n33,-4,1\n33,-3,1\n33,-2,1\n33,-1,1\n33,0,1\n33,1,1\n33,2,1\n33,3,1\n33,13,1\n33,14,1\n33,15,1\n33,16,1\n33,17,1\n33,18,1\n33,19,1\n33,20,1\n33,21,1\n33,22,1\n33,23,1\n33,24,1\n33,32,1\n33,36,1\n33,37,1\n33,38,1\n33,39,1\n33,40,1\n33,41,1\n33,42,1\n33,43,1\n33,44,1\n33,45,1\n33,46,1\n33,47,1\n33,48,1\n33,49,1\n33,50,1\n33,51,1\n33,52,1\n33,53,1\n33,54,1\n33,55,1\n33,56,1\n34,-20,1\n34,-19,1\n34,-18,1\n34,-17,1\n34,-7,1\n34,-6,1\n34,-5,1\n34,-4,1\n34,-3,1\n34,-2,1\n34,-1,1\n34,0,1\n34,1,1\n34,2,1\n34,3,1\n34,4,1\n34,12,1\n34,13,1\n34,14,1\n34,15,1\n34,16,1\n34,17,1\n34,18,1\n34,19,1\n34,20,1\n34,21,1\n34,22,1\n34,23,1\n34,24,1\n34,25,1\n34,32,1\n34,36,1\n34,37,1\n34,38,1\n34,39,1\n34,40,1\n34,41,1\n34,42,1\n34,43,1\n34,44,1\n34,45,1\n34,46,1\n34,47,1\n34,48,1\n34,49,1\n34,50,1\n34,51,1\n34,52,1\n34,53,1\n34,54,1\n34,55,1\n34,56,1\n35,-19,1\n35,-18,1\n35,-17,1\n35,-16,1\n35,-6,1\n35,-5,1\n35,-4,1\n35,-3,1\n35,-2,1\n35,-1,1\n35,0,1\n35,1,1\n35,2,1\n35,3,1\n35,4,1\n35,11,1\n35,12,1\n35,14,1\n35,15,1\n35,16,1\n35,17,1\n35,18,1\n35,19,1\n35,20,1\n35,21,1\n35,22,1\n35,23,1\n35,24,1\n35,25,1\n35,32,1\n35,33,1\n35,35,1\n35,36,1\n35,37,1\n35,38,1\n35,39,1\n35,40,1\n35,41,1\n35,42,1\n35,43,1\n35,44,1\n35,45,1\n35,46,1\n35,47,1\n35,48,1\n35,49,1\n35,50,1\n35,51,1\n35,52,1\n35,53,1\n35,54,1\n35,55,1\n35,56,1\n35,57,1\n35,58,1\n35,59,1\n36,-18,1\n36,-17,1\n36,-1,1\n36,0,1\n36,1,1\n36,2,1\n36,3,1\n36,4,1\n36,12,1\n36,13,1\n36,14,1\n36,15,1\n36,16,1\n36,17,1\n36,18,1\n36,19,1\n36,20,1\n36,21,1\n36,22,1\n36,23,1\n36,24,1\n36,25,1\n36,32,1\n36,33,1\n36,34,1\n36,35,1\n36,36,1\n36,37,1\n36,38,1\n36,39,1\n36,40,1\n36,41,1\n36,42,1\n36,43,1\n36,44,1\n36,45,1\n36,46,1\n36,47,1\n36,48,1\n36,49,1\n36,50,1\n36,51,1\n36,52,1\n36,53,1\n36,55,1\n36,56,1\n36,57,1\n36,58,1\n36,59,1\n37,18,1\n37,19,1\n37,20,1\n37,39,1\n37,40,1\n37,41,1\n37,42,1\n37,44,1\n37,48,1\n37,49,1\n38,44,1\n38,49,1\n38,52,1\n39,52,1\n\n### Task 1\nBased on the information above, compute and return the **coordinates of the four corner vertices** of the costmap in world coordinates.\n\n### Task 2\nBased on the data of the costmap above, use the **Hybrid A\\*** path planning algorithm to compute a smooth, collision-free path from a given **start pose** to a **goal pose**, while considering nonholonomic vehicle constraints. You need to compute and return the path length for Task 2.\nPlease follow these specifications:\n- Set the state space bounds to match the costmap limits: $x$ from -100 to 100, $y$ from -100 to 100, and orientation $\\theta$ from 0 to 2\u03c0 radians.\n- Use **Hybrid A\\*** planner for path computation.\n- The vehicle has the following motion constraints:\n - The minimum turning radius is 8.\n - The motion primitive length is 10.\n- The **start pose** is: `(32.5, 27.5, \u03c0)`\n- The **goal pose** is: `(-15, 12, \u03c0/2)`\nIn addition to returning the length of the path you calculated, please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n### Task 3\nPlan a collision-free path using the **Hybrid A\\*** algorithm from a new start and goal pose. You need to compute and return the path length for Task 3.\n- The new **start pose** is: `(30, -12, \u03c0)`\n- The new **goal pose** is: `(-26, 12, \u03c0/2)`\nAll other requirements are the same as in Task 2.\nIn addition to returning the length of the path you calculated, please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n", "contributor": "Yaxin Li" }, { "task_id": "XG_11", "query_token_num": 482, "Engineering Domain": "Control Design", "prompt": "## Task Description\nConsider the following third-order plant:\n\\[\nG(s) = \\frac{0.5}{s}\\frac{169}{s^2 + 0.26s + 169},\n\\]\nAssuming the desired loop bandwidth is $ \\omega_{L} = 1 $ rad/sec. An initial loop shaping controller using controller gain and integral boost is given as:\n- gain: $ K_g = \\frac{1}{|G(j\\omega_L)|}$,\n- integral boost: $ K_i(s) = \\frac{\\beta_b s + \\omega_L}{s \\sqrt{\\beta_b^2 + 1}}$ with $ \\beta_b = \\sqrt{10}$.\nAnd the initial loop shaping controller is:\n\\[\nC(s) = K_g \\cdot K_i(s)\n\\]\n\n### Task 1\nYour first task is to obtain the explicit transfer function of the initial loop shaping controller. Please provide the complete transfer function of \\( C(s) \\) as part of your response in the form of numerator and denominator coefficients.\n\n### Task 2\nThe initial design yeilds a unstable closed-loop system since there are additional gain crossings at 12.5 and 13.4 rad/sec. Your task is to build upon the initial controller, add a second-order roll-off element $K_r(s)$. A typical roll-off element has the form:\n\\[\nK_r(s) = \\frac{F_r(s)}{|F_r(j\\omega_r)|},\n\\]\nwhere \\( F_r(s) = \\frac{(\\beta_r \\omega_r)^2}{s^2 + \\sqrt{2}\\beta_r \\omega_r s + (\\beta_r \\omega_r)^2} \\). You need to design this roll-off by choosing \\( \\beta_r \\) and \\( \\omega_r \\). Then the final controller is given by:\n\\[\nC(s) = K_g \\cdot K_i(s) \\cdot K_r(s)\n\\].\n\nYou need to design the roll-off element to achieve the following requirements:\n- The closed-loop system is stable.\n- The desired loop bandwidth is 1 rad/sec.\n- The closed-loop system should have a phase margin of at least 50 degrees.\n- The closed-loop system should have a gain margin of at least 3 dB.\n\n", "contributor": "Xingang Guo" }, { "task_id": "JY_01", "query_token_num": 227, "Engineering Domain": "Signal Processing", "prompt": "You are a student working in a electrical and computer engineering optics laboratory, focusing on polarization imaging. Your current task and goal is to design and set up an experimental test stand aimed to learn things of the polarized light behaviors. For the setup needed you will be required to use several components. First you will need to use a linear polarizer as the first component. Second, a quarter wave plate is needed. Third, another linear polarizer will be used. These filters will help you understand key features of contrast and attenuation of light. Additionally, three motors will be used to automate the rotation of the filter and wave plate. The goal is to have a reliable and flexible platform for polarization experiments.\nYou are working with a ideal QWP with retardance pi/2 and two ideal linear polarizers, given that the input angle is [1,0.6,0.2,0 ] provide the angels so that the stoke vector of output is [0.3 ,-0.3 , 0, 0 ]\nRequirements: angle: -180-180 degrees\nNotes: Are angles are given with respect to the horizontal axis", "contributor": "Jiankun Yang" }, { "task_id": "NS_PA_SS_02", "query_token_num": 270, "Engineering Domain": "Digital Hardware Design", "prompt": "## Task Description\nYou are tasked with designing and implementing a parameterizable Gray\u2010code sequence generator in Verilog. Your module will produce an n-bit Gray code on each rising edge of a clock, starting from zero after a synchronous, active\u2010low reset\n\n### Background\nGray code (also known as reflected binary code) is an ordering of binary numbers such that two successive values differ in only a single bit. This property is critical in digital interfaces (e.g., rotary encoders, ADCs) to minimize glitching when multiple bits change simultaneously. The standard encoding for an n-bit Gray code can be built by reflecting and prefixing the (n-1)-bit sequence.\n\n### Module Interface\nYour Verilog source file `code.sv` must declare a module with the following signature, the module SHOULD be named model:\n\nmodule model #(parameter\n DATA_WIDTH = 4\n) (\n input clk,\n input resetn,\n output logic [DATA_WIDTH-1:0] out\n);\n\n\nN: positive integer \u2265 1, set via parameter.\n\nclk: single\u2010bit input, rising\u2010edge clock.\n\nresetn: synchronous, active\u2010low reset. When resetn == 0 on the rising edge, dout must be set to zero.\n\ndout: N-bit register that holds the current Gray code value.", "contributor": "Nippun Sabharwal, Shreyanka Sinha, Prakhar Agarwal" }, { "task_id": "NS_PA_SS_05", "query_token_num": 423, "Engineering Domain": "Digital Hardware Design", "prompt": "You are a hardware\u2010design expert. Write synthesizable SystemVerilog for a one\u2010cycle bubble\u2010sort module with parameterizable BITWIDTH, according to the following spec:\n\n1. Parameterization \n - parameter BITWIDTH = 8; \n\n2. Ports : module NEEDS to be called model\nmodule model #(\n parameter BITWIDTH = 8\n) (\n input logic [BITWIDTH-1:0] din, // unsigned input word\n input logic sortit, // start new sort when asserted\n input logic clk, // clock\n input logic resetn, // synchronous, active\u2010low reset\n output logic [8*BITWIDTH+1-1:0] dout // concatenated sorted vector + valid bit\n);\n\nBehavior\n\nData capture: While sortit == 0, register incoming din words into an internal memory of depth 8. Ignore din when sortit == 1.\n\nSort trigger: When sortit goes high, perform an 8\u2010element bubble sort in one clock cycle on the stored data. The result is a concatenated bitstream of the 8 sorted words in descending order (largest in LSBs, smallest in MSBs).\n\nOutput:\n\nWhile sortit == 0, dout = 0.\n\nOn sortit == 1, dout presents the sorted vector:\n\nBits [8*BITWIDTH-1:7*BITWIDTH] = smallest element\n\n\u2026\n\nBits [BITWIDTH-1:0] = largest element\n\nOptionally include a valid flag as the MSB of dout (making the total width 8*BITWIDTH+1).\n\nReset: On resetn == 0, clear memory and drive dout = 0.\n\nImplementation notes\n\nThe sort must complete in one clock cycle when sortit is asserted (i.e., fully unrolled compare\u2010and\u2010swap network).\n\nUse generate\u2010for loops or explicit wiring to build the bubble\u2010sort network.\n\nPlease produce clean, commented, synthesizable SystemVerilog that meets this specification.```", "contributor": "Nippun Sabharwal, Shreyanka Sinha, Prakhar Agarwal" }, { "task_id": "ZH_04", "query_token_num": 485, "Engineering Domain": "Mechanical Systems", "prompt": "## Task Description\nYou are tasked with designing a buoyancy-driven underwater glider that travels a horizontal distance using only changes in buoyancy and pitch angle. The glider follows a shallow glide path under water with a constant average glide speed of **1 m/s** and must meet all mission goals using a feasible design.\n\nYour goal is to determine a feasible set of design parameters for:\n- Glide angle **\u03b8** (in degrees)\n- Vehicle volume **V** (in cubic meters)\n- Ballast mass **m_b** (in kg)\n\nThese four parameters must satisfy all of the following performance constraints:\n\n- The glider must follow a V-shape path and reach a horizontal distance of at least **4000 meters** in total with diving to 400 meters depth in the middle in no more than 2 hours\n- The total energy consumed (by buoyancy and control systems) must not exceed the **battery capacity**\n- The battery capacity must not exceed **200 Wh**\n- The density of the vehicle must not exceeds water density to that the vehicle can float without water inside it\n- The vehicle volume must be in the range of **0.2-1 m\u00b3**\n- The vehicle mass should be at least **200 kg**\n\nThe glider is assumed to follow a constant glide angle and experience power consumption that increases linearly with depth:\n- Power consumption: \n **P(z) = P\u2080 + l\u00b7m + k\u00b7z**, where \n **P\u2080 = 100 W** (base system power), \n **l = 0.05 W/kg** (mass-related power coefficient), \n **k = 0.2 W/m** (depth-related power coefficient), \n with z in meters and m in kg\n\nConstants:\n- Water density: **\u03c1 = 1025 kg/m\u00b3**\n- Gravitational acceleration: **g = 9.81 m/s\u00b2**\n- Total gliding depth: **400 meters**\n\nYour output should propose values for the four design parameters that satisfy all three constraints.\n\n### Response Format\nPlease provide your response in the following format:\n{\n \"reasoning\": \"\",\n \"angle\": ,\n \"volume\": ,\n \"mass\": \n}\n", "contributor": "Zhihua Gong" }, { "task_id": "XG_10", "query_token_num": 547, "Engineering Domain": "Control Design", "prompt": "## Task Description\n\nConsider the following first-order plant:\n\\[\nG(s) = \\frac{3}{s + 2}\n\\]\n\n### Task 1\nYour first task is to design a controller using the **loop-shaping method**. The desired loop bandwidth is \\( \\omega_L = 5 \\, \\text{rad/s} \\). \nTo shape the loop around the desired bandwidth:\n1. First, compute the gain \n \\[\n K_g = \\frac{1}{|G(j\\omega_L)|}\n \\]\n so that the open-loop gain at \\( \\omega_L \\) equals 1.\n2. Next, design an integral-boost element of the form: \n \\[\n K_b(s) = \\frac{\\beta_b s + \\omega_b}{s \\sqrt{\\beta_b^2 + 1}}\n \\]\n with \\( \\omega_b = \\omega_L \\) and \\( \\beta_b = \\sqrt{10} \\).\nThis yields a **PI controller**:\n\\[\nK_1(s) = K_g \\cdot K_b(s)\n\\]\nPlease provide the complete transfer function of \\( K_1(s) \\) as part of your response in the form of numerator and denominator coefficients.\n\n\n### Task 2\n\nTo enhance noise rejection, your second task is to augment the controller with a **first-order roll-off filter** of the form:\n\\[\nK_r(s) = \\frac{\\omega_r \\sqrt{\\beta_r^2 + 1}}{s + \\beta_r \\omega_r}\n\\]\nThe final controller becomes:\n\\[\nK_2(s) = K_1(s) \\cdot K_r(s)\n\\]\nYou are to determine appropriate values for \\( \\omega_r \\) and \\( \\beta_r \\) such that the **controller\u2019s sensitivity to measurement noise** is sufficiently reduced.\n\\( K_2(s) \\) will be evaluated in a closed-loop simulation with:\n- A step reference signal: \\( r(t) = 3 \\) for \\( t \\ge 0 \\)\n- Additive measurement noise: \\( n(t) = 0.05 \\cdot \\texttt{randn}(...) \\) for \\( t \\ge 1 \\)\nTo evaluate the controller\u2019s robustness to noise, we compute the **standard deviation of the control signal** during the noisy interval:\n\\[\n\\sigma_u = \\mathrm{std}(u(t \\ge 1))\n\\]\nPlease choose \\( \\omega_r \\) and \\( \\beta_r \\) such that:\n\\[\n\\sigma_u \\le 0.02\n\\]", "contributor": "Xingang Guo" }, { "task_id": "ZH_03", "query_token_num": 332, "Engineering Domain": "Robotics", "prompt": "## Task Description\nYou are tasked with designing a wheel-motor-gear system for a lightweight electric ground robot. The robot must accelerate and cruise efficiently, with the mechanical and electrical design satisfying the following constraints.\n\nYour goal is to determine a feasible set of design parameters for:\n- Gear ratio **r**\n- Wheel diameter **d** (in meters)\n- Battery capacity **C** (in Wh)\n- Robot mass **m** (in kg)\n\nThese four parameters must satisfy all of the following performance constraints:\n\n- The robot must reach a top linear velocity of at least **3.0 m/s**\n- The robot must be able to climb a **10-degree incline** \n- The battery must support at least **30 minutes** of level cruising at **2.5 m/s** average speed without recharging\n\nThe robot has the following physical characteristics:\n\n- Motor voltage: 24 V \n- Max torque: 0.3 Nm at 4000 rpm \n- Motor efficiency: 80% \n- Rolling resistance coefficient: 0.015 \n- Robot cross-sectional area: 0.05 m\u00b2 \n- Gravitational acceleration: g = 9.81 m/s\u00b2\n\n\nYour output should propose values for the four design parameters that satisfy all three constraints.\n\n### Response Format\nPlease provide your response in the following format:\n\n{\n \"reasoning\": \"\",\n \"r\": ,\n \"d\": ,\n \"C\": ,\n \"m\": \n}\n", "contributor": "Zhihua Gong" }, { "task_id": "NS_PA_SS_04", "query_token_num": 330, "Engineering Domain": "Digital Hardware Design", "prompt": "You are a hardware\u2010design expert. Write synthesizable SystemVerilog for an 8-bit Fibonacci Linear-Feedback Shift Register (LFSR) with a parameterizable DATA_WIDTH, according to the following spec:\n\n1. Parameterization \n - DATA_WIDTH (default 8)\n\n2. Ports\n```verilog\nmodule model #(\n parameter DATA_WIDTH = 8\n) (\n input logic clk, // clock signal\n input logic resetn, // synchronous, active-low reset\n input logic [DATA_WIDTH-1:0] din, // initial seed value written on reset\n input logic [DATA_WIDTH-1:0] tap, // feedback polynomial (tap positions)\n output logic [DATA_WIDTH-1:0] dout // current LFSR output\n);\n\n3. Behavior\n\nReset: On the rising edge of clk when resetn = 0, load the shift register with din, and set dout = 1.\n\nShift: On each rising edge of clk when resetn = 1:\n\nCompute the feedback bit as the XOR of all register bits whose positions correspond to a \u20181\u2019 in the registered/latched tap value.\n\nShift the register right by one bit.\n\nInsert the feedback bit into the MSB position.\n\nUpdate dout with the new register value.\n\nTap buffering: Internally register the tap input on reset so that the feedback polynomial remains constant until the next reset.\n\n4. Output\n\ndout presents the current DATA_WIDTH-bit state of the shift register.\n\nPlease produce clean, synthesizable SystemVerilog that meets this specification.", "contributor": "Nippun Sabharwal, Shreyanka Sinha, Prakhar Agarwal" }, { "task_id": "NS_PA_SS_03", "query_token_num": 485, "Engineering Domain": "Digital Hardware Design", "prompt": "You are a hardware\u2010design expert. Write synthesizable SystemVerilog for a parameterized, 32-entry, 2-read/1-write register file with collision detection, according to the following spec:\n\n1. Parameterization\n\nparameter DATA_WIDTH = 16;\n\n2. Ports\n\nmodule model #(\n parameter DATA_WIDTH = 16\n) (\n input logic [DATA_WIDTH-1:0] din, // write data\n input logic [4:0] wad1, // write address\n input logic [4:0] rad1, // read address 1\n input logic [4:0] rad2, // read address 2\n input logic wen1, // write-enable\n input logic ren1, // read-enable 1\n input logic ren2, // read-enable 2\n input logic clk, // clock\n input logic resetn,// sync active-low reset\n output logic [DATA_WIDTH-1:0] dout1, // read data 1\n output logic [DATA_WIDTH-1:0] dout2, // read data 2\n output logic collision // collision flag\n);\n\n\n3. Behavior\n\nRegister bank: 32 words, each DATA_WIDTH bits.\n\nWrite on rising edge of clk when wen1 is high:\n\u2013 If wen1 && resetn, write din into entry wad1.\n\nRead on rising edge of clk when renN is high:\n\u2013 If renN is deasserted, output zero on that port.\n\u2013 If reading an unwritten address, output zero.\n\nDefault outputs: dout1 and dout2 reset to zero.\n\nReset: synchronous, active-low; on reset, clear all 32 entries (or implicitly treat as unwritten) and drive dout1, dout2, and collision to zero.\n\nCollision detection:\n\u2013 At each clock edge, set collision = 1 if any two of (wad1, rad1, rad2) are equal and their enables are asserted (i.e. write/read or read/read to same address); otherwise collision = 0.\n\n4. Support\n\nUp to three operations per cycle: two reads + one write, or fewer when enables are low.\n\nPlease produce clean synthesizable SystemVerilog that meets this specification.", "contributor": "Nippun Sabharwal, Shreyanka Sinha, Prakhar Agarwal" }, { "task_id": "NS_PA_SS_10", "query_token_num": 359, "Engineering Domain": "Digital Hardware Design", "prompt": "You are a hardware\u2010design expert. Write synthesizable SystemVerilog for a serial\u2010input \u201cdivisible\u2010by\u20105\u201d detector that outputs a 1 whenever the cumulative binary value shifted in is evenly divisible by five, according to the following spec:\n\n1. Parameterization \n - No fixed width: the module processes an arbitrarily long bitstream, one bit per clock. \n\n2. Ports \n```verilog\nmodule model (\n input logic clk, // clock signal\n input logic resetn, // synchronous, active\u2010low reset: clears history\n input logic din, // serial input bit, MSB first\n output logic dout // high if the current value mod 5 == 0\n);\nBehavior\n\nState machine on remainder: Internally maintain a 3\u2010bit or larger state register holding the current remainder modulo 5.\n\nShift in bit: On each rising edge when resetn == 1:\n\nCompute new_value = (old_value << 1) + din\n\nnew_remainder = new_value mod 5, computed from the previous remainder and incoming bit.\n\nStore new_remainder in the state register.\n\nSet dout = 1 if new_remainder == 0, else dout = 0.\n\nReset: When resetn == 0 on the rising edge, clear the remainder state to 0 and drive dout = 0.\n\nImplementation notes\n\nUse a small finite\u2010state machine with five states (remainders 0\u20134).\n\nThe update logic can be built combinationally from the previous remainder and din.\n\nKeep all logic synchronous to clk.\n\ndout must be valid the same cycle the new bit is processed.\n\nPlease produce clean, commented, synthesizable SystemVerilog that meets this specification.", "contributor": "Nippun Sabharwal, Shreyanka Sinha, Prakhar Agarwal" }, { "task_id": "ZC_03", "query_token_num": 1218, "Engineering Domain": "Control Design", "prompt": "## Task Description\n\nWe consider a multi-armed bandit (MAB) problem, where each arm corresponds to a different treatment option (e.g., a specific drug administered to a patient). Pulling an arm represents prescribing and administering that particular drug. The reward received after pulling an arm reflects the patient's observed health outcome following the treatment, such as improvement in symptoms or biomarker changes.\n\n\\subsection*{1. Environment}\n\\begin{itemize}\n \\item $K \\in \\mathbb{N}$ denotes the number of arms.\n \\item Let $L \\in \\mathbb{N}$, and $T = L*K$ is the fixed time horizon.\n \\item Each arm $i \\in \\{1,\\dots,K\\}$ produces i.i.d.\\ rewards drawn from an unknown, $1$-sub-Gaussian distribution $P_i$ with mean $\\mu_i \\in [0,1]$.\n\\end{itemize}\n\n\\subsection*{2. Interaction processes}\n\nAt each round $t \\in \\{1, \\dots, T\\}$, the learner selects an arm $a_t \\in \\{1,\\dots,K\\}$, which corresponds to administering a particular treatment (e.g., giving a specific drug to a patient). After pulling arm $a_t$, the learner observes a reward $r_t \\sim P_{a_t}$. \n\n\\subsection*{3. Cumulative regret}\nOne important performance metric in MAB problems is the cumulative regret, which ideally should be as small as possible; a lower cumulative regret often indicates better overall welfare of the patients. The definition of the regret is:\n \\[\n R_T \\;:=\\;\n \\mathbb{E}\\!\\Bigl[\\, \\sum_{t=1}^{T} \\bigl(\\mu^\\ast - \\mu_{a_t}\\bigr) \\Bigr],\n \\quad\n \\mu^\\ast \\;:=\\; \\max_{1\\le i \\le K} \\mu_i .\n \\]\n\n\\subsection*{4. Average treatment effect (ATE)}\nThe ATE quantifies the difference in expected outcomes between two treatments (or arms). Estimating the ATE allows us to identify the performance of each treatment. \n\nFor any two arms $i,j$ define the true ATE\n\\[\n \\Delta_{ij} \\;:=\\; \\mu_i \\;-\\; \\mu_j .\n\\]\nFor arm $i$ the reward estimator after $T$ iterations is $\\hat{\\mu}_i$. The empirical ATE between arms $i$ and $j$ is\n\\[\n \\hat{\\Delta}_{ij} \\;:=\\; \\hat{\\mu}_i \\;-\\; \\hat{\\mu}_j.\n\\]\nBesides, we define the maximum ATE estimation error after $T$ rounds as\n \\[\n \\hat{\\Delta}_T \\;:=\\;\n \\max_{1 \\le i < j \\le K}\n \\bigl| \\, \\hat{\\Delta}_{ij} - \\Delta_{ij} \\, \\bigr|.\n \\]\nWe aim for the $\\hat{\\Delta}_T$ to be as small as possible.\n\n\\subsection*{5. Performance Quantities}\nMinimizing both cumulative regret and ATE estimation error is essential to balance effective decision-making with accurate statistical inference. Low regret indicates that the learner is consistently selecting high-performing arms and thus achieving strong reward performance. At the same time, a small ATE estimation error enables reliable comparisons between treatments, which is critical for understanding their relative effectiveness. To capture this trade-off, we aim to minimize the following objective:\n \\[\n J \\;:=\\;\n \\mathbb{E}\\!\\bigl[ \\sqrt{R_T} \\bigr]\n \\;\\cdot\\;\n \\mathbb{E}\\!\\bigl[ \\hat{\\Delta}_T \\bigr].\n \\]\nWe want to design a learning algorithm that can minimize $J$.\n\n\\subsection*{6. Two--phase algorithm design}\nWe aim to design a two-phase algorithm to minimize \\(J\\). Let \\(\\alpha\\) and \\(\\beta\\) satisfy \\(1 \\le K^{\\alpha}L^{\\beta} \\le T\\). The algorithm proceeds in two stages: an initial uniform exploration phase, followed by an adaptive exploitation phase based on the collected data.\n\n\\paragraph{Exploration phase (rounds $1,\\dots,K^{\\alpha}L^{\\beta}$).}\nPull every arm in a round--robin fashion.\n\n\n\\paragraph{Exploitation phase (rounds $K^{\\alpha}L^{\\beta}+1,\\dots,T$).}\nRun the standard UCB rule.\n\nThe resulting $J$ is denoted $J(\\alpha,\\beta)$.\n \n### Task\u00a0\n\nHere we analyze the asymptotic behavior of $J$, focusing only on the constants $K$ and $L$, ignoring the logarithmic term and other constant factors.\n\n \\textbf{Goal:} Find the upper bounds and lower bounds of $\\alpha$ and $\\beta$ $\\{\\bar\\alpha,\\bar\\beta,\\underline{\\alpha},\\underline{\\beta}\\}$ such that\n \\[\n \\forall \\alpha \\in [\\bar\\alpha,\\underline{\\alpha}],\\ \\forall \\beta\\in[\\bar\\beta,\\underline{\\beta}];\\quad J(\\alpha,\\beta) = \\min_{x,y \\in S} J(x,y) \n \\]\n where\n \\[\n S \\;:=\\; \\bigl\\{\\, \\alpha,\\beta \\in \\mathbb{R} \\,:\\; 1 \\le K^{\\alpha}L^\\beta \\le T \\bigr\\}.\n \\]", "contributor": "Zichen Wang" }, { "task_id": "Yiqi_02", "query_token_num": 4385, "Engineering Domain": "Computer Architecture Design", "prompt": "# Problem Definition of T10 Benchmark\n\nTo compute a matrix multiplication operator on an inter-core connected AI chip, we need you to derive an execution plan using T10's abstraction. For more information about this problem, please refer to \"Background Information of T10 Benchmark\".\n\n**The Computation Task:** \nThe matrix multiplication (MatMul) to be computed is defined as $C[m,n] += A[m,k]*B[k,n]$, where $m = 32$, $k = 5120$, and $n = 15360$. The input and output tensors are all in FP16 format (2 bytes per data element). To find better partitioning plans, you may consider padding this operator along any of its dimensions. However, there will be performance overhead if you pad too much.\n\n**The Hardware:** \nWe use an inter-core connected AI chip called IPU Mk2. An IPU chip has 1,472 cores, and each core executes independent threads in parallel with a private 624KB scratchpad memory, which adds up to a total of 896MB on-chip memory. The IPU cores are interconnected by high-bandwidth low-latency links. Each core can access the scratchpad memory of another core at 5.5GB/s, offering an aggregated inter-core all-to-all bandwidth of $1472 \\times 5.5$ GB/s $\\approx 8$ TB/s [1]. Inside each core, there is a systolic array of shape $16 \\times 16$, which can compute a partition of the MatMul operator at high throughput. If the sub-MatMul to be computed on each core does not have a shape that is a multiple of the systolic array shape, this sub-MatMul must be padded to align with the systolic array shape.\n\n**The Execution Plan:** \nIn this problem, we need you to derive a fast execution plan that computes the above MatMul on an IPU chip. First, this plan should ensure that at any time during execution, the sub-tensor partitions on each core do not overflow the per-core SRAM size. Second, the partition factors in this plan should comply with all constraints defined in T10's background information. Third, this plan should use no more than 1,472 cores. Finally, this plan should try to minimize the total execution time, which is the sum of per-core computation time and inter-core communication time.\n\n**The Output Format:** \nYou should output the execution plan in the following format:\n\n- `F_op`: a list of integers with length 3, which are the operator partition factors on dimensions $m$, $k$, and $n$, respectively.\n- `f_t_A_m`: integer, which is the temporal partition factor of tensor A on dimension $m$.\n- `f_t_A_k`: integer, which is the temporal partition factor of tensor A on dimension $k$.\n- `f_t_B_k`: integer, which is the temporal partition factor of tensor B on dimension $k$.\n- `f_t_B_n`: integer, which is the temporal partition factor of tensor B on dimension $n$.\n- `f_t_C_m`: integer, which is the temporal partition factor of tensor C on dimension $m$.\n- `f_t_C_n`: integer, which is the temporal partition factor of tensor C on dimension $n$.\n\n---\n\n# Background Information of T10 Benchmark\n\n## 1. Inter-core Connected AI Chip\n\nDeep learning accelerators, such as GPUs and TPUs, are widely recognized for their exceptional computing throughput (e.g., hundreds of Tera-FLOPS), making them ideal for handling large-scale models and high-dimensional data in deep learning. Such effectiveness is largely attributed to their massive parallel cores and specialized accelerator units, e.g., TensorCore. However, to saturate the high computing throughput, they usually require a high-throughput memory system, e.g., a large shared memory with multi-hierarchical cache layers in accelerators. Also, an efficient deep learning compiler [7, 8] is necessary to optimize data reuse across the memory hierarchy, ensuring the computing units are fully utilized. This combination of hardware and software design often yields orders of magnitude higher performance than traditional CPUs for critical deep learning operations, including matrix multiplication and convolution.\n\nDespite the success of existing accelerators, the constantly increasing demand for processing large deep-learning models with higher computation throughput presents a significant challenge to the underlying memory system. To address this challenge, the community is exploring a more scalable architecture with fully distributed memory, such as the Graphcore IPU [2], SambaNova SN10 [5], and Cerebras WSE [3]. Rather than relying on shared-memory architecture, they typically associate each computation core with local memory, and connect the cores via a high-bandwidth on-chip network, creating a large aggregated on-chip memory. However, this unique architecture renders previous deep learning compilers designed for shared-memory architectures, which cannot fully leverage the new architecture's scalability, resulting in significant memory waste.\n\nDesigning a deep learning compiler for distributed memory-based accelerators presents several unique challenges:\n1. Due to the absence of global shared memory, it is necessary to partition the operators, along with their input and output tensors, into sub-operators that can operate independently on each core with only local memory access.\n2. As the local memory on each core is mostly on-chip memory, the aggregated memory capacity is considerably smaller than the off-chip memory. Thus, the compiler must effectively utilize the limited memory capacity to support a model size as large as possible, without compromising on computing performance.\n3. Given that there is usually a trade-off between memory consumption and computation performance for each operator, an end-to-end model compilation must consider the trade-offs among all operators, generating a combinatorial optimization space that is infeasible to solve using existing compilers.\n\nIn this problem, we focus on a representative example of the inter-core connected AI chip: the Graphcore Intelligence Processing Unit (IPU) MK2 [2]. An IPU chip has 1,472 cores, and each core executes independent threads in parallel with a private 624KB scratchpad memory, which adds up to a total of 896MB on-chip memory. Compared to the global shared memory architecture, a key distinction is that IPU cores are interconnected by high-bandwidth low-latency links. Each core can access the scratchpad memory of another core at 5.5GB/s, offering an aggregated inter-core all-to-all bandwidth of $1472 \\times 5.5$GB/s $\\approx 8$TB/s [1].\n\n---\n\n## 2. Background of T10\n\nTo eliminate the excessive memory footprint and redundant inter-core communications of VGM, we map the DNN computation to a _compute-shift_ pattern. In each step, each core independently computes a sub-task with data received from its upstream neighbors and shifts the data to its downstream. The feasibility of this approach for general DNNs comes from this observation: most DNN operators can be divided into regular computation tasks, which load and produce consecutive data tiles of the input and output tensors, respectively.\n\n![Figure 1](./images/figure1.png)\nFigure 1 shows an example that maps a MatMul operator to two cores with the compute-shift style execution. \nBoth (b) and (c) are valid compute-shift execution plans, but with different tradeoffs between memory footprint and communication overhead.\n\n**Example: Mapping MatMul to Two Cores**\nWe show an example that maps a matrix multiplication (MatMul) operator to two cores in Figure 1 (a). \n1. **Partitioning:** We first partition the operator along dimension $m$ onto two cores in Figure 1 (b). By default, both cores hold a copy of the weight tensor, which incurs memory capacity overhead. \n2. **Memory Optimization:** To reduce memory footprint, in Figure 1 (c), we further split the weight tensor along dimension $n$ into two parts and place each part on one of the cores. Then, the computation must be conducted in two steps, as each core holds half of the weight tensor and performs half of its computation per step. Between the computation steps, each core circularly shifts its partition to the next core, forming a shift ring of two cores.\n\n**Advantages of Compute-Shift Pattern**\n1. Eliminates the need for a global memory to store shared data, improving memory capacity utilization. \n2. Evenly distributes communication volume across inter-core connections. \n3. Aligns computation with data tile, avoiding redundant communications to many cores.\n\n**Tradeoff Between Memory Footprint and Communication Overhead**\nFor example, both Figure 1 (b) and (c) show valid execution plans:\n- **Plan (b):** Finishes the entire computation in one step without inter-core communication, but has a higher memory footprint. \n- **Plan (c):** Has less memory footprint but incurs more communication overhead.\n\nIn reality, deriving the best tradeoff is challenging due to multi-dimensional DNN operators and thousands of cores on an IPU chip. An efficient compute-shift execution plan may contain numerous nested shift rings along multiple tensor dimensions, composing a massive tradeoff space to search through.\n\n---\n\n## 3. T10's Execution Plan Format\n\n### $r$Tensor: A New Tensor Abstraction\nT10 introduces a distributed tensor abstraction called RotatingTensor ($r$Tensor). $r$Tensor describes how each tensor is partitioned, mapped, and shifted on the interconnected cores (summarized in Table 1).\n\n**Table 1. Terminologies used in T10**\n| **Symbol** | **Name** | **Description** |\n|------------|------------------------------|-------------------------------------------------------------------------------|\n| `f_s^X` | Spatial Partition Factor | Spatially partitions a tensor X into sub-tensors. |\n| `f_t^X` | Temporal Partition Factor | Temporally partitions a sub-tensor of X into sub-tensor partitions. |\n| `F_op` | Operator Partition Factor | Spatially partitions an entire operator into sub-operators. |\n\nFirst, T10 partitions the computation of an operator onto multiple cores. Based on the data dependency, the computation partitioning will imply how each of its input/output tensor is partitioned. This gives a spatial partition factor ($f_s$), which splits a tensor into sub-tensors. Second, each sub-tensor may be required by multiple cores. To share a sub-tensor among them, we specify how the sub-tensor is further partitioned among the cores using a temporal partition factor ($f_t$). $f_t$ also specifies how the partitions of a sub-tensor are circularly shifted among the cores. Altogether, a set of $r$Tensors of an operator defines a compute-shift execution plan. The numerous possible $r$Tensor configurations of an operator generate a huge search space of execution plans.\n\n![Figure 2](./images/figure2.png)\nFigure 2 shows the llustration of rTensor partitioning and rotating.\n\nSpecifically, $f_s$ and $f_t$ are vectors with a length equal to the number of dimensions of a tensor, indicating how the tensor is partitioned along each dimension. For example, in Figure 2 (a), a tensor $T$ of shape $[6,8]$ is partitioned onto 8 cores by a spatial factor $f_s=[2,1]$, forming 2 sub-tensors of shape $[3,8]$. Thus, to share each sub-tensor among 4 cores without incurring high memory footprint, a temporal factor $f_t=[1,2]$ further partitions each sub-tensor into 2 partitions with shape $[3,4]$, as shown in Figure 2 (b). It forms $\\frac{4}{2} = 2$ rotation rings with 2 cores in each, where cores share the sub-tensor by circularly shifting its partitions. In comparison, Figure 2 (c) shows how another $f_t=[1,4]$ splits the same sub-tensor to 4 partitions, on $\\frac{4}{4}=1$ rotation ring with 4 cores.\n\n---\n\n## 3.2. Compute-Shift Execution Plan\n\nUsing the $r$Tensor abstraction, T10 organizes the computation of a general DNN operator into a compute-shift pattern, where the operator's computation and tensors are partitioned to individual cores and their local memories. The entire computation involves multiple compute-shift steps until each tensor has been shifted across all cores. Each compute step is defined as a *sub-task*. In each compute-shift step, each core computes a sub-task and shifts local tensors to its neighbors. We now discuss how T10 partitions DNN operators into compute-shift-based execution plans.\n\n### Operator representation.\nTo represent an operator's computation, T10 uses tensor expression [6], which defines how each output tensor value is computed from the input values. For example, a matrix multiplication of tensors $A$ in shape $[M,K]$ and $B$ in $[K,N]$ into $C$ is defined as\n\n$C[m,n] \\longleftarrow A[m,k]*B[k,n]$,\n\nwhere $m$, $k$, and $n$ are axes to index the elements in each tensor. Equation (1) indicates that any value in $C$ indexed by $m$ and $n$ (i.e., $C[m,n]$) is computed by summing $A[m,k]*B[k,n]$ over all possible indices $k$. T10 supports all common operators, like MatMult and Convolution, from DNN workloads in both inference and training. For a few special cases like Sort, which cannot be represented in tensor expression, T10 uses the implementations from the vendor library.\n\n### Partitioning an operator.\nTo map an operator to interconnected cores, T10 first partitions it into parallel *sub-operators* along all unique axes in its tensor expression, using an *operator partition factor* ($F_{op}$). For example, Equation (1) contains axes $m$, $k$, and $n$, then $F_{op}$ is a vector of three integer factors specifying how the three axes are spatially partitioned. The total number of sub-operators is the product of all elements in $F_{op}$. For example, $F_{op}=[2,1,4]$ for $[m,k,n]$ slices the operator into 8 sub-operators on 8 cores, each computing a $\\lceil\\frac{M}{2},\\frac{K}{1}\\rceil \\times \\lceil\\frac{K}{1},\\frac{N}{4}\\rceil$ sub-matrix multiplication.\n\n### Partitioning $r$Tensors.\nT10 then uses $F_{op}$ to derive the spatial partition factor $f_s$ for each tensor, following the data dependencies in tensor expression. With the same example, for $F_{op}=[2,1,4]$ on $[m,k,n]$, the spatial partition factor for the tensor A is $f_s^A=[2,1]$ for axes $m$ and $k$. Similarly, for tensors B and C, we have $f_s^B=[1,4]$ and $f_s^C=[2,4]$.\n\nIf a tensor's dimensions do not include some axis in $F_{op}$, each of the sliced sub-tensors is required by multiple sub-operators along the missing axis. Thus, once the spatial factor determines the number of cores that will share a sub-tensor, the temporal factor determines how we split the sub-tensor across these cores into rotation ring(s). In the above example, $F_{op}$ partitions the entire operator onto $2 \\times 1 \\times 4 = 8$ cores, and $f_s^B$ spatially partitions tensor B into $1 \\times 4 = 4$ sub-tensors. Thus, each sub-tensor is shared by $P=\\frac{8}{4}=2$ cores. Then, a temporal factor $f_t^B=[2,1]$ further splits each sub-tensor into $2 \\times 1 = 2$ partitions, forming $\\frac{P}{2}=1$ rotation ring.\n\nT10 enforces that the product of elements in $f_t$, or $\\prod f_t$, is a divisor of the number of cores that shares the sub-tensor ($P$), so that the number of rotation rings (i.e., $\\frac{P}{\\prod f_t}$) is an integer. If there is more than one rotation ring, we replicate each sub-tensor $\\frac{P}{\\prod f_t}$ times to ensure that each ring shares one copy of the sub-tensor. While the duplication consumes memory space, it may reduce the number of rotation steps by allowing a larger sub-task on each core at each step, which enables a trade-off between memory usage and communication cost.\n\n![Figure 3](./images/figure3.png)\nFigure 3 shows an example of the rotation of rTensor.\nThe compute-shift executions of the sub-operators need to be aligned.\n\n### Aligning the rotations of $r$Tensors.\nSince a general DNN operator can have various tensor shapes, a naive partitioning plan can easily cause the tensor shifting and the sub-task computing at an unaligned pace. In Figure 3 (a), we still use the MatMult operator in Equation (1) as an example. We partition it into a $2 \\times 4$ grid in Figure 3 (b), with the specified partition factors. Note that both A and B are temporally partitioned along axis $k$, but with different $f_t$ factors.\n\nThe rotating paces of tensors in one operator must be aligned to ensure correct data dependency. In Figure 3 (b), tensors A and B are shifted with different paces along axis $k$. To synchronizes the paces, each core shifts A for 2 times along $k$ for each time B is shifted, and computes a sub-task (i.e., a sub-MatMult) of shape $[\\text{m=1, k=1, n=1}]$ for each time A is shifted. This requires 4 compute steps to finish the sub-operator on this core, where A is shifted after each step and B is shifted every 2 steps.\n\n### Alignment constraints.\nTo ensure that a $r$Tensor configuration can be translated into a valid execution plan, the product of the temporal partition factors of a tensor (i.e., the total number of temporal partitions) should be a factor of the replication number caused by spatial partitioning. Additionally, for different tensors of an operator that share a common dimension, all their temporal factors on this dimension should be aligned. Thus, any pair of temporal factors should be a factor or multiple of each other. This approach allows each tensor or sub-tensor to flow across cores at a different pace, while ensuring that corresponding tensor partitions can meet at the same time step on a specific core. For instance, in the matrix multiplication illustrated in Figure 3(b), tensor A has a temporal factor of 4 along dimension $k$, tensor B has a factor of 2, and these factors along $k$ (i.e., 4 and 2) must be a factor or multiple of each other.\n\n### Sub-operator scheduling.\nWith the above constraints, we can organize an operator's computation into a valid compute-shift execution plan. At each step, each sub-operator computes a sub-task partitioned by $F_{op}$ and the $f_t$ along each axis. Each sub-operator iterates over all its sub-tasks by nested-looping through the axes of this operator. Between sub-tasks, an $r$Tensor is rotated along the currently iterating axis for all its sub-tensors, until all sub-tasks are enumerated.\n\nSpecifically, T10 organizes the computation on each core as nested loops of interleaved compute and shift stages. Each loop corresponds to a temporally partitioned dimension. For example, if there are two dimensions to shift, $m$ and $n$, with $m$ shifting twice and $n$ shifting once, then there are two valid 5-time shift schedules: (1) $m$ is the inner loop, i.e., $\\text{shift}(m) \\times 2 \\rightarrow \\text{shift}(n) \\rightarrow \\text{shift}(m) \\times 2$; and (2) $n$ is the inner loop, i.e., $\\text{shift}(n) \\rightarrow \\text{shift}(m) \\rightarrow \\text{shift}(n) \\rightarrow \\text{shift}(m) \\rightarrow \\text{shift}(n)$. To determine the optimal loop order, T10 designates the dimension belonging to the tensor with the smaller size as the inner loop to reduce the total communication volume, as the inner loop is executed more times. To generate local computations for each core, T10 invokes the corresponding compute function with the partition configuration and the tensor expression.\n\n---\n\n# References\n[1] Zhe Jia, Blake Tillman, Marco Maggioni, and Daniele Paolo Scarpazza. 2019. Dissecting the Graphcore IPU Architecture via Microbenchmarking. \n[2] Simon Knowles. 2021. Graphcore Colossus Mk2 IPU. \n[3] Sean Lie. 2021. Multi-Million Core, Multi-Wafer AI Cluster. \n[4] Yiqi Liu et al. 2024. Scaling Deep Learning Computation over the Inter-Core Connected Intelligence Processor with T10. \n[5] Raghu Prabhakar and Sumti Jairath. 2021. SambaNova SN10 RDU. \n[6] Nicolas Vasilache et al. 2018. Tensor Comprehensions. \n[7] Lianmin Zheng et al. 2020. Ansor. \n[8] Hongyu Zhu et al. 2022. ROLLER. ", "contributor": "Yiqi Liu" }, { "task_id": "XW_01", "query_token_num": 1116, "Engineering Domain": "Operating System Design", "prompt": "## Task Description\nIn this task, you will be provided with a filesystem image. You are required to develop separate programs\u2014each implementing a different filesystem operation (e.g., create, read, update, delete)\u2014to modify the corresponding sections of that image. Your objective is to ensure that each program correctly performs its assigned operation on the intended part of the filesystem image while preserving its overall integrity.\n\nHere is the class definition for your reference:\n\nfrom dataclasses import dataclass, field\nfrom typing import List, Dict, Optional\n\n@dataclass\nclass SuperBlock:\n \"\"\"File system superblock, stores metadata.\"\"\"\n block_size: int # Size of each block (bytes)\n total_blocks: int # Total number of blocks\n inode_count: int # Total number of inodes\n free_block_bitmap: List[bool] # Free block bitmap, True = free\n\n@dataclass\nclass Inode:\n \"\"\"Inode structure, stores file/directory metadata.\"\"\"\n ino: int # Inode number\n is_dir: bool # Whether this inode is a directory\n size: int # File size (bytes)\n direct_blocks: List[int] # List of direct block indices\n # Optional: add indirect block pointers, multi-level indexing, permissions, timestamps, etc.\n\n@dataclass\nclass DirEntry:\n \"\"\"Directory entry: maps a filename to an inode.\"\"\"\n name: str\n inode: int\n\n@dataclass\nclass FileSystemImage:\n \"\"\"Complete file system image structure.\"\"\"\n superblock: SuperBlock\n inodes: Dict[int, Inode] = field(default_factory=dict)\n # Directory tree: inode -> list of entries in that directory; valid only for is_dir=True inodes\n directories: Dict[int, List[DirEntry]] = field(default_factory=dict)\n # Data block storage area: index corresponds to block number, content is bytes\n data_blocks: List[Optional[bytes]] = field(default_factory=list)\n\n def __post_init__(self):\n # Initialize data block storage area\n if not self.data_blocks:\n self.data_blocks = [None] * self.superblock.total_blocks\n\n def allocate_block(self) -> int:\n \"\"\"Allocate a block from the free bitmap and return its index; raise if none available.\"\"\"\n for idx, free in enumerate(self.superblock.free_block_bitmap):\n if free:\n self.superblock.free_block_bitmap[idx] = False\n self.data_blocks[idx] = b'' # Initialize with empty content\n return idx\n raise RuntimeError(\"No free blocks available\")\n\n def free_block(self, block_idx: int):\n \"\"\"Free the specified block index.\"\"\"\n if 0 <= block_idx < self.superblock.total_blocks:\n self.superblock.free_block_bitmap[block_idx] = True\n self.data_blocks[block_idx] = None\n else:\n raise IndexError(\"Block index out of range\")\n\n def create_inode(self, is_dir: bool) -> Inode:\n \"\"\"Create a new inode and return it.\"\"\"\n new_ino = len(self.inodes) + 1\n if new_ino > self.superblock.inode_count:\n raise RuntimeError(\"No free inodes\")\n inode = Inode(\n ino=new_ino,\n is_dir=is_dir,\n size=0,\n direct_blocks=[]\n )\n self.inodes[new_ino] = inode\n if is_dir:\n self.directories[new_ino] = []\n return inode\n\n def add_dir_entry(self, dir_ino: int, name: str, inode: int):\n \"\"\"Add a directory entry to the directory with inode dir_ino.\"\"\"\n if dir_ino not in self.directories:\n raise RuntimeError(\"Not a directory inode\")\n self.directories[dir_ino].append(DirEntry(name=name, inode=inode))\n\n\n### Task 1\ndef read(fs_img: FileSystemImage, name: str, pos: int, length: int) -> str:\n \"\"\"\n Read up to `length` bytes from the file called `name` in the given FileSystemImage,\n starting at byte offset `pos`, and return the data as a Python string (decoded as UTF\u20118).\n\n Parameters:\n - fs_img: the FileSystemImage instance containing inodes, directories, and data blocks.\n - name: an absolute or relative path to the target file within `fs_img`.\n - pos: the byte offset within the file at which to begin reading.\n - length: the maximum number of bytes to read.\n\n Returns:\n - A Python `str` containing the bytes read, decoded from UTF\u20118.\n\n Behavior:\n 1. If the file `name` does not exist or refers to a directory, raise a `FileNotFoundError` or `IsADirectoryError` respectively.\n 2. If `pos` is negative or exceeds the file\u2019s size, raise an `ValueError`.\n 3. If `pos + length` extends beyond the end of file, read only up to EOF.\n 4. Read the appropriate data blocks from `fs_img.data_blocks` according to the file\u2019s inode `direct_blocks`, concatenating and slicing as needed.\n 5. Decode the resulting bytes to a UTF\u20118 string and return it.\n \"\"\"\n # Your implementation here\u2026\n\n", "contributor": "Licheng Xu,Jinwen Wang" }, { "task_id": "HJ_01", "query_token_num": 192, "Engineering Domain": "Robotics", "prompt": "## Task Description\nThe company let you assembly a car for track following design competition. The car control is simply a look ahead point tracking model. A path with length of 56 meters is given, and your car should finish test in 10 sec with max tolerance 1 meters of track-off distance. You are given 300 dolors budget. You can control four different value: refresh rate, acceleration, max velocity and lookahead distance. The refreshing cost is 5 dollar/hz; the acceleration cost is 10 dolors/ m/s^2; the max motor velocity is 8 dolors/ m/s, and the look ahead camera distance cost 1 dolor/ meter. \n\n### Task \nYour task is to design the car setup with: refresh rate, acceleration, max velocity and lookahead distance so that: \nTotal runtime < 10 sec\nMax off-track error < 1 meter\nBudget cost < 300 dollars\n\n", "contributor": "Jingjie He" }, { "task_id": "ZC_02", "query_token_num": 420, "Engineering Domain": "Control Design", "prompt": "## Task Description\nConsider the discrete\u2010time Lurye feedback interconnection composed of the following blocks:\n\nNonlinear block:\n \\[\n w_k = \\phi(v_k), \n \\quad\n \\phi:\\mathbb R\\to\\mathbb R\\text{ satisfies }\n 0 \\;\\le\\; \\frac{\\phi(v_1)-\\phi(v_2)}{v_1-v_2}\\;\\le\\;1,\n \\;\\forall v_1\\neq v_2.\n \\]\n \nLinear time\u2010invariant block:\n \\[\n \\begin{cases}\n x_{k+1} = A\\,x_k + \\alpha\\,B\\,w_k,\\\\\n y_k = C\\,x_k + D\\,w_k,\n \\end{cases}\n \\quad\n \\alpha>0\\text{ multiplies the input matrix }B,\n \\]\n with numerical values\n \\[\n A = \\begin{bmatrix}0.5000 & 0 \\\\1.0000 & 0\\end{bmatrix},\n B = \\begin{bmatrix}1 \\\\0\\end{bmatrix},\\quad\n C = \\begin{bmatrix}2.0000 & 0.9200\\end{bmatrix},\n D = [\\,0\\,].\n \\]\n \nInterconnection\uff1a\n \\[\n v_k = d_k - y_k,\\qquad\n w_k = \\phi(v_k),\\qquad\n e_k = w_k.\n \\]\n \n### Task\u00a0\nCalculate the $\\alpha$ where\n\\[\n \\alpha_{\\max}\n = \\max\\bigl\\{\\alpha>0 \\mid \\text{the closed\u2010loop is absolutely stable for all }\\phi\\text{ in the sector}\\bigr\\}.\n\\]\nPlease note the properties of the nonlinear operator $\\phi$, you are encouraged to use semidefinite programming and bisection.\n", "contributor": "Zichen Wang" }, { "task_id": "Ziheng_01", "query_token_num": 593, "Engineering Domain": "Control Design", "prompt": "## Task Description\nYou are given an aircraft pitch-axis plant model and asked to design a Robust-Servo LQR (RS-LQR) controller. Consider the continuous\u2010time state\u2013space model\n\\[\n\\dot{\\bm x}_p = A_p\\,\\bm x_p + B_p\\,u,\\quad\ny = C_p\\,\\bm x_p + D_p\\,u,\n\\]\nwhere\n\\[\n\\bm x_p = [\\alpha,\\; q,\\; \\delta_e,\\;\\dot\\delta_e]^T,\\quad\nu = \\delta_{\\mathrm{cmd}},\\quad\ny = [A_z,\\;\\alpha,\\;q,\\;\\delta_e,\\;\\dot\\delta_e]^T.\n\\]\nThe plant matrices are\n\\[\nA_p = \\begin{bmatrix}\n-1.3046 & 1.0 & -0.21420 & 0 \\\\\n 47.71 & 0 & -104.83 & 0 \\\\\n 0 & 0 & 0 & 1.0 \\\\\n 0 & 0 & -12769.0 & -135.6\n\\end{bmatrix},\\quad\nB_p = [0,\\;0,\\;0,\\;12769.0]^T,\n\\]\n\\[\nC_p = \\begin{bmatrix}\n-1156.9 & 0 & -189.95 & 0 \\\\\n 1 & 0 & 0 & 0 \\\\\n 0 & 1 & 0 & 0 \\\\\n 0 & 0 & 1 & 0 \\\\\n 0 & 0 & 0 & 1\n\\end{bmatrix},\\quad\nD_p = \\mathbf{0}_{5\\times1}.\n\\]\nDesign a dynamic state\u2013feedback controller\n\\[\n\\dot{\\bm x}_c = A_c\\,\\bm x_c + B_{c1}\\,y + B_{c2}\\,r,\\quad\nu = C_c\\,\\bm x_c + D_{c1}\\,y + D_{c2}\\,r,\n\\]\nsuch that:\n\\begin{itemize}\n \\item The closed\u2010loop rise time of \\(A_z\\) is \\(<0.2\\)\u00a0s.\n \\item The system is stable.\n \\item The gain margin is \\(>3\\) dB.\n \\item The phase margin is \\(>30\\) degrees.\n\\end{itemize}\n\nPlease output all six controller matrices Ac, Bc1, Bc2, Cc, Dc1, Dc2 that satisfies the above requirements.", "contributor": "Ziheng Guo" }, { "task_id": "XG_02", "query_token_num": 681, "Engineering Domain": "Control Design", "prompt": "Consider a nanopositioning stage modeled by the following seventh-order linear state-space system. This model is fitted to frequency response data collected from the physical device:\nA = \\begin{bmatrix}\n-3360.27884342382 & 24650.4407238876 & -24650.4407238876 & 24650.4407238876 & -24650.4407238876 & 24650.4407238876 & -6162.61018097190 \\\\\n-3270.26403683917 & 10278.7248098086 & -7476.39347226054 & 7476.39347226054 & -7476.39347226054 & 7476.39347226054 & -1869.09836806513 \\\\\n-2657.10970968037 & 10628.4388387215 & -13430.7701762696 & 16233.1015138177 & -16233.1015138177 & 16233.1015138177 & -4058.27537845441 \\\\\n-3954.03177459846 & 15816.1270983939 & -15816.1270983939 & 13013.7957608458 & -10211.4644232977 & 10211.4644232977 & -2552.86610582443 \\\\\n-2325.45756017668 & 9301.83024070671 & -9301.83024070671 & 9301.83024070671 & -12104.1615782548 & 14906.4929158029 & -3726.62322895072 \\\\\n-1665.81075466004 & 6663.24301864017 & -6663.24301864017 & 6663.24301864017 & -6663.24301864017 & 3860.91168109210 & -264.645085886005 \\\\\n-1596.51916299641 & 6386.07665198562 & -6386.07665198562 & 6386.07665198562 & -6386.07665198562 & 6386.07665198562 & -4398.85050054448 \\\\\n\\end{bmatrix},\nB = \\begin{bmatrix}\n33.1501 \\\\\n29.2147 \\\\\n49.7430 \\\\\n55.4071 \\\\\n43.2351 \\\\\n22.8726 \\\\\n24.9153 \\\\\n\\end{bmatrix},\nC = \\begin{bmatrix}\n41.1585 & -164.6342 & 164.6342 & -164.6342 & 164.6342 & -164.6342 & 41.1585\n\\end{bmatrix}\nD = \\begin{bmatrix}\n0\n\\end{bmatrix}.\n\nYour task is to design a robust feedback controller using the loop shaping method that satisfies the following frequency-domain performance requirements:\n-Closed-loop bandwidth: approximately 85 Hz (\u00b110 Hz tolerance)\n-Gain margin: greater than 1.5 dB\n-Phase margin: greater than 60 degrees\n\n", "contributor": "Xingang Guo" }, { "task_id": "XG_05", "query_token_num": 378, "Engineering Domain": "Control Design", "prompt": "## Task Description\nIn this task, you are required to design a feedback controller to regulate the temperature of a chemical reactor using a heat exchanger system. The reactor, modeled as a stirred tank, is shown in the accompanying figure. A liquid stream enters the tank from the top inlet and is continuously mixed. To maintain the liquid at a desired constant temperature, the amount of steam supplied to the heat exchanger (located at the bottom of the tank) must be adjusted. This is achieved by modulating the control valve that governs steam flow. Your objective is to design a controller that ensures the reactor temperature remains stable and responds effectively to disturbances and setpoint changes.\n\n### Task 1\nYour first task is to derive a first-order with delay transfer function $G(s) = exp(-theta*s)/(1+tau*s)$ to model the dynamics of the stirred tank. The second figure shows a measured step response of the stirred tank, with $t_1 = 23$ s and $t_2 = 36$ s. The values of $t_1$ and $t_2$ are the times where the step response reaches 28.3% and 63.2% of its final value, respectively. Please determine the value of $\\theta$ and $\\tau$ from the step response figure using the given information. Then the transfer function will be $G(s) = exp(-theta*s)/(1+tau*s)$.\n\n### Task 2\nYour second task is to design a feedback controller to regulate the temperature of the stirred tank using the model you derived in Task 1 that satisfies the following requirements:\n- Gain margin: >= 7 dB\n- Phase margin: >= 60 degrees\n- Overshoot: <= 10% (for a step reference input)\n- Settling time: <= 150 s (for a step reference input)\n", "contributor": "Xingang Guo" }, { "task_id": "YF_05", "query_token_num": 454, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nIn this task, you are required to determine a suitable cross-sectional area A for a specified member of a simple 2D truss, which will be evaluated using a static linear-elastic finite-element model in MATLAB.\n\nThe truss is defined by three nodes and three pin-connected members forming a right triangle:\nYou are given the following fixed parameters:\n\n- Nodes (coordinates in mm):\nNode1 - (0,0) (ux=uy=0)\nNode2 - (1000,0)(uy = 0)\nNode3 - (1000,1000)\n\n- A vertical downward force of 4000 N applied at Node 3\n\n- Members (element connectivity):\n Node 1 \u2192 Node 2 (A = 100mm^2)\n\n Node 2 \u2192 Node 3 \u2190 design this member\u2019s area\n\n Node 1 \u2192 Node 3 (A = 100mm^2)\n\n- Material properties:\n - Young\u2019s modulus: 210,000 MPa\n - Poisson\u2019s ratio: 0.3\n\nPerformance criterion:\nThe maximum nodal displacement must satisfy \u03b4 max < 0.5mm\nThe score depends on the ratio of the maximum measured angle to the allowable threshold. If that ratio falls between seventy percent and ninety percent, the beam earns the full 100 points. If the ratio is below seventy percent, partial credit is awarded in direct proportion to how close it is to seventy-percent (with zero displacement scoring zero and seventy-percent scoring 100). If the ratio lies between ninety percent and one hundred percent, points are deducted in proportion to how far it exceeds ninety percent (dropping from 100 at ninety percent down to zero at the full threshold). Any ratio below zero or above one hundred percent results in a score of zero.\n---\n\n### Task\n\nYour task is to:\n- a structurally sound value for the area A (in mm\u00b2) of the member between Node 2 and Node 3. You must have a numerical computation and analysis.\n- Provide a brief justification for your choice of thickness, considering stiffness, loading, and geometric constraints\n\nYou do **not** need to evaluate the angle yourself. The simulation and evaluation will be done separately.\n\n", "contributor": "Yufan Zhang" }, { "task_id": "YF_02", "query_token_num": 450, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nIn this task, you are required to determine a suitable thickness (Th) of a rectangular steel beam subjected to a dual-point load, applied at the quarter-span locations, and evaluated using 3D structural simulation in MATLAB\u2019s PDE Toolbox.\n\nThe beam is modeled as a simply supported rectangular beam with a solid rectangular cross-section (width \u00d7 thickness). It is loaded vertically downward by two equal forces applied symmetrically at 1/4 and 3/4 of the beam span.\n\nYou are given the following fixed parameters:\n\n- 'L = 1000' mm (Total span length)\n- 'w = 40' mm (Beam width, constant)\n\n- 'Height = Th' mm (Beam thickness to be designed)\n- Two vertical downward forces: F = 1000 N each, applied at quarter-span locations\n- Material properties:\n - Young\u2019s modulus: 210,000 MPa\n - Poisson\u2019s ratio: 0.3\n\nThe beam will be evaluated using a static linear elasticity model in 3D (extruded along the beam width). The performance criterion is that the maximum vertical displacement (uy) must be less than 1 mm under the given load.\nThe score depends on the ratio of the maximum measured displacement to the allowable threshold. If that ratio falls between seventy percent and ninety percent, the beam earns the full 100 points. If the ratio is below seventy percent, partial credit is awarded in direct proportion to how close it is to seventy-percent (with zero displacement scoring zero and seventy-percent scoring 100). If the ratio lies between ninety percent and one hundred percent, points are deducted in proportion to how far it exceeds ninety percent (dropping from 100 at ninety percent down to zero at the full threshold). Any ratio below zero or above one hundred percent results in a score of zero.\n\n---\n\n### Task\n\nYour task is to:\n- Propose a structurally sound value for `Th` (thickness of the beam, in mm)\n- Provide a brief justification for your choice of thickness, considering stiffness, loading, and geometric constraints\n\nYou do **not** need to evaluate the displacement yourself. The simulation and evaluation will be done separately.\n\n", "contributor": "Yufan Zhang" }, { "task_id": "qjlim2_01", "query_token_num": 356, "Engineering Domain": "Signal Processing", "prompt": "## Background\n\nMicrostrip patch antennas are widely used in modern wireless communication due to their low profile, ease of fabrication, and compatibility with printed circuit board (PCB) technology. \n\nIn this task, you are to design a rectangular microstrip patch antenna that satisfy the task objective and constraints stated below.\n\nThe antenna is centered at the origin with the patch facing the +z direction. The feed point lies in the x-y plane. The dielectric substrate must be selected from commercially available Rogers low-loss laminates, and the chosen material's permittivity will influence the design.\n\n## Task Objective and Constraints\n\nYour task is to design a rectangular microstrip patch antenna that meets the following specifications:\n\n- Resonant Frequency: 1.537 GHz (S11 <= \u201310 dB)\n- Bandwidth: >= 50 MHz\n- Gain: >= 3 dBi\n- Volume Constraint (Ground Plane Size) [ Length \u00d7 Width \u00d7 Height ]: <= 100 mm \u00d7 100 mm \u00d7 10 mm\n- Feed Method: 50-ohm coaxial pin feed (from below substrate)\n- Substrate Material: Rogers low-loss laminate (commercially available)\n\n## Design Inputs\n\nDetermine the optimal design parameters to satisfy the task objectives:\n\n- Length of Metallic Patch in mm: length_mm\n- Width of Metallic Patch in mm: width_mm\n- Substrate height in mm: height_mm\n- Relative permittivity of selected Rogers material: epsilon_r\n- Feed position in the x direction relative to patch center: feed_offset_x_mm\n- Confidence of your design: confidence\n\n## Design Context\n\n- Ground Plane Size is 1.5 times max(Length, Width)\n- Patch size (Length and Width) have to be smaller than ground plane size\n", "contributor": "Qi Jian Lim\n" }, { "task_id": "XZ_03", "query_token_num": 1485, "Engineering Domain": "Robotics", "prompt": "## Task Description\nYou are given a Webots world file named 'construction_site.wbt' with some walls (obstacles) and a controller file named \"robot_controller.py\", you should first read the world info as shown below, then choose a path planning algorithm to generate the shortest path from start point to goal point without hitting any obstacles or walls. The path should satisfy the following requirements: The small inspection robot's starting position is at the site entrance (0,0,0), and we set the goal position to the far corner inspection point (49,39,0). Suppose this inspection robot can only navigate on grid nodes (i.e., x and y values are integers). \n\nThe construction_site.wbt contains the following world info:\n#VRML_SIM R2025a utf8\n\nEXTERNPROTO \"https://raw.githubusercontent.com/cyberbotics/webots/R2025a/projects/objects/backgrounds/protos/TexturedBackground.proto\"\nEXTERNPROTO \"https://raw.githubusercontent.com/cyberbotics/webots/R2025a/projects/objects/backgrounds/protos/TexturedBackgroundLight.proto\"\n\nWorldInfo {\n basicTimeStep 16\n}\n\nViewpoint {\n orientation 0.57 -0.495 -0.656 4.55\n position 3.88 -16.8 99.5\n}\n\nTexturedBackground {\n}\n\nTexturedBackgroundLight {\n}\n\nDEF FLOOR Solid {\n translation 25 20 0\n name \"floor\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.8 0.8 0.8\n roughness 1\n metalness 0\n }\n geometry Box {\n size 50 40 0.1\n }\n }\n ]\n boundingObject Box {\n size 50 40 0.1\n }\n}\n\n# Vertical wall from (10,5) to (10,35) \nDEF VERTICAL_WALL_1 Solid {\n translation 10 20 0.5\n name \"vertical_wall_1\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 30 1\n }\n }\n ]\n boundingObject Box {\n size 1 30 1\n }\n}\n\n# Horizontal wall from (10,20) to (40,20) \nDEF HORIZONTAL_WALL Solid {\n translation 25 20 0.5\n name \"horizontal_wall\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 30 1 1\n }\n }\n ]\n boundingObject Box {\n size 30 1 1\n }\n}\n\n# Vertical wall from (30,0) to (30,15)\nDEF VERTICAL_WALL_2 Solid {\n translation 30 7.5 0.5\n name \"vertical_wall_2\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 15 1\n }\n }\n ]\n boundingObject Box {\n size 1 15 1\n }\n}\n\n# Obstacle cluster from (20,25) to (25,30) \nDEF OBSTACLE_CLUSTER Solid {\n translation 22.5 27.5 0.5\n name \"obstacle_cluster\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 5 5 1\n }\n }\n ]\n boundingObject Box {\n size 5 5 1\n }\n}\n\n# Random obstacles \nDEF OBSTACLE_1 Solid {\n translation 15 10 0.5\n name \"obstacle_1\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n boundingObject Box {\n size 1 1 1\n }\n}\n\nDEF OBSTACLE_2 Solid {\n translation 25 5 0.5\n name \"obstacle_2\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n boundingObject Box {\n size 1 1 1\n }\n}\n\nDEF OBSTACLE_3 Solid {\n translation 35 25 0.5\n name \"obstacle_3\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n boundingObject Box {\n size 1 1 1\n }\n}\n\nDEF OBSTACLE_4 Solid {\n translation 40 30 0.5\n name \"obstacle_4\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n boundingObject Box {\n size 1 1 1\n }\n}\n\nDEF OBSTACLE_5 Solid {\n translation 45 15 0.5\n name \"obstacle_5\"\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n boundingObject Box {\n size 1 1 1\n }\n}\n\n# Robot node - simplified to avoid physical features\nRobot {\n translation 0 0 0.5\n name \"robot\"\n controller \"robot_controller\"\n supervisor TRUE\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 1 0 0\n roughness 1\n metalness 0\n }\n geometry Sphere {\n radius 0.500000\n subdivision 2\n }\n }\n ]\n boundingObject Sphere {\n radius 0.500000\n }\n}\n\n\n## Required Results:\n1. The complete path as an ordered list of coordinates from start to goal\n2. The total path length (in meters)\n3. The algorithm used (A*, Dijkstra, etc.)\n4. The number of nodes explored during the search\n5. Whether 4-connected or 8-connected movement was used", "contributor": "Xiayu Zhao\n" }, { "task_id": "XZ_04", "query_token_num": 1452, "Engineering Domain": "Robotics", "prompt": "## Task Description\nYou are given a Webots world file named 'construction_site.wbt' with some walls (obstacles) and a controller file named \"robot_controller.py\", you should first read the world info as shown below, then generate a trajectory from start point to goal point without hitting any obstacles. The trajectory should satisfy the following requirements: \n\n 1. The format of trajectory should be written as (t, X, Y, Z, v, a), where t is time, X, Y, Z are the 3D coordinates of the robot, v is velocity, a is acceleration. The small inspection robot's starting position is at the site entrance (0,0,0,0,0,0), and we set the goal position to the far corner inspection point (t,19,24,0,0,a). \n 2. The trajectory should follow the safety constraints: \n 2.1 In the WHITE_ZONE solid area, the robot's maximum speed should not exceed 1m/s;\n 2.2 In the RED_ZONE solid area, the robot's maximum speed should not exceed 2m/s;\n 2.3 In the GREEN_ZONE solid area, the robot's maximum speed should not exceed 0.5m/s;\n 3. The entire trajectory can only be in the above three zones, i.e., the robot can not move out from those zones.\n\nThe construction_site.wbt contains the following world info (the length unit is meter):\n#VRML_SIM R2025a utf8\n\nEXTERNPROTO \"https://raw.githubusercontent.com/cyberbotics/webots/R2025a/projects/objects/backgrounds/protos/TexturedBackground.proto\"\nEXTERNPROTO \"https://raw.githubusercontent.com/cyberbotics/webots/R2025a/projects/objects/backgrounds/protos/TexturedBackgroundLight.proto\"\n\nWorldInfo {\n basicTimeStep 16\n}\nViewpoint {\n orientation 0.5228920141164687 -0.5800081356561211 -0.6246394993481706 4.784396651657472\n position -24.923416016240427 -15.86980776668673 82.27805548757286\n}\nTexturedBackground {\n}\nTexturedBackgroundLight {\n}\nDEF WHITE_ZONE Solid {\n translation 0.11 7.12 0\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.8 0.8 0.8\n roughness 1\n metalness 0\n }\n geometry Box {\n size 10 15 0.1\n }\n }\n ]\n name \"floor\"\n boundingObject Box {\n size 10 15 0.1\n }\n}\nDEF RED_ZONE Solid {\n translation 0.11 22.11 0\n children [\n Shape {\n appearance DEF red PBRAppearance {\n baseColor 0.666667 0 0\n roughness 1\n metalness 0\n }\n geometry Box {\n size 10 15 0.1\n }\n }\n ]\n name \"floor(1)\"\n boundingObject Box {\n size 10 15 0.1\n }\n}\nDEF GREEN_ZONE Solid {\n translation 12.63 24.61 0\n rotation 0 0 1 -1.5707953071795862\n children [\n Shape {\n appearance DEF green PBRAppearance {\n baseColor 0 0.333333 0\n roughness 1\n metalness 0\n }\n geometry Box {\n size 10 15 0.1\n }\n }\n ]\n name \"floor(2)\"\n boundingObject Box {\n size 10 15 0.1\n }\n}\nDEF OBSTACLE_2 Solid {\n translation -0.41 4.78 0.5\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n name \"obstacle_4\"\n boundingObject Box {\n size 1 1 1\n }\n}\nDEF OBSTACLE_3 Solid {\n translation 1.58 11.04 0.5\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n name \"obstacle_5\"\n boundingObject Box {\n size 1 1 1\n }\n}\nDEF OBSTACLE_1 Solid {\n translation 3.24 21.69 0.5\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n name \"obstacle_5(1)\"\n boundingObject Box {\n size 1 1 1\n }\n}\nDEF OBSTACLE_4 Solid {\n translation -1.76 18.4 0.5\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n name \"obstacle_5(3)\"\n boundingObject Box {\n size 1 1 1\n }\n}\nDEF OBSTACLE_5 Solid {\n translation 13.45 24.52 0.5\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 0.6 0.6 0.6\n }\n geometry Box {\n size 1 1 1\n }\n }\n ]\n name \"obstacle_5(2)\"\n boundingObject Box {\n size 1 1 1\n }\n}\nRobot {\n translation 0 0 0.5\n children [\n Shape {\n appearance PBRAppearance {\n baseColor 1 0 0\n roughness 1\n metalness 0\n }\n geometry Sphere {\n radius 0.5\n subdivision 2\n }\n }\n ]\n boundingObject Sphere {\n radius 0.5\n }\n controller \"robot_controller\"\n supervisor TRUE\n}\n\n\n## Required Results:\n1. The complete trajectory from start to goal\n2. The total travel time (in second)\n3. The total path length (in meters)\n4. The number of nodes explored during the search", "contributor": "Xiayu Zhao\n" }, { "task_id": "YZ_04", "query_token_num": 340, "Engineering Domain": "Mechanical Systems", "prompt": "## Task Description\nIn this task, you are required to design a battery module for electric vehicle applications using the data from a Lithium-Ferrous-Phosphate (LFP) cell characterized at multiple temperatures. The battery must support a 100\u202fA fast-charge for up to 20\u202fminutes, and the resulting temperature rise in each cell should stay within specified limits. You will also design and parameterize a cooling system (with a parallel channel configuration) so that the maximum temperature gradient across the module and the pressure drop of the coolant remain within their respective constraints.\n\n### Task 1\nThe given HPPC data uses a 40\u202fA pulse, but your final design must handle a continuous charge rate of 100\u202fA, so that you need to specify the following parameters of battery module to satisfy this need:\n- numCells_p, the number of cells in the parallel set.\n- numCells_s, the number of series connected parallel set.\n\n### Task 2\nYour second task is to determine the desired parameters for the cooling plate. As a result, the cooling plate you designed must keep the battery within reasonable temperatures during its operation. Below are the detailed requirements:\n- The maximum rise in cell temperature must be lower than or equal to 10 degree Celsius.\n- The maximum temperature gradient within a module must not exceed 5 degree Celsius.\n- The maximum acceptable pressure drop for the module cooling system must be less than 20kPa.\n\nThe design parameters for the cooling plate you need to specify includes:\n- NumChannel, the number of cooling channels.\n- Flowrate, the applicable coolant flow-rate.\n- ChannelDia, the channel diameter, typically < 0.01.", "contributor": "Yizhou Zhao" }, { "task_id": "YZ_03", "query_token_num": 619, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\nIn this task, you are required to design a helical antenna for use in mobile and satellite communications, operating in axial mode to produce circularly polarized radiation along its main axis. The helical antenna must be designed to meet specific frequency and performance criteria. Your final goal is to determine appropriate parameters for a helical antenna implemented using the MATLAB antenna toolbox, ensuring it satisfies specific requirements in terms of directivity variation and axial ratio. Notably, the helix model in the toolbox uses a strip approximation, which relates the width of the strip to the radius of an equivalent cylinder.\n\n### Task 1\nYour first task is to calculate the relative bandwidth (less than 1), based on the following frequency range and center frequency:\n- Frequency range: 1.3 - 2 GHz\n- Center frequency: 1.65 GHz\n\n\n### Task 2\nYour second task is to determine a set of appropriate parameters for the helical antenna design using the MATLAB toolbox. Since the helix model in the toolbox has a circular ground plane, the radius of the ground plane should be set to half the side length of an equivalent square ground plane. Specifically, the parameters you need to consider include:\n- $r$, the radius of cylinder, must be less than 0.0005\n- $D$, the diameter of the helical antenna, must satisfy $0.05 < D < 0.06$.\n- $turns$, the number of helical turns\n- $pitch$, the pitch of the helix, which must be greater than 5 deg\n- $side$, the side length of the square ground plane, must be greater than 0.3.\nThe helical antenna will be created and evaluated using the MATLAB code shown below. The frequency range and center frequency are given in Task 1:\n\n% design helix antenna\nwidth = cylinder2strip(r);\nfeedheight = 3*r;\nradius = D/2;\nspacing = helixpitch2spacing(pitch,radius);\nradiusGP = side/2;\nhx = helix(Radius=radius,Width=width,Turns=turns,...\n Spacing=spacing,GroundPlaneRadius=radiusGP,...\n FeedStubHeight=feedheight);\n% directivity as a function of frequency\nfreq = [1.3e9, 1.65e9, 2.0e9]; \nNf = length(freq);\nD = nan(1, Nf);\nfor i = 1:Nf\n D(i) = pattern(hx, freq(i), 0, 90);\nend\n% axial ratio at center frequency\nar_dB = axialRatio(hx, freq, 0, 90);\n\nThe helix antenna you design must satisfy the following requirements:\n- r: < D / (20 * 3.14)\n- Directivity range: 13 dBi +/- 1.5 dBi\n- Axial Ratio: < 1.5", "contributor": "Yizhou Zhao" }, { "task_id": "YJ_01", "query_token_num": 423, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nIn this task, you are required to determine the optimal material distribution within a 2D design domain to minimize structural compliance under a given set of physical constraints. The domain is a fixed-size grid of **64 \u00d7 64 elements**. Each design must satisfy the specified boundary conditions, load configurations, and a volume fraction constraint.\n\n## Input\n\nThe input consists of a 5-channel tensor, where each channel is a **64 \u00d7 64 NumPy array (.npy format)** representing:\n\n- **Channel 1**: volume fraction, prescribed uniformly or non-uniformly across the grid. \n- **Channel 2**: von Mises stress under the given loading and boundary conditions. \n- **Channel 3**: Strain energy distribution under the same conditions. \n- **Channel 4**: x-direction load magnitude at each node (0 if none). \n- **Channel 5**: y-direction load magnitude at each node (0 if none). \n\nThe inputs are specified in five 64x64 numpy array:\n- channel 1: A 64x64 matrix with each element equal 0.48\n- channel 2:[[3.02378885e-06 4.47539433e-06 7.50072817e-06 1.20186311e-05\n 1.80109097e-05 2.54543330e-05 3.43215513e-05 4.45822821e-05\n 5.62047910e-05 6.91577125e-05 8.34122703e-05 9.89449821e-05\n 1.15740968e-04 1.33798037e-04 1.53131780e-04 1.73782043e-04\n 1.95821249e-04 2.19365323e-04 2.44588274e-04 2.71741967e-04\n 3.01183312e-04 3.33411876e-04 3.69121785e-04 4.09269653e-04\n 4.55158574e-04 5.08461270e-04 5.71189253e-04 6.43753731e-04\n 7.24444883e-04 8.61603091e-04 7.41751328e-03 1.26088212e-02\n 2.28558406e-02 1.90377994e-02 2.29648198e-03 5.74503268e-04\n 1.70806693e-04 5.59472407e-05 2.40936179e-05 2.09785195e-05\n 2.83383866e-05 3.92710245e-05 5.09601691e-05 6.22304338e-05\n 7.26109646e-05 8.19471512e-05 9.02286714e-05 9.75098238e-05\n 1.03871446e-04 1.09402429e-04 1.14190775e-04 1.18319405e-04\n 1.21864365e-04 1.24894237e-04 1.27470146e-04 1.29646034e-04\n 1.31469059e-04 1.32980001e-04 1.34213660e-04 1.35199214e-04\n 1.35960520e-04 1.36516369e-04 1.36880691e-04 1.35381261e-04]\n [9.99441870e-06 1.12235038e-05 1.38634008e-05 1.78071154e-05\n 2.30355207e-05 2.95237637e-05 3.72418210e-05 4.61551870e-05\n 5.62256893e-05 6.74124195e-05 7.96727639e-05 9.29635022e-05\n 1.07241926e-04 1.22466889e-04 1.38599632e-04 1.55604117e-04\n 1.73446380e-04 1.92092012e-04 2.11500144e-04 2.31610822e-04\n 2.52319841e-04 2.73429263e-04 2.94549893e-04 3.14907379e-04\n 3.32953288e-04 3.45612379e-04 3.47097711e-04 3.29221765e-04\n 3.12111234e-04 6.08510000e-04 3.59270247e-03 5.18087526e-03\n 1.32168194e-02 1.43017050e-02 4.15618859e-03 1.41871086e-03\n 5.49137011e-04 2.31669836e-04 1.07999778e-04 5.93808033e-05\n 4.26299521e-05 4.00876239e-05 4.39482247e-05 5.05486821e-05\n 5.81038451e-05 6.57295301e-05 7.29931730e-05 7.96957838e-05\n 8.57614630e-05 9.11794279e-05 9.59727398e-05 1.00181083e-04\n 1.03851151e-04 1.07031244e-04 1.09768251e-04 1.12105984e-04\n 1.14084301e-04 1.15738676e-04 1.17100023e-04 1.18194668e-04\n 1.19044384e-04 1.19666461e-04 1.20073785e-04 1.20337789e-04]\n [2.35636661e-05 2.45563331e-05 2.67028106e-05 2.99060067e-05\n 3.41460670e-05 3.93967071e-05 4.56253381e-05 5.27931715e-05\n 6.08552585e-05 6.97604009e-05 7.94508362e-05 8.98615592e-05\n 1.00919068e-04 1.12539220e-04 1.24623702e-04 1.37054362e-04\n 1.49684198e-04 1.62323090e-04 1.74715204e-04 1.86503157e-04\n 1.97171221e-04 2.05956267e-04 2.11713348e-04 2.12736162e-04\n 2.06620301e-04 1.90685736e-04 1.65312082e-04 1.51134218e-04\n 2.63334631e-04 9.20941119e-04 2.44746839e-03 3.68516374e-03\n 5.18872672e-03 6.36497638e-03 4.67760144e-03 2.25661676e-03\n 1.08103309e-03 5.35911749e-04 2.79099804e-04 1.54861824e-04\n 9.41517471e-05 6.52404603e-05 5.27898861e-05 4.90300096e-05\n 4.98626330e-05 5.30562941e-05 5.73679019e-05 6.20960998e-05\n 6.68450510e-05 7.13951408e-05 7.56300484e-05 7.94945337e-05\n 8.29694529e-05 8.60566908e-05 8.87699298e-05 9.11289252e-05\n 9.31559195e-05 9.48733840e-05 9.63025915e-05 9.74627149e-05\n 9.83702607e-05 9.90387162e-05 9.94783327e-05 9.97591586e-05]\n [4.16295394e-05 4.23891394e-05 4.40496624e-05 4.65237958e-05\n 4.97912972e-05 5.38249610e-05 5.85903740e-05 6.40455261e-05\n 7.01402094e-05 7.68151090e-05 8.40004479e-05 9.16139943e-05\n 9.95581552e-05 1.07715765e-04 1.15944019e-04 1.24065760e-04\n 1.31857062e-04 1.39029690e-04 1.45206841e-04 1.49891012e-04\n 1.52425636e-04 1.51962080e-04 1.47475242e-04 1.37966593e-04\n 1.23280995e-04 1.06798444e-04 1.03599745e-04 1.62552795e-04\n 4.06523400e-04 9.86394132e-04 1.78374670e-03 2.44852323e-03\n 3.09814326e-03 3.61013837e-03 3.30263275e-03 2.31434577e-03\n 1.38602652e-03 8.04681374e-04 4.70304174e-04 2.82003698e-04\n 1.75940806e-04 1.16167394e-04 8.28164575e-05 6.47941377e-05\n 5.57792162e-05 5.20891459e-05 5.15337521e-05 5.27874077e-05\n 5.50369816e-05 5.77795579e-05 6.07034385e-05 6.36165751e-05\n 6.64026399e-05 6.89935579e-05 7.13520420e-05 7.34603211e-05\n 7.53127692e-05 7.69110295e-05 7.82607593e-05 7.93694404e-05\n 8.02449011e-05 8.08943190e-05 8.13235561e-05 8.15972663e-05]\n [6.28043506e-05 6.33317118e-05 6.45084511e-05 6.62570029e-05\n 6.85570438e-05 7.13809340e-05 7.46931813e-05 7.84496781e-05\n 8.25966380e-05 8.70691320e-05 9.17890915e-05 9.66626042e-05\n 1.01576278e-04 1.06392396e-04 1.10942558e-04 1.15019509e-04\n 1.18367091e-04 1.20668876e-04 1.21537814e-04 1.20513575e-04\n 1.17084793e-04 1.10778431e-04 1.01417249e-04 8.97817565e-05\n 7.92062724e-05 7.91830708e-05 1.12506768e-04 2.24775284e-04\n 4.76587523e-04 8.80236310e-04 1.32859982e-03 1.70887193e-03\n 2.06440694e-03 2.35597015e-03 2.33335753e-03 1.93868583e-03\n 1.40315628e-03 9.40361914e-04 6.13516650e-04 3.99514561e-04\n 2.63633738e-04 1.78364548e-04 1.25188815e-04 9.22934977e-05\n 7.22593285e-05 6.04225455e-05 5.38282608e-05 5.05846143e-05\n 4.94673385e-05 4.96765694e-05 5.06857439e-05 5.21464951e-05\n 5.38279511e-05 5.55774453e-05 5.72947348e-05 5.89148629e-05\n 6.03966303e-05 6.17147546e-05 6.28544892e-05 6.38079028e-05\n 6.45712985e-05 6.51434252e-05 6.55242540e-05 6.57699295e-05]\n [8.59151283e-05 8.62095004e-05 8.69013337e-05 8.79229117e-05\n 8.92542314e-05 9.08678555e-05 9.27281912e-05 9.47905077e-05\n 9.69996367e-05 9.92882860e-05 1.01574885e-04 1.03760883e-04\n 1.05727442e-04 1.07331535e-04 1.08401644e-04 1.08733659e-04\n 1.08088435e-04 1.06194270e-04 1.02761238e-04 9.75218274e-05\n 9.03273087e-05 8.13586461e-05 7.15654221e-05 6.35363223e-05\n 6.31073670e-05 8.19320611e-05 1.40196660e-04 2.64734202e-04\n 4.73105995e-04 7.44987039e-04 1.02115664e-03 1.26404811e-03\n 1.48750640e-03 1.66928411e-03 1.71064384e-03 1.55490925e-03\n 1.26543758e-03 9.51567463e-04 6.83433932e-04 4.80834304e-04\n 3.36772910e-04 2.37459280e-04 1.70093164e-04 1.24843620e-04\n 9.47045888e-05 7.48415115e-05 6.19596809e-05 5.38197404e-05\n 4.88961722e-05 4.61450322e-05 4.48481892e-05 4.45091888e-05\n 4.47834349e-05 4.54310914e-05 4.62850648e-05 4.72290501e-05\n 4.81823462e-05 4.90892683e-05 4.99117104e-05 5.06238947e-05\n 5.12086554e-05 5.16548189e-05 5.19553835e-05 5.21558529e-05]\n [1.09995072e-04 1.10055300e-04 1.10260289e-04 1.10552438e-04\n 1.10912671e-04 1.11314695e-04 1.11724215e-04 1.12097926e-04\n 1.12382233e-04 1.12511723e-04 1.12407371e-04 1.11974584e-04\n 1.11101250e-04 1.09656207e-04 1.07488953e-04 1.04432174e-04\n 1.00310074e-04 9.49580202e-05 8.82635871e-05 8.02469800e-05\n 7.12121341e-05 6.20199264e-05 5.45591786e-05 5.24983455e-05\n 6.23136825e-05 9.42061151e-05 1.61499614e-04 2.75859632e-04\n 4.37162452e-04 6.25517604e-04 8.11038178e-04 9.78734036e-04\n 1.13128329e-03 1.25484628e-03 1.30460798e-03 1.24561986e-03\n 1.09128298e-03 8.90542783e-04 6.91177899e-04 5.20106518e-04\n 3.85148286e-04 2.83709608e-04 2.09598063e-04 1.56373036e-04\n 1.18577749e-04 9.19755466e-05 7.34150254e-05 6.06020212e-05\n 5.18834588e-05 4.60729358e-05 4.23194166e-05 4.00116502e-05\n 3.87097191e-05 3.80963535e-05 3.79423532e-05 3.80819893e-05\n 3.83954437e-05 3.87962229e-05 3.92221022e-05 3.96285939e-05\n 3.99842387e-05 4.02672316e-05 4.04630454e-05 4.06054038e-05]\n [1.34271035e-04 1.34096754e-04 1.33814665e-04 1.33377704e-04\n 1.32768609e-04 1.31963557e-04 1.30931467e-04 1.29633156e-04\n 1.28020365e-04 1.26034740e-04 1.23606905e-04 1.20655871e-04\n 1.17089256e-04 1.12805095e-04 1.07696630e-04 1.01662410e-04\n 9.46256145e-05 8.65690750e-05 7.75963688e-05 6.80350069e-05\n 5.86045481e-05 5.06772072e-05 4.66501910e-05 5.03992811e-05\n 6.76357157e-05 1.05676268e-04 1.71761945e-04 2.69275748e-04\n 3.93213421e-04 5.29590167e-04 6.62797101e-04 7.85258425e-04\n 8.95578332e-04 9.84539893e-04 1.02972329e-03 1.01077905e-03\n 9.27723408e-04 8.01463281e-04 6.59841821e-04 5.24784817e-04\n 4.08053901e-04 3.13196190e-04 2.39068301e-04 1.82580011e-04\n 1.40244777e-04 1.08883844e-04 8.58599853e-05 6.90907827e-05\n 5.69766766e-05 4.83080573e-05 4.21780848e-05 3.79099583e-05\n 3.49996021e-05 3.30718554e-05 3.18475407e-05 3.11189287e-05\n 3.07315406e-05 3.05706739e-05 3.05514382e-05 3.06113953e-05\n 3.07051458e-05 3.08003835e-05 3.08750760e-05 3.09509514e-05]\n [1.58147346e-04 1.57740032e-04 1.56974536e-04 1.55814875e-04\n 1.54246772e-04 1.52250584e-04 1.49800838e-04 1.46865737e-04\n 1.43406736e-04 1.39378345e-04 1.34728420e-04 1.29399370e-04\n 1.23330952e-04 1.16465743e-04 1.08758987e-04 1.00195450e-04\n 9.08172600e-05 8.07685963e-05 7.03652855e-05 6.01993668e-05\n 5.12882653e-05 4.52704134e-05 4.46234565e-05 5.28207475e-05\n 7.42324562e-05 1.13451720e-04 1.73751313e-04 2.54883967e-04\n 3.51542736e-04 4.54522988e-04 5.54964970e-04 6.48023026e-04\n 7.31091113e-04 7.97809541e-04 8.35949162e-04 8.33674732e-04\n 7.88208403e-04 7.08282621e-04 6.09261305e-04 5.06293024e-04\n 4.10148520e-04 3.26488793e-04 2.57054527e-04 2.01247227e-04\n 1.57373218e-04 1.23413697e-04 9.74259140e-05 7.77137701e-05\n 6.28731828e-05 5.17778260e-05 4.35415014e-05 3.74753306e-05\n 3.30478827e-05 2.98511722e-05 2.75729917e-05 2.59750066e-05\n 2.48757001e-05 2.41372357e-05 2.36554154e-05 2.33520562e-05\n 2.31692524e-05 2.30651129e-05 2.30106677e-05 2.30162206e-05]\n [1.81186691e-04 1.80550446e-04 1.79310760e-04 1.77443324e-04\n 1.74938244e-04 1.71782062e-04 1.67957638e-04 1.63444162e-04\n 1.58217453e-04 1.52250780e-04 1.45516556e-04 1.37989466e-04\n 1.29651801e-04 1.20502230e-04 1.10569689e-04 9.99348328e-05\n 8.87622853e-05 7.73477602e-05 6.61844024e-05 5.60513640e-05\n 4.81223529e-05 4.40786948e-05 4.61849560e-05 5.72423592e-05\n 8.02878702e-05 1.17904624e-04 1.71151884e-04 2.38486452e-04\n 3.15468961e-04 3.95958950e-04 4.74376263e-04 5.47124691e-04\n 6.11476478e-04 6.62921642e-04 6.94316854e-04 6.98639363e-04\n 6.73188383e-04 6.21562592e-04 5.52134853e-04 4.74702914e-04\n 3.97628522e-04 3.26534558e-04 2.64336409e-04 2.11918727e-04\n 1.68909839e-04 1.34298576e-04 1.06841087e-04 8.52939849e-05\n 6.85292881e-05 5.55781770e-05 4.56361138e-05 3.80494056e-05\n 3.22946185e-05 2.79568140e-05 2.47094243e-05 2.22968566e-05\n 2.05200366e-05 1.92246944e-05 1.82920387e-05 1.76314406e-05\n 1.71747750e-05 1.68721239e-05 1.66886041e-05 1.66242740e-05]\n [2.03089063e-04 2.02231073e-04 2.00532911e-04 1.97982487e-04\n 1.94575815e-04 1.90307763e-04 1.85172354e-04 1.79163384e-04\n 1.72275523e-04 1.64506211e-04 1.55858735e-04 1.46347097e-04\n 1.36003461e-04 1.24889299e-04 1.13111688e-04 1.00846564e-04\n 8.83709569e-05 7.61060354e-05 6.46715603e-05 5.49490602e-05\n 4.81441114e-05 4.58257111e-05 4.99023409e-05 6.24746443e-05\n 8.55003601e-05 1.20251206e-04 1.66667422e-04 2.22902527e-04\n 2.85450720e-04 3.50024362e-04 4.12751797e-04 4.70766817e-04\n 5.21602116e-04 5.61992327e-04 5.87530700e-04 5.93954358e-04\n 5.79231709e-04 5.44845081e-04 4.95420483e-04 4.37154258e-04\n 3.76083179e-04 3.16951760e-04 2.62836772e-04 2.15304762e-04\n 1.74801109e-04 1.41057963e-04 1.13422356e-04 9.10826957e-05\n 7.32077811e-05 5.90224530e-05 4.78420844e-05 3.90825875e-05\n 3.22571340e-05 2.69665513e-05 2.28874457e-05 1.97602481e-05\n 1.73782581e-05 1.55781281e-05 1.42318773e-05 1.32403657e-05\n 1.25280795e-05 1.20390676e-05 1.17338811e-05 1.16039171e-05]\n [2.23669850e-04 2.22600517e-04 2.20466338e-04 2.17267845e-04\n 2.13008483e-04 2.07693524e-04 2.01330841e-04 1.93932130e-04\n 1.85514816e-04 1.76104924e-04 1.65741338e-04 1.54481992e-04\n 1.42412698e-04 1.29659476e-04 1.16405392e-04 1.02912898e-04\n 8.95523604e-05 7.68365688e-05 6.54589763e-05 5.63296798e-05\n 5.05969828e-05 4.96338336e-05 5.49595265e-05 6.80640100e-05\n 9.01169365e-05 1.21590227e-04 1.61902355e-04 2.09267515e-04\n 2.60918969e-04 3.13697431e-04 3.64707795e-04 4.11599097e-04\n 4.52265905e-04 4.84305229e-04 5.04882377e-04 5.11358258e-04\n 5.02348987e-04 4.78493636e-04 4.42439933e-04 3.98118892e-04\n 3.49756504e-04 3.01062452e-04 2.54798911e-04 2.12703595e-04\n 1.75633669e-04 1.43796122e-04 1.16975898e-04 9.47205850e-05\n 7.64721847e-05 6.16521512e-05 4.97110031e-05 4.01535814e-05\n 3.25488159e-05 2.65303556e-05 2.17922995e-05 1.80826907e-05\n 1.51963564e-05 1.29679726e-05 1.12658015e-05 9.98628917e-06\n 9.04957102e-06 8.39585888e-06 7.98265304e-06 7.79448077e-06]\n [2.42838116e-04 2.41570887e-04 2.39029523e-04 2.35227343e-04\n 2.30176597e-04 2.23894805e-04 2.16405972e-04 2.07742382e-04\n 1.97947186e-04 1.87078053e-04 1.75212259e-04 1.62453641e-04\n 1.48941949e-04 1.34865118e-04 1.20474950e-04 1.06106382e-04\n 9.21998951e-05 7.93253698e-05 6.82035784e-05 5.97182682e-05\n 5.49075451e-05 5.49189185e-05 6.09104926e-05 7.38861053e-05\n 9.44707021e-05 1.22666640e-04 1.57672915e-04 1.97869515e-04\n 2.41029601e-04 2.84708897e-04 3.26629593e-04 3.64842746e-04\n 3.97599626e-04 4.23109720e-04 4.39492688e-04 4.45093658e-04\n 4.39028010e-04 4.21621758e-04 3.94478291e-04 3.60144345e-04\n 3.21558254e-04 2.81515996e-04 2.42309860e-04 2.05576963e-04\n 1.72313560e-04 1.42983678e-04 1.17660057e-04 9.61581405e-05\n 7.81449159e-05 6.32184245e-05 5.09609969e-05 4.09719026e-05\n 3.28852362e-05 2.63779303e-05 2.11715873e-05 1.70307307e-05\n 1.37592108e-05 1.11958665e-05 9.21010896e-06 7.69780902e-06\n 6.57768561e-06 5.78828675e-06 5.28559147e-06 5.04907683e-06]\n [2.60575971e-04 2.59126934e-04 2.56212727e-04 2.51859308e-04\n 2.46088843e-04 2.38932532e-04 2.30432211e-04 2.20642608e-04\n 2.09634429e-04 1.97498515e-04 1.84351332e-04 1.70342084e-04\n 1.55661749e-04 1.40554212e-04 1.25329485e-04 1.10378531e-04\n 9.61884563e-05 8.33555780e-05 7.25921109e-05 6.47199693e-05\n 6.06429259e-05 6.12872465e-05 6.75029374e-05 7.99255741e-05\n 9.88141920e-05 1.23902006e-04 1.54314651e-04 1.88608884e-04\n 2.24948555e-04 2.61368645e-04 2.96018651e-04 3.27276838e-04\n 3.53710070e-04 3.73972045e-04 3.86789451e-04 3.91121830e-04\n 3.86441326e-04 3.72976106e-04 3.51773250e-04 3.24540984e-04\n 2.93340967e-04 2.60250647e-04 2.27095697e-04 1.95297986e-04\n 1.65834144e-04 1.39272400e-04 1.15850276e-04 9.55634906e-05\n 7.82478681e-05 6.36459071e-05 5.14562028e-05 4.13674248e-05\n 3.30799139e-05 2.63181200e-05 2.08366805e-05 1.64223443e-05\n 1.28933597e-05 1.00974594e-05 7.90919878e-06 6.22713586e-06\n 4.97115347e-06 4.08009920e-06 3.50984075e-06 3.23651245e-06]\n [2.76919706e-04 2.75307033e-04 2.72058650e-04 2.67212648e-04\n 2.60801858e-04 2.52872078e-04 2.43483959e-04 2.32715577e-04\n 2.20665805e-04 2.07458655e-04 1.93248736e-04 1.78227964e-04\n 1.62633563e-04 1.46757256e-04 1.30955203e-04 1.15657778e-04\n 1.01377521e-04 8.87125860e-05 7.83417358e-05 7.10057584e-05\n 6.74694457e-05 6.84591192e-05 7.45742043e-05 8.61786964e-05\n 1.03289303e-04 1.25488641e-04 1.51897567e-04 1.81232349e-04\n 2.11945736e-04 2.42413771e-04 2.71103393e-04 2.96663312e-04\n 3.17927154e-04 3.33876675e-04 3.43640069e-04 3.46571154e-04\n 3.42389382e-04 3.31307549e-04 3.14071341e-04 2.91879186e-04\n 2.66207426e-04 2.38599991e-04 2.10482058e-04 1.83034136e-04\n 1.57135024e-04 1.33362014e-04 1.12028169e-04 9.32370659e-05\n 7.69403807e-05 6.29896000e-05 5.11779494e-05 4.12718420e-05\n 3.30328905e-05 2.62322485e-05 2.06591493e-05 1.61253084e-05\n 1.24665422e-05 9.54262661e-06 7.23614358e-06 5.45083305e-06\n 4.10980148e-06 3.15381494e-06 2.53982053e-06 2.24210658e-06]\n [2.91943155e-04 2.90186467e-04 2.86645556e-04 2.81369769e-04\n 2.74402935e-04 2.65805781e-04 2.55657995e-04 2.44060940e-04\n 2.31141088e-04 2.17054238e-04 2.01990555e-04 1.86180400e-04\n 1.69900794e-04 1.53482144e-04 1.37314558e-04 1.21852581e-04\n 1.07616622e-04 9.51885616e-05 8.51984048e-05 7.82983655e-05\n 7.51211538e-05 7.62209086e-05 8.19988756e-05 9.26216838e-05\n 1.07946990e-04 1.27476762e-04 1.50358581e-04 1.75446387e-04\n 2.01413993e-04 2.26893704e-04 2.50600190e-04 2.71406854e-04\n 2.88368126e-04 3.00711879e-04 3.07840667e-04 3.09367645e-04\n 3.05181530e-04 2.95507128e-04 2.80922500e-04 2.62312130e-04\n 2.40763594e-04 2.17436186e-04 1.93435118e-04 1.69716305e-04\n 1.47032353e-04 1.25917522e-04 1.06701912e-04 8.95430003e-05\n 7.44641655e-05 6.13928050e-05 5.01938097e-05 4.06965733e-05\n 3.27153493e-05 2.60636535e-05 2.05637937e-05 1.60526609e-05\n 1.23848096e-05 9.43367842e-06 7.09161435e-06 5.26919598e-06\n 3.89421274e-06 2.91054916e-06 2.27714261e-06 1.96766665e-06]\n [3.05743492e-04 3.03863213e-04 3.00073059e-04 2.94432377e-04\n 2.86995898e-04 2.77839019e-04 2.67059932e-04 2.54782321e-04\n 2.41158639e-04 2.26373944e-04 2.10650200e-04 1.94250900e-04\n 1.77485659e-04 1.60714282e-04 1.44349457e-04 1.28856900e-04\n 1.14751313e-04 1.02586136e-04 9.29347965e-05 8.63613454e-05\n 8.33791976e-05 8.43986381e-05 8.96668641e-05 9.92084073e-05\n 1.12777758e-04 1.29838070e-04 1.49577731e-04 1.70969023e-04\n 1.92861087e-04 2.14087407e-04 2.33562303e-04 2.50346216e-04\n 2.63674649e-04 2.72962642e-04 2.77805346e-04 2.77990181e-04\n 2.73520995e-04 2.64639996e-04 2.51828297e-04 2.35773005e-04\n 2.17302281e-04 1.97301790e-04 1.76630829e-04 1.56053896e-04\n 1.36196476e-04 1.17526304e-04 1.00355936e-04 8.48599140e-05\n 7.10997100e-05 5.90508982e-05 4.86288168e-05 3.97106350e-05\n 3.21530274e-05 2.58054926e-05 2.05198182e-05 1.61563871e-05\n 1.25880474e-05 9.70219862e-06 7.40164621e-06 5.60465968e-06\n 4.24456775e-06 3.26913584e-06 2.63990062e-06 2.33087105e-06]\n [3.18429500e-04 3.16446271e-04 3.12450549e-04 3.06510106e-04\n 2.98690042e-04 2.89079609e-04 2.77794287e-04 2.64978320e-04\n 2.50807669e-04 2.35493248e-04 2.19284290e-04 2.02471543e-04\n 1.85389883e-04 1.68419728e-04 1.51986397e-04 1.36556321e-04\n 1.22628736e-04 1.10721369e-04 1.01348682e-04 9.49917226e-05\n 9.20597042e-05 9.28451655e-05 9.74770229e-05 1.05878454e-04\n 1.17738612e-04 1.32507410e-04 1.49419946e-04 1.67551222e-04\n 1.85893875e-04 2.03444561e-04 2.19281832e-04 2.32622012e-04\n 2.42848583e-04 2.49520599e-04 2.52371423e-04 2.51307641e-04\n 2.46411009e-04 2.37938505e-04 2.26311934e-04 2.12090733e-04\n 1.95927828e-04 1.78514740e-04 1.60525607e-04 1.42569438e-04\n 1.25156728e-04 1.08682436e-04 9.34237950e-05 7.95493583e-05\n 6.71349980e-05 5.61829927e-05 4.66412535e-05 3.84207892e-05\n 3.14104240e-05 2.54884640e-05 2.05314451e-05 1.64203381e-05\n 1.30446794e-05 1.03051033e-05 8.11470495e-06 6.39959912e-06\n 5.09896441e-06 4.16479959e-06 3.56155880e-06 3.26427086e-06]\n [3.30112179e-04 3.28046357e-04 3.23888099e-04 3.17711727e-04\n 3.09591803e-04 2.99630117e-04 2.87957632e-04 2.74736750e-04\n 2.60163806e-04 2.44471590e-04 2.27931635e-04 2.10855937e-04\n 1.93597596e-04 1.76549770e-04 1.60142132e-04 1.44833893e-04\n 1.31102370e-04 1.19426109e-04 1.10261885e-04 1.04015485e-04\n 1.01007258e-04 1.01434865e-04 1.05337428e-04 1.12566843e-04\n 1.22772913e-04 1.35408316e-04 1.49756828e-04 1.64983732e-04\n 1.80202045e-04 1.94543842e-04 2.07224546e-04 2.17590566e-04\n 2.25146271e-04 2.29562625e-04 2.30673930e-04 2.28469358e-04\n 2.23082934e-04 2.14781518e-04 2.03947809e-04 1.91055638e-04\n 1.76637305e-04 1.61245863e-04 1.45417271e-04 1.29637623e-04\n 1.14319275e-04 9.97875093e-05 8.62773048e-05 7.39382839e-05\n 6.28452350e-05 5.30116204e-05 4.44039056e-05 3.69551661e-05\n 3.05770347e-05 2.51695628e-05 2.06289300e-05 1.68531677e-05\n 1.37461839e-05 1.12204173e-05 9.19844483e-06 7.61383140e-06\n 6.41146676e-06 5.54758548e-06 4.98962204e-06 4.71408089e-06]\n [3.40897463e-04 3.38768743e-04 3.34489540e-04 3.28138625e-04\n 3.19798772e-04 3.09582581e-04 2.97634216e-04 2.84131345e-04\n 2.69287102e-04 2.53351821e-04 2.36614240e-04 2.19401757e-04\n 2.02079254e-04 1.85045876e-04 1.68729073e-04 1.53575185e-04\n 1.40035857e-04 1.28549786e-04 1.19519679e-04 1.13284945e-04\n 1.10091588e-04 1.10061906e-04 1.13167772e-04 1.19212150e-04\n 1.27823637e-04 1.38467866e-04 1.50477264e-04 1.63097321e-04\n 1.75543871e-04 1.87063145e-04 1.96985608e-04 2.04766372e-04\n 2.10008664e-04 2.12471115e-04 2.12062733e-04 2.08830409e-04\n 2.02942670e-04 1.94671334e-04 1.84370944e-04 1.72455398e-04\n 1.59371886e-04 1.45573547e-04 1.31493282e-04 1.17521417e-04\n 1.03989337e-04 9.11601106e-05 7.92259712e-05 6.83115577e-05\n 5.84813327e-05 4.97494627e-05 4.20906440e-05 3.54507016e-05\n 2.97561816e-05 2.49225123e-05 2.08605895e-05 1.74818328e-05\n 1.47018804e-05 1.24431436e-05 1.06364584e-05 9.22205943e-06\n 8.15007432e-06 7.38070429e-06 6.88422271e-06 6.63888561e-06]\n [3.50880753e-04 3.48707920e-04 3.44347402e-04 3.37880143e-04\n 3.29395610e-04 3.19015143e-04 3.06893473e-04 2.93220298e-04\n 2.78221700e-04 2.62161102e-04 2.45339424e-04 2.28094005e-04\n 2.10795812e-04 1.93844391e-04 1.77659995e-04 1.62672385e-04\n 1.49305901e-04 1.37960685e-04 1.28990368e-04 1.22677134e-04\n 1.19205874e-04 1.18639947e-04 1.20901827e-04 1.25762302e-04\n 1.32841612e-04 1.41624850e-04 1.51491984e-04 1.61760307e-04\n 1.71734559e-04 1.80758204e-04 1.88258941e-04 1.93782834e-04\n 1.97014072e-04 1.97780372e-04 1.96046548e-04 1.91899915e-04\n 1.85531082e-04 1.77212613e-04 1.67276890e-04 1.56093779e-04\n 1.44048596e-04 1.31521150e-04 1.18867033e-04 1.06402376e-04\n 9.43930636e-05 8.30488492e-05 7.25221803e-05 6.29110406e-05\n 5.42647648e-05 4.65916942e-05 3.98676207e-05 3.40441698e-05\n 2.90565216e-05 2.48301109e-05 2.12861498e-05 1.83459697e-05\n 1.59342770e-05 1.39814750e-05 1.24252257e-05 1.12114242e-05\n 1.02947457e-05 9.63890129e-06 9.21671505e-06 9.00834299e-06]\n [3.60142945e-04 3.57943755e-04 3.53539343e-04 3.47010427e-04\n 3.38451429e-04 3.27990113e-04 3.15788883e-04 3.02046017e-04\n 2.86996568e-04 2.70912610e-04 2.54102455e-04 2.36908415e-04\n 2.19702648e-04 2.02880638e-04 1.86851878e-04 1.72027440e-04\n 1.58804316e-04 1.47546705e-04 1.38564865e-04 1.32092681e-04\n 1.28265728e-04 1.27102169e-04 1.28489259e-04 1.32178286e-04\n 1.37790302e-04 1.44833942e-04 1.52734971e-04 1.60875254e-04\n 1.68637024e-04 1.75447118e-04 1.80815696e-04 1.84364996e-04\n 1.85845577e-04 1.85139811e-04 1.82254383e-04 1.77304758e-04\n 1.70494838e-04 1.62094580e-04 1.52417540e-04 1.41799574e-04\n 1.30579467e-04 1.19082043e-04 1.07604256e-04 9.64047103e-05\n 8.56968658e-05 7.56459186e-05 6.63690585e-05 5.79385189e-05\n 5.03866825e-05 4.37124488e-05 3.78881314e-05 3.28662823e-05\n 2.85860015e-05 2.49784576e-05 2.19714899e-05 1.94932755e-05\n 1.74751204e-05 1.58534863e-05 1.45713838e-05 1.35792668e-05\n 1.28355575e-05 1.23069131e-05 1.19683300e-05 1.18019344e-05]\n [3.68747646e-04 3.66538831e-04 3.62125739e-04 3.55586393e-04\n 3.47018265e-04 3.36553043e-04 3.24357742e-04 3.10635651e-04\n 2.95626795e-04 2.79607587e-04 2.62889252e-04 2.45814642e-04\n 2.28752997e-04 2.12092294e-04 1.96228891e-04 1.81554322e-04\n 1.68439349e-04 1.57215679e-04 1.48156180e-04 1.41454865e-04\n 1.37208392e-04 1.35401220e-04 1.35896700e-04 1.38436274e-04\n 1.42648375e-04 1.48067600e-04 1.54163362e-04 1.60375723e-04\n 1.66154772e-04 1.70999101e-04 1.74488937e-04 1.76310317e-04\n 1.76268205e-04 1.74288250e-04 1.70408534e-04 1.64763768e-04\n 1.57564858e-04 1.49076583e-04 1.39595576e-04 1.29430133e-04\n 1.18882777e-04 1.08236055e-04 9.77417715e-05 8.76136790e-05\n 7.80234433e-05 6.90996015e-05 6.09290579e-05 5.35605693e-05\n 4.70096191e-05 4.12640869e-05 3.62901824e-05 3.20382121e-05\n 2.84478687e-05 2.54528466e-05 2.29846923e-05 2.09758832e-05\n 1.93621818e-05 1.80843561e-05 1.70893687e-05 1.63311466e-05\n 1.57710371e-05 1.53780426e-05 1.51289140e-05 1.50077815e-05]\n [3.76739275e-04 3.74536660e-04 3.70148135e-04 3.63646514e-04\n 3.55130297e-04 3.44732464e-04 3.32621476e-04 3.19002014e-04\n 3.04115125e-04 2.88237418e-04 2.71678896e-04 2.54779045e-04\n 2.37900789e-04 2.21422025e-04 2.05724576e-04 1.91180551e-04\n 1.78136414e-04 1.66895332e-04 1.57698776e-04 1.50708697e-04\n 1.45991968e-04 1.43508966e-04 1.43108216e-04 1.44528715e-04\n 1.47410958e-04 1.51316748e-04 1.55756740e-04 1.60223447e-04\n 1.64226491e-04 1.67326315e-04 1.69162680e-04 1.69474990e-04\n 1.68112725e-04 1.65035718e-04 1.60305405e-04 1.54069158e-04\n 1.46540330e-04 1.37976597e-04 1.28658814e-04 1.18871981e-04\n 1.08889343e-04 9.89600607e-05 8.93005504e-05 8.00892625e-05\n 7.14645340e-05 6.35250190e-05 5.63321523e-05 4.99140854e-05\n 4.42705555e-05 3.93782004e-05 3.51959102e-05 3.16699007e-05\n 2.87382884e-05 2.63350366e-05 2.43932222e-05 2.28476303e-05\n 2.16367286e-05 2.07041006e-05 1.99994284e-05 1.94791206e-05\n 1.91066750e-05 1.88528557e-05 1.86957535e-05 1.86215308e-05]\n [3.84141808e-04 3.81960528e-04 3.77628281e-04 3.71210147e-04\n 3.62803540e-04 3.52540013e-04 3.40586240e-04 3.27144665e-04\n 3.12453480e-04 2.96785539e-04 2.80445813e-04 2.63766986e-04\n 2.47102879e-04 2.30819458e-04 2.15283368e-04 2.00848125e-04\n 1.87838381e-04 1.76532975e-04 1.67147828e-04 1.59820018e-04\n 1.54594635e-04 1.51416079e-04 1.50125388e-04 1.50464804e-04\n 1.52090167e-04 1.54590894e-04 1.57516299e-04 1.60406079e-04\n 1.62822066e-04 1.64377970e-04 1.64764037e-04 1.63764168e-04\n 1.61264092e-04 1.57250450e-04 1.51801741e-04 1.45073036e-04\n 1.37276793e-04 1.28662180e-04 1.19495018e-04 1.10039944e-04\n 1.00545786e-04 9.12346359e-05 8.22946230e-05 7.38760968e-05\n 6.60907276e-05 5.90129408e-05 5.26830755e-05 4.71116916e-05\n 4.22845098e-05 3.81675542e-05 3.47121576e-05 3.18595879e-05\n 2.95451349e-05 2.77015779e-05 2.62620146e-05 2.51620760e-05\n 2.43415889e-05 2.37457601e-05 2.33259702e-05 2.30402613e-05\n 2.28536005e-05 2.27379882e-05 2.26724739e-05 2.26452958e-05]\n [3.90957953e-04 3.88812746e-04 3.84567552e-04 3.78277195e-04\n 3.70035810e-04 3.59970739e-04 3.48243591e-04 3.35050945e-04\n 3.20624332e-04 3.05229071e-04 2.89161559e-04 2.72744638e-04\n 2.56320731e-04 2.40242577e-04 2.24861584e-04 2.10514015e-04\n 1.97505553e-04 1.86095034e-04 1.76478457e-04 1.68774626e-04\n 1.63013902e-04 1.59131587e-04 1.56967209e-04 1.56270647e-04\n 1.56715336e-04 1.57918086e-04 1.59464169e-04 1.60935566e-04\n 1.61939759e-04 1.62136174e-04 1.61257669e-04 1.59125004e-04\n 1.55653178e-04 1.50849556e-04 1.44804693e-04 1.37677549e-04\n 1.29677219e-04 1.21043371e-04 1.12027365e-04 1.02875586e-04\n 9.38159487e-05 8.50480590e-05 7.67370119e-05 6.90105155e-05\n 6.19588064e-05 5.56367338e-05 5.00673770e-05 4.52466091e-05\n 4.11481070e-05 3.77284023e-05 3.49316766e-05 3.26940972e-05\n 3.09475755e-05 2.96228997e-05 2.86522443e-05 2.79711004e-05\n 2.75196923e-05 2.72439591e-05 2.70961875e-05 2.70353736e-05\n 2.70273926e-05 2.70450388e-05 2.70679938e-05 2.70866396e-05]\n [3.97168590e-04 3.95074161e-04 3.90946592e-04 3.84827930e-04\n 3.76806787e-04 3.67003440e-04 3.55571108e-04 3.42696868e-04\n 3.28601831e-04 3.13540111e-04 2.97796199e-04 2.81680339e-04\n 2.65521621e-04 2.49658677e-04 2.34428019e-04 2.20150355e-04\n 2.07115464e-04 1.95566519e-04 1.85684994e-04 1.77577498e-04\n 1.71265948e-04 1.66682449e-04 1.63669952e-04 1.61989369e-04\n 1.61333192e-04 1.61344939e-04 1.61643036e-04 1.61847130e-04\n 1.61604371e-04 1.60613145e-04 1.58641966e-04 1.55541800e-04\n 1.51250928e-04 1.45792352e-04 1.39264624e-04 1.31827638e-04\n 1.23685306e-04 1.15067142e-04 1.06210571e-04 9.73453639e-05\n 8.86811685e-05 8.03985448e-05 7.26435274e-05 6.55253869e-05\n 5.91170642e-05 5.34576480e-05 4.85562602e-05 4.43967647e-05\n 4.09428069e-05 3.81427991e-05 3.59345733e-05 3.42495221e-05\n 3.30161345e-05 3.21628957e-05 3.16205708e-05 3.13239271e-05\n 3.12129664e-05 3.12337500e-05 3.13389011e-05 3.14878639e-05\n 3.16469910e-05 3.17895233e-05 3.18955121e-05 3.19575770e-05]\n [4.02732362e-04 4.00703796e-04 3.96725049e-04 3.90822886e-04\n 3.83078082e-04 3.73600929e-04 3.62532869e-04 3.50047802e-04\n 3.36352648e-04 3.21686700e-04 3.06319314e-04 2.90545549e-04\n 2.74679461e-04 2.59044953e-04 2.43964260e-04 2.29744449e-04\n 2.16662589e-04 2.04950510e-04 1.94780344e-04 1.86252168e-04\n 1.79385130e-04 1.74113294e-04 1.70287158e-04 1.67681318e-04\n 1.66008176e-04 1.64936895e-04 1.64116173e-04 1.63198876e-04\n 1.61866269e-04 1.59849541e-04 1.56946611e-04 1.53032759e-04\n 1.48064332e-04 1.42075655e-04 1.35169950e-04 1.27505730e-04\n 1.19280416e-04 1.10713026e-04 1.02027604e-04 9.34387140e-05\n 8.51398589e-05 7.72952642e-05 7.00350180e-05 6.34532731e-05\n 5.76089976e-05 5.25286665e-05 4.82102698e-05 4.46280686e-05\n 4.17376159e-05 3.94806694e-05 3.77897314e-05 3.65920492e-05\n 3.58129936e-05 3.53787971e-05 3.52186800e-05 3.52664253e-05\n 3.54614780e-05 3.57496554e-05 3.60835513e-05 3.64227147e-05\n 3.67336731e-05 3.69898616e-05 3.71715080e-05 3.72735793e-05]\n [4.07585337e-04 4.05638546e-04 4.01841351e-04 3.96202725e-04\n 3.88793229e-04 3.79710171e-04 3.69079740e-04 3.57058894e-04\n 3.43836528e-04 3.29633452e-04 3.14700657e-04 2.99315476e-04\n 2.83775321e-04 2.68388872e-04 2.53464843e-04 2.39298708e-04\n 2.26158083e-04 2.14267750e-04 2.03795520e-04 1.94840303e-04\n 1.87423706e-04 1.81486363e-04 1.76889842e-04 1.73424495e-04\n 1.70823015e-04 1.68778839e-04 1.66967926e-04 1.65072017e-04\n 1.62801211e-04 1.59913761e-04 1.56231269e-04 1.51648011e-04\n 1.46133802e-04 1.39730572e-04 1.32543470e-04 1.24727843e-04\n 1.16473744e-04 1.07989641e-04 9.94868829e-05 9.11661416e-05\n 8.32066307e-05 7.57585106e-05 6.89384836e-05 6.28282992e-05\n 5.74756878e-05 5.28971400e-05 4.90819358e-05 4.59968694e-05\n 4.35912054e-05 4.18015018e-05 4.05560446e-05 3.97787350e-05\n 3.93923505e-05 3.93211682e-05 3.94929813e-05 3.98405721e-05\n 4.03027206e-05 4.08248341e-05 4.13592828e-05 4.18655208e-05\n 4.23100628e-05 4.26663750e-05 4.29147327e-05 4.30525639e-05]\n [4.11640741e-04 4.09792932e-04 4.06212480e-04 4.00888069e-04\n 3.93877592e-04 3.85262274e-04 3.75149457e-04 3.63675253e-04\n 3.51006555e-04 3.37341885e-04 3.22910516e-04 3.07969428e-04\n 2.92797722e-04 2.77688362e-04 2.62937328e-04 2.48830588e-04\n 2.35629604e-04 2.23556396e-04 2.12779404e-04 2.03401553e-04\n 1.95451857e-04 1.88881760e-04 1.83567001e-04 1.79315319e-04\n 1.75879688e-04 1.72976147e-04 1.70304748e-04 1.67571741e-04\n 1.64510915e-04 1.60902110e-04 1.56585247e-04 1.51468716e-04\n 1.45531673e-04 1.38820442e-04 1.31439845e-04 1.23540751e-04\n 1.15305371e-04 1.06931882e-04 9.86198159e-05 9.05573212e-05\n 8.29110798e-05 7.58192300e-05 6.93873171e-05 6.36870084e-05\n 5.87571181e-05 5.46063938e-05 5.12174941e-05 4.85516300e-05\n 4.65534182e-05 4.51555972e-05 4.42833554e-05 4.38581169e-05\n 4.38007097e-05 4.40339030e-05 4.44843474e-05 4.50839795e-05\n 4.57709711e-05 4.64903066e-05 4.71940745e-05 4.78415514e-05\n 4.83991476e-05 4.88402744e-05 4.91451813e-05 4.93138572e-05]\n [4.14788752e-04 4.13058895e-04 4.09733780e-04 4.04779309e-04\n 3.98238181e-04 3.90172329e-04 3.80666504e-04 3.69831878e-04\n 3.57809139e-04 3.44770468e-04 3.30919816e-04 3.16490941e-04\n 3.01742778e-04 2.86951934e-04 2.72402366e-04 2.58372609e-04\n 2.45121294e-04 2.32872006e-04 2.21798779e-04 2.12013703e-04\n 2.03558037e-04 1.96398066e-04 1.90426518e-04 1.85469817e-04\n 1.81300856e-04 1.77656288e-04 1.74256847e-04 1.70828787e-04\n 1.67124421e-04 1.62939810e-04 1.58128044e-04 1.52607065e-04\n 1.46361631e-04 1.39439686e-04 1.31943941e-04 1.24019922e-04\n 1.15841954e-04 1.07598551e-04 9.94785659e-05 9.16591610e-05\n 8.42962867e-05 7.75180312e-05 7.14208445e-05 6.60683919e-05\n 6.14926126e-05 5.76964614e-05 5.46577939e-05 5.23338895e-05\n 5.06661812e-05 4.95848508e-05 4.90130492e-05 4.88705874e-05\n 4.90770250e-05 4.95541414e-05 5.02278217e-05 5.10294167e-05\n 5.18966554e-05 5.27741924e-05 5.36138754e-05 5.43748083e-05\n 5.50232809e-05 5.55326229e-05 5.58830316e-05 5.60771221e-05]\n [4.16896470e-04 4.15305745e-04 4.12278851e-04 4.07756441e-04\n 4.01763431e-04 3.94339144e-04 3.85541821e-04 3.75453370e-04\n 3.64183760e-04 3.51874421e-04 3.38699988e-04 3.24867737e-04\n 3.10614220e-04 2.96198767e-04 2.81893833e-04 2.67972520e-04\n 2.54693981e-04 2.42287795e-04 2.30938697e-04 2.20773210e-04\n 2.11849735e-04 2.04153390e-04 1.97596547e-04 1.92025348e-04\n 1.87231892e-04 1.82971082e-04 1.78980556e-04 1.75001786e-04\n 1.70800261e-04 1.66182845e-04 1.61010747e-04 1.55207120e-04\n 1.48758932e-04 1.41713396e-04 1.34169806e-04 1.26267994e-04\n 1.18174835e-04 1.10070238e-04 1.02133889e-04 9.45337555e-05\n 8.74170161e-05 8.09037290e-05 7.50832586e-05 7.00132180e-05\n 6.57205234e-05 6.22040667e-05 5.94384901e-05 5.73785793e-05\n 5.59638604e-05 5.51230737e-05 5.47782862e-05 5.48484950e-05\n 5.52526460e-05 5.59120520e-05 5.67522391e-05 5.77042789e-05\n 5.87056806e-05 5.97009246e-05 6.06417206e-05 6.14870631e-05\n 6.22031572e-05 6.27632683e-05 6.31475475e-05 6.33612480e-05]\n [4.17808169e-04 4.16380362e-04 4.13699651e-04 4.09679038e-04\n 4.04323029e-04 3.97644927e-04 3.89672384e-04 3.80453444e-04\n 3.70062475e-04 3.58605279e-04 3.46222633e-04 3.33091513e-04\n 3.19423339e-04 3.05458796e-04 2.91459056e-04 2.77693651e-04\n 2.64425645e-04 2.51895231e-04 2.40303227e-04 2.29796166e-04\n 2.20454722e-04 2.12286960e-04 2.05227497e-04 1.99142987e-04\n 1.93843643e-04 1.89099756e-04 1.84661576e-04 1.80280522e-04\n 1.75729552e-04 1.70820714e-04 1.65418272e-04 1.59446426e-04\n 1.52891292e-04 1.45797482e-04 1.38260125e-04 1.30413594e-04\n 1.22418344e-04 1.14447283e-04 1.06672898e-04 9.92561229e-05\n 9.23375688e-05 8.60314194e-05 8.04219922e-05 7.55627345e-05\n 7.14772593e-05 6.81619454e-05 6.55896062e-05 6.37137605e-05\n 6.24731065e-05 6.17958818e-05 6.16038780e-05 6.18159656e-05\n 6.23510522e-05 6.31304581e-05 6.40797340e-05 6.51299763e-05\n 6.62187102e-05 6.72904208e-05 6.82968110e-05 6.91968607e-05\n 6.99567553e-05 7.05497395e-05 7.09559457e-05 7.11832034e-05]\n [4.17346052e-04 4.16107864e-04 4.13826990e-04 4.10386503e-04\n 4.05767902e-04 3.99955028e-04 3.92940721e-04 3.84734301e-04\n 3.75369228e-04 3.64910222e-04 3.53458978e-04 3.41157594e-04\n 3.28188873e-04 3.14772853e-04 3.01159194e-04 2.87615511e-04\n 2.74412219e-04 2.61805029e-04 2.50016673e-04 2.39219775e-04\n 2.29522868e-04 2.20961352e-04 2.13494733e-04 2.07010740e-04\n 2.01336115e-04 1.96253016e-04 1.91519266e-04 1.86890254e-04\n 1.82140131e-04 1.77080157e-04 1.71572485e-04 1.65538357e-04\n 1.58960384e-04 1.51879274e-04 1.44385940e-04 1.36610284e-04\n 1.28708110e-04 1.20847601e-04 1.13196595e-04 1.05911605e-04\n 9.91292078e-05 9.29600580e-05 8.74855378e-05 8.27567851e-05\n 7.87957173e-05 7.55975804e-05 7.31345381e-05 7.13598489e-05\n 7.02122431e-05 6.96201903e-05 6.95058347e-05 6.97884549e-05\n 7.03873735e-05 7.12242993e-05 7.22251248e-05 7.33212315e-05\n 7.44503718e-05 7.55572033e-05 7.65935537e-05 7.75184888e-05\n 7.82982494e-05 7.89061137e-05 7.93222328e-05 7.95568596e-05]\n [4.15311768e-04 4.14292988e-04 4.12471642e-04 4.09698827e-04\n 4.05930560e-04 4.01117846e-04 3.95214455e-04 3.88185888e-04\n 3.80018955e-04 3.70731185e-04 3.60379114e-04 3.49064420e-04\n 3.36936826e-04 3.24192856e-04 3.11069794e-04 2.97834679e-04\n 2.84768777e-04 2.72148617e-04 2.60225327e-04 2.49204452e-04\n 2.39228656e-04 2.30365526e-04 2.22602210e-04 2.15847792e-04\n 2.09943316e-04 2.04678361e-04 1.99812246e-04 1.95097352e-04\n 1.90301937e-04 1.85229992e-04 1.79736247e-04 1.73735199e-04\n 1.67203821e-04 1.60178389e-04 1.52746465e-04 1.45035431e-04\n 1.37199141e-04 1.29404176e-04 1.21816973e-04 1.14592786e-04\n 1.07867057e-04 1.01749484e-04 9.63207019e-05 9.16313599e-05\n 8.77031612e-05 8.45314086e-05 8.20885661e-05 8.03283909e-05\n 7.91902566e-05 7.86033632e-05 7.84906205e-05 7.87720618e-05\n 7.93677197e-05 8.01999436e-05 8.11951835e-05 8.22852906e-05\n 8.34083998e-05 8.45094715e-05 8.55405654e-05 8.64609195e-05\n 8.72368981e-05 8.78418643e-05 8.82560245e-05 8.84917978e-05]\n [4.11489076e-04 4.10722560e-04 4.09426423e-04 4.07418124e-04\n 4.04626006e-04 4.00965118e-04 3.96345999e-04 3.90685134e-04\n 3.83916539e-04 3.76003724e-04 3.66950990e-04 3.56812849e-04\n 3.45700212e-04 3.33782062e-04 3.21281556e-04 3.08466050e-04\n 2.95631204e-04 2.83080191e-04 2.71099900e-04 2.59936683e-04\n 2.49774577e-04 2.40718863e-04 2.32787262e-04 2.25910105e-04\n 2.19939594e-04 2.14667012e-04 2.09845647e-04 2.05216531e-04\n 2.00533857e-04 1.95587217e-04 1.90218465e-04 1.84331915e-04\n 1.77897539e-04 1.70947721e-04 1.63568760e-04 1.55888734e-04\n 1.48063432e-04 1.40261983e-04 1.32653506e-04 1.25395758e-04\n 1.18626360e-04 1.12456820e-04 1.06969265e-04 1.02215588e-04\n 9.82185820e-05 9.49745542e-05 9.24569393e-05 9.06204597e-05\n 8.94054536e-05 8.87420769e-05 8.85541682e-05 8.87626431e-05\n 8.92883502e-05 9.00543743e-05 9.09878114e-05 9.20210648e-05\n 9.30927299e-05 9.41481415e-05 9.51396557e-05 9.60267390e-05\n 9.67759266e-05 9.73607048e-05 9.77613640e-05 9.79921170e-05]\n [4.05648093e-04 4.05169459e-04 4.04469616e-04 4.03331307e-04\n 4.01653536e-04 3.99312779e-04 3.96172558e-04 3.92095233e-04\n 3.86955602e-04 3.80655611e-04 3.73139105e-04 3.64405215e-04\n 3.54518683e-04 3.43615370e-04 3.31901350e-04 3.19644512e-04\n 3.07158448e-04 2.94779469e-04 2.82838777e-04 2.71632835e-04\n 2.61395621e-04 2.52276506e-04 2.44326916e-04 2.37497743e-04\n 2.31647919e-04 2.26562909e-04 2.21980467e-04 2.17620097e-04\n 2.13212361e-04 2.08524568e-04 2.03380193e-04 1.97670546e-04\n 1.91358394e-04 1.84474269e-04 1.77106964e-04 1.69390102e-04\n 1.61486779e-04 1.53574057e-04 1.45828761e-04 1.38415569e-04\n 1.31477963e-04 1.25132176e-04 1.19464017e-04 1.14528182e-04\n 1.10349582e-04 1.06926147e-04 1.04232601e-04 1.02224744e-04\n 1.00843858e-04 1.00020966e-04 9.96807153e-05 9.97447839e-05\n 1.00134730e-04 1.00774292e-04 1.01591152e-04 1.02518232e-04\n 1.03494570e-04 1.04465876e-04 1.05384811e-04 1.06211087e-04\n 1.06911426e-04 1.07459455e-04 1.07835565e-04 1.08055268e-04]\n [3.97551688e-04 3.97398646e-04 3.97370264e-04 3.97214368e-04\n 3.96799800e-04 3.95962734e-04 3.94516644e-04 3.92265095e-04\n 3.89017189e-04 3.84605123e-04 3.78902819e-04 3.71844044e-04\n 3.63437954e-04 3.53779663e-04 3.43053509e-04 3.31527133e-04\n 3.19535500e-04 3.07455364e-04 2.95672336e-04 2.84544197e-04\n 2.74365204e-04 2.65336377e-04 2.57546186e-04 2.50964513e-04\n 2.45450719e-04 2.40774417e-04 2.36645616e-04 2.32749692e-04\n 2.28782288e-04 2.24479743e-04 2.19641838e-04 2.14145139e-04\n 2.07946743e-04 2.01079505e-04 1.93640703e-04 1.85776482e-04\n 1.77664434e-04 1.69496382e-04 1.61462902e-04 1.53740644e-04\n 1.46482908e-04 1.39813584e-04 1.33824160e-04 1.28573360e-04\n 1.24088829e-04 1.20370296e-04 1.17393639e-04 1.15115413e-04\n 1.13477430e-04 1.12411127e-04 1.11841531e-04 1.11690688e-04\n 1.11880532e-04 1.12335181e-04 1.12982689e-04 1.13756333e-04\n 1.14595482e-04 1.15446136e-04 1.16261213e-04 1.17000634e-04\n 1.17631296e-04 1.18126958e-04 1.18468105e-04 1.18670940e-04]\n [3.86964658e-04 3.87175851e-04 3.87895913e-04 3.88838784e-04\n 3.89843593e-04 3.90705895e-04 3.91187386e-04 3.91029116e-04\n 3.89968366e-04 3.87758967e-04 3.84194160e-04 3.79130303e-04\n 3.72508949e-04 3.64374120e-04 3.54881428e-04 3.44295997e-04\n 3.32977299e-04 3.21350806e-04 3.09868634e-04 2.98963616e-04\n 2.89002975e-04 2.80248445e-04 2.72829034e-04 2.66730663e-04\n 2.61804121e-04 2.57789597e-04 2.54353461e-04 2.51131227e-04\n 2.47770252e-04 2.43966511e-04 2.39491444e-04 2.34206950e-04\n 2.28068607e-04 2.21118764e-04 2.13472169e-04 2.05297142e-04\n 1.96795162e-04 1.88181241e-04 1.79666790e-04 1.71445984e-04\n 1.63686012e-04 1.56521127e-04 1.50050074e-04 1.44336285e-04\n 1.39410167e-04 1.35272814e-04 1.31900559e-04 1.29249870e-04\n 1.27262209e-04 1.25868582e-04 1.24993619e-04 1.24559059e-04\n 1.24486641e-04 1.24700393e-04 1.25128371e-04 1.25703919e-04\n 1.26366517e-04 1.27062299e-04 1.27744322e-04 1.28372642e-04\n 1.28914276e-04 1.29343080e-04 1.29639615e-04 1.29820045e-04]\n [3.73666372e-04 3.74279625e-04 3.75823482e-04 3.77980696e-04\n 3.80562959e-04 3.83326964e-04 3.85982966e-04 3.88207469e-04\n 3.89660791e-04 3.90009760e-04 3.88954969e-04 3.86260968e-04\n 3.81786454e-04 3.75510426e-04 3.67549515e-04 3.58161831e-04\n 3.47733836e-04 3.36749096e-04 3.25740912e-04 3.15234249e-04\n 3.05685132e-04 2.97427005e-04 2.90632914e-04 2.85299751e-04\n 2.81256776e-04 2.78196216e-04 2.75719926e-04 2.73393793e-04\n 2.70801173e-04 2.67587899e-04 2.63493927e-04 2.58369549e-04\n 2.52176850e-04 2.44979005e-04 2.36921150e-04 2.28206770e-04\n 2.19073145e-04 2.09768601e-04 2.00533373e-04 1.91584984e-04\n 1.83108348e-04 1.75250243e-04 1.68117504e-04 1.61778129e-04\n 1.56264479e-04 1.51577810e-04 1.47693505e-04 1.44566494e-04\n 1.42136489e-04 1.40332788e-04 1.39078489e-04 1.38294062e-04\n 1.37900246e-04 1.37820326e-04 1.37981838e-04 1.38317788e-04\n 1.38767456e-04 1.39276879e-04 1.39799084e-04 1.40294138e-04\n 1.40729091e-04 1.41077842e-04 1.41320989e-04 1.41473824e-04]\n [3.57467584e-04 3.58517425e-04 3.60953929e-04 3.64433532e-04\n 3.68745225e-04 3.73611532e-04 3.78694634e-04 3.83607193e-04\n 3.87929356e-04 3.91232982e-04 3.93113154e-04 3.93225635e-04\n 3.91327056e-04 3.87312725e-04 3.81245493e-04 3.73368629e-04\n 3.64096816e-04 3.53982277e-04 3.43657510e-04 3.33761176e-04\n 3.24858145e-04 3.17367059e-04 3.11508244e-04 3.07281184e-04\n 3.04474897e-04 3.02708102e-04 3.01490529e-04 3.00293618e-04\n 2.98618519e-04 2.96051529e-04 2.92300899e-04 2.87213120e-04\n 2.80770469e-04 2.73073976e-04 2.64317138e-04 2.54755594e-04\n 2.44677124e-04 2.34375088e-04 2.24127113e-04 2.14179705e-04\n 2.04738619e-04 1.95964283e-04 1.87971289e-04 1.80830885e-04\n 1.74575481e-04 1.69204317e-04 1.64689586e-04 1.60982533e-04\n 1.58019159e-04 1.55725317e-04 1.54021095e-04 1.52824447e-04\n 1.52054092e-04 1.51631751e-04 1.51483792e-04 1.51542378e-04\n 1.51746202e-04 1.52040913e-04 1.52379289e-04 1.52721255e-04\n 1.53033779e-04 1.53290723e-04 1.53472673e-04 1.53593137e-04]\n [3.38231947e-04 3.39746332e-04 3.43131372e-04 3.48024751e-04\n 3.54200690e-04 3.61356143e-04 3.69112862e-04 3.77024470e-04\n 3.84591036e-04 3.91283304e-04 3.96577739e-04 4.00001757e-04\n 4.01185939e-04 3.99917056e-04 3.96183038e-04 3.90199519e-04\n 3.82408379e-04 3.73442237e-04 3.64055086e-04 3.55026896e-04\n 3.47057142e-04 3.40666377e-04 3.36124680e-04 3.33420641e-04\n 3.32275847e-04 3.32200052e-04 3.32574223e-04 3.32744318e-04\n 3.32108834e-04 3.30186999e-04 3.26660387e-04 3.21386873e-04\n 3.14390716e-04 3.05835472e-04 2.95987302e-04 2.85175579e-04\n 2.73756075e-04 2.62080105e-04 2.50471209e-04 2.39209581e-04\n 2.28523489e-04 2.18586464e-04 2.09518821e-04 2.01392160e-04\n 1.94235651e-04 1.88043155e-04 1.82780485e-04 1.78392300e-04\n 1.74808339e-04 1.71948838e-04 1.69729052e-04 1.68062930e-04\n 1.66865970e-04 1.66057376e-04 1.65561600e-04 1.65309383e-04\n 1.65238393e-04 1.65293555e-04 1.65427155e-04 1.65598791e-04\n 1.65775222e-04 1.65930183e-04 1.66044184e-04 1.66127975e-04]\n [3.15902507e-04 3.17898712e-04 3.22267078e-04 3.28637284e-04\n 3.36780620e-04 3.46382069e-04 3.57036303e-04 3.68248578e-04\n 3.79444186e-04 3.89990193e-04 3.99232340e-04 4.06547904e-04\n 4.11411933e-04 4.13469831e-04 4.12604650e-04 4.08984171e-04\n 4.03072563e-04 3.95595515e-04 3.87456346e-04 3.79612195e-04\n 3.72930774e-04 3.68055487e-04 3.65306970e-04 3.64641512e-04\n 3.65673539e-04 3.67754353e-04 3.70087448e-04 3.71854939e-04\n 3.72330974e-04 3.70964755e-04 3.67425142e-04 3.61607783e-04\n 3.53612126e-04 3.43698911e-04 3.32238867e-04 3.19661583e-04\n 3.06410698e-04 2.92908728e-04 2.79532518e-04 2.66598634e-04\n 2.54357100e-04 2.42991510e-04 2.32623554e-04 2.23320257e-04\n 2.15102567e-04 2.07954273e-04 2.01830572e-04 1.96665856e-04\n 1.92380490e-04 1.88886506e-04 1.86092233e-04 1.83905927e-04\n 1.82238536e-04 1.81005707e-04 1.80129172e-04 1.79537635e-04\n 1.79167272e-04 1.78961937e-04 1.78873165e-04 1.78860035e-04\n 1.78888962e-04 1.78933456e-04 1.78973885e-04 1.79017243e-04]\n [2.90532847e-04 2.93012620e-04 2.98368342e-04 3.06235940e-04\n 3.16400126e-04 3.28553518e-04 3.42284362e-04 3.57068225e-04\n 3.72268678e-04 3.87152751e-04 4.00926523e-04 4.12794208e-04\n 4.22039877e-04 4.28124615e-04 4.30784463e-04 4.30108067e-04\n 4.26570419e-04 4.21003207e-04 4.14494055e-04 4.08224524e-04\n 4.03275207e-04 4.00438911e-04 4.00084428e-04 4.02101969e-04\n 4.05940399e-04 4.10723127e-04 4.15411531e-04 4.18977453e-04\n 4.20550157e-04 4.19515173e-04 4.15557296e-04 4.08653005e-04\n 3.99025812e-04 3.87080905e-04 3.73334099e-04 3.58346292e-04\n 3.42670079e-04 3.26811171e-04 3.11204298e-04 2.96201531e-04\n 2.82070194e-04 2.68997446e-04 2.57099000e-04 2.46429919e-04\n 2.36996020e-04 2.28764864e-04 2.21675746e-04 2.15648371e-04\n 2.10590116e-04 2.06401912e-04 2.02982857e-04 2.00233725e-04\n 1.98059524e-04 1.96371278e-04 1.95087190e-04 1.94133320e-04\n 1.93443893e-04 1.92961353e-04 1.92636231e-04 1.92426907e-04\n 1.92299319e-04 1.92226660e-04 1.92189095e-04 1.92188860e-04]\n [2.62321627e-04 2.65265868e-04 2.71571508e-04 2.80898505e-04\n 2.93066103e-04 3.07800944e-04 3.24714307e-04 3.43281170e-04\n 3.62827487e-04 3.82533861e-04 4.01464480e-04 4.18628814e-04\n 4.33078834e-04 4.44035958e-04 4.51030402e-04 4.54023932e-04\n 4.53479991e-04 4.50347949e-04 4.45943877e-04 4.41737003e-04\n 4.39081138e-04 4.38952592e-04 4.41760079e-04 4.47274495e-04\n 4.54692714e-04 4.62812378e-04 4.70267437e-04 4.75765309e-04\n 4.78276065e-04 4.77145253e-04 4.72125669e-04 4.63341919e-04\n 4.51211304e-04 4.36345873e-04 4.19455869e-04 4.01267766e-04\n 3.82463109e-04 3.63638942e-04 3.45287230e-04 3.27789116e-04\n 3.11419530e-04 2.96358185e-04 2.82703798e-04 2.70489263e-04\n 2.59696279e-04 2.50268568e-04 2.42123264e-04 2.35160350e-04\n 2.29270241e-04 2.24339676e-04 2.20256156e-04 2.16911168e-04\n 2.14202422e-04 2.12035306e-04 2.10323740e-04 2.08990577e-04\n 2.07967685e-04 2.07195792e-04 2.06624209e-04 2.06210456e-04\n 2.05919879e-04 2.05725273e-04 2.05606549e-04 2.05560229e-04]\n [2.31647883e-04 2.35011369e-04 2.42177254e-04 2.52850316e-04\n 2.66909835e-04 2.84149788e-04 3.04243841e-04 3.26708355e-04\n 3.50870754e-04 3.75853972e-04 4.00590348e-04 4.23878697e-04\n 4.44493959e-04 4.61348171e-04 4.73684430e-04 4.81265461e-04\n 4.84502786e-04 4.84470799e-04 4.82769811e-04 4.81242693e-04\n 4.81599668e-04 4.85044998e-04 4.92008674e-04 5.02058141e-04\n 5.14009358e-04 5.26195832e-04 5.36812734e-04 5.44244153e-04\n 5.47302669e-04 5.45348118e-04 5.38289805e-04 5.26501970e-04\n 5.10692065e-04 4.91758200e-04 4.70661718e-04 4.48328782e-04\n 4.25584738e-04 4.03118357e-04 3.81469688e-04 3.61034456e-04\n 3.42078589e-04 3.24757789e-04 3.09138566e-04 2.95218428e-04\n 2.82943937e-04 2.72226070e-04 2.62952773e-04 2.54998887e-04\n 2.48233745e-04 2.42526804e-04 2.37751683e-04 2.33788905e-04\n 2.30527660e-04 2.27866815e-04 2.25715369e-04 2.23992513e-04\n 2.22627425e-04 2.21558886e-04 2.20734815e-04 2.20111752e-04\n 2.19654368e-04 2.19334999e-04 2.19133260e-04 2.19039093e-04]\n [1.99102573e-04 2.02809575e-04 2.10684567e-04 2.22499665e-04\n 2.38222750e-04 2.57754391e-04 2.80879997e-04 3.07214075e-04\n 3.36143907e-04 3.66785412e-04 3.97969708e-04 4.28282778e-04\n 4.56178735e-04 4.80175577e-04 4.99118499e-04 5.12463017e-04\n 5.20498771e-04 5.24422117e-04 5.26187790e-04 5.28131144e-04\n 5.32435987e-04 5.40593452e-04 5.53017794e-04 5.68939166e-04\n 5.86598645e-04 6.03669669e-04 6.17766347e-04 6.26894263e-04\n 6.29744348e-04 6.25796961e-04 6.15261549e-04 5.98910132e-04\n 5.77868518e-04 5.53416105e-04 5.26824731e-04 4.99247872e-04\n 4.71658029e-04 4.44822912e-04 4.19308892e-04 3.95500978e-04\n 3.73630916e-04 3.53807488e-04 3.36045366e-04 3.20290575e-04\n 3.06441784e-04 2.94367392e-04 2.83918752e-04 2.74940087e-04\n 2.67275671e-04 2.60774839e-04 2.55295311e-04 2.50705240e-04\n 2.46884325e-04 2.43724242e-04 2.41128613e-04 2.39012655e-04\n 2.37302643e-04 2.35935269e-04 2.34856957e-04 2.34023203e-04\n 2.33397952e-04 2.32953052e-04 2.32667799e-04 2.32524815e-04]\n [1.65509606e-04 1.69451568e-04 1.77817683e-04 1.90469421e-04\n 2.07492193e-04 2.28935701e-04 2.54754760e-04 2.84734059e-04\n 3.18402336e-04 3.54949120e-04 3.93167307e-04 4.31454804e-04\n 4.67912745e-04 5.00568516e-04 5.27721711e-04 5.48359924e-04\n 5.62532448e-04 5.71532408e-04 5.77755970e-04 5.84197979e-04\n 5.93684778e-04 6.08073953e-04 6.27694546e-04 6.51224382e-04\n 6.76035138e-04 6.98863131e-04 7.16566499e-04 7.26740669e-04\n 7.28057379e-04 7.20309316e-04 7.04230466e-04 6.81199019e-04\n 6.52921413e-04 6.21163759e-04 5.87560637e-04 5.53503411e-04\n 5.20094341e-04 4.88147134e-04 4.58215448e-04 4.30634781e-04\n 4.05567738e-04 3.83046661e-04 3.63010631e-04 3.45335775e-04\n 3.29859029e-04 3.16396082e-04 3.04754452e-04 2.94742677e-04\n 2.86176503e-04 2.78882813e-04 2.72701900e-04 2.67488569e-04\n 2.63112412e-04 2.59457541e-04 2.56421981e-04 2.53916851e-04\n 2.51865457e-04 2.50202365e-04 2.48872494e-04 2.47830286e-04\n 2.47038959e-04 2.46469871e-04 2.46102002e-04 2.45910082e-04]\n [1.31927190e-04 1.35963938e-04 1.44537763e-04 1.57617697e-04\n 1.75431724e-04 1.98219563e-04 2.26166876e-04 2.59313471e-04\n 2.97436308e-04 3.39917483e-04 3.85622538e-04 4.32833599e-04\n 4.79298289e-04 5.22455904e-04 5.59870444e-04 5.89825677e-04\n 6.11932752e-04 6.27511877e-04 6.39504810e-04 6.51804464e-04\n 6.68129576e-04 6.90813986e-04 7.19974122e-04 7.53385522e-04\n 7.87098940e-04 8.16524369e-04 8.37564797e-04 8.47439351e-04\n 8.45026282e-04 8.30758921e-04 8.06233435e-04 7.73713985e-04\n 7.35678334e-04 6.94479797e-04 6.52142950e-04 6.10274458e-04\n 5.70055960e-04 5.32285971e-04 4.97444639e-04 4.65763739e-04\n 4.37291723e-04 4.11949027e-04 3.89572317e-04 3.69948233e-04\n 3.52838106e-04 3.37995376e-04 3.25177360e-04 3.14152801e-04\n 3.04706359e-04 2.96640948e-04 2.89778602e-04 2.83960363e-04\n 2.79045562e-04 2.74910738e-04 2.71448378e-04 2.68565597e-04\n 2.66182830e-04 2.64232605e-04 2.62658413e-04 2.61413703e-04\n 2.60461013e-04 2.59771248e-04 2.59323092e-04 2.59083022e-04]\n [9.96185561e-05 1.03584553e-04 1.12028611e-04 1.25037618e-04\n 1.42997473e-04 1.66369607e-04 1.95627398e-04 2.31156461e-04\n 2.73111298e-04 3.21229916e-04 3.74627325e-04 4.31619641e-04\n 4.89667244e-04 5.45549841e-04 5.95866518e-04 6.37857522e-04\n 6.70369060e-04 6.94591629e-04 7.14127684e-04 7.34114329e-04\n 7.59542462e-04 7.93377317e-04 8.35290330e-04 8.81576107e-04\n 9.26265776e-04 9.62904796e-04 9.86251563e-04 9.93332860e-04\n 9.83678306e-04 9.58899881e-04 9.21941986e-04 8.76306124e-04\n 8.25438380e-04 7.72344367e-04 7.19412087e-04 6.68385562e-04\n 6.20427962e-04 5.76225346e-04 5.36098682e-04 5.00106254e-04\n 4.68128689e-04 4.39935074e-04 4.15231792e-04 3.93697017e-04\n 3.75004033e-04 3.58836211e-04 3.44896012e-04 3.32909818e-04\n 3.22629970e-04 3.13834989e-04 3.06328688e-04 2.99938623e-04\n 2.94514242e-04 2.89924904e-04 2.86057932e-04 2.82816758e-04\n 2.80119216e-04 2.77896016e-04 2.76089388e-04 2.74651919e-04\n 2.73545565e-04 2.72740843e-04 2.72216192e-04 2.71929710e-04]\n [6.99807729e-05 7.36975970e-05 8.16443354e-05 9.40237549e-05\n 1.11378686e-04 1.34404951e-04 1.63903192e-04 2.00687314e-04\n 2.45430207e-04 2.98432235e-04 3.59317140e-04 4.26701502e-04\n 4.97948939e-04 5.69190466e-04 6.35816938e-04 6.93552002e-04\n 7.39942878e-04 7.75725550e-04 8.05265517e-04 8.35452891e-04\n 8.73145318e-04 9.22164514e-04 9.81310114e-04 1.04442095e-03\n 1.10241864e-03 1.14626476e-03 1.16948769e-03 1.16942019e-03\n 1.14706347e-03 1.10605142e-03 1.05133523e-03 9.88048439e-04\n 9.20756640e-04 8.53094345e-04 7.87690882e-04 7.26267337e-04\n 6.69808928e-04 6.18750799e-04 5.73144494e-04 5.32792368e-04\n 4.97348641e-04 4.66391261e-04 4.39470485e-04 4.16140068e-04\n 3.95976005e-04 3.78586762e-04 3.63617852e-04 3.50752845e-04\n 3.39712212e-04 3.30250974e-04 3.22155760e-04 3.15241682e-04\n 3.09349246e-04 3.04341454e-04 3.00101143e-04 2.96528613e-04\n 2.93539539e-04 2.91063149e-04 2.89040675e-04 2.87424033e-04\n 2.86174740e-04 2.85263028e-04 2.84667160e-04 2.84336995e-04]\n [4.44231827e-05 4.77184301e-05 5.48076821e-05 6.59919679e-05\n 8.19477161e-05 1.03588251e-04 1.32047280e-04 1.68619246e-04\n 2.14623842e-04 2.71156516e-04 3.38696501e-04 4.16586688e-04\n 5.02493870e-04 5.92100638e-04 6.79409273e-04 7.58007937e-04\n 8.23286445e-04 8.74880486e-04 9.17940817e-04 9.61865168e-04\n 1.01633912e-03 1.08637721e-03 1.16911040e-03 1.25424373e-03\n 1.32788137e-03 1.37750905e-03 1.39567322e-03 1.38113389e-03\n 1.33779876e-03 1.27257363e-03 1.19322652e-03 1.10687335e-03\n 1.01920408e-03 9.34288684e-04 8.54727614e-04 7.81949682e-04\n 7.16532321e-04 6.58481638e-04 6.07451016e-04 5.62899009e-04\n 5.24196555e-04 4.90695669e-04 4.61770668e-04 4.36840762e-04\n 4.15380529e-04 3.96922886e-04 3.81057637e-04 3.67427645e-04\n 3.55723892e-04 3.45680220e-04 3.37068174e-04 3.29692224e-04\n 3.23385441e-04 3.18005684e-04 3.13432280e-04 3.09563160e-04\n 3.06312423e-04 3.03608267e-04 3.01391261e-04 2.99612904e-04\n 2.98234455e-04 2.97225991e-04 2.96565684e-04 2.96195584e-04]\n [2.41942825e-05 2.69253858e-05 3.28528885e-05 4.23419706e-05\n 5.61540378e-05 7.53652387e-05 1.01397424e-04 1.36018858e-04\n 1.81271885e-04 2.39263029e-04 3.11736701e-04 3.99374462e-04\n 5.00864531e-04 6.12014810e-04 7.25505972e-04 8.32082264e-04\n 9.23637089e-04 9.97453094e-04 1.05923519e-03 1.12200779e-03\n 1.19989311e-03 1.29961755e-03 1.41511853e-03 1.52900858e-03\n 1.61990520e-03 1.67090781e-03 1.67468669e-03 1.63372850e-03\n 1.55722410e-03 1.45705464e-03 1.34462880e-03 1.22915616e-03\n 1.11714286e-03 1.01262316e-03 9.17697447e-04 8.33108548e-04\n 7.58730847e-04 6.93936662e-04 6.37848226e-04 5.89499293e-04\n 5.47931767e-04 5.12248618e-04 4.81638878e-04 4.55385749e-04\n 4.32865057e-04 4.13538690e-04 3.96945801e-04 3.82693433e-04\n 3.70447461e-04 3.59924287e-04 3.50883477e-04 3.43121367e-04\n 3.36465591e-04 3.30770435e-04 3.25912928e-04 3.21789567e-04\n 3.18313587e-04 3.15412691e-04 3.13027184e-04 3.11108444e-04\n 3.09617687e-04 3.08524989e-04 3.07808536e-04 3.07403275e-04]\n [1.01689779e-05 1.22481680e-05 1.68180203e-05 2.42605444e-05\n 3.53511663e-05 5.12352044e-05 7.35158439e-05 1.04340520e-04\n 1.46443674e-04 2.03064218e-04 2.77603469e-04 3.72850288e-04\n 4.89649505e-04 6.25159346e-04 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0.02966847 0.02653299 0.02355942 0.02083393\n 0.01839621 0.01625592 0.01440529 0.01282732 0.01150066 0.01040211\n 0.00950776 0.00879344 0.00823503 0.00780881 0.00749203 0.00726356\n 0.00710444 0.00699823 0.00693113 0.00689194 0.00687176 0.00686373\n 0.00686268 0.00686485 0.00686764 0.00687321]\n [0.01445538 0.01443947 0.01441043 0.01436594 0.01430486 0.01422563\n 0.01412628 0.01400438 0.01385705 0.01368094 0.01347228 0.01322698\n 0.01294083 0.01260994 0.01223152 0.01180533 0.01133627 0.0108389\n 0.01034489 0.00991427 0.00964836 0.00969484 0.01022701 0.01139078\n 0.01325033 0.01577255 0.01884496 0.02229405 0.02589399 0.02937807\n 0.03246396 0.03489214 0.03646671 0.03708641 0.03675694 0.03558215\n 0.03373698 0.0314299 0.02886604 0.02622034 0.02362484 0.02116827\n 0.018903 0.01685448 0.01503009 0.01342598 0.01203178 0.01083372\n 0.00981628 0.00896321 0.0082579 0.00768362 0.00722369 0.00686179\n 0.00658224 0.00637041 0.00621307 0.00609861 0.00601717 0.00596065\n 0.00592261 0.00589812 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0.01278723 0.01154066\n 0.01040573 0.00937895 0.00845532 0.00762908 0.00689411 0.0062443\n 0.00567371 0.00517674 0.00474821 0.0043834 0.00407817 0.00382896\n 0.00363286 0.00348761 0.00339161 0.00334628]\n [0.01733943 0.01729653 0.01721096 0.0170822 0.01690977 0.0166931\n 0.01643157 0.0161246 0.01577181 0.0153732 0.01492955 0.01444287\n 0.01391723 0.01335984 0.01278284 0.01220554 0.0116576 0.01118226\n 0.01083846 0.01069873 0.01083919 0.0113217 0.01217537 0.01338804\n 0.01491094 0.01667003 0.01857609 0.02053138 0.02243449 0.02418544\n 0.02569192 0.02687631 0.027682 0.02807802 0.02806067 0.02765195\n 0.02689506 0.02584795 0.02457614 0.02314598 0.02161935 0.02005007\n 0.01848221 0.01694979 0.01547751 0.01408212 0.01277383 0.01155788\n 0.01043576 0.00940633 0.00846668 0.00761282 0.00684016 0.00614392\n 0.00551944 0.00496243 0.00446916 0.00403671 0.00366313 0.00334765\n 0.00309083 0.00289444 0.00276113 0.00269554]\n [0.0178754 0.01782838 0.01773431 0.01759297 0.01740413 0.01716754\n 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0.01411421 0.01373703 0.0134668\n 0.01333484 0.01336821 0.0135847 0.01398874 0.01456951 0.01530193\n 0.01614983 0.01706987 0.01801541 0.01893959 0.01979784 0.02054998\n 0.02116183 0.02160662 0.02186591 0.02193009 0.02179826 0.02147759\n 0.02098222 0.02033172 0.01954945 0.01866085 0.01769183 0.01666748\n 0.01561106 0.0145433 0.01348201 0.01244198 0.01143505 0.01047036\n 0.00955461 0.00869242 0.00788671 0.00713901 0.00644981 0.00581881\n 0.00524522 0.00472799 0.00426608 0.00385864 0.00350528 0.0032063\n 0.00296279 0.00277671 0.00265053 0.00258612]\n [0.01983479 0.01977865 0.0196669 0.0195001 0.01927934 0.01900621\n 0.01868299 0.0183128 0.01789988 0.01744988 0.01697029 0.01647082\n 0.01596398 0.01546546 0.01499452 0.01457397 0.01422952 0.01398829\n 0.01387604 0.01391367 0.01411336 0.01447567 0.01498854 0.01562829\n 0.0163623 0.01715219 0.01795707 0.01873618 0.0194511 0.02006746\n 0.02055639 0.02089549 0.0210696 0.02107102 0.0208994 0.02056115\n 0.02006849 0.01943829 0.01869069 0.0178477 0.01693197 0.01596567\n 0.01496962 0.01396266 0.01296133 0.01197964 0.01102915 0.01011905\n 0.00925641 0.00844643 0.00769271 0.00699753 0.00636208 0.00578669\n 0.00527099 0.00481409 0.00441467 0.00407109 0.00378151 0.00354401\n 0.00335669 0.00321786 0.00312612 0.00307998]\n [0.02012342 0.02006738 0.0199562 0.01979046 0.01957145 0.01930109\n 0.01898202 0.01861782 0.01821325 0.01777451 0.0173096 0.01682869\n 0.01634447 0.01587243 0.015431 0.01504127 0.01472613 0.01450874\n 0.01441004 0.0144459 0.0146242 0.01494286 0.01538927 0.01594136\n 0.01656974 0.01724047 0.01791764 0.01856572 0.01915145 0.01964533\n 0.0200228 0.02026505 0.02035954 0.02030019 0.02008716 0.01972635\n 0.01922863 0.01860884 0.01788466 0.01707551 0.01620148 0.01528243\n 0.01433722 0.01338319 0.01243578 0.0115084 0.01061233 0.00975685\n 0.00894933 0.00819547 0.00749942 0.00686402 0.00629087 0.0057805\n 0.00533238 0.00494502 0.00461595 0.00434189 0.00411884 0.00394241\n 0.00380809 0.00371165 0.00364952 0.00361872]\n [0.0203876 0.02033216 0.02022267 0.02005961 0.01984448 0.01957944\n 0.01926746 0.01891248 0.01851963 0.01809551 0.01764845 0.01718877\n 0.01672908 0.01628437 0.01587194 0.01551098 0.01522161 0.01502337\n 0.01493309 0.01496261 0.01511656 0.01539104 0.01577337 0.01624311\n 0.01677385 0.01733551 0.01789652 0.01842586 0.01889463 0.01927745\n 0.01955332 0.01970641 0.01972636 0.01960846 0.01935334 0.01896664\n 0.01845822 0.01784142 0.01713208 0.01634762 0.01550617 0.01462577\n 0.01372376 0.01281628 0.01191795 0.01104169 0.01019862 0.00939812\n 0.00864786 0.00795391 0.00732082 0.00675164 0.00624797 0.00580988\n 0.00543597 0.0051233 0.00486758 0.00466338 0.00450452 0.00438454\n 0.00429723 0.00423704 0.00419952 0.0041813 ]\n [0.02063003 0.02057567 0.02046886 0.02030995 0.0201006 0.01984317\n 0.01954084 0.01919783 0.01881953 0.01841275 0.01798595 0.01754941\n 0.01711539 0.01669815 0.01631368 0.01597921 0.01571223 0.01552907\n 0.01544311 0.01546296 0.01559082 0.01582157 0.01614278 0.01653557\n 0.01697623 0.01743805 0.01789326 0.01831469 0.01867722 0.01895891\n 0.01914183 0.01921261 0.01916276 0.01898873 0.01869166 0.01827702\n 0.01775401 0.01713484 0.01643397 0.0156673 0.01485147 0.01400313\n 0.01313848 0.01227274 0.01141994 0.01059267 0.00980201 0.00905747\n 0.00836695 0.00773676 0.00717151 0.00667406 0.00624535 0.00588433\n 0.00558792 0.00535118 0.00516765 0.00502984 0.00492982 0.00485988\n 0.00481298 0.00478321 0.00476595 0.00475803]\n [0.02085271 0.02079984 0.02069663 0.02054321 0.02034134 0.02009352\n 0.01980309 0.01947441 0.01911302 0.01872579 0.01832111 0.01790903\n 0.01750128 0.01711119 0.01675339 0.01644316 0.01619554 0.01602407\n 0.01593927 0.01594717 0.01604816 0.01623635 0.01649971 0.01682089\n 0.01717856 0.017549 0.01790771 0.01823088 0.01849664 0.01868601\n 0.01878366 0.01877836 0.01866322 0.01843572 0.0180975 0.01765399\n 0.01711394 0.01648875 0.01579186 0.01503806 0.01424285 0.01342188\n 0.01259046 0.01176323 0.01095379 0.0101746 0.00943674 0.00874984\n 0.00812194 0.00755929 0.00706618 0.00664464 0.00629428 0.00601222\n 0.00579322 0.00563011 0.0055144 0.00543702 0.00538903 0.00536221\n 0.00534942 0.00534489 0.00534427 0.00534477]\n [0.02105692 0.02100594 0.02090716 0.02076042 0.02056757 0.02033115\n 0.0200546 0.01974231 0.01939982 0.01903393 0.01865283 0.01826614\n 0.01788492 0.01752149 0.01718902 0.01690096 0.01667016 0.0165077\n 0.01642173 0.01641628 0.01649037 0.01663766 0.01684665 0.0171014\n 0.01738272 0.01766951 0.01794013 0.01817371 0.01835116 0.01845611\n 0.01847546 0.01839985 0.01822379 0.01794571 0.01756773 0.01709537\n 0.01653708 0.01590373 0.01520802 0.01446392 0.01368612 0.01288956\n 0.01208896 0.01129856 0.01053176 0.00980095 0.00911727 0.00849039\n 0.00792821 0.00743655 0.00701878 0.00667548 0.00640429 0.00620003\n 0.00605516 0.00596048 0.005906 0.00588177 0.00587849 0.00588803\n 0.0059036 0.00591982 0.00593277 0.00594015]\n [0.02124327 0.02119454 0.02110094 0.02096201 0.02077958 0.02055621\n 0.02029531 0.02000122 0.01967938 0.01933636 0.01898001 0.01861942\n 0.01826485 0.01792752 0.0176192 0.0173516 0.01713556 0.01698012\n 0.01689145 0.01687198 0.01691974 0.01702818 0.01718637 0.01737969\n 0.01759087 0.0178011 0.01799128 0.01814308 0.01823989 0.01826758\n 0.01821506 0.01807458 0.01784192 0.01751638 0.0171006 0.01660025\n 0.01602365 0.01538133 0.01468548 0.01394952 0.0131876 0.01241416\n 0.01164359 0.01088989 0.01016638 0.00948544 0.00885818 0.00829408\n 0.00780056 0.00738245 0.00704158 0.00677648 0.00658242 0.00645183\n 0.00637513 0.00634165 0.00634056 0.00636165 0.00639585 0.00643544\n 0.0064742 0.00650728 0.00653121 0.00654417]\n [0.02141169 0.02136555 0.02127788 0.0211478 0.0209771 0.0207683\n 0.0205247 0.02025049 0.01995087 0.01963211 0.01930157 0.0189677\n 0.0186399 0.01832826 0.01804316 0.01779471 0.01759199 0.01744223\n 0.01735 0.01731648 0.017339 0.01741091 0.01752192 0.01765863\n 0.01780547 0.0179457 0.01806243 0.01813958 0.01816275 0.01811979\n 0.01800138 0.01780123 0.0175163 0.01714671 0.01669562 0.01616892\n 0.01557496 0.01492405 0.01422812 0.01350023 0.01275418 0.01200415\n 0.01126434 0.01054862 0.00987029 0.00924163 0.00867353 0.00817493\n 0.00775222 0.00740869 0.00714407 0.00695445 0.00683269 0.00676916\n 0.00675278 0.00677208 0.00681603 0.0068747 0.00693952 0.00700344\n 0.00706081 0.00710737 0.00714004 0.00715746]\n [0.0215615 0.0215183 0.02143724 0.02131703 0.02115935 0.02096659\n 0.02074186 0.02048914 0.02021328 0.01992011 0.01961645 0.01930999\n 0.01900922 0.01872309 0.01846066 0.01823054 0.01804025 0.01789549\n 0.0177995 0.01775247 0.01775122 0.01778918 0.01785665 0.01794138\n 0.01802936 0.01810566 0.01815538 0.01816448 0.01812046 0.018013\n 0.01783437 0.01757963 0.01724681 0.01683684 0.01635342 0.01580276\n 0.01519329 0.01453532 0.01384063 0.01312209 0.01239334 0.01166841\n 0.0109614 0.01028614 0.00965577 0.00908231 0.00857606 0.00814494\n 0.00779377 0.00752375 0.00733217 0.00721271 0.00715612 0.00715127\n 0.00718629 0.00724954 0.0073303 0.00741921 0.0075084 0.00759148\n 0.00766345 0.00772051 0.00775998 0.0077809 ]\n [0.02169138 0.02165145 0.02157772 0.02146839 0.02132501 0.02114976\n 0.02094552 0.02071591 0.02046538 0.02019923 0.01992362 0.01964544\n 0.01937221 0.01911177 0.0188719 0.01865983 0.01848169 0.01834187\n 0.01824251 0.01818301 0.01815986 0.01816662 0.01819422 0.01823148\n 0.01826577 0.01828383 0.01827255 0.01821968 0.01811451 0.01794836\n 0.01771494 0.01741059 0.01703435 0.01658796 0.01607568 0.01550411\n 0.01488187 0.01421936 0.01352833 0.01282162 0.01211281 0.01141585\n 0.01074476 0.01011319 0.00953398 0.00901853 0.00857609 0.00821303\n 0.0079321 0.00773211 0.00760794 0.00755116 0.00755102 0.00759557\n 0.00767279 0.00777136 0.00788118 0.00799362 0.00810155 0.00819925\n 0.00828226 0.00834724 0.00839181 0.00841537]\n [0.02179938 0.02176307 0.0216974 0.02160001 0.02147226 0.02131607\n 0.02113399 0.02092924 0.02070575 0.02046822 0.02022207 0.01997333\n 0.01972853 0.01949439 0.01927748 0.01908375 0.01891809 0.01878376\n 0.01868198 0.01861153 0.01856869 0.01854722 0.01853866 0.01853281\n 0.01851835 0.01848354 0.01841687 0.01830776 0.01814713 0.01792781\n 0.01764487 0.01729586 0.0168808 0.01640223 0.01586502 0.01527618\n 0.01464465 0.01398097 0.01329699 0.01260558 0.01192029 0.01125498\n 0.0106235 0.01003912 0.00951404 0.0090586 0.00868052 0.00838414\n 0.00816989 0.00803419 0.00796984 0.00796688 0.00801372 0.00809826\n 0.00820878 0.00833461 0.00846644 0.00859641 0.00871811 0.00882642\n 0.00891737 0.008988 0.0090362 0.00906165]\n [0.02188291 0.02185061 0.02179379 0.02170946 0.02159877 0.02146332\n 0.02130526 0.0211273 0.0209328 0.02072576 0.02051079 0.02029304\n 0.020078 0.01987129 0.01967831 0.01950383 0.01935162 0.01922395\n 0.01912124 0.01904183 0.01898185 0.01893529 0.01889431 0.01884966\n 0.01879122 0.01870863 0.01859189 0.01843198 0.01822129 0.0179541\n 0.01762679 0.01723804 0.01678887 0.01628261 0.01572476 0.01512284\n 0.0144861 0.01382533 0.0131525 0.01248053 0.01182289 0.01119327\n 0.01060511 0.01007103 0.00960213 0.00920727 0.00889219 0.00865898\n 0.00850575 0.00842683 0.0084135 0.00845491 0.00853927 0.00865479\n 0.00879041 0.00893625 0.00908383 0.00922606 0.00935718 0.00947261\n 0.00956879 0.00964309 0.00969361 0.00972029]\n [0.02193876 0.02191089 0.02186376 0.02179374 0.0217017 0.02158886\n 0.02145688 0.02130792 0.02114468 0.02097037 0.02078876 0.02060403\n 0.02042062 0.02024305 0.0200756 0.01992194 0.01978479 0.01966555\n 0.01956399 0.01947806 0.0194038 0.01933552 0.01926596 0.01918677\n 0.01908896 0.01896348 0.01880175 0.01859619 0.01834063 0.01803071\n 0.01766407 0.01724051 0.01676202 0.01623275 0.01565887 0.0150484\n 0.01441098 0.01375763 0.01310045 0.01245233 0.01182658 0.01123648\n 0.01069478 0.01021304 0.0098009 0.00946531 0.00920986 0.00903437\n 0.00893489 0.0089042 0.00893263 0.00900909 0.00912204 0.00926033\n 0.00941372 0.00957319 0.00973107 0.00988098 0.01001774 0.01013724\n 0.0102363 0.01031254 0.01036425 0.01039159]\n [0.02196301 0.02194006 0.02190358 0.02184927 0.02177765 0.02168953\n 0.02158602 0.02146863 0.02133932 0.02120046 0.02105489 0.02090576\n 0.02075648 0.02061045 0.02047082 0.02034024 0.02022045 0.02011207\n 0.02001427 0.01992471 0.01983942 0.019753 0.0196588 0.01954932\n 0.01941666 0.01925303 0.01905118 0.01880492 0.01850948 0.01816179\n 0.01776075 0.01730726 0.01680429 0.0162568 0.01567166 0.01505738\n 0.01442399 0.01378271 0.01314571 0.01252571 0.01193564 0.01138812\n 0.01089486 0.010466 0.01010938 0.00982985 0.00962884 0.00950413\n 0.00945021 0.00945885 0.00952 0.00962278 0.00975622 0.00991\n 0.01007476 0.01024234 0.01040581 0.01055945 0.0106986 0.01081955\n 0.01091944 0.01099611 0.01104804 0.01107551]\n [0.0219511 0.0219336 0.02190886 0.02187183 0.02182268 0.0217617\n 0.02168941 0.02160659 0.02151437 0.02141423 0.02130798 0.02119773\n 0.02108578 0.02097439 0.02086565 0.02076116 0.02066175 0.0205673\n 0.02047649 0.02038669 0.02029398 0.02019326 0.02007848 0.01994299\n 0.01977996 0.01958277 0.0193455 0.0190633 0.01873277 0.01835213\n 0.01792149 0.01744286 0.01692019 0.01635927 0.0157676 0.01515423\n 0.01452949 0.01390474 0.01329204 0.0127038 0.0121523 0.01164918\n 0.01120479 0.01082758 0.0105234 0.01029503 0.01014191 0.01006022\n 0.01004337 0.01008263 0.01016807 0.01028928 0.01043609 0.01059904\n 0.01076967 0.01094061 0.01110565 0.01125964 0.01139837 0.01151851\n 0.01161746 0.01169328 0.01174456 0.01177172]\n [0.02189772 0.02188629 0.02187451 0.02185657 0.02183221 0.02180117\n 0.02176328 0.02171855 0.02166717 0.02160965 0.02154671 0.02147937\n 0.02140873 0.02133594 0.02126197 0.02118738 0.02111216 0.02103545\n 0.02095546 0.02086933 0.02077321 0.02066231 0.02053119 0.02037404\n 0.02018504 0.01995879 0.01969064 0.01937709 0.01901605 0.01860706\n 0.01815144 0.01765229 0.01711454 0.01654477 0.01595113 0.01534309\n 0.01473122 0.01412687 0.01354184 0.01298795 0.01247659 0.01201813\n 0.01162134 0.01129281 0.0110364 0.010853 0.01074041 0.01069369\n 0.0107056 0.01076738 0.01086948 0.01100218 0.01115616 0.01132286\n 0.01149465 0.01166493 0.0118281 0.01197954 0.01211545 0.01223284\n 0.01232933 0.01240316 0.01245305 0.0124795 ]\n [0.02179681 0.02179217 0.02179474 0.02179795 0.02180106 0.02180318\n 0.0218034 0.02180083 0.02179471 0.02178443 0.0217696 0.02175001\n 0.02172557 0.02169623 0.02166181 0.02162185 0.02157545 0.02152105\n 0.0214564 0.02137844 0.02128335 0.02116672 0.02102369 0.02084929\n 0.02063875 0.02038782 0.02009317 0.01975263 0.01936544 0.01893246\n 0.01845619 0.01794085 0.01739231 0.01681791 0.01622638 0.01562754\n 0.01503203 0.01445106 0.01389592 0.01337764 0.01290646 0.01249127\n 0.01213914 0.01185479 0.01164028 0.01149487 0.01141516 0.01139545\n 0.01142833 0.01150526 0.01161726 0.0117554 0.01191124 0.01207704\n 0.01224599 0.01241216 0.01257054 0.01271696 0.01284801 0.01296096\n 0.01305368 0.01312455 0.01317242 0.01319781]\n [0.02164156 0.02164452 0.02166305 0.02168975 0.02172337 0.02176235\n 0.02180493 0.02184928 0.02189355 0.02193598 0.02197492 0.02200889\n 0.0220365 0.02205646 0.02206738 0.02206775 0.02205573 0.02202907\n 0.02198503 0.02192034 0.02183125 0.02171368 0.0215634 0.02137628\n 0.02114858 0.02087727 0.02056031 0.02019689 0.01978761 0.01933462\n 0.01884166 0.01831402 0.01775847 0.01718309 0.01659705 0.01601042\n 0.01543379 0.01487797 0.01435359 0.01387065 0.01343808 0.01306319\n 0.01275134 0.01250552 0.01232623 0.01221147 0.012157 0.01215678\n 0.01220346 0.01228894 0.01240491 0.01254325 0.01269635 0.01285731\n 0.01302 0.01317913 0.01333021 0.0134695 0.01359393 0.01370103\n 0.01378885 0.01385594 0.01390122 0.01392526]\n [0.02142438 0.02143585 0.02147214 0.02152501 0.02159261 0.02167266\n 0.02176249 0.02185922 0.02195984 0.02206131 0.02216067 0.02225503\n 0.02234165 0.02241787 0.02248105 0.02252852 0.02255748 0.02256492\n 0.02254759 0.02250197 0.0224244 0.02231111 0.02215849 0.02196328\n 0.0217228 0.02143526 0.02109995 0.02071744 0.02028972 0.01982027\n 0.01931404 0.01877737 0.0182179 0.01764434 0.01706626 0.01649377\n 0.01593726 0.015407 0.01491275 0.01446334 0.01406627 0.01372733\n 0.01345024 0.01323649 0.01308531 0.0129938 0.01295724 0.01296948\n 0.01302344 0.01311159 0.01322633 0.01336032 0.01350675 0.01365945\n 0.01381296 0.01396255 0.01410421 0.01423457 0.01435088 0.01445089\n 0.01453286 0.01459545 0.01463768 0.0146601 ]\n [0.0211369 0.02115793 0.02121401 0.02129604 0.02140155 0.02152744\n 0.02167006 0.02182541 0.0219892 0.02215704 0.02232451 0.02248725\n 0.02264102 0.0227817 0.02290529 0.02300786 0.02308556 0.02313452\n 0.02315094 0.02313102 0.02307109 0.02296776 0.022818 0.02261945\n 0.02237054 0.02207074 0.02172073 0.02132251 0.02087949 0.0203965\n 0.01987969 0.01933646 0.01877524 0.01820529 0.01763643 0.01707874\n 0.01654221 0.01603642 0.01557012 0.01515094 0.01478494 0.01447645\n 0.01422775 0.01403911 0.0139088 0.01383331 0.01380768 0.01382589\n 0.01388127 0.01396686 0.01407578 0.01420146 0.0143378 0.0144793\n 0.01462111 0.01475902 0.01488943 0.01500933 0.01511624 0.01520813\n 0.01528343 0.01534091 0.0153797 0.01540026]\n [0.02077005 0.0208018 0.02087994 0.02099448 0.02114228 0.02131936\n 0.02152101 0.02174201 0.02197673 0.02221929 0.02246372 0.02270407\n 0.02293446 0.02314918 0.0233427 0.02350975 0.02364524 0.02374438\n 0.02380267 0.02381597 0.02378057 0.02369338 0.02355201 0.023355\n 0.02310192 0.02279358 0.02243211 0.02202101 0.02156515 0.02107073\n 0.02054514 0.01999678 0.01943483 0.01886903 0.01830933 0.01776563\n 0.01724742 0.01676348 0.01632151 0.0159279 0.01558739 0.01530298\n 0.01507576 0.01490502 0.01478836 0.0147219 0.01470067 0.01471889\n 0.01477034 0.0148487 0.01494776 0.01506163 0.0151849 0.01531266\n 0.01544061 0.01556499 0.0156826 0.01579073 0.01588715 0.01597005\n 0.01603798 0.01608985 0.01612486 0.01614337]\n [0.02031412 0.02035789 0.02046059 0.02061134 0.02080627 0.02104047\n 0.02130809 0.02160261 0.02191695 0.02224367 0.02257513 0.02290365\n 0.02322156 0.02352142 0.023796 0.02403844 0.02424232 0.02440169\n 0.02451124 0.02456635 0.0245632 0.02449895 0.02437185 0.02418135\n 0.02392824 0.02361475 0.02324452 0.02282263 0.0223555 0.02185076\n 0.02131703 0.02076371 0.0202007 0.01963812 0.01908598 0.0185539\n 0.0180508 0.0175846 0.01716197 0.01678811 0.01646658 0.01619923\n 0.01598621 0.01582608 0.01571598 0.01565189 0.01562893 0.01564167\n 0.01568437 0.0157513 0.01583688 0.01593587 0.01604345 0.01615526\n 0.01626748 0.01637676 0.01648023 0.01657549 0.01666051 0.01673368\n 0.01679368 0.01683951 0.01687046 0.01688676]\n [0.01975895 0.01981614 0.01994612 0.02013712 0.02038449 0.02068228\n 0.02102348 0.02140018 0.02180379 0.02222521 0.02265504 0.02308371\n 0.02350165 0.02389943 0.02426795 0.02459854 0.02488314 0.02511446\n 0.02528614 0.02539291 0.02543073 0.02539693 0.02529035 0.02511143\n 0.02486223 0.02454647 0.02416944 0.02373793 0.02325999 0.02274474\n 0.02220209 0.02164247 0.02107646 0.02051452 0.01996667 0.01944221\n 0.01894945 0.01849547 0.01808594 0.01772501 0.01741521 0.01715745\n 0.01695116 0.01679437 0.01668395 0.01661588 0.01658547 0.01658766\n 0.0166172 0.01666891 0.01673779 0.01681918 0.01690877 0.01700272\n 0.0170976 0.01719043 0.01727866 0.01736011 0.01743299 0.01749582\n 0.01754742 0.01758687 0.01761353 0.01762748]\n [0.01909413 0.01916626 0.01932646 0.01956206 0.01986754 0.02023592\n 0.02065891 0.02112718 0.02163059 0.02215833 0.02269913 0.02324145\n 0.0237736 0.02428402 0.02476139 0.02519495 0.0255747 0.02589165\n 0.02613813 0.02630794 0.02639663 0.02640161 0.02632227 0.02616004\n 0.02591834 0.02560253 0.02521971 0.02477849 0.02428874 0.02376119\n 0.02320714 0.02263806 0.02206527 0.02149956 0.02095096 0.02042844\n 0.0199397 0.01949107 0.01908731 0.01873164 0.01842574 0.01816979\n 0.01796265 0.01780203 0.01768466 0.01760659 0.01756339 0.01755035\n 0.01756272 0.01759579 0.0176451 0.01770648 0.0177761 0.01785052\n 0.01792669 0.01800195 0.01807401 0.01814092 0.01820105 0.01825306\n 0.01829589 0.01832871 0.01835091 0.0183624 ]\n [0.01830942 0.0183981 0.01859164 0.01887642 0.01924603 0.01969234\n 0.02020579 0.02077563 0.02139013 0.02203677 0.0227024 0.02337339\n 0.02403581 0.02467566 0.02527913 0.02583296 0.02632476 0.02674343\n 0.02707954 0.02732563 0.02747656 0.02752963 0.02748472 0.02734426\n 0.02711318 0.02679862 0.02640969 0.0259571 0.0254527 0.02490906\n 0.02433902 0.02375522 0.02316976 0.02259386 0.02203756 0.02150957\n 0.02101706 0.02056564 0.02015933 0.01980055 0.01949029 0.01922816\n 0.01901262 0.01884115 0.01871045 0.01861671 0.01855574 0.0185232\n 0.01851473 0.01852611 0.0185533 0.01859258 0.0186405 0.018694\n 0.01875033 0.01880712 0.01886228 0.01891405 0.01896097 0.01900182\n 0.01903561 0.01906159 0.01907922 0.01908817]\n [0.01739519 0.01750211 0.01773224 0.01807098 0.01851091 0.01904272\n 0.01965556 0.02033729 0.02107469 0.02185361 0.02265904 0.02347525\n 0.02428592 0.02507435 0.02582387 0.02651818 0.02714196 0.02768138\n 0.02812466 0.0284626 0.02868892 0.02880058 0.02879783 0.02868414\n 0.02846604 0.02815273 0.02775566 0.02728792 0.0267637 0.02619771\n 0.02560454 0.02499825 0.02439187 0.02379713 0.0232242 0.02268159\n 0.02217603 0.02171255 0.0212945 0.02092368 0.02060049 0.02032411\n 0.02009269 0.01990357 0.01975349 0.01963875 0.01955541 0.01949946\n 0.01946689 0.01945386 0.01945673 0.01947211 0.0194969 0.01952834\n 0.01956394 0.01960155 0.01963927 0.01967551 0.0197089 0.01973835\n 0.01976293 0.01978197 0.01979493 0.01980129]\n [0.01634315 0.01647004 0.01674012 0.01713766 0.01765412 0.01827895\n 0.01900002 0.01980393 0.02067619 0.0216012 0.0225623 0.0235417\n 0.02452062 0.02547941 0.02639804 0.02725659 0.028036 0.02871887\n 0.02929028 0.02973853 0.03005567 0.03023789 0.03028561 0.0302034\n 0.02999959 0.02968578 0.02927616 0.02878673 0.02823453 0.0276368\n 0.02701033 0.02637085 0.02573258 0.02510793 0.02450734 0.02393921\n 0.02340995 0.02292408 0.02248439 0.02209215 0.02174727 0.02144858\n 0.02119399 0.02098073 0.02080556 0.0206649 0.02055503 0.02047217\n 0.02041263 0.02037286 0.02034954 0.02033955 0.02034009 0.0203486\n 0.02036282 0.02038077 0.02040071 0.02042117 0.02044088 0.02045881\n 0.02047413 0.02048617 0.02049446 0.02049821]\n [0.01514721 0.01529586 0.0156093 0.01607046 0.01666945 0.01739439\n 0.01823197 0.01916779 0.0201864 0.02127123 0.02240431 0.02356606\n 0.02473526 0.02588908 0.02700359 0.02805442 0.02901774 0.02987147\n 0.03059635 0.03117715 0.03160339 0.03186993 0.03197712 0.03193058\n 0.03174077 0.03142218 0.03099243 0.03047114 0.02987889 0.02923617\n 0.02856249 0.02787569 0.02719152 0.02652328 0.02588181 0.02527554\n 0.0247106 0.02419109 0.0237193 0.02329599 0.02292065 0.02259175\n 0.022307 0.02206349 0.02185798 0.02168696 0.02154685 0.02143406\n 0.02134511 0.02127669 0.02122569 0.02118923 0.02116469 0.02114971\n 0.02114217 0.02114023 0.02114226 0.02114687 0.02115289 0.02115934\n 0.02116542 0.02117051 0.02117415 0.0211753 ]\n [0.01380456 0.01397682 0.01433713 0.0148666 0.01555365 0.01638491\n 0.01734604 0.01842206 0.01959723 0.02085468 0.02217585 0.02353988\n 0.02492332 0.0263 0.0276415 0.02891796 0.03009943 0.03115746\n 0.03206689 0.0328074 0.03336477 0.03373168 0.03390796 0.03390039\n 0.03372193 0.03339077 0.03292891 0.03236069 0.03171132 0.03100545\n 0.03026612 0.02951389 0.02876637 0.02803804 0.02734029 0.0266816\n 0.02606787 0.02550275 0.02498802 0.02452393 0.02410951 0.02374285\n 0.02342138 0.02314204 0.0229015 0.02269624 0.02252274 0.02237752\n 0.02225724 0.02215871 0.02207899 0.02201534 0.02196527 0.02192654\n 0.02189715 0.02187533 0.02185954 0.02184846 0.02184095 0.02183607\n 0.02183306 0.02183132 0.0218304 0.02182899]\n [0.01231709 0.01251497 0.01292588 0.0135282 0.01430803 0.01525028\n 0.01633981 0.01756177 0.01890113 0.0203419 0.02186602 0.02345229\n 0.02507558 0.0267064 0.02831118 0.02985328 0.03129473 0.03259854\n 0.03373121 0.03466515 0.03538059 0.03586679 0.03612247 0.03615558\n 0.03598232 0.03562571 0.03511366 0.03447687 0.03374672 0.03295342\n 0.03212455 0.0312841 0.03045204 0.02964421 0.0288726 0.02814573\n 0.02746917 0.02684603 0.02627746 0.02576308 0.02530137 0.02488994\n 0.02452586 0.02420579 0.02392621 0.02368352 0.02347415 0.02329464\n 0.02314166 0.02301211 0.02290311 0.02281198 0.02273632 0.02267394\n 0.02262291 0.02258152 0.02254825 0.02252182 0.02250111 0.02248522\n 0.02247338 0.02246501 0.02245967 0.02245578]\n [0.01069289 0.01091887 0.0113847 0.0120644 0.01294057 0.01399603\n 0.01521532 0.01658478 0.01809166 0.01972258 0.02146174 0.02328912\n 0.02517896 0.02709878 0.02900929 0.03086548 0.03261883 0.03422058\n 0.03562551 0.03679551 0.03770258 0.03833067 0.03867655 0.03874945\n 0.03856991 0.03816761 0.03757872 0.03684277 0.03599962 0.03508687\n 0.03413802 0.03318134 0.03223952 0.03132988 0.0304649 0.02965295\n 0.02889899 0.02820536 0.02757234 0.02699873 0.02648224 0.02601987\n 0.02560814 0.02524332 0.02492158 0.0246391 0.02439216 0.02417719\n 0.02399083 0.02382994 0.02369163 0.02357323 0.02347235 0.02338682\n 0.02331472 0.02325434 0.02320418 0.02316297 0.0231296 0.02310315\n 0.02308287 0.02306817 0.02305861 0.02305235]\n [0.00894815 0.00920584 0.00973248 0.01049445 0.01146889 0.01263607\n 0.01398106 0.01549318 0.01716419 0.01898583 0.02094711 0.02303157\n 0.02521468 0.02746192 0.02972796 0.03195749 0.03408806 0.03605463\n 0.03779516 0.03925617 0.04039741 0.04119479 0.04164178 0.04174923\n 0.04154374 0.04106468 0.04036016 0.03948227 0.03848267 0.03740889\n 0.03630196 0.03519524 0.03411438 0.03307801 0.03209869 0.03118413\n 0.03033826 0.02956216 0.0288549 0.0282141 0.02763647 0.02711813\n 0.02665488 0.02624242 0.02587645 0.02555281 0.0252675 0.02501676\n 0.02479707 0.0246052 0.02443815 0.02429323 0.02416798 0.02406021\n 0.02396796 0.02388951 0.02382334 0.02376816 0.02372284 0.02368645\n 0.02365824 0.0236376 0.02362409 0.02361562]\n [0.0071093 0.00740516 0.00800216 0.00885242 0.00992452 0.01119607\n 0.01265454 0.01429497 0.01611674 0.01812011 0.02030244 0.02265433\n 0.0251556 0.02777175 0.0304517 0.03312783 0.03571922 0.03813796\n 0.04029763 0.04212206 0.04355259 0.04455288 0.04511122 0.04524065\n 0.04497686 0.04437383 0.04349745 0.04241817 0.04120413 0.03991607\n 0.03860427 0.03730778 0.03605495 0.03486498 0.03374969 0.03271527\n 0.03176382 0.03089453 0.03010468 0.02939031 0.02874674 0.02816894\n 0.02765177 0.02719014 0.02677914 0.02641412 0.02609069 0.0258048\n 0.02555269 0.02533093 0.0251364 0.02496628 0.02481802 0.02468936\n 0.02457828 0.02448301 0.02440199 0.02433389 0.02427755 0.02423202\n 0.02419652 0.02417043 0.02415329 0.02414279]\n [0.0052161 0.00556405 0.00624933 0.00719579 0.00835976 0.0097184\n 0.01126555 0.01300609 0.01495104 0.01711327 0.01950306 0.02212304\n 0.02496233 0.02799048 0.03115246 0.03436661 0.03752761 0.04051512\n 0.04320677 0.04549226 0.04728508 0.04853015 0.04920774 0.04933426\n 0.04895976 0.04816111 0.04703155 0.04566866 0.04416368 0.04259436\n 0.04102177 0.03949035 0.03803 0.03665897 0.03538679 0.03421678\n 0.03314804 0.03217701 0.03129847 0.03050633 0.02979412 0.02915534\n 0.02858363 0.02807294 0.02761759 0.0272123 0.02685219 0.02653281\n 0.0262501 0.02600037 0.02578031 0.02558694 0.02541758 0.02526986\n 0.02514168 0.02503119 0.02493678 0.02485706 0.02479085 0.02473713\n 0.02469512 0.02466416 0.02464379 0.02463149]\n [0.00333089 0.00376653 0.00457538 0.00562347 0.00685906 0.00826865\n 0.00985997 0.01165279 0.0136738 0.01595274 0.01851804 0.02139099\n 0.02457767 0.02805912 0.03178129 0.03564825 0.03952299 0.0432386\n 0.0466186 0.04950038 0.05175462 0.05329737 0.05409646 0.05417412\n 0.0536041 0.05250068 0.05100028 0.04924095 0.0473457 0.04541318\n 0.04351537 0.04170022 0.03999639 0.03841841 0.03697109 0.03565293\n 0.03445859 0.03338057 0.03241038 0.03153919 0.0307583 0.0300594\n 0.02943469 0.02887697 0.02837963 0.02793665 0.02754259 0.02719252\n 0.02688201 0.02660709 0.0263642 0.02615017 0.02596218 0.02579771\n 0.02565458 0.02553083 0.0254248 0.02533503 0.02526028 0.02519951\n 0.02515189 0.02511676 0.02509361 0.02507978]\n [0.00163042 0.00224056 0.00320305 0.0043135 0.00555572 0.00694317\n 0.0085036 0.01027399 0.0122984 0.01462625 0.01730925 0.02039547\n 0.02391927 0.0278862 0.03225452 0.03691828 0.04170097 0.04636812\n 0.05065957 0.05433047 0.05718454 0.05909278 0.06000356 0.05994956\n 0.05904582 0.05747017 0.05542881 0.05312008 0.05070902 0.04831713\n 0.04602424 0.04387668 0.04189669 0.04009068 0.03845533 0.03698181\n 0.03565856 0.03447293 0.03341227 0.03246441 0.03161801 0.03086267\n 0.03018895 0.02958834 0.02905321 0.02857674 0.02815283 0.02777606\n 0.0274416 0.02714516 0.02688291 0.02665149 0.02644789 0.02626949\n 0.02611396 0.02597928 0.02586369 0.02576567 0.02568394 0.02561743\n 0.02556525 0.02552671 0.0255013 0.02548625]\n [0.00116384 0.00171071 0.00256573 0.00354011 0.00463315 0.0058686\n 0.00728301 0.00892349 0.0108478 0.01312461 0.01583248 0.01905521\n 0.02287096 0.02733158 0.0324311 0.0380691 0.04402509 0.04996605\n 0.05549807 0.06024231 0.06389569 0.0662579 0.06724546 0.06691081\n 0.06544467 0.06313768 0.06031085 0.05725041 0.05417204 0.05121571\n 0.04845935 0.04593746 0.04365751 0.04161159 0.03978401 0.03815576\n 0.03670718 0.03541926 0.03427439 0.0332566 0.03235159 0.03154667\n 0.03083062 0.03019358 0.02962683 0.02912272 0.02867451 0.02827627\n 0.02792275 0.02760934 0.02733197 0.02708707 0.02687147 0.02668241\n 0.02651745 0.0263745 0.02625171 0.0261475 0.02606056 0.02598975\n 0.02593417 0.0258931 0.02586602 0.02585008]\n [0.00213265 0.0023765 0.00284792 0.00346983 0.00423676 0.00516715\n 0.00629552 0.00767139 0.00936097 0.01144966 0.01404432 0.01727277\n 0.02127604 0.02618551 0.0320761 0.03889487 0.04638857 0.0540828\n 0.06136013 0.06761279 0.07236377 0.07529786 0.07627587 0.07538755\n 0.07297257 0.06953093 0.06557338 0.06150648 0.05759302 0.05397204\n 0.05069798 0.0477767 0.0451893 0.04290617 0.04089462 0.03912271\n 0.03756104 0.03618333 0.03496648 0.03389044 0.0329378 0.03209357\n 0.03134474 0.0306801 0.03008991 0.02956573 0.02910019 0.02868689\n 0.02832022 0.02799528 0.02770777 0.02745393 0.02723046 0.02703447\n 0.02686345 0.0267152 0.02658784 0.02647973 0.02638951 0.02631601\n 0.02625832 0.02621568 0.02618756 0.02617109]\n [0.00333928 0.00342028 0.00360987 0.00390342 0.00431654 0.00487533\n 0.00561936 0.00660495 0.0079095 0.00963699 0.01192507 0.0149525\n 0.0189424 0.02414936 0.03080688 0.03900796 0.04853102 0.05871438\n 0.06854898 0.07700601 0.08331963 0.08699048 0.08776243 0.08580358\n 0.08176963 0.07656744 0.07101487 0.06565176 0.06074902 0.05639411\n 0.05258165 0.04926601 0.04638877 0.04389134 0.04172019 0.03982848\n 0.03817615 0.03672925 0.03545917 0.0343418 0.03335682 0.03248702\n 0.03171783 0.0310368 0.03043331 0.02989823 0.0294237 0.02900291\n 0.02862996 0.02829972 0.02800772 0.02775006 0.02752332 0.02732456\n 0.02715116 0.0270009 0.02687184 0.02676231 0.02667092 0.02659648\n 0.02653805 0.02649488 0.02646641 0.02644981]\n [0.00422335 0.00425169 0.00432662 0.00444839 0.00463062 0.00489547\n 0.00527795 0.00583213 0.00663986 0.00782195 0.00955103 0.0120661\n 0.01568995 0.02084468 0.02803121 0.0376904 0.04985001 0.06368346\n 0.07745898 0.08929377 0.09793801 0.10259001 0.10272073 0.09865313\n 0.09180834 0.08391157 0.07620557 0.06929603 0.0633225 0.05823506\n 0.05392121 0.05026067 0.04714466 0.04448095 0.04219347 0.04022018\n 0.03851061 0.03702366 0.03572573 0.03458923 0.03359133 0.03271309\n 0.03193863 0.03125462 0.03064977 0.03011446 0.02964048 0.02922078\n 0.02884926 0.02852067 0.02823042 0.02797454 0.02774958 0.02755253\n 0.02738076 0.02723201 0.02710432 0.02699603 0.02690571 0.02683219\n 0.0267745 0.02673188 0.02670379 0.02668747]\n [0.00467043 0.00469073 0.00474272 0.00482081 0.00492637 0.00506378\n 0.00524383 0.00548991 0.00584903 0.00641049 0.00733651 0.00890669\n 0.01156469 0.01595333 0.02295652 0.03367208 0.04897477 0.06827346\n 0.08855187 0.1058616 0.11817017 0.12431252 0.12270196 0.11429795\n 0.10253862 0.09067911 0.0803962 0.07187864 0.06491261 0.05920976\n 0.05451226 0.05061216 0.0473475 0.0445932 0.04225262 0.04025053\n 0.03852797 0.03703825 0.0357441 0.03461544 0.03362782 0.03276117\n 0.03199891 0.0313272 0.03073443 0.03021078 0.02974792 0.0293387\n 0.02897701 0.02865757 0.02837578 0.0281277 0.02790987 0.02771929\n 0.02755337 0.02740985 0.02728678 0.02718251 0.02709563 0.02702495\n 0.02696953 0.02692862 0.02690165 0.02688605]\n [0.00461015 0.00465384 0.00475191 0.00489297 0.00507027 0.0052754\n 0.00549868 0.00573044 0.00596452 0.00620807 0.00650508 0.00698469\n 0.00796121 0.01017754 0.01513353 0.02510049 0.04287252 0.07008567\n 0.10200122 0.12887463 0.14763549 0.15624296 0.15009441 0.13209201\n 0.11174985 0.0952497 0.0825223 0.07272585 0.06508627 0.05903291\n 0.05416177 0.05018675 0.04690268 0.04416002 0.0418479 0.03988282\n 0.03820089 0.03675257 0.03549891 0.03440893 0.03345772 0.03262501\n 0.03189417 0.03125144 0.0306853 0.0301861 0.02974561 0.02935687\n 0.02901387 0.02871146 0.02844518 0.02821116 0.02800604 0.0278269\n 0.0276712 0.02753675 0.02742164 0.02732426 0.02724323 0.0271774\n 0.02712584 0.0270878 0.02706275 0.0270483 ]\n [0.00400406 0.00411526 0.00435016 0.00468185 0.00509379 0.00557057\n 0.00609743 0.00665813 0.00723165 0.00778771 0.00828208 0.00865851\n 0.00889196 0.00917207 0.01011043 0.01341459 0.02677122 0.06125853\n 0.1162629 0.16030552 0.19158705 0.21046445 0.18647204 0.14466476\n 0.11540243 0.09547258 0.08144926 0.07120386 0.06347012 0.05747435\n 0.05272269 0.04888781 0.04574538 0.0431372 0.04094891 0.039096\n 0.03751485 0.03615668 0.03498356 0.03396552 0.03307862 0.0323035\n 0.03162432 0.031028 0.03050365 0.03004211 0.02963564 0.02927763\n 0.02896242 0.02868512 0.02844151 0.02822794 0.0280412 0.02787852\n 0.02773749 0.02761601 0.02751226 0.02742468 0.02735196 0.027293\n 0.02724688 0.02721291 0.02719056 0.02717772]\n [0.00286901 0.00315649 0.00370335 0.00440595 0.00522548 0.00614658\n 0.007166 0.00828695 0.00951551 0.01085696 0.01231003 0.01385519\n 0.01542859 0.01686313 0.01776104 0.01793951 0.02206899 0.03889525\n 0.12949873 0.19243208 0.27995462 0.30889352 0.19755023 0.14044966\n 0.10925212 0.08965714 0.07641055 0.06692623 0.05985649 0.05441791\n 0.05012888 0.04667772 0.04385471 0.04151393 0.03955093 0.03788917\n 0.03647128 0.03525349 0.03420183 0.03328951 0.03249514 0.03180142\n 0.03119419 0.03066173 0.03019428 0.02978361 0.02942272 0.02910564\n 0.02882724 0.02858307 0.02836928 0.02818249 0.02801977 0.02787855\n 0.0277566 0.02765195 0.02756292 0.02748804 0.02742607 0.02737598\n 0.02733691 0.02730819 0.02728932 0.02727851]\n [0.00181297 0.00238365 0.00331567 0.00440021 0.0055991 0.00691361\n 0.00836194 0.00997336 0.01178789 0.01385833 0.01625445 0.01906906\n 0.02242724 0.02649207 0.03148512 0.03749572 0.04470774 0.05375671\n 0.18208981 0.29559719 0.39820416 0.36825408 0.18676491 0.12959535\n 0.10079519 0.08296934 0.0710817 0.06262618 0.05634626 0.05152063\n 0.04771377 0.04464701 0.04213444 0.04004742 0.03829425 0.03680777\n 0.03553773 0.03444575 0.03350201 0.03268296 0.03196975 0.03134707\n 0.03080237 0.03032523 0.02990693 0.02954008 0.02921838 0.02893645\n 0.02868961 0.0284738 0.02828548 0.02812157 0.02797935 0.02785642\n 0.0277507 0.02766037 0.02758382 0.02751969 0.0274668 0.02742417\n 0.02739099 0.02736661 0.02735058 0.02733755]]\n- channel 4: A 64\u00d764 matrix of zeros with a single non-zero value 0.5 located at position (63, 20)\n- channel 5: A 64\u00d764 matrix representing a y-direction load distribution, with a single point load of 0.8660254 located at position (63, 19)\n\n###Task\nBased on these five input channels, compute and return the following outputs:\n- C_y_hat (float): The compliance (objective value) of the optimized material layout.\n- VF_y_hat (float): The volume fraction of the optimized layout you generated, calculated as the proportion of material (1's) in y_hat.\n\n#### Constraints\n- The design must minimize compliance.\n- All boundary conditions and external loads must be satisfied.\n- The volume fraction constraint must not be violated.\n- The final outputs should be provided according to the specified field descriptions.", "contributor": "Yilan Jiang" }, { "task_id": "XZ_02", "query_token_num": 581, "Engineering Domain": "Robotics", "prompt": "## Task Description\nYou are given a 2D gridmap of a construction site, where each node is represented as a triplet (x, y, 0/1). This map follows the specifications below:\n-The construction site spans an area that is 50 meters wide and 40 meters long.\n-Each grid cell is 1 meter \u00d7 1 meter.\n-The bottom-left corner of the site map corresponds to world coordinates (0, 0).\n-The value 0 or 1 in (x, y, 0/1) represents: A value of 1 denotes an obstacle (construction material, equipment, barricade, etc.), while a 0 indicates traversable space.\n\nThe construction site contains the following obstacles:\n-A vertical wall from (10,5) to (10,35)\n-A horizontal wall from (10,20) to (40,20)\n-A vertical wall from (30,0) to (30,15)\n-A cluster of obstacles in the region from (20,25) to (25,30)\n-Several random obstacles at: (15,10), (25,5), (35,25), (40,30), (45,15)\n\nYour goal is to perform path planning for an autonomous construction robot navigating this site. You can choose any suitable algorithm to compute collision-free paths. We use an autonomous construction vehicle with a radius of 0.5 meters, which can navigate continuously on the site (not just on grid nodes). Based on the site map described above, use a path planning algorithm to compute a smooth, efficient (as short as possible), and collision-free path from the given start pose to the goal pose, while considering the vehicle's turning constraints.\n\nPlease follow these specifications:\n1. Set the state space bounds to match the site limits: x from 0 to 49, y from 0 to 39, and orientation \u03b8 from 0 to 2\u03c0 radians.\n2. The construction vehicle has the following motion constraints:\n\t-The minimum turning radius is 4 meters due to its wheelbase and steering mechanism.\n\t-The vehicle moves at a constant forward speed of 1 meter per second for safety on the construction site.\n3. The start pose is: (0, 0, \u03c0) (at the site entrance, facing left)\n4. The goal pose is: (49, 39, \u03c0/2) (at the far corner delivery area, facing up)\n\n## Required Results:\n1. Path representation: Output the path as a list of tuples (x, y, \u03b8) at regular intervals (e.g., every 1 meter along the path or at fixed time steps)\n2. Total path length (in meters)\n3. Minimum distance to obstacles (in meters)\n4. Maximum curvature (to verify turning radius constraint)\n5. Number of nodes/states explored \n", "contributor": "Xiayu Zhao\n" }, { "task_id": "YF_03", "query_token_num": 469, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nIn this task, you are required to determine a suitable thickness (Th) of a rectangular steel cantilever beam subjected to uniform loads and evaluated using 3D structural simulation in MATLAB\u2019s PDE Toolbox.\n\nThe beam is modeled as a cantilever with one end fully fixed (all degrees of freedom constrained) and the other end free. A constant downward pressure is applied only on the outer half of the top face\u2014that is, over the region from L/2 to L(Stay away from the end)\n\nYou are given the following fixed parameters:\n\n- 'L = 1000' mm (Total span length)\n- 'w = 40' mm (Beam width, constant)\n\n- 'Height = Th' mm (Beam thickness to be designed)\n- Uniform load magnitude: 1000/(L/2*w)N/mm^2,applied only over the half\u2010length area(Stay away from the fixed end)\n- Material properties:\n - Young\u2019s modulus: 210,000 MPa\n - Poisson\u2019s ratio: 0.3\n\nThe beam will be evaluated using a static linear elasticity model in 3D (extruded along the beam width). The performance criterion is that the maximum vertical displacement (uy) must be less than 2 mm under the given load.\nThe score depends on the ratio of the maximum measured displacement to the allowable threshold. If that ratio falls between seventy percent and ninety percent, the beam earns the full 100 points. If the ratio is below seventy percent, partial credit is awarded in direct proportion to how close it is to seventy-percent (with zero displacement scoring zero and seventy-percent scoring 100). If the ratio lies between ninety percent and one hundred percent, points are deducted in proportion to how far it exceeds ninety percent (dropping from 100 at ninety percent down to zero at the full threshold). Any ratio below zero or above one hundred percent results in a score of zero.\n\n---\n\n### Task\n\nYour task is to:\n- Propose a structurally sound value for `Th` (thickness of the beam, in mm)\n- Provide a brief justification for your choice of thickness, considering stiffness, loading, and geometric constraints\n\nYou do **not** need to evaluate the displacement yourself. The simulation and evaluation will be done separately.\n\n", "contributor": "Yufan Zhang" }, { "task_id": "CY_03", "query_token_num": 2938, "Engineering Domain": "Operating System Design", "prompt": "### Task Description\n\nYour task is to design the read function for a virtio block device driver. The relevant data structures have been provided.\nPlease follow the function headers provided, complete the specified helper functions, and finally put the helper functions together to complete the read function.\n\nThe relevant data structures and some helper functions you can use are:\n```python\n\nfrom dataclasses import dataclass, field\nfrom typing import Optional, Union, List, Callable, Optional\n\n# COMPILE-TIME PARAMETERS\nVIOBLK_INTR_PRIO = 1\nVIOBLK_NAME = \"vioblk\"\nVIOBLK_IRQ_PRIO = 1\n\n# INTERNAL CONSTANT DEFINITIONS\nVIRTIO_BLK_F_SIZE_MAX = 1\nVIRTIO_BLK_F_SEG_MAX = 2\nVIRTIO_BLK_F_GEOMETRY = 4\nVIRTIO_BLK_F_RO = 5\nVIRTIO_BLK_F_BLK_SIZE = 6\nVIRTIO_BLK_F_FLUSH = 9\nVIRTIO_BLK_F_TOPOLOGY = 10\nVIRTIO_BLK_F_CONFIG_WCE = 11\nVIRTIO_BLK_F_MQ = 12\nVIRTIO_BLK_F_DISCARD = 13\nVIRTIO_BLK_F_WRITE_ZEROES = 14\nVIRTIO_BLK_F_LIFETIME = 15\nVIRTIO_BLK_F_SECURE_ERASE = 16\n\n# Virtio device status bits\nVIRTIO_STAT_ACKNOWLEDGE = (1 << 0)\nVIRTIO_STAT_DRIVER = (1 << 1)\nVIRTIO_STAT_FEATURES_OK = (1 << 3)\nVIRTIO_STAT_DRIVER_OK = (1 << 2)\nVIRTIO_STAT_DEVICE_NEEDS_RESET = (1 << 6)\nVIRTIO_STAT_FAILED = (1 << 7)\n\n# Virtio feature bits (number, not mask)\nVIRTIO_F_INDIRECT_DESC = 28\nVIRTIO_F_EVENT_IDX = 29\nVIRTIO_F_ANY_LAYOUT = 27\nVIRTIO_F_RING_RESET = 40\nVIRTIO_F_IN_ORDER = 35\n\n# Virtqueue constants\nVIRTQ_LEN_MAX = 32768\n\nVIRTQ_USED_F_NO_NOTIFY = 1\nVIRTQ_AVAIL_F_NO_INTERRUPT = 1\n\nVIRTQ_DESC_F_NEXT = (1 << 0)\nVIRTQ_DESC_F_WRITE = (1 << 1)\nVIRTQ_DESC_F_INDIRECT = (1 << 2)\n\n# Feature vector length\nVIRTIO_FEATLEN = 4\n\n# Virtio interrupt status bits\nUSED_BUFFER_NOTIFICATION = (1 << 0)\nCONFIGURATION_CHANGE_NOTIFICATION = (1 << 1)\n\n\n# vioblk vq request type\nVIRTIO_BLK_T_IN = 0\nVIRTIO_BLK_T_OUT = 1\n\n\n@dataclass\nclass Geometry:\n cylinders: int # uint16_t\n heads: int # uint8_t\n sectors: int # uint8_t\n\n@dataclass\nclass Topology:\n physical_block_exp: int # uint8_t\n alignment_offset: int # uint8_t\n min_io_size: int # uint16_t\n opt_io_size: int # uint32_t\n\n@dataclass\nclass BlockConfig:\n capacity: int # uint64_t\n size_max: int # uint32_t\n seg_max: int # uint32_t\n geometry: Geometry\n blk_size: int # uint32_t\n topology: Topology\n writeback: int # uint8_t\n unused0: int # char\n num_queues: int # uint16_t\n max_discard_sectors: int # uint32_t\n max_discard_seg: int # uint32_t\n discard_sector_alignment: int # uint32_t\n max_write_zeroes_sectors: int # uint32_t\n max_write_zeroes_seg: int # uint32_t\n write_zeroes_may_unmap: int # uint8_t\n max_secure_erase_sectors: int # uint32_t\n max_secure_erase_seg: int # uint32_t\n secure_erase_sector_alignment: int # uint32_t\n\n@dataclass\nclass VirtioMmioRegs:\n magic_value: int = 0 # uint32_t\n version: int = 0 # uint32_t\n device_id: int = 0 # uint32_t\n vendor_id: int = 0 # uint32_t\n device_features: int = 0 # uint32_t\n device_features_sel: int = 0 # uint32_t\n driver_features: int = 0 # uint32_t\n driver_features_sel: int = 0 # uint32_t\n queue_sel: int = 0 # uint32_t\n queue_num_max: int = 0 # uint32_t\n queue_num: int = 0 # uint32_t\n queue_ready: int = 0 # uint32_t\n queue_notify: int = 0 # uint32_t\n interrupt_status: int = 0 # uint32_t\n interrupt_ack: int = 0 # uint32_t\n status: int = 0 # uint32_t\n queue_desc: int = 0 # uint64_t\n queue_driver: int = 0 # uint64_t\n queue_device: int = 0 # uint64_t\n shm_sel: int = 0 # uint32_t\n shm_len: int = 0 # uint64_t\n shm_base: int = 0 # uint64_t\n queue_reset: int = 0 # uint32_t\n \n\n config: Union[BlockConfig, bytes] = field(default_factory=lambda: BlockConfig(\n capacity=4,\n size_max=512,\n seg_max=1,\n geometry=Geometry(cylinders=1, heads=1, sectors=4),\n blk_size=512,\n topology=Topology(physical_block_exp=0, alignment_offset=0, min_io_size=512, opt_io_size=512),\n writeback=0,\n unused0=0,\n num_queues=1,\n max_discard_sectors=0,\n max_discard_seg=0,\n discard_sector_alignment=0,\n max_write_zeroes_sectors=0,\n max_write_zeroes_seg=0,\n write_zeroes_may_unmap=0,\n max_secure_erase_sectors=0,\n max_secure_erase_seg=0,\n secure_erase_sector_alignment=0\n ))\n\n\n\n# define the iointf interface\n@dataclass\nclass IoIntf:\n close: Optional[Callable[['Io'], None]]\n cntl: Optional[Callable[['Io', int, object], int]]\n read: Optional[Callable[['Io', int, object, int], int]]\n write: Optional[Callable[['Io', int, object, int], int]]\n\n# define the io struct\n@dataclass\nclass Io:\n intf: Optional[IoIntf]\n refcnt: int\n\n\n@dataclass\nclass VirtqDesc:\n addr: int = 0 # uint64_t\n len: int = 0 # uint32_t\n flags: int = 0 # uint16_t\n next: int = 0 # int16_t\n\n@dataclass\nclass VirtqAvail:\n flags: int = 0 # uint16_t\n idx: int = 0 # uint16_t\n ring: List[int] = field(default_factory=list)\n\n\n@dataclass\nclass VirtqUsedElem:\n id: int = 0 # uint32_t\n len: int = 0 # uint32_t\n\n@dataclass\nclass VirtqUsed:\n flags: int = 0 # uint16_t\n idx: int = 0 # uint16_t\n ring: List[VirtqUsedElem] = field(default_factory=list)\n\ndef virtio_notify_avail(regs: VirtioMmioRegs, qid: int) -> None:\n regs.queue_notify = qid\n\n## Thread and Condition Variable\n@dataclass\nclass Thread:\n id: int = -1\n\n## Your program will be running on curr_thread:\ncurr_thread = Thread(id = 1)\n\n@dataclass\nclass ThreadList:\n threads: List[Thread] = field(default_factory=list)\n\n def add_thread(self, thread: Thread):\n self.threads.append(thread)\n\n def clear(self):\n self.threads.clear()\n\n@dataclass\nclass Condition:\n name: Optional[str] = None\n wait_list: ThreadList = field(default_factory=ThreadList)\n```\n\nHere are some functions for condition variables you can use.\nYou should use condition_wait but you don't need to know the details.\n`condition_init(cond: Condition, name: Optional[str] = None)`\n`condition_wait(cond: Condition, thread: Thread)`\n`condition_broadcast(cond: Condition)`\n\n\n```python\n# Lock\n@dataclass\nclass Lock:\n owner: Optional[Thread] = None\n lkrelease: Condition = field(default_factory=Condition)\n```\nHere are some functions for condition variables you can use.\nYou should use lock_acquire and lock_release but you don't need to know the details.\n`lock_init(lock: Lock)`\n`lock_acquire(lock: Lock, thread: Thread)`\n`lock_release(lock: Lock)`\n\n```python\n# vioblk_req\n@dataclass\nclass VioblkReq:\n type: int\n reserved: int\n sector: int\n\n# vioblk_device\n@dataclass\nclass VioblkDevice:\n regs: VirtioMmioRegs\n io: Io\n irqno: int = 2\n instno: int = 0\n\n @dataclass\n class Vq:\n last_used_idx: int = 0\n\n avail: Union[VirtqAvail, bytes] = field(default_factory=lambda: VirtqAvail())\n\n used: Union[VirtqUsed, bytes] = field(default_factory=lambda: VirtqUsed()) # \u586b\u5145\n desc: list = field(default_factory=lambda: [VirtqDesc() for _ in range(4)]) # 4 descriptors\n\n req: VioblkReq = field(default_factory=lambda: VioblkReq(-1, -1, -1))\n status: int = 0\n \n vq: Vq = field(default_factory=Vq)\n\n readbufcnt: int = 0\n readbuf: Optional[bytes] = None\n\n writebufcnt: int = 0\n writebuf: Optional[bytes] = None\n\n vioblk_used_updated: Condition = field(default_factory=Condition)\n vioblk_lock: Lock = field(default_factory=Lock)\n\n blksz: int = 512\n is_open: int = 1\n pos: int = 0\n capacity: int = 2048\n```\n\nAbout interrupts, you only need to know these three functions:\n\n`disable_interrupts()` Disables interrupts and returns an identifier used to restore interrupts.\n`restore_interrupts(orig: int)` Restores interrupts using an identifier /orig/.\n`enable_interrupts()` Enables interrupts and returns an identifier used to restore interrupts.\n\n\nHere are two tasks for you:\nFirst, please implement a vioblk_read function, which:\n- Reads bufsz number of bytes (must be aligned to VirtIO block size) from the disk and writes them to buf.\n- Achieves this by repeatedly setting the appropriate registers to request a block from the disk.\n- Thread sleeps while waiting for the disk to service the request.\n- Return the number of bytes successfully read from the disk, or -1 on failure.\n- Remember to check input.\n\n```python\ndef vioblk_read(vioblk:VioblkDevice, pos: int, buf: bytes, bufsz: int):\n # vioblk - a VioblkDevice instance\n # pos - the position to read data from, may not be multiples of block size\n # buf - the buffer to pass your read data into\n # bufsz - number of bytes needed to be read, may not be multiples of block size\n # Your Implementation here:\n return -1\n```\n\nSecond, please implement a vioblk_write function, which:\n- Writes bufsz number of bytes (must be aligned to VirtIO block size) into the disk from buf.\n- Achieves this by repeatedly setting the appropriate registers to send requests to the device.\n- Data should be written into vioblk device's writebuf only from which the driver will read data into its disk.\n- But you still need to set up relevant virt queue descriptors.\n- Thread sleeps while waiting for the disk to service the request.\n- Return the number of bytes successfully written to the disk, or -1 on failure.\n- Remember to check input.\n- Hint: you should call your read function.\n\n```python\ndef vioblk_write(vioblk:VioblkDevice, pos: int, buf: bytes, bufsz: int):\n # vioblk - a VioblkDevice instance\n # pos - the position to write data into, may not be multiples of block size\n # buf - the buffer where your data is from\n # bufsz - number of bytes needed to be written, may not be multiples of block size\n # Your Implementation here:\n return -1\n```\n\nPlease give me your code in two python code_blocks:\n\n```python\nYour code here\n```", "contributor": "Chongying Yue" }, { "task_id": "HC_03", "query_token_num": 199, "Engineering Domain": "Signal Processing", "prompt": "In this task, you will be given a set of 2D points.\n\n## Task Description\nYou are given a list of (x, y) pairs that roughly follow a quadratic (second-order) polynomial relationship, but include some noise.\n\nYour task is to estimate the best-fit second-order polynomial function of the form:\n y = a * x^2 + b * x + c\n\nwhere:\n- a, b, c are real-valued coefficients.\n\nYou must provide the estimated coefficients (a, b, c) and minimize the mean squared error (MSE) of the fit.\n\n## Output Format\nYou must provide the following:\n\n### coefficients\n a\n b\n c\n\n## Data points:\nx = [-2, -1, 0, 1, 2, 3]\ny = [7.9, 2.0, 0.1, 2.2, 6.0, 12.1]\n", "contributor": "Hao Chen\n" }, { "task_id": "YF_04", "query_token_num": 427, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nIn this task, you are required to determine a suitable diameter d of a solid cylindrical steel shaft, which will be subjected to an applied torque and evaluated using 3D structural simulation in MATLAB\u2019s PDE Toolbox.\n\nThe shaft is modeled as a cantilever: one end is fully fixed (all degrees of freedom constrained), and the other end is free. A torque T is applied uniformly over the free\u2010end circular face about the shaft axis.\nYou are given the following fixed parameters:\n\n- 'L = 1000' mm \n- 'diameter' mm (to be designed)\n\n\n- Applied torque: T=1\u00d710^6 N\u00b7mm (equivalent to 1 kN\u00b7m)\n- Material properties:\n - Young\u2019s modulus: 210,000 MPa\n - Poisson\u2019s ratio: 0.3\n\nThe shaft will be evaluated using a static linear\u2010elastic 3D model. The performance criterion is that the maximum twist angle \u03d5 between the free end and the fixed end (rotation about the longitudinal axis) must satisfy\n0.05rad. The score depends on the ratio of the maximum measured angle to the allowable threshold. If that ratio falls between seventy percent and ninety percent, the beam earns the full 100 points. If the ratio is below seventy percent, partial credit is awarded in direct proportion to how close it is to seventy-percent (with zero displacement scoring zero and seventy-percent scoring 100). If the ratio lies between ninety percent and one hundred percent, points are deducted in proportion to how far it exceeds ninety percent (dropping from 100 at ninety percent down to zero at the full threshold). Any ratio below zero or above one hundred percent results in a score of zero.\n---\n\n### Task\n\nYour task is to:\n- Propose a structurally sound value for `D` (diameter of the shaft, in mm)\n- Provide a brief justification for your choice of thickness, considering stiffness, loading, and geometric constraints\n\nYou do **not** need to evaluate the angle yourself. The simulation and evaluation will be done separately.\n\n", "contributor": "Yufan Zhang" }, { "task_id": "Yuqi_01", "query_token_num": 2348, "Engineering Domain": "Computer Architecture Design", "prompt": "## Neural Processing Unit Architecture\nNeural processing units (NPUs) are specialized accelerators for machine learning (ML) workloads. A typical example is Google TPU [1,2], the state-of-the-art NPU architecture widely deployed in production.\nIt consists of weight-stationary systolic arrays (SAs) for matrix multiplications and convolutions, and SIMD vector units (VUs) for generic vector operations.\nAn SA consists of a 2D array of processing elements (PEs) that are connected in a mesh topology. Each PE can perform a multiply-accumulate (MAC) operation.\nEach VU takes 8$\\times$128$ vectors as inputs and can output a 8$\\times$128$ vector per cycle.\nEach chip has an off-chip high-bandwidth memory (HBM) to store the ML model weights and input/output data, and an on-chip SRAM to exploit on-chip data reuse and hide HBM access latency.\nA DMA engine performs asynchronous memory copy between the HBM and SRAM, and the DMA operation are performed in parallel with the computation in the SAs and VUs.\nMultiple NPU chips can be interconnected via high-speed inter-chip interconnect (ICI) links, which form an NPU pod. The NPU chips in a pod are arranged as a 3D torus, which is optimized for all-reduce bandwidth [3,10]. The DMA engine performs peer-to-peer RDMA operations to access another chip's HBM or SRAM.\n\n\n## Distributed Large Language Model Serving\nLarge language models (LLMs) are auto-regressive transformer-based language models.\nTo serve an input request, the LLM performs two stages of computations: prefill and decode.\nDuring prefill, the LLM computes the forward pass for the input sequence and generate the key-value (KV) cache for each input token. It also generates the first output token.\nDuring decode, the LLM iteratively generates the next output token based on the KV cache of the input tokens and the previously generated output tokens.\nIn state-of-the-art LLM serving systems, the prefill and decode stages are disaggregated and performed in a pipelined manner.\nTherefore, we can treat the prefill and decode stages as two separate workloads and optimize them independently.\n\nSince the LLM is too large to fit into a single NPU chip, we need to shard the model weights, KV cache, and activation tensors across multiple chips.\nTypically, there are three tunable sharding parameters: data parallelism (DP), tensor parallelism (TP), and pipeline parallelism (PP).\n\nIn DP, the input batch is sharded across chips such that each chip independently computes the forward pass for its own local batch.\n\nIn TP, the model weights are sharded across chips follwing the Megatron-LM approach [6]. For the attention layers, each attention head is assigned to a different chip. For the FFN layers, the FNN matrices are sharded across chips, and it requires all-reduce (or reduce-scatter plus all-gather) communication to aggregate the final output of the FNN layers.\n\nIn PP, different transformer layers in the LLM are assigned to different chips, forming a pipeline. There will be peer-to-peer (P2P) inter-chip communications to receive and send the input/output tensors of each pipeline stage.\n\n\n## SLO Metrics for LLM Serving\nFor prefill, the latency SLO metric is the time-to-first-token (TTFT) for each request, which is the time taken to process all input tokens of the request.\nFor decode, the latency SLO metric is the time-per-output-token (TPOT) for each request, which is the time taken to generate each output token.\nFor both prefill and decode, the throughput metric is tokens per second, which is the number of tokens processed per second.\n\n\n## Task Description\nIn this task, you will act as a computer architect to tune the hardware specifications of a neural processing unit (NPU). You are given a large language model (LLM) inference workload with the average input and output sequence lengths for each request. You first need to determine some critical architectural parameters for each NPU chip.\nThen, you will consider deploying the given LLM workload at scale. You need to act as the cluster NPU allocator [4,5] to figure out how to allocate NPU resourcess to the given workload.\nSpecifically, you need to tune the NPU cluster configuration for serving the given LLM workload, including the number of chips, network topology, the model shardings, and the batch size, to meet latency and throughput service-level objective (SLO) constraints.\nFor the following tasks, assume each task is independent, and you do not need to consider the previous tasks when answering the next task.\n\n### Task 1: Systolic Array (SA) Width\nWe want to first decide the width of the SA based on the tensor operator semantics in the LLM model. Assume the SA is square.\nConsider a matrix multiplication operator $C = A \\times B$, where the input matrix $A$ is of size $m \\times k$, the input matrix $B$ is of size $k \\times n$, and the output matrix $C$ is of size $m \\times n$.\nFor a weight-stationary SA, if $m$ is less than its width, the SA will be diagonally underutilized; if $n$ is less than its width, some columns in the SA will be underutilized; if $k$ is less than its width, some rows in the SA will be underutilized.\nThe SA is fully utilized when $m$, $k$, and $n$ are all greater than or equal to its width.\nConsider a specific matrix multiplication operator where $m=1024$, $k=128$, and $n=128$.\nIf we want to make sure the FLOPs (floating-point operations) per second utilization of the SA is at least 70%, what is the maximum width of the SA?\nYour answer should be a a positive integer, which is the width of the SA.\n\n### Task 2: HBM Bandwidth\nNow we tune the memory subsystem.\nSpecifically, we need to determine how much HBM bandwidth is required to avoid stalling the computation.\nSuppose we have four SAs, each with width 128 and running at 940 MHz.\nFor simplicity, assume the SRAM bandwidth is infinite, and the VUs will not be a performance bottleneck.\nConsider a matrix multiplication operator $C = A \\times B$, where the input matrix $A$ is of size $m \\times k$, the input matrix $B$ is of size $k \\times n$, and the output matrix $C$ is of size $m \\times n$.\nWe perform tiled matrix multiplication [7] to exploit on-chip data reuse and reduce the HBM bandwidth pressure.\nEach SA computes separate output tiles.\nYou may refer to the JAX documentation [9] for the tiling strategy for multiple SAs on an NPU.\nThe tile size is restricted by the SRAM size, and we need to keep at least 10 tiles in the SRAM for each SA, in order to hide the HBM access latency.\nAssume the on-chip SRAM is 32 MB, and all elements in the matrices are float16 (2 bytes).\nFor a matrix multiplication operator where $m=4096$, $k=8192$, and $n=28672$, what is the minimum required HBM bandwidth in GB/s (including both read and write traffic) such that the SA computation will not be stalled?\n\n### Task 3: NPU Allocations for Prefill and Decode\nConsider an NPU chip with the following specifications:\n{\n \"num_sa\": 8,\n \"num_vu\": 6,\n \"hbm_bw_GBps\": 2765,\n \"vmem_size_MB\": 128,\n \"freq_GHz\": 1.75,\n \"sa_dim\": 128,\n \"hbm_size_GB\": 95,\n \"ici_link_bw_GBps\": 100,\n}\nwhere \"num_sa\" is the number of SAs, \"num_vu\" is the number of VUs, \"hbm_bw_GBps\" is the HBM bandwidth in GB/s, \"vmem_size_MB\" is the size of the on-chip SRAM in MB, \"freq_GHz\" is the frequency of the chip in GHz, \"sa_dim\" is the width of the SA, \"hbm_size_GB\" is the size of the HBM in GB, and \"ici_link_bw_GBps\" is the bandwidth of each ICI link in GB/s.\nEach NPU chip has 6 ICI links that are directly connected to 6 neighboring chips, and all NPU chips in an NPU pod are connected in a 3D torus topology.\nYou are given the Llama3.1-405B LLM model, and you need to find the optimal NPU pod configuration and the optimal model sharding and batch size for serving the LLM model. The detailed model specifications are as follows:\n{\n \"d_model\": 16384,\n \"num_heads\": 128,\n \"d_head\": 128,\n \"num_kv_heads\": 8,\n \"d_ff\": 53248,\n \"num_layers\": 126,\n \"use_flash_attention\": true,\n}\nwhere \"d_model\" is the embedding dimension, \"num_heads\" is the number of attention heads, \"d_head\" is the dimension of each attention head, \"num_kv_heads\" is the number of key-value heads (for grouped-query attention), \"d_ff\" is the hidden dimension of the feed-forward network (FFN), \"num_layers\" is the number of transformer layers, and \"use_flash_attention\" indicates whether to use flash attention [8] (only used for prefill) or not.\nThe average input sequence length is 4096 tokens for prefill, and the average output sequence length is 512 tokens for decode.\nThe latency SLO is 500 ms TTFT for prefill and 20 ms TPOT for decode.\nAssume we have a 4$\\times$4$\\times$4 NPU pod for prefill, and another 4$\\times$4$\\times$4 NPU pod for decode. Please find the optimal allocations for each of them to achieve the best throughput (tokens per second), while ensuring that the latency SLO is met.\nYou should output two allocations plans, one for prefill and one for decode.\nEach allocation plan should include the following parameters:\n - DP: data parallelism degree. Must be a multiple of 2.\n - TP: tensor parallelism degree. Must be a multiple of 2.\n - PP: pipeline parallelism degree. Must be a multiple of 2.\n - batch_size: the number of requests in a batch. Must be a power of 2.\n - mem_per_chip_GB: the HBM memory footprint on each NPU chip in GB.\nYou need to ensure that the product of DP, TP, and PP does not exceed 64 chips (but each parallelism degree can exceed 4 by taking multiple ICI axes). You also need to ensure that the allocation plan meets the 95GB per-chip HBM memory capacity constraint.", "contributor": "Yuqi Xue" }, { "task_id": "DL_01", "query_token_num": 3181, "Engineering Domain": "Computer Architecture Design", "prompt": "# Solid-State Drive Design Task - Single Configuration Parameter\n\nIn this problem, you will finalize a set of Solid-State Drive (SSD) designs that meet the performance requirements for a specific workload type. Initially, you must determine which parameters to tune\u2014and to what extent\u2014to satisfy the given performance criteria.\n\n## Background\n\n![fig_ssd_arch](./images/ssdhardware.png)\n\nThe internal architecture of a typical SSD is presented in the above Figure. An SSD consists of five major components: a set of flash memory packages, an SSD controller having embedded processors like ARM, off-chip DRAM (SSD DRAM), flash controllers, and the I/O interface that includes SATA and NVMe protocols. The flash packages are organized in a hierarchical manner. Each SSD has multiple channels, and each channel can process read/write commands independently. Each channel is shared by multiple flash packages. Each package has multiple flash chips. Within each chip, there are multiple planes. Each plane includes multiple flash blocks, and each block has multiple flash pages. The page size varies in different SSDs. When a free flash page is written once, that page is no longer available for future writes until that page is erased. However, erase operation is expensive and performed at block granularity. As each flash block has limited endurance, it is important for blocks to age uniformly (i.e., wear leveling). Modern SSD controllers employ out-of-place write, GC, and wear leveling to overcome these shortcomings and maintain indirections for the address translation in their flash translation layer (FTL).\n\nIn this problem, our aim is to design SSDs that allow developers to customize SSD hardware according to the application needs.\n\n## Task Description\n\nSSD customers typically evaluate SSD performance using key metrics including I/O throughput, average latency and tail latency. In this section, you should optimize the given SSD configuration by tuning the top-5 most significant parameter to reach the given performance requirement. You should first select the top-5 critical parameters, and answer what is the final value of each parameter if you tune it ALONE to reach the performance requirements. If the requirement cannot be reached, please answer \"impossible\" instead of the final parameter value. Please always provide your reasoning.\n\n### Formal Problem Definition\n\nGiven a parameter set $S$ and a workload set $W$, select 5 top parameter $s \\in S$ that affects the I/O throughput, average latency or both of them for each workload $w \\in W$. Specifically, address the following question for this 5 parameters:\n\nIf we want to get 20\\% performance improvement on I/O throughput or on average latency comparing to the baseline configuration (see next section), how should we tune this single parameter? If this is impossible, please answer \"impossible\" instead of providing the number and explain why. Note that the correlation between performance and parameter values are usurally not linear.\n\n### Configuration Set\n\nPlease provide answer for each parameter listed in the table below. The third column of this table listed the baseline configuration (Samsung 983 DCT 1.92TB SSD). We provide typical values for each parameter, you can also choose value outside the listed parameters (we assume that these design can be achieved with advanced manufacture techniques, to create next-generation SSDs), but the parameter should follow the general trend in the listed parameters (e.g., number of channels should be descrete numbers). \n\n| Parameter Name | Description | Baseline |\n|:--------------------------|:----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:-----------|\n| PCIe_Lane_Bandwidth | The PCIe bandwidth per lane in GB/s. Typical values: 0.5, 1.0, 2.0, 4.0, 8.0. | 8.0 |\n| PCIe_Lane_Count | The number of PCIe lanes. Typical values: 1, 2, 4, 8, 16. | 4 |\n| HostInterface_Type | The type of host interface. Typical values: NVME, SATA. | NVME |\n| IO_Queue_Depth | the length of the host-side I/O queue. Typical values: 4, 8, 16, 32, 64, 128, 256. | 16 |\n| Queue_Fetch_Size | The maximum number of requests that can be served in parallel in a queue. Typical values: 4, 8, 16, 32, 64, 128, 256. | 16 |\n| Data_Cache_Capacity | The size of the DRAM Data Cache in bytes. Typical values:100663296, 167772160, 234881024, 301989888, 369098752, 436207616. | 536870912 |\n| Data_Cache_DRAM_Row_Size | The size of the DRAM rows in bytes. values:1024, 2048, 4096, 8192, 16384. | 4096 |\n| Data_Cache_DRAM_Data_Rate | The DRAM data transfer rate in MT/s. Typical values:100, 200, 400, 800, 1600, 2133, 2400, 2666, 3200. | 800 |\n| Data_Cache_DRAM_Data_Burst_Size | The number of bytes that are transferred in one DRAM burst (depends on the number of DRAM chips). Typical values: 1, 2, 4, 8, 16. | 8 |\n| Data_Cache_DRAM_tRCD | The value of the timing parameter tRCD in nanoseconds used to access DRAM in the data cache. Typical values:4, 7, 14, 21, 28 | 9 |\n| Data_Cache_DRAM_tCL | The value of the timing parameter tCL in nanoseconds used to access DRAM in the data cache. Typical values:4, 7, 14, 21, 28 | 9 |\n| Data_Cache_DRAM_tRP | The value of the timing parameter tRP in nanoseconds used to access DRAM in the data cache. Typical values:4, 7, 14, 21, 28 | 9 |\n| Address_Mapping | The logical-to-physical address mapping policy implemented in the Flash Translation Layer (FTL).Typical values: PAGE_LEVEL, HYBRID | PAGE_LEVEL |\n| CMT_Capacity | The size of the SRAM/DRAM space in bytes used to cache the address mapping table (Cached Mapping Table). Typical values: 67108864, 134217728, 201326592, 268435456, 335544320, 402653184, 469762048, 536870912 | 268435456 |\n| Plane_Allocation_Scheme | The scheme for plane allocation priorities (C-Channel, W-Way, D-Die, P-Plane). Typical values: CWDP, CWPD, CDWP, CDPW, CPWD, CPDW, WCDP, WCPD, WDCP, WDPC, WPCD, WPDC, DCWP, DCPW, DWCP, DWPC, DPCW, DPWC, PCWD, PCDW, PWCD, PWDC, PDCW, PDWC | CWDP |\n| Overprovisioning_Ratio | The ratio of reserved storage space with respect to the available flash storage capacity. Typical values:0.1, 0.15, 0.2, 0.25, 0.3 | 0.126 |\n| GC_Exect_Threshold | The threshold for starting Garbage Collection (GC). Typical values: 0.1, 0.15, 0.2, 0.25, 0.3 | 0.05 |\n| GC_Block_Selection_Policy | The GC block selection policy. Typical values: GREEDY, RGA, RANDOM, RANDOM P, RANDOM PP, FIFO | GREEDY |\n| Use_Copyback_for_GC | Whether GC Copyback is enabled. Typical values: true, false | false |\n| Preemptible_GC_Enabled | The toggle to enable pre-emptible GC. Typical values:true, false | true |\n| GC_Hard_Threshold | The threshold to stop pre-emptible GC execution. Typical values:0.1, 0.15, 0.2, 0.25, 0.3 | 1 |\n| Dynamic_Wearleveling_Enabled | The toggle to enable dynamic wear-leveling. Typical values: true, false | true |\n| Static_Wearleveling_Enabled | The toggle to enable static wear-leveling. Typical values: true, false | true |\n| Static_Wearleveling_Threshold | The threshold for starting static wear-leveling. Typical values: 50, 60, 70, 80, 90, 100 | 100 |\n| Preferred_suspend_erase_time_for_read | The reasonable time to suspend an ongoing flash erase operation in favor of a recently-queued read operation. Typical values:100000, 200000, 300000, 400000, 500000 | 100000 |\n| Preferred_suspend_erase_time_for_write | The reasonable time to suspend an ongoing flash erase operation in favor of a recently-queued read operation. Typical values:100000, 200000, 300000, 400000, 500000 | 100000 |\n| Preferred_suspend_write_time_for_read | The reasonable time to suspend an ongoing flash erase operation in favor of a recently-queued program operation. Typical values:100000, 200000, 300000, 400000, 500000 | 100000 |\n| Flash_Channel_Count | The number of flash channels in the SSD back end. Typical values:4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32 | 8 |\n| Flash_Channel_Width | The width of each flash channel in byte. Typical values:1, 2, 4, 8 | 8 |\n| Channel_Transfer_Rate | The transfer rate of flash channels in the SSD back end in MT/s. Typical values:100, 200, 333, 800 | 800 |\n| Chip_No_Per_Channel | The number of flash chips attached to each channel in the SSD back end. Typical values:1, 2, 3, 4, 5, 6, 7, 8 | 4 |\n| Flash_Technology | Typical values:TLC, MLC, SLC | MLC |\n| CMD_Suspension_Support | The type of suspend command support by flash chips. Typical values:NONE, PROGRAM, PROGRAM ERASE, ERASE | None |\n| Page_Read_Latency_LSB | The latency of reading LSB bits of flash memory cells in nanoseconds. Typical values:25000, 50000, 59975, 75000, 100000 | 5000 |\n| Page_Read_Latency_CSB | Similar as above. Typical values:0, 25000, 50000, 75000, 100000 | 0 |\n| Page_Read_Latency_MSB | Similar as above. Typical values:25000, 50000, 75000, 100000, 104956 | 10000 |\n| Page_Program_Latency_LSB | Similar as above. Typical values:82062, 250000, 500000, 750000, 1000000 | 30000 |\n| Page_Program_Latency_CSB | Similar as above. Typical values:0, 250000, 500000, 750000, 1000000 | 0 |\n| Page_Program_Latency_MSB | Similar as above. Typical values:250000, 500000, 750000, 1000000, 1250000, 1500000, 1750000, 2000000, 2250000 | 800000 |\n| Block_Erase_Latency | The latency of erasing a flash block in nanoseconds.Typical values:3000000, 3800000 | 1000000 |\n| Block_PE_Cycles_Limit | The PE limit of each flash block. Typical values:10000, 20000, 30000, 40000, 50000 | 10000 |\n| Suspend_Erase_Time | The time taken to suspend an ongoing erase operation in nanoseconds.Typical values:700000, 800000, 900000, 1000000, 1100000 | 700000 |\n| Suspend_Program_Time | The time taken to suspend an ongoing program operation in nanoseconds. Typical values:60000, 70000, 80000, 90000, 100000 | 100000 |\n| Die_No_Per_Chip | The number of dies in each flash chip. Typical values:1, 2, ..., 16 | 8 |\n| Plane_No_Per_Die | The number of planes in each die. Typical values:1, 2, ..., 16 | 2 |\n| Block_No_Per_Plane | The number of flash blocks in each plane. Typical values:128, 256, ..., 1024 | 1364 |\n| Page_No_Per_Block | The number of physical pages in each flash block. Typical values:128, 256, ..., 1024 | 768 |\n| Page_Capacity | The size of each physical flash page in bytes. Typical values:4096 | 4096 |\n| Page_Metadat_Capacity | The size of the metadata area of each physical flash page in bytes. Typical values:224, 448, 672, 896, 1120 | 448 |\n\n### Target Workload Set\n\nPlease provide answer for each workload mentioned below:\n\n#### Real-world Workloads\n\nThese workloads represents typical storage-intensive application patterns.\n\n| **Workload Category** | **Description** |\n|-----------------------|-----------------|\n| Big Data Analytics | MapReduce workloads running in data centers. |\n| Cloud Storage | Cloud storage workloads running in data centers. |\n| Key-Value Store | YCSB benchmarks are executed against RocksDB. |\n| Maps | Maps workloads running on enterprise servers. |\n| Database | TPCC/TPCH executed against Windows SQL Server. |\n| WebSearch | WebSearch services trace from UMassTraceRepository. |\n| Advertisement | Advertisement workloads running on servers. |\n\n## Response Instruction\n\nYour response should be structured in the following format:\n\nFor each workload, create a workload_result class for the tuning result. In each workload_result, \n\nPlease strictly follow the format, do not include any other text or comments.\n\n\n\n", "contributor": "Daixuan Li" }, { "task_id": "YZ_02", "query_token_num": 1250, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\nIn this task, you are required to design four Savitzky\u2013Golay (SG) filters using different weighting strategies. SG filters are digital FIR lowpass filters that operate by performing a moving least-squares polynomial fit on the input data samples within a specified window. They are widely used to smooth or differentiate signal data while reducing noise and preserving the underlying shape of the signal. The key to implementing an SG filter is to approximate its cutoff frequency using predefined characteristic parameters and to capture the relationship between the filter\u2019s characteristics and its frequency response.\n\n### Task 1\nYour first task is to derive an analytical expression that relates the cutoff frequency $F_{-3dB}$ to the SG filter characteristic parameters $(m,n_h)$ and a sample rate $F_s$. The analytical expression (1) is given by $F_{-3dB} = \\frac{F_s}{b_0(n_h+0.5)/(m+b_1)-(b_2+b_3*m)/(n_h+0.5)}$. This expression is obtained via least-squares fitting. You need to determine the unknown coefficients $(b_0,b_1,b_2,b_3)$ in this formula under the following predefined parameters for an SG filter with no weighting:\n- filter polynomial order $m = 6$\n- half-width interval $n_h = 50$\nThen the following requirement must be satisfied: \n- the estimated cutoff frequency $F_{-3dB}$: $abs(F_{-3dB}/F_s - 0.023) <= 0.003$\nIt is crucial to verify that the $F_{-3dB}$ value calculated using your derived analytical expression meets this requirement, as it is essential for the subsequent tasks.\n\n### Task 2\nYour second task is to design SG filters with four weighting strategies. The first step in this task is to obtain a wider half-magnitude interval $n_{hW}$, which is defined by the analytical expression (2): $n_{hW} = round(\\frac{c_0 + c_1 * m + c_2 * m^2}{F_{-3dB}/F_s} - 1)$, where the cutoff frequency is obtained from Task 1. The MATLAB code examples below outline the construction of weighted SG filters with three different weighting strategies. They also provide the implementation for the unweighted SG filter and the metrics for evaluating filter performance.\n\n#### MATLAB code for designing a SG filter with squared Hann weighting:\n\nflW = 2*nhW+1;\nweightsSqHann = hann(flW+2).^2;\nweightsSqHann([1 end]) = [];\n[~,gSGwSqHann] = sgolay(m,flW,weightsSqHann);\ngSGwSqHann = gSGwSqHann(:,1);\nHSGwSqHann = freqz(gSGwSqHann,1,NDFT,Fs);\n\n\n#### MATLAB code for designing a SG filter with optimal weighting:\n\nTn = toeplitz([2 -1 zeros(1,flW-2)]);\nv = ones(flW,1);\nweightsOptimal = Tn\\v;\n[~,gSGwOptimal] = sgolay(m,flW,weightsOptimal);\ngSGwOptimal = gSGwOptimal(:,1);\nHSGwOptimal = freqz(gSGwOptimal,1,NDFT,Fs);\n\n\n#### MATLAB code for designing a SG filter with triangular weighting:\n\nweightsTriang = triang(flW);\n[~,gSGwTriang] = sgolay(m,flW,weightsTriang);\ngSGwTriang = gSGwTriang(:,1);\nHSGwTriang = freqz(gSGwTriang,1,NDFT,Fs);\n\n\n#### MATLAB code for designing a SG filter with no weighting:\n\n[~,gSGwNone] = sgolay(m,flW);\ngSGwNone = gSGwNone(:,1);\nHSGwNone = freqz(gSGwNone,1,NDFT,Fs);\n\n\n#### MATLAB code for measuring the performance of SG filter with four weighting strategies, metrics are output vs. input noise ratios, r, and smoothness parameter values, s:\n\nrSGwNone = gSGwNone'*gSGwNone;\nsSGwNone = diff([0;gSGwNone;0]);\nsSGwNone = sum(abs(sSGwNone).^2)/2;\n\nrSGwSqHann = gSGwSqHann'*gSGwSqHann;\nsSGwSqHann = diff([0;gSGwSqHann;0]);\nsSGwSqHann = sum(abs(sSGwSqHann).^2)/2;\n\nrSGwTriang = gSGwTriang'*gSGwTriang;\nsSGwTriang = diff([0;gSGwTriang;0]); \nsSGwTriang = sum(abs(sSGwTriang).^2)/2;\n\nrSGwOptimal = gSGwOptimal'*gSGwOptimal;\nsSGwOptimal = diff([0;gSGwOptimal;0]); \nsSGwOptimal = sum(abs(sSGwOptimal).^2)/2;\n\n\nSimilar to Task 1, your objective in Task 2 is to derive the unknown coefficients (c_0, c_1, c_2) for the expression (2) such that the following requirements are satisfied:\n- half-magnitude interval $n_{hW}$: > n_h\n- sSGwOptimal < sSGwTriang < sSGwSqHann < sSGwNone < -70 (dB)\n- rSGwNone < rSGwOptimal < rSGwTriang < rSGwSqHann < -26 (dB)\n", "contributor": "Yizhou Zhao" }, { "task_id": "RK_01", "query_token_num": 193, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nThis is an asymmetric design load problem.\nDesign domain is a 2D rectangular region in cartesian coordinates, with vertices at (0,0), (6,0), (6,1), (0,1). \nA vertically downward point load is applied at (2,1). Pin support is at (0,0) and roller support is at (6,0). \nLx = 6 and Ly = 1.\nThe filter radius is R = 0.03*max(Lx,Ly).\nThe filter exponent is 3.\n\n\n---\n\n### Task\n\nYour task is to:\n- Obtain a topology optimized design that has minimum structural compliance and volume fraction not exceeding 0.25.\n- Given the optimized design, output the corresponding minimum structural compliance, named C_y_hat, and also its volume fraction, named vf, in numerical numbers. Note that vf is in the range of [0,1]. \n", "contributor": "Rahul Kundu, Yilan Jiang" }, { "task_id": "XY_03", "query_token_num": 1066, "Engineering Domain": "Digital Hardware Design", "prompt": "# FPGA Hexadecimal Display Driver Design Challenge\n\n## Introduction\nYou are designing a 4-digit hexadecimal display driver for an FPGA. The display shows values from 0\u2013F using time-division multiplexing. Each digit must refresh at least 60Hz to avoid flickering. The FPGA clock frequency is 50 MHz.\n\n## Your Tasks\n\n1. Compute the total refresh frequency required.\n2. Compute the division ratio needed from 50 MHz to achieve that.\n3. Determine the **minimum** number of counter bits `n` such that `2^n >= division_ratio`.\n4. Select two appropriate counter bits to use for digit selection (ensure they cycle through 4 values).\n5. Justify your digit bit selection.\n6. Calculate the maximum possible delay between refreshes of the same digit under worst-case conditions. You should consider the clock tolerance of \u00b1100 ppm (parts per million, or 0.0001), the potential delay of up to 5 clock cycles in the display driver logicand the current refresh period based on calculations from tasks 1-2\n7. Determine if this maximum delay could cause perceptible flicker. Use 30Hz as the flicker threshold (i.e., if delay exceeds 33.33ms, flicker is possible).\n\n## Output Instructions\nYou must return only a structured Python response like this:\n config=ConfigFile(\n counter_bits=,\n division_ratio=,\n digit_select_bits=,\n bit_select_reasoning=\"\",\n max_delay_ms=,\n is_flicker_possible=,\n )\n\n\n## the following is an example of hex_driver written in system verily for referencing:\nmodule hex_driver (\n input logic clk,\n input logic reset,\n\n input logic [3:0] in[4],\n\n output logic [7:0] hex_seg,\n output logic [3:0] hex_grid\n);\n \n module nibble_to_hex(\n input logic [3:0] nibble,\n output logic [7:0] hex\n );\n always_comb begin\n case(nibble)\n 4'b0000 : hex = 8'b00111111; // '0'\n 4'b0001 : hex = 8'b00000110; // '1'\n 4'b0010 : hex = 8'b01011011; // '2'\n 4'b0011 : hex = 8'b01001111; // '3'\n 4'b0100 : hex = 8'b01100110; // '4'\n 4'b0101 : hex = 8'b01101101; // '5'\n 4'b0110 : hex = 8'b01111101; // '6'\n 4'b0111 : hex = 8'b00000111; // '7'\n 4'b1000 : hex = 8'b01111111; // '8'\n 4'b1001 : hex = 8'b01101111; // '9'\n 4'b1010 : hex = 8'b01110111; // 'A'\n 4'b1011 : hex = 8'b01111100; // 'b'\n 4'b1100 : hex = 8'b00111001; // 'C'\n 4'b1101 : hex = 8'b01011110; // 'd'\n 4'b1110 : hex = 8'b01111001; // 'E'\n 4'b1111 : hex = 8'b01110001; // 'F'\n endcase\n end\n endmodule\n\n logic [7:0] hex [4];\n\n genvar i;\n generate\n for(i = 0; i < 4; i++) begin\n nibble_to_hex nibble_to_hex_(\n .nibble(in[i]),\n .hex(hex[i])\n );\n end\n endgenerate\n\n logic [16:0] counter;\n\n always_ff @( posedge clk ) begin\n if (reset) begin\n counter <= '0;\n end else begin\n counter <= counter + 1;\n end\n end\n\n always_comb begin\n if (reset) begin\n hex_grid = '1;\n hex_seg = '1;\n end else begin\n case (counter [16:15])\n 2'b00: begin\n hex_seg = ~hex[0];\n hex_grid = 4'b1110;\n end\n 2'b01: begin\n hex_seg = ~hex[1];\n hex_grid = 4'b1101;\n end\n 2'b10: begin\n hex_seg = ~hex[2];\n hex_grid = 4'b1011;\n end\n 2'b11: begin\n hex_seg = ~hex[3];\n hex_grid = 4'b0111;\n end\n endcase\n end\n end\n\nendmodule", "contributor": "XiangYi Kong" }, { "task_id": "libin2_03", "query_token_num": 330, "Engineering Domain": "Operating System Design", "prompt": "## Task Description\n\nIn this task, you need to design a proper cluster size in a file system. You and required to handle a great amount of files, and should use the space as effectively as possible. \nThe following informatiion is given:\n- Partition size: 1\u202fTB\n- Total number of files: 1\u202f000\u202f000 \n\n### 1. Continuous function for the proportion of small files\nP_small(T) = 0.8 \u00d7 (1 \u2212 exp(\u2212\u202fT /\u202f4.1)) \n\nwhere \n- T is the \u201csmall\u2011file threshold\u201d, in KB (see the candidate values below) \n- P_small(T) \u2208 [0,\u202f0.8] represents the fraction of files whose size \u2264\u202fT\u202fKB \n- The remaining 1 \u2212 P_small(T) is treated as \u201clarge files\u201d (>\u202fT\u202fKB)\n\n### 2. Average file sizes\navg_small_kb(T) = 2 + 0.05 \u00d7\u202fT \u2003// in KB \navg_large_kb(T) = 512 + 0.50 \u00d7\u202fT \u2003// in KB \n\n## Design requirements:\n1. Fragmentation overhead \u2264\u202f0.5\u202f% \n - Average wasted space for small files:\u2003W_small = cluster_size\u202fB \u2212 2\u202fKB \n - Average wasted space for large files:\u2003W_large = cluster_size\u202fB /\u202f2 \n\n2. Metadata (cluster mapping table) overhead \u2264\u202f0.05\u202f%\n - Each cluster requires 4 B of mapping information\n", "contributor": "Libin Wang" }, { "task_id": "XY_04", "query_token_num": 526, "Engineering Domain": "Digital Hardware Design", "prompt": "## Task Description\n\nYou are tasked to design a flexible and efficient color mapping system for a Tetris game implemented on an FPGA development board with VGA output. The objective is to ensure distinct visual representation of all gameplay elements while operating under hardware resource constraints.\n\nA VGA display of 640x480 pixels and RGB444 color depth is available. Only a maximum of 10 distinct color mappings can be active at any time due to memory limitations. Additionally, your design should handle dynamic gameplay states, including a Night Mode that adjusts the color palette for low-light visibility.\n\n\n### Task 1: Define Color Mapping and Screen Regions\nDefine color schemes for different game elements such as the Tetris playfield, active tetrominoes, next piece preview, background, UI panels, and game over screen.\nEach tetromino (I, J, L, O, S, T, Z) must have distinguishable default colors.\nDesignate display regions for playfield, next piece preview, and score display by specifying pixel coordinate boundaries.\nRespect the 10-color definition constraint.\n\n### Task 2: Design Dynamic Mode Handling\nCreate a Night Mode theme that switches colors to darker palettes suitable for low-light gameplay.\nEnsure smooth and logical color remapping when transitioning between normal and Night Mode.\n\n### Task 3: Optimize Hardware Resource Usage\nImplement bit slicing strategies for efficient pixel-to-grid mapping.\nAvoid expensive multiplication or division in hardware logic.\n\n### Task 4: Validate and Discuss Your Design\nPropose a simple method to validate that color mappings are correctly applied under different game states.\nDiscuss trade-offs made between visual richness, resource constraints, and adaptability.\nSuggest one innovative feature or future improvement to the color mapping system.\n\n\n## Output Format\n\nYour response must include:\n\n1. task_report:\nIntroduction\nTask Analysis\nMethodology\nResults\nDiscussion and Trade-offs\nInnovation and Future Improvements\n\n2. config:\ncolor_mapping: Colors for different elements\ndisplay_regions: Regions for game components\ntetromino_colors: Specific color schemes for each tetromino\nui_elements: Colors for UI states\nbit_slicing: Expressions mapping pixels to grid positions\ndynamic_modes: Color adjustments for Night Mode\nresource_constraints: Statement about the 10-color limit\n\n\n## Technical Specifications\n\n1.Clock frequency: 50 MHz\n2.VGA resolution: 640x480 pixels\n3.Color depth: RGB444\n4.Tetris playfield grid: 10 blocks wide by 20 blocks tall\n5.Game states: start menu, in-progress gameplay, game over, Night Mode (dynamic)\n\nFollow the structured output format precisely to ensure full evaluation credit.\n\n", "contributor": "XiangYi Kong" }, { "task_id": "AB_03", "query_token_num": 737, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\n\nYou are an expert Python programmer specializing in Computer Vision using the OpenCV library. Your task is to process the image located at 'images/test_shape.png' to find the largest contour and then compute its approximate polygon and convex hull representations.\n\n**Constraint: You MUST use the OpenCV functions `cv2.findContours`, `cv2.contourArea`, `cv2.arcLength`, `cv2.approxPolyDP`, and `cv2.convexHull` as appropriate to solve this task.**\n\n## Implementation Steps\n\nThe implementation should follow this specific logic:\n\n1. **Load Image:** Load the image directly from the hardcoded path 'images/test_shape.png'. Handle potential loading errors.\n2. **Preprocess:** Convert the loaded image to grayscale. Apply binary thresholding (e.g., `cv2.threshold` with `cv2.THRESH_BINARY`) to create a binary image where the object is white and the background is black.\n3. **Find Contours:** Find all external contours in the binary image using `cv2.findContours`. Use the retrieval mode `cv2.RETR_EXTERNAL` and the approximation method `cv2.CHAIN_APPROX_SIMPLE`. Handle the case where no contours are found.\n4. **Identify Largest Contour:** Iterate through the found contours and identify the one with the largest area using `cv2.contourArea`. If no contours were found, proceed to return `(None, None)`.\n5. **Calculate Approximate Polygon:** For the largest contour found (`cnt`):\n * Calculate its perimeter (arc length) using `cv2.arcLength(cnt, True)`.\n * Calculate the epsilon value for approximation using the formula: `epsilon = 0.01 * arc_length`.\n * Compute the approximate polygon vertices using `cv2.approxPolyDP(cnt, epsilon, True)`.\n6. **Calculate Convex Hull:** For the *same* largest contour (`cnt`), compute the convex hull vertices using `cv2.convexHull(cnt)`.\n7. **Return Results:** Return the computed vertices as a tuple: `(approx_vertices, hull_vertices)`.\n\n## Input Specification\n\nThe solution code's main function must internally use the hardcoded path 'images/test_shape.png' for image loading. It should **not** accept any arguments.\n\n## Output Specification\n\nYour response must be structured according to the `CodeSolutionOutput` Pydantic model, containing the following fields:\n\n1. **`reasoning`**: Provide a clear, step-by-step explanation of how the code follows the Implementation Steps above to find the largest contour and compute its simplified representations.\n2. **`solution_code`**: Provide the complete Python code.\n * The code must include necessary imports (e.g., `numpy`, `cv2`).\n * The core logic must be encapsulated within a function named `get_simplified_contours` that takes **no arguments**.\n * This function must load the image using the hardcoded path 'images/test_shape.png'.\n * This function must **return** a tuple containing two elements: `(approx_vertices, hull_vertices)`.\n * `approx_vertices`: The NumPy array of vertices returned by `cv2.approxPolyDP`.\n * `hull_vertices`: The NumPy array of vertices returned by `cv2.convexHull`.\n * If the image cannot be loaded or no contours are found, the function should return `(None, None)`.\n * The code should **not** include any code for displaying images (`cv2.imshow`) or saving files (`cv2.imwrite`).", "contributor": "Ayush Barik" }, { "task_id": "RS_01", "query_token_num": 324, "Engineering Domain": "Mechanical Systems", "prompt": "Given two files: TrackFile.txt and SetupFile.json.\nTrackFile.txt has a row segment containing length and curvature (1/radius of curvature; zero for straights):\n0\t0.000024\n10\t-1.16667E-05\n20\t2.13333E-05\n30\t0.000066\n40\t-6.76667E-05\n50\t-9.03333E-05\n60\t0.000075\n70\t0.000233667\n80\t0.000324667\n90\t0.000143\n100\t8.43333E-05\n110\t0.000111667\n120\t0.000057\n130\t-0.000149\n140\t-0.000243333\n150\t-0.000328\n160\t-0.000163\n170\t0.000211333\n180\t0.000574\n190\t0.00069\n200\t0.000623\n210\t0.000397\n220\t0.000301333\n230\t0.000765333\n240\t0.002166\n250\t0.00457\n260\t0.01237\n270\t0.03242\n280\t0.040309333\n290\t0.018050333\n300\t0.010655\n310\t0.005606\n320\t0.003332667\n330\t0.000466\n340\t0.000744667\n350\t0.000555333\n360\t0.000675\n370\t0.000519667\n380\t0.000605\n390\t0.000773\n400\t0.000960667\n410\t0.001043\n420\t0.00081\n430\t0.001081\n440\t0.001226667\n450\t0.001234\n460\t0.001321\n470\t0.001166333\n480\t0.001054\n490\t0.000896\n500\t0.001024667\n510\t0.001272\n520\t0.001207\n530\t0.001307333\n540\t0.001434\n550\t0.001476667\n560\t0.001555\n570\t0.001498\n580\t0.001545333\n590\t0.001889667\n600\t0.00191\n610\t0.001684\n620\t0.001412\n630\t0.001269\n640\t0.001077333\n650\t0.000808\n660\t0.000444\n670\t0.000007\n680\t-0.000346667\n690\t-0.000424\n700\t-0.000367\n710\t-0.00031\n720\t-0.000192\n730\t-2.56667E-05\n740\t7.83333E-05\n750\t0.000173\n760\t0.000192667\n770\t0.000074\n780\t-0.000005\n790\t-0.000118333\n800\t-0.000335\n810\t-0.000559\n820\t-0.000643667\n830\t-0.000698667\n840\t-0.001024\n850\t-0.001753667\n860\t-0.002447333\n870\t-0.002669\n880\t-0.002064\n890\t-0.002478\n900\t-0.002609\n910\t-0.002733333\n920\t-0.002021667\n930\t-0.001064\n940\t0.000234\n950\t0.001743333\n960\t0.003549\n970\t0.00475\n980\t0.006055333\n990\t0.004918\n1000\t0.004290667\n1010\t0.003958\n1020\t0.003061\n1030\t0.001792\n1040\t0.001072\n1050\t-0.000314\n1060\t-0.002452\n1070\t-0.002665667\n1080\t-0.002002\n1090\t-0.001633333\n1100\t-0.001453667\n1110\t-0.001527\n1120\t-0.001441333\n1130\t-0.001281667\n1140\t-0.000958\n1150\t-0.000786333\n1160\t-0.00063\n1170\t-0.000408\n1180\t-0.000346333\n1190\t-0.000261333\n1200\t-0.000154\n1210\t-0.000126\n1220\t-0.000091\n1230\t-0.000029\n1240\t0.000158\n1250\t0.000302667\n1260\t0.000422\n1270\t0.000544\n1280\t0.000679667\n1290\t0.000873\n1300\t0.001100333\n1310\t0.001444667\n1320\t0.00183\n1330\t0.001885667\n1340\t0.001816333\n1350\t0.001788\n1360\t0.001714333\n1370\t0.001587667\n1380\t0.001565\n1390\t0.001533333\n1400\t0.001515333\n1410\t0.001463\n1420\t0.001379667\n1430\t0.001165333\n1440\t0.000857\n1450\t0.000675333\n1460\t0.000497333\n1470\t0.000269\n1480\t0.000183333\n1490\t0.000165333\n1500\t0.000192\n1510\t0.000175\n1520\t0.000200667\n1530\t0.00024\n1540\t0.000225667\n1550\t0.000192333\n1560\t0.000161\n1570\t0.000194\n1580\t0.000148667\n1590\t-0.000035\n1600\t0.000005\n1610\t0.000137\n1620\t0.000055\n1630\t-3.66667E-05\n1640\t2.26667E-05\n1650\t0.000012\n1660\t-0.000079\n1670\t-0.000099\n1680\t-0.000167\n1690\t-0.000207333\n1700\t-0.000227\n1710\t-0.000223\n1720\t-0.000222\n1730\t-0.000154667\n1740\t-0.000078\n1750\t-0.000119\n1760\t-0.000168\n1770\t-0.000119\n1780\t-0.000121667\n1790\t-0.000143\n1800\t-0.000054\n1810\t0.000024\n1820\t2.33333E-06\n1830\t-0.000025\n1840\t3.33333E-07\n1850\t4.46667E-05\n1860\t0.000038\n1870\t-1.36667E-05\n1880\t-5.63333E-05\n1890\t-0.000068\n1900\t-4.86667E-05\n1910\t-3.63333E-05\n1920\t-0.000014\n1930\t5.56667E-05\n1940\t0.000120333\n1950\t0.00008\n1960\t1.23333E-05\n1970\t2.33333E-06\n1980\t-0.000009\n1990\t-5.53333E-05\n2000\t-0.000139\n2010\t-0.00018\n2020\t-0.000151333\n2030\t-0.000053\n2040\t0.000006\n2050\t-0.000068\n2060\t-0.000011\n2070\t0.000245\n2080\t0.000428\n2090\t0.000492333\n2100\t0.000877\n2110\t0.002114\n2120\t0.004145333\n2130\t0.006308\n2140\t0.008737333\n2150\t0.010928333\n2160\t0.015221\n2170\t0.016506667\n2180\t0.010118\n2190\t-0.004162\n2200\t-0.012450667\n2210\t-0.014274667\n2220\t-0.015427\n2230\t-0.013374\n2240\t-0.009006667\n2250\t-0.003579\n2260\t0.005610667\n2270\t0.009615333\n2280\t0.010004\n2290\t0.009913\n2300\t0.010784667\n2310\t0.010727\n2320\t0.010896333\n2330\t0.009149333\n2340\t0.008374\n2350\t0.006517333\n2360\t0.004706333\n2370\t0.00303\n2380\t0.001536333\n2390\t0.000351\n2400\t-0.000581\n2410\t-0.000668333\n2420\t-0.000734667\n2430\t-0.000519\n2440\t-0.000685333\n2450\t-0.000889\n2460\t-0.000631\n2470\t-0.000444\n2480\t-0.00038\n2490\t-0.000271\n2500\t-0.000588333\n2510\t-0.000776333\n2520\t-0.000355\n2530\t-0.000100333\n2540\t-0.000235667\n2550\t-0.000323\n2560\t0.000136\n2570\t0.000852667\n2580\t0.001818\n2590\t0.003843667\n2600\t0.005362\n2610\t0.00755\n2620\t0.009662333\n2630\t0.010069667\n2640\t0.018863\n2650\t0.020548667\n2660\t0.022625667\n2670\t0.021145\n2680\t0.019562\n2690\t0.017756333\n2700\t0.016504\n2710\t0.015486667\n2720\t0.014131667\n2730\t0.011333\n2740\t0.007868667\n2750\t0.008469\n2760\t0.008073\n2770\t0.006241333\n2780\t0.003563\n2790\t0.00049\n2800\t-0.001542333\n2810\t-0.004198\n2820\t-0.006062\n2830\t-0.008759667\n2840\t-0.012348333\n2850\t-0.011128\n2860\t-0.009510667\n2870\t-0.008321\n2880\t-0.006072\n2890\t-0.003494667\n2900\t-0.002556\n2910\t-0.001183\n2920\t-0.000485667\n2930\t0.000131667\n2940\t0.000578\n2950\t0.001170333\n2960\t0.000837333\n2970\t0.000659\n2980\t0.001185667\n2990\t0.001364\n3000\t0.001348\n3010\t0.001305\n3020\t0.001296333\n3030\t0.001025\n3040\t0.000975333\n3050\t0.001000333\n3060\t0.000872\n3070\t0.000852\n3080\t0.000906333\n3090\t0.000973\n3100\t0.000796667\n3110\t0.000647667\n3120\t0.000625\n3130\t0.000425333\n3140\t0.000233333\n3150\t0.000096\n3160\t-1.73333E-05\n3170\t-0.000185333\n3180\t-0.00019\n3190\t-5.63333E-05\n3200\t-4.43333E-05\n3210\t0.000024\n3220\t-0.000146\n3230\t-0.000319333\n3240\t-0.000389\n3250\t-0.000722333\n3260\t-0.001367667\n3270\t-0.002464\n3280\t-0.004044667\n3290\t-0.005740667\n3300\t-0.006801\n3310\t-0.007030667\n3320\t-0.007430667\n3330\t-0.007836\n3340\t-0.008042667\n3350\t-0.007583667\n3360\t-0.007634\n3370\t-0.006841667\n3380\t-0.005936333\n3390\t-0.005774\n3400\t-0.005605667\n3410\t-0.005634333\n3420\t-0.005491\n3430\t-0.005477667\n3440\t-0.005563667\n3450\t-0.005694\n3460\t-0.005568333\n3470\t-0.005536333\n3480\t-0.005497\n3490\t-0.005480667\n3500\t-0.005576\n3510\t-0.005383\n3520\t-0.005383\n3530\t-0.005246333\n3540\t-0.005166\n3550\t-0.004881667\n3560\t-0.004504667\n3570\t-0.003667\n3580\t-0.002981667\n3590\t-0.002318667\n3600\t-0.001536\n3610\t-0.001161333\n3620\t-0.000904333\n3630\t-0.000695\n3640\t-0.000704\n3650\t-0.000717667\n3660\t-0.000516\n3670\t-0.000264333\n3680\t-0.000217667\n3690\t-0.000355\n3700\t-0.000393\n3710\t-0.000423\n3720\t-0.000461\n3730\t-0.000425333\n3740\t-0.000239333\n3750\t-0.000073\n3760\t-6.96667E-05\n3770\t0.000015\n3780\t0.000261\n3790\t0.000564667\n3800\t0.000743\n3810\t0.000814\n3820\t0.001088333\n3830\t0.001446\n3840\t0.002031\n3850\t0.003003667\n3860\t0.004454\n3870\t0.006528\n3880\t0.007872333\n3890\t0.009518\n3900\t0.010766\n3910\t0.011522333\n3920\t0.013053333\n3930\t0.013552\n3940\t0.013813\n3950\t0.013885333\n3960\t0.012555\n3970\t0.013071\n3980\t0.012528667\n3990\t0.011411\n4000\t0.007893\n4010\t0.001871667\n4020\t-0.006091\n4030\t-0.010214333\n4040\t-0.011719\n4050\t-0.011786\n4060\t-0.011460667\n4070\t-0.011470667\n4080\t-0.010756\n4090\t-0.010565\n4100\t-0.008367333\n4110\t-0.006189\n4120\t-0.005072667\n4130\t-0.002471667\n4140\t-0.001364\n4150\t-0.001567667\n4160\t-0.002122333\n4170\t-0.002496\n4180\t-0.001945\n4190\t-0.001223\n4200\t-0.000308\n4210\t0.000477\n4220\t0.000630667\n4230\t0.001528\n4240\t0.002781333\n4250\t0.003392333\n4260\t0.004682\n4270\t0.007125333\n4280\t0.010582\n4290\t0.013069\n4300\t0.015796\n4310\t0.016065\n4320\t0.013539\n4330\t0.013631333\n4340\t0.011672667\n4350\t0.010116\n4360\t0.008764667\n4370\t0.006085\n4380\t0.002755\n4390\t0.001196667\n4400\t0.000386667\n4410\t-0.000047\n4420\t0.000356333\n4430\t0.001528667\n4440\t0.004112\n4450\t0.006018333\n4460\t0.006968\n4470\t0.007622\n4480\t0.007682\n4490\t0.007854\n4500\t0.007835\n4510\t0.006713333\n4520\t0.006462667\n4530\t0.006042\n4540\t0.00545\n4550\t0.004076\n4560\t0.003074\n4570\t0.003070333\n4580\t0.003237\n4590\t0.002936\n4600\t0.00245\n4610\t0.002323\n4620\t0.002372\n4630\t0.00236\n4640\t0.002281\n4650\t0.002285\n4660\t0.002192667\n4670\t0.002210667\n4680\t0.002043\n4690\t0.001917667\n4700\t0.001819\n4710\t0.001665\n4720\t0.001829667\n4730\t0.001832667\n4740\t0.001749\n4750\t0.001643\n4760\t0.001580333\n4770\t0.001521\n4780\t0.001303333\n4790\t0.001361333\n4800\t0.00148\n4810\t0.001660333\n4820\t0.001864333\n4830\t0.002016\n4840\t0.001941667\n4850\t0.001824333\n4860\t0.00187\n4870\t0.001788667\n4880\t0.001729333\n4890\t0.001661\n4900\t0.001551333\n4910\t0.001335667\n4920\t0.001102\n4930\t0.000939333\n4940\t0.000744\n4950\t0.00065\n4960\t0.000567667\n4970\t0.000396667\n4980\t0.000207\n4990\t4.66667E-05\n5000\t-0.000145333\n5010\t-0.000277\n5020\t-0.000442\n5030\t-0.000677333\n5040\t-0.000849\n5050\t-0.001077\n5060\t-0.001342333\n5070\t-0.001556\n5080\t-0.001844333\n5090\t-0.002048333\n5100\t-0.002106\n5110\t-0.002032667\n5120\t-0.002021\n5130\t-0.002245\n5140\t-0.002624\n5150\t-0.002745667\n5160\t-0.00289\n5170\t-0.002954333\n5180\t-0.002967667\n5190\t-0.002948\n5200\t-0.002829667\n5210\t-0.002800667\n5220\t-0.00291\n5230\t-0.002752\n5240\t-0.002656667\n5250\t-0.002461\n5260\t-0.002427667\n5270\t-0.002415667\n5280\t-0.002216\n5290\t-0.001773\n5300\t-0.001381333\n5310\t-0.00112\n5320\t-0.00092\n5330\t-0.000716\n5340\t-0.000537\n5350\t-0.000584333\n5360\t-0.000802333\n5370\t-0.000959\n5380\t-0.001319333\n5390\t-0.002064\n5400\t-0.003083\n5410\t-0.004068\n5420\t-0.004532667\n5430\t-0.004454\n5440\t-0.004671333\n5450\t-0.004853333\n5460\t-0.004758\n5470\t-0.004564667\n5480\t-0.004783\n5490\t-0.004748\n5500\t-0.004566667\n5510\t-0.004406333\n5520\t-0.004094\n5530\t-0.003749\n5540\t-0.003350333\n5550\t-0.002997\n5560\t-0.002488\n5570\t-0.002137333\n5580\t-0.001735\n5590\t-0.001266667\n5600\t-0.00102\n5610\t-0.000817\n5620\t-0.000644667\n5630\t-0.000488667\n5640\t-0.000235\n5650\t-4.73333E-05\n5660\t0.000158333\n5670\t0.000307\n5680\t0.000520333\n5690\t0.000845333\n5700\t0.000997\n5710\t0.001062333\n5720\t0.001221667\n5730\t0.001368\n5740\t0.001652\n5750\t0.001762667\n5760\t0.001631\n5770\t0.001563667\n5780\t0.001673667\n5790\t0.001788\n5800\t0.001747667\n5810\t0.001633667\n5820\t0.001504\n5830\t0.001398333\n5840\t0.001274667\n5850\t0.001063\n5860\t0.000743667\n5870\t0.000491333\n5880\t0.000233\n5890\t4.66667E-05\n5900\t0.000188667\n5910\t0.000227\n5920\t0.00018\n5930\t0.000007\n5940\t-0.000029\n5950\t0.000385667\n5960\t0.000569333\n5970\t0.000679\n5980\t0.002694\n5990\t0.005252\n6000\t0.017234\n6010\t0.031803333\n6020\t0.035275667\n6030\t0.020078\n6040\t-0.024973333\n6050\t-0.045326333\n6060\t-0.039965\n6070\t-0.031691667\n6080\t-0.017527\n6090\t-0.010846\n6100\t-0.004321\n6110\t-0.001869\n6120\t-0.000669\n6130\t0.000133667\n6140\t0.000476667\n6150\t0.000523\n6160\t0.000494\n6170\t-0.000202667\n6180\t-0.000084\n6190\t0.000014\n6200\t-0.000167\n6210\t-0.000189\n6220\t-0.000149\n6230\t0.000094\n6240\t-0.000123\n6250\t-7.46667E-05\n6260\t-8.43333E-05\n6270\t-0.00015\n6280\t-0.00005\n6290\t0.000221333\n6300\t0.000249\n6310\t-0.000025\n6320\t3.46667E-05\n6330\t0.000054\n6340\t0.000029\n6350\t-1E-06\n6360\t-0.000031\n6370\t-0.000061\n6380\t-0.000091\n6390\t-0.000121\n6400\t-0.000151\n6410\t-0.000181\n6420\t-0.000211\n6430\t-0.000241\n6440\t-0.000271\n6450\t-0.000301\n6460\t-0.000331\n6470\t-0.000361\n6480\t-0.000391\n6490\t-0.000421\n6500\t-0.000451\n6510\t-0.000481\n6520\t-0.000511\n6530\t-0.000541\n6540\t-0.000571\n6550\t-0.000601\n6560\t-0.000631\n6570\t-0.000661\n6580\t-0.000691\n6590\t-0.000721\n6600\t-0.000751\n6610\t-0.000781\n6620\t-0.000811\n6630\t-0.000841\n6640\t-0.000871\n6650\t-0.000901\n6660\t-0.000931\n6670\t-0.000961\n6680\t-0.000991\n6690\t-0.001021\n6700\t-0.001051\n6710\t-0.001081\n6720\t-0.001111\n6730\t-0.001141\n6740\t-0.001171\n6750\t-0.001201\n6760\t-0.001231\n6770\t-0.001261\n6780\t-0.001291\n6790\t-0.001321\n6800\t-0.001351\n6810\t-0.001381\n6820\t-0.001411\n6830\t-0.001441\n6840\t-0.001471\n6850\t-0.001501\n6860\t-0.001531\n6870\t-0.001561\n6880\t-0.001591\n6890\t-0.001621\n6900\t-0.001651\n6910\t-0.001681\n6920\t-0.001711\n6930\t-0.001741\n6940\t-0.001771\n6950\t-0.001801\n\n\nSetupFile.json includes parameters:\n{\n \"setupName\" : \"Gp2Dummy\",\n \"mcar\"\t: 728,\n \"clt\"\t: 3.1,\n \"cx\"\t: 1.0,\n \"afrcar\"\t: 1.0,\n \"mbrk\"\t: 7000,\n \"gripx\"\t: 1.15,\n \"gripy\"\t: 1.40,\n \"loadEff\"\t: 0.10,\n \"rtyre\"\t: 0.32,\n \"rGearRat\"\t: [10.0,7.8,6.1,7.8,5.2,4.5,4.0],\n \"reff\"\t: 0.95,\n \"EngNm\"\t: [200,300,430,380],\n \"EngRpm\"\t: [0,3000,7000,10000],\n \"rho\"\t: 1.22\n}\n\nBased on the information above, complete the following tasks:\n\n#Task 1\nCompute the maximum possible speed the car achieves anywhere on the lap.\n\n#Task 2\nThe minimum possible lap time the car can achieve over a single lap.\n\nPlease use consistent SI units and convert top speed in km/hr and lap time into seconds(s).", "contributor": "Rushabh Prasad Shetty" }, { "task_id": "AB_02", "query_token_num": 691, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\n\nYou are an expert Python programmer specializing in Computer Vision using the OpenCV library. Your task is to implement the **Watershed algorithm** (`cv2.watershed`) for image segmentation specifically for the image located at 'images/8_of_hearts.png'.\n\nThe goal is to segment the foreground objects (the red heart pips and '8' numerals) from the white background in this specific image.\n\n**Constraint: You MUST use the OpenCV Watershed algorithm (`cv2.watershed`) for the core segmentation step. Using any other segmentation method (e.g., color thresholding alone, contour finding alone, GrabCut, etc.) will result in a failed evaluation.**\n\n## Implementation Steps\n\nThe implementation should follow this specific logic:\n1. Loading the image directly from the path 'images/8_of_hearts.png' and converting it to grayscale.\n2. Thresholding the grayscale image (using THRESH_BINARY_INV | THRESH_OTSU).\n3. Morphological opening to remove noise (kernel = np.ones((3,3), np.uint8), iterations = 2).\n4. Finding sure background via dilation (kernel = np.ones((3,3), np.uint8), iterations=3).\n5. Finding sure foreground via distance transform (cv2.DIST_L2, mask size 5) and thresholding. Use a threshold based on the distance transform's maximum value (e.g., 0.7 * dist_transform.max()) to determine the sure foreground region.\n6. Identifying the unknown region by subtracting sure foreground from sure background.\n7. Labeling components using `cv2.connectedComponents` on the sure foreground.\n8. Preparing markers for watershed (incrementing labels, setting unknown region to 0).\n9. Applying `cv2.watershed` using the original color image loaded from 'images/8_of_hearts.png'. **This step is mandatory.**\n10. Generating a final binary mask from the watershed markers.\n\n## Input Specification\n\nThe solution code's main function should *not* take an image path as an argument. It must internally use the hardcoded path 'images/8_of_hearts.png' for all image loading and processing operations.\n\n## Output Specification\n\nYour response must be structured according to the CodeSolutionOutput Pydantic model, containing the following fields:\n\n1. reasoning: Provide a clear, step-by-step explanation of how the code implements the Watershed segmentation process for the specified image ('images/8_of_hearts.png') according to the requirements. Explain each major step.\n2. solution_code: Provide the complete Python code.\n * The code must include necessary imports (numpy, cv2).\n * The core logic should be encapsulated within a function named `segment_image` that takes **no arguments**.\n * This function must load the image using the hardcoded path `'images/8_of_hearts.png'`.\n * This function must **return** the final binary segmentation mask as a NumPy array (dtype=uint8), where foreground pixels (segmented objects) are 255 and background/boundaries are 0.\n * The code should **not** include any code for displaying images or saving files directly. It should only perform the calculation and return the mask array.\n * Include basic error handling for image loading (return None if the image cannot be loaded from the hardcoded path).", "contributor": "Ayush Barik" }, { "task_id": "XY_05", "query_token_num": 975, "Engineering Domain": "Digital Hardware Design", "prompt": "# SLC-3 CPU Design\n\nThis assessment evaluate the SLC-3 CPU's control logic and state machine implementation.\n\n## PART 1: Control Signal Settings\n\nFor each instruction, determine the precise configuration of all control signals during the execution phase. \n\nThe response MUST be structured as follows:\n\n\"ports_table\": {\n \"ADD\": {\n \"ld_reg\": \"\",\n \"ld_ir\": \"\",\n \"ld_pc\": \"\",\n \"ld_cc\": \"\",\n \"gateALU\": \"\",\n \"gateMDR\": \"\",\n \"mem_en\": \"\",\n \"mem_we\": \"\"\n },\n \"AND\": {\n // Control signals for AND\n },\n // Continue for each instruction...\n}\n\n\n## PART 2: State Machine Implementation\n\nThe SLC-3 CPU uses the following key states in its finite state machine:\n\n- s_18: Common fetch cycle state\n- s_32: Decode state\n- s_1: ADD execution state\n- s_5: AND execution state\n- s_9: NOT execution state\n- s_0: BR evaluation state\n- s_22: BR taken state\n- s_12: JMP execution state\n- s_4: JSR execution state\n- s_21: JSR linkage state\n- s_6: LDR address calculation state\n- s_25_1, s_25_2, s_25_3: LDR memory access sequence states\n- s_27: LDR data ready state\n- s_7: STR address calculation state\n- s_23: STR memory prepare state\n- s_16_1, s_16_2, s_16_3: STR memory write sequence states\n\nYour state_transitions MUST use this exact format:\n\n\"state_transitions\": {\n \"ADD\": {\n \"current\": \"s_1\",\n \"next\": \"\"\n },\n \"AND\": {\n \"current\": \"s_5\",\n \"next\": \"\"\n },\n // For BR, use this special format\n \"BR\": {\n \"current\": \"s_0\",\n \"next_taken\": \"\",\n \"next_not_taken\": \"\",\n \"sequence_taken\": \",\"\n },\n // Multi-cycle example (use comma-separated string)\n \"LDR\": {\n \"current\": \"s_6\",\n \"next\": \"\",\n \"sequence\": \",,,,\"\n }\n}\n\nIMPORTANT: For multi-cycle instructions and branch paths, use comma-separated strings (NOT arrays or nested objects).\n\n## PART 3: Explanations\n\nYou must also provide a detailed explanation for each instruction:\n\"explanation\": {\n \"ADD\": \"Explanation for ADD instruction...\",\n \"AND\": \"Explanation for AND instruction...\",\n // Continue for each instruction...\n}\n\n## Instructions to Analyze:\n\n1. ADD - Arithmetic addition\n2. AND - Bitwise AND\n3. NOT - Bitwise complement\n4. LDR - Load from memory to register\n5. STR - Store register to memory\n6. BR - Conditional branch\n7. JMP - Unconditional jump\n8. JSR - Jump to subroutine\n9. SWAP - Exchange registers (custom instruction)\n\n## Critical Design Constraints:\n\nHardware safety: No multiple components may drive the bus simultaneously\nControl accuracy: PC updates occur only during branch and jump operations\nState consistency: All execution paths must eventually return to s_18 (fetch cycle)\nCycle requirements: Memory operations must follow proper sequence states\nInstruction integrity: JSR must save return address to R7 before jumping\nPower efficiency: Minimize active control signals whenever possible\n\n## REQUIRED OUTPUT FORMAT:\n\nYour complete response MUST follow this exact structure:\n{\n \"config\": {\n \"ports_table\": {\n \"ADD\": { \"ld_reg\": \"1\", \"ld_ir\": \"0\", ... },\n \"AND\": { ... },\n // All instructions\n },\n \"explanation\": {\n \"ADD\": \"Explanation text...\",\n \"AND\": \"Explanation text...\",\n // All instructions\n },\n \"state_transitions\": {\n \"ADD\": { \"current\": \"s_1\", \"next\": \"\" },\n \"AND\": { \"current\": \"s_5\", \"next\": \"\" },\n \"BR\": { \"current\": \"s_0\", \"next_taken\": \"s_22\", \"next_not_taken\": \"\", \"sequence_taken\": \",\" },\n \"LDR\": { \"current\": \"s_6\", \"next\": \"\", \"sequence\": \"\" },\n // All instructions\n }\n }\n}\n\nEnsure you follow this structure exactly. Use strings for all values, and comma-separated strings (not arrays) for sequences. Any validation errors will result in automatic failure.", "contributor": "XiangYi Kong\n" }, { "task_id": "libin2_02", "query_token_num": 310, "Engineering Domain": "Operating System Design", "prompt": "### Task Description\n\nIn this task, you need to choose an appropriate Round-Robin time quantum (time_quantum) for a set of threads in order to minimize the **combined cost**. \nWe will calculate three cost components: \n1. Average waiting time(avg_waiting_time), in milliseconds (ms). Smaller is better. \n2. Number of context switches(context_switches). Each switch counts as 1 ms of overhead. Fewer is better. \n3. Time quantum cost(quantum_cost), reflecting the negative impact of too long a time quantum, defined as: quantum_cost = time_quantum * 0.5\n\nThe combined cost(combined_cost) is the sum of these three components.\n\n\n### Input\nThe thread list is given as tuples (arrival_time, burst_time), both in ms:\ncase1 = [(0,5),(2,3),(4,8),(6,6),(8,4)]\ncase2 = [(0,10),(1,2),(3,7),(5,5)]\ncase3 = [(0,2),(2,2),(4,2),(6,2),(8,2),(10,2)]\n\n### Requirements\nChoose a single time quantum such that the combined cost for each case does not exceed: \n- case1: 17 ms \n- case2: 17 ms \n- case3: 8 ms \n\nReturn the chosen time_quantum and, for each case, the corresponding avg_waiting_time, context_switches, and quantum_cost.", "contributor": "Libin Wang" }, { "task_id": "NS_PA_SS_08", "query_token_num": 357, "Engineering Domain": "Digital Hardware Design", "prompt": "You are a hardware\u2010design expert. Write synthesizable SystemVerilog for a target\u2010sequence detector that pulses a 1 on `seen` whenever a specified 5-bit pattern appears in a serial bitstream, according to the following spec:\n\n1. Parameterization \n - parameter TARGET_WIDTH = 5; \n\n2. Ports \n```verilog\nmodule model #(\n parameter TARGET_WIDTH = 5\n) (\n input logic clk, // clock signal\n input logic resetn, // synchronous, active-low reset\n input logic [TARGET_WIDTH-1:0] init,// target sequence, loaded on reset\n input logic din, // serial input bit\n output logic seen // pulses high for one cycle on match\n);\nBehavior\n\nTarget loading: On each rising edge when resetn==0, latch init into an internal target register.\n\nShift register: Maintain a TARGET_WIDTH-bit shift register of the last received bits. On each rising edge when resetn==1, shift in din.\n\nDetection: Compare the internal shift register to target. If they match, assert seen=1 for one clock cycle; otherwise seen=0.\n\nSequence reset: When resetn==0, clear the shift register (so previous bits are forgotten) and drive seen=0.\n\nPadding: Treat shorter init values as zero-padded on the high side (e.g. 3'b11 \u2192 5'b00011).\n\nImplementation notes\n\nFully synchronous logic.\n\nUse a generate or loop to build the comparator if desired.\n\nseen should be a one-cycle pulse on each detection, overlapping matches allowed (i.e. detect overlapping patterns).\n\nProduce clean, commented, synthesizable SystemVerilog that meets this specification.``", "contributor": "Nippun Sabharwal, Shreyanka Sinha, Prakhar Agarwal" }, { "task_id": "JY_02", "query_token_num": 151, "Engineering Domain": "Signal Processing", "prompt": "You are working with a image and want to develop a real kernel that detects the edges of the image. Create the kernel and return the convoluted edge output as an array \nYou should follow the following\n1, Apply a gaussian blur to smooth the image.\n2, Design a filtering mechanizim to filter only the significant edges with one x direction kernel and y direction kernel of the same size and shape. \n3, Design a threshold of max and min value to filter out noisy edges.\n\nbased on the data of the input image array, you should choose the optimal size of the gaussian and edge filtering kernels and the values in them. \nIn the end, we will compare your response with the baseline response using edge density, connectivity and entropy. \n\nInput image: \n[\n[76, 77, 74, 75, 75, 73, 71, 71, 72, 74, 70, 69, 67, 66, 66, 68, 70, 71, 68, 65, 61, 57, 57, 59, 63, 66, 75, 75, 74, 71, 66, 63, 62, 62, 58, 61, 65, 69, 71, 71, 70, 69, 68, 65, 63, 65, 68, 70, 66, 63, 60, 60, 61, 63, 66, 67, 66, 64, 63, 63, 64, 66, 67, 69, 70, 71, 69, 68, 66, 65, 64, 66, 67, 69, 63, 63, 64, 65, 67, 71, 74, 76, 72, 69, 67, 68, 72, 75, 76, 76, 74, 73, 71, 70, 69, 69, 70, 71, 64, 66]\n[75, 77, 74, 74, 74, 71, 68, 67, 67, 69, 68, 67, 66, 65, 67, 69, 72, 74, 74, 71, 67, 64, 65, 70, 76, 80, 79, 79, 79, 76, 72, 69, 69, 69, 66, 70, 77, 81, 82, 78, 73, 69, 70, 66, 64, 66, 70, 72, 68, 63, 64, 65, 66, 70, 73, 74, 73, 72, 70, 71, 72, 73, 73, 72, 71, 70, 73, 72, 69, 68, 68, 69, 71, 72, 67, 67, 67, 68, 70, 72, 75, 77, 74, 70, 68, 69, 73, 77, 78, 78, 76, 75, 73, 71, 70, 70, 71, 72, 69, 70]\n[75, 75, 76, 75, 75, 74, 75, 76, 77, 77, 79, 77, 75, 73, 73, 75, 77, 78, 76, 77, 77, 77, 76, 75, 73, 72, 74, 76, 78, 80, 82, 81, 80, 80, 73, 74, 75, 76, 76, 76, 76, 75, 66, 68, 69, 71, 71, 71, 69, 69, 72, 72, 71, 71, 71, 72, 73, 74, 74, 74, 74, 73, 73, 73, 73, 72, 68, 69, 70, 71, 72, 72, 72, 72, 70, 71, 73, 74, 75, 75, 74, 73, 70, 69, 68, 71, 76, 80, 79, 78, 77, 78, 78, 77, 77, 77, 80, 82, 80, 79]\n[78, 78, 80, 79, 78, 77, 76, 76, 75, 75, 75, 74, 74, 73, 73, 74, 75, 76, 80, 79, 79, 78, 78, 78, 78, 78, 77, 77, 76, 76, 77, 77, 78, 78, 82, 81, 80, 78, 76, 75, 74, 73, 72, 73, 74, 75, 75, 75, 75, 74, 75, 74, 74, 73, 73, 74, 75, 75, 73, 73, 72, 72, 72, 72, 72, 72, 72, 73, 74, 75, 76, 77, 77, 77, 76, 77, 79, 80, 80, 80, 79, 78, 75, 74, 74, 76, 81, 83, 83, 81, 80, 83, 87, 87, 85, 84, 85, 87, 87, 86]\n[81, 81, 83, 83, 83, 82, 81, 79, 78, 77, 71, 72, 73, 74, 74, 75, 75, 74, 78, 78, 77, 77, 78, 78, 79, 80, 83, 81, 79, 77, 76, 77, 79, 80, 83, 81, 79, 76, 73, 72, 72, 72, 75, 75, 75, 75, 76, 76, 77, 77, 77, 76, 75, 75, 75, 75, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 75, 75, 75, 76, 77, 79, 81, 82, 81, 82, 84, 86, 88, 89, 89, 89, 85, 84, 84, 86, 89, 91, 91, 90, 89, 95, 101, 102, 98, 94, 95, 97, 93, 93]\n[86, 87, 88, 89, 89, 90, 89, 88, 86, 85, 79, 80, 83, 85, 85, 85, 83, 82, 81, 82, 83, 85, 86, 86, 86, 85, 88, 87, 86, 85, 85, 86, 87, 88, 84, 82, 80, 78, 77, 78, 80, 81, 79, 79, 79, 79, 80, 80, 81, 81, 86, 85, 84, 83, 82, 82, 82, 83, 84, 84, 85, 85, 86, 87, 87, 87, 83, 83, 83, 84, 85, 88, 90, 91, 91, 93, 95, 98, 101, 104, 106, 107, 103, 103, 103, 104, 106, 107, 107, 107, 104, 110, 115, 113, 107, 103, 105, 108, 101, 102]\n[100, 100, 101, 101, 101, 100, 99, 97, 96, 95, 94, 96, 98, 100, 101, 100, 98, 96, 92, 95, 99, 102, 103, 102, 100, 98, 92, 94, 95, 97, 98, 98, 97, 97, 93, 92, 91, 90, 91, 93, 96, 97, 92, 93, 93, 94, 94, 94, 95, 95, 101, 100, 99, 97, 96, 96, 96, 96, 93, 93, 94, 95, 96, 97, 98, 98, 100, 101, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 115, 117, 119, 120, 119, 120, 121, 122, 123, 123, 124, 125, 120, 123, 124, 121, 115, 112, 114, 118, 113, 113]\n[116, 117, 118, 117, 114, 112, 109, 108, 107, 107, 105, 106, 108, 110, 110, 108, 106, 105, 103, 106, 110, 113, 114, 113, 110, 108, 100, 102, 105, 108, 109, 109, 108, 107, 106, 106, 105, 106, 108, 110, 113, 114, 112, 113, 115, 117, 117, 116, 115, 114, 117, 116, 114, 113, 111, 110, 110, 110, 107, 107, 108, 110, 111, 113, 114, 114, 119, 120, 121, 122, 123, 123, 123, 123, 125, 124, 123, 123, 122, 123, 124, 124, 127, 129, 131, 132, 132, 132, 135, 136, 138, 138, 136, 133, 131, 130, 131, 133, 126, 125]\n[124, 126, 126, 125, 122, 120, 120, 121, 123, 125, 120, 121, 121, 122, 121, 119, 117, 116, 115, 116, 117, 118, 118, 118, 118, 118, 116, 116, 117, 118, 118, 119, 119, 119, 119, 121, 124, 128, 132, 136, 139, 140, 142, 144, 148, 150, 151, 149, 146, 144, 142, 141, 139, 137, 135, 134, 133, 133, 131, 132, 133, 135, 137, 138, 139, 140, 142, 144, 146, 148, 148, 146, 144, 143, 140, 139, 138, 137, 137, 138, 139, 140, 142, 145, 148, 149, 148, 149, 152, 155, 157, 155, 154, 156, 158, 159, 158, 156, 153, 149]\n[125, 126, 126, 125, 124, 124, 127, 132, 138, 141, 139, 139, 139, 138, 137, 135, 134, 133, 128, 126, 124, 122, 123, 125, 128, 130, 130, 128, 126, 125, 125, 125, 127, 128, 133, 136, 142, 150, 157, 163, 168, 170, 172, 175, 179, 182, 183, 180, 176, 174, 170, 168, 166, 164, 162, 161, 160, 160, 153, 154, 156, 157, 159, 161, 163, 163, 166, 168, 171, 173, 173, 170, 166, 164, 155, 155, 155, 156, 158, 161, 164, 165, 164, 168, 171, 172, 172, 173, 176, 180, 171, 170, 170, 176, 182, 184, 180, 175, 183, 177]\n[127, 128, 132, 126, 122, 124, 133, 141, 146, 147, 147, 151, 156, 161, 161, 158, 154, 150, 147, 144, 140, 136, 134, 133, 134, 135, 135, 139, 142, 139, 133, 131, 135, 140, 153, 159, 169, 178, 183, 183, 181, 179, 180, 182, 185, 189, 191, 191, 187, 183, 181, 179, 178, 178, 180, 182, 182, 181, 175, 174, 173, 172, 172, 173, 174, 175, 182, 179, 177, 178, 181, 182, 180, 177, 171, 172, 174, 175, 177, 178, 178, 178, 181, 182, 185, 187, 188, 187, 185, 184, 180, 178, 179, 185, 192, 195, 192, 188, 191, 188]\n[148, 148, 151, 147, 144, 146, 151, 155, 154, 152, 159, 160, 163, 165, 167, 167, 167, 167, 166, 165, 163, 161, 159, 157, 156, 156, 147, 152, 159, 164, 166, 165, 163, 162, 164, 168, 172, 175, 175, 172, 167, 164, 172, 174, 178, 183, 187, 188, 186, 183, 182, 182, 182, 183, 184, 184, 182, 180, 177, 178, 179, 180, 180, 180, 179, 179, 175, 173, 172, 175, 179, 182, 181, 179, 177, 177, 178, 178, 178, 178, 177, 176, 179, 181, 183, 185, 185, 184, 183, 182, 174, 171, 171, 175, 183, 188, 187, 185, 188, 186]\n[159, 157, 166, 165, 165, 167, 171, 170, 166, 162, 169, 168, 166, 165, 165, 168, 171, 173, 174, 175, 175, 175, 173, 171, 169, 167, 156, 158, 162, 170, 176, 179, 176, 173, 174, 174, 173, 171, 166, 161, 155, 152, 165, 167, 171, 177, 182, 184, 183, 181, 178, 179, 181, 184, 184, 182, 176, 172, 172, 174, 177, 179, 181, 180, 179, 178, 169, 168, 168, 172, 179, 183, 183, 182, 181, 181, 181, 180, 178, 176, 174, 173, 177, 179, 180, 181, 182, 181, 180, 179, 171, 168, 166, 168, 173, 177, 178, 177, 177, 177]\n[160, 158, 169, 170, 171, 175, 178, 178, 175, 172, 177, 174, 170, 166, 165, 166, 169, 170, 176, 176, 176, 175, 175, 174, 173, 172, 170, 166, 163, 161, 164, 169, 175, 178, 181, 179, 177, 173, 169, 165, 162, 160, 166, 167, 169, 174, 177, 178, 176, 174, 173, 176, 180, 184, 184, 179, 172, 166, 163, 165, 167, 170, 173, 175, 176, 176, 167, 166, 167, 171, 178, 183, 183, 182, 178, 178, 177, 176, 174, 172, 170, 169, 174, 175, 176, 176, 176, 175, 174, 173, 172, 170, 168, 168, 170, 170, 168, 166, 163, 163]\n[167, 166, 170, 170, 171, 173, 175, 176, 176, 175, 179, 178, 176, 175, 174, 173, 174, 174, 178, 176, 174, 172, 172, 173, 174, 175, 180, 178, 173, 166, 162, 166, 176, 185, 186, 184, 180, 177, 175, 174, 174, 174, 169, 168, 169, 170, 171, 170, 167, 164, 170, 173, 178, 183, 184, 179, 171, 165, 156, 156, 157, 159, 162, 167, 172, 175, 166, 165, 164, 168, 174, 178, 178, 176, 170, 170, 171, 170, 170, 169, 168, 167, 169, 169, 169, 169, 168, 167, 166, 166, 167, 168, 169, 171, 171, 168, 164, 161, 155, 156]\n[173, 174, 174, 173, 172, 171, 170, 170, 170, 170, 169, 171, 174, 176, 177, 178, 177, 176, 169, 167, 164, 161, 160, 162, 164, 166, 168, 172, 174, 171, 166, 166, 173, 180, 180, 178, 175, 172, 170, 171, 172, 173, 170, 169, 168, 167, 167, 165, 161, 158, 163, 165, 170, 175, 177, 174, 168, 163, 152, 151, 150, 150, 153, 158, 163, 167, 165, 163, 162, 165, 170, 172, 171, 169, 166, 166, 168, 169, 169, 169, 169, 169, 167, 167, 166, 165, 164, 163, 162, 162, 161, 164, 169, 172, 173, 171, 167, 165, 161, 160]\n[169, 171, 174, 174, 173, 171, 168, 165, 164, 164, 160, 162, 167, 171, 173, 174, 174, 173, 163, 162, 160, 158, 157, 157, 158, 158, 156, 161, 165, 167, 167, 167, 168, 170, 173, 172, 169, 168, 167, 168, 170, 171, 171, 170, 169, 169, 170, 169, 166, 164, 161, 162, 166, 171, 174, 174, 171, 168, 161, 159, 158, 157, 157, 159, 162, 164, 167, 164, 163, 165, 170, 172, 171, 169, 169, 170, 171, 173, 174, 174, 175, 175, 173, 172, 171, 169, 168, 167, 166, 166, 164, 168, 172, 175, 176, 175, 174, 173, 173, 171]\n[164, 166, 169, 170, 171, 171, 168, 164, 162, 161, 161, 163, 166, 169, 171, 171, 171, 170, 171, 172, 172, 171, 170, 168, 166, 165, 164, 163, 163, 166, 171, 174, 174, 173, 175, 174, 173, 173, 174, 176, 179, 180, 172, 172, 172, 173, 175, 176, 175, 173, 168, 169, 172, 176, 181, 183, 182, 180, 177, 177, 175, 174, 173, 172, 171, 170, 170, 167, 166, 169, 173, 176, 175, 173, 174, 175, 176, 178, 179, 179, 179, 179, 181, 180, 178, 177, 175, 174, 173, 173, 174, 176, 178, 179, 179, 178, 178, 179, 182, 178]\n[164, 170, 169, 170, 172, 175, 177, 177, 175, 173, 174, 174, 173, 174, 176, 179, 181, 183, 176, 178, 180, 181, 179, 176, 172, 170, 166, 167, 170, 172, 175, 176, 177, 178, 177, 176, 176, 177, 179, 179, 178, 176, 181, 181, 182, 184, 186, 186, 184, 182, 180, 181, 183, 184, 184, 183, 181, 180, 180, 181, 182, 181, 179, 178, 178, 179, 174, 173, 173, 176, 178, 177, 172, 167, 167, 170, 175, 180, 183, 184, 184, 183, 183, 185, 186, 186, 183, 180, 178, 178, 176, 178, 180, 180, 178, 177, 177, 178, 178, 178]\n[173, 176, 178, 179, 181, 183, 184, 184, 183, 181, 177, 177, 176, 177, 178, 180, 182, 183, 182, 183, 185, 185, 184, 182, 179, 177, 173, 174, 174, 175, 176, 176, 176, 176, 174, 174, 175, 178, 181, 183, 182, 181, 182, 182, 182, 184, 186, 186, 184, 181, 182, 183, 184, 185, 185, 184, 182, 181, 184, 184, 183, 181, 180, 180, 182, 185, 182, 180, 179, 180, 181, 179, 175, 171, 172, 173, 176, 178, 179, 179, 178, 177, 183, 185, 187, 188, 186, 185, 185, 186, 179, 181, 182, 181, 180, 179, 180, 181, 184, 184]\n[182, 182, 179, 181, 184, 187, 188, 189, 189, 189, 183, 183, 182, 182, 183, 183, 184, 185, 188, 189, 189, 189, 189, 188, 186, 186, 184, 183, 182, 181, 179, 178, 177, 176, 173, 173, 175, 178, 182, 185, 185, 184, 183, 183, 183, 185, 187, 187, 184, 182, 184, 185, 186, 186, 186, 184, 182, 181, 185, 184, 183, 180, 179, 181, 185, 188, 188, 186, 183, 182, 181, 180, 177, 175, 176, 176, 175, 174, 173, 172, 170, 170, 173, 175, 178, 180, 180, 181, 182, 184, 181, 182, 182, 181, 180, 180, 181, 183, 185, 184]\n[184, 182, 176, 178, 182, 184, 186, 187, 188, 189, 189, 188, 188, 187, 187, 187, 187, 187, 190, 190, 190, 190, 190, 190, 190, 190, 191, 190, 188, 186, 183, 181, 180, 180, 176, 175, 176, 178, 181, 182, 181, 180, 180, 180, 181, 183, 186, 187, 185, 183, 184, 185, 185, 186, 185, 183, 181, 180, 180, 181, 181, 180, 179, 180, 183, 186, 187, 185, 182, 180, 179, 178, 178, 178, 179, 177, 175, 172, 170, 168, 168, 168, 165, 167, 170, 171, 172, 173, 175, 177, 180, 181, 181, 180, 179, 179, 181, 184, 184, 183]\n[181, 181, 184, 187, 188, 187, 185, 183, 184, 186, 189, 189, 188, 188, 187, 186, 185, 185, 187, 187, 187, 188, 189, 190, 190, 191, 191, 190, 188, 185, 184, 182, 182, 182, 182, 181, 179, 179, 179, 178, 176, 173, 174, 174, 176, 179, 182, 183, 181, 180, 182, 183, 184, 184, 184, 182, 181, 179, 178, 180, 183, 184, 184, 183, 183, 183, 185, 184, 182, 180, 178, 179, 180, 182, 183, 181, 178, 176, 174, 174, 174, 175, 171, 172, 173, 173, 172, 172, 174, 176, 181, 182, 183, 183, 182, 182, 184, 186, 186, 187]\n[183, 186, 204, 205, 204, 198, 190, 184, 182, 183, 187, 187, 187, 187, 186, 185, 183, 182, 185, 186, 187, 189, 191, 191, 192, 192, 189, 188, 186, 183, 182, 182, 183, 183, 189, 187, 184, 183, 182, 180, 176, 173, 173, 173, 174, 176, 178, 179, 177, 175, 180, 181, 182, 183, 183, 183, 181, 180, 180, 184, 188, 189, 188, 186, 184, 184, 185, 185, 185, 183, 181, 181, 183, 186, 186, 185, 184, 183, 182, 183, 184, 185, 178, 178, 178, 177, 174, 174, 175, 177, 184, 186, 189, 190, 189, 188, 189, 190, 185, 186]\n[193, 196, 216, 216, 213, 205, 194, 186, 184, 185, 189, 189, 190, 190, 189, 188, 186, 185, 186, 188, 191, 194, 196, 197, 196, 195, 193, 191, 189, 186, 185, 186, 187, 187, 193, 191, 190, 189, 189, 187, 184, 182, 183, 182, 181, 182, 182, 180, 177, 174, 179, 180, 182, 184, 185, 184, 184, 183, 184, 186, 188, 189, 187, 185, 184, 185, 187, 188, 188, 186, 183, 181, 183, 185, 186, 186, 186, 186, 186, 187, 188, 188, 182, 183, 182, 179, 177, 176, 177, 179, 185, 188, 192, 194, 193, 192, 191, 191, 186, 187]\n[203, 206, 215, 216, 213, 205, 194, 187, 186, 188, 193, 194, 195, 195, 195, 193, 192, 190, 188, 191, 196, 199, 202, 202, 200, 199, 199, 197, 194, 192, 190, 190, 191, 192, 195, 194, 193, 194, 195, 195, 193, 191, 195, 193, 191, 190, 188, 185, 180, 177, 179, 181, 183, 185, 186, 186, 186, 185, 185, 186, 186, 185, 182, 181, 183, 184, 187, 189, 189, 186, 182, 179, 179, 181, 183, 183, 184, 184, 185, 185, 186, 186, 188, 188, 187, 184, 182, 181, 183, 185, 182, 187, 192, 195, 194, 192, 190, 190, 192, 192]\n[205, 203, 202, 201, 199, 195, 192, 190, 191, 193, 198, 198, 198, 197, 195, 192, 189, 187, 189, 190, 192, 192, 192, 193, 196, 198, 203, 203, 203, 201, 198, 194, 191, 188, 190, 187, 184, 184, 187, 191, 194, 195, 195, 193, 190, 190, 191, 189, 184, 180, 179, 180, 183, 184, 185, 185, 183, 183, 180, 181, 182, 183, 183, 182, 180, 179, 181, 182, 182, 181, 178, 177, 178, 180, 181, 180, 180, 179, 180, 181, 183, 184, 184, 185, 188, 188, 187, 184, 180, 177, 175, 178, 182, 187, 189, 189, 189, 188, 193, 194]\n[201, 201, 199, 200, 199, 198, 196, 193, 192, 192, 193, 193, 193, 193, 193, 191, 190, 189, 189, 190, 192, 192, 191, 192, 194, 196, 202, 202, 200, 199, 198, 197, 197, 196, 193, 190, 187, 186, 188, 190, 190, 190, 193, 192, 190, 191, 192, 191, 188, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 183, 181, 180, 179, 177, 178, 178, 177, 176, 177, 180, 182, 181, 182, 182, 182, 182, 181, 180, 179, 179, 179, 181, 181, 182, 182, 182, 181, 177, 178, 180, 181, 181, 180, 178, 177, 185, 187]\n[195, 197, 195, 196, 198, 198, 198, 195, 193, 191, 188, 188, 189, 189, 189, 190, 190, 190, 186, 188, 189, 189, 188, 188, 190, 192, 196, 195, 193, 193, 193, 195, 198, 200, 195, 192, 190, 189, 189, 189, 188, 187, 189, 188, 188, 189, 190, 190, 188, 186, 184, 183, 181, 180, 179, 179, 179, 179, 182, 182, 182, 181, 181, 180, 180, 180, 178, 178, 178, 176, 175, 176, 178, 181, 178, 179, 182, 184, 184, 183, 181, 180, 181, 180, 179, 179, 179, 180, 182, 183, 182, 182, 182, 181, 180, 179, 178, 178, 179, 180]\n[189, 191, 191, 191, 191, 192, 193, 193, 191, 189, 190, 189, 188, 188, 187, 187, 187, 187, 182, 184, 185, 185, 183, 182, 183, 184, 184, 184, 184, 185, 186, 188, 190, 192, 191, 189, 188, 189, 190, 190, 189, 187, 186, 185, 185, 185, 185, 184, 183, 182, 182, 182, 182, 182, 181, 181, 180, 179, 177, 177, 177, 178, 178, 179, 179, 180, 181, 183, 183, 182, 179, 176, 176, 176, 174, 176, 179, 181, 184, 186, 187, 187, 190, 188, 186, 184, 182, 181, 181, 181, 182, 181, 181, 181, 182, 183, 185, 186, 179, 179]\n[185, 186, 188, 186, 183, 184, 186, 188, 188, 187, 194, 193, 191, 189, 187, 185, 183, 182, 179, 181, 182, 182, 179, 177, 177, 177, 175, 177, 179, 181, 182, 183, 183, 182, 185, 184, 184, 186, 189, 191, 191, 190, 186, 186, 185, 184, 182, 181, 181, 181, 183, 185, 188, 190, 190, 189, 187, 186, 180, 180, 180, 180, 179, 178, 177, 177, 181, 184, 188, 188, 186, 181, 178, 176, 179, 178, 178, 179, 181, 184, 188, 191, 191, 191, 190, 188, 186, 183, 181, 179, 177, 176, 176, 176, 178, 180, 183, 185, 182, 182]\n[185, 184, 187, 183, 179, 179, 183, 186, 186, 185, 192, 192, 192, 191, 189, 185, 182, 180, 180, 182, 183, 183, 180, 177, 175, 175, 174, 176, 179, 182, 183, 183, 182, 181, 182, 181, 180, 181, 185, 187, 188, 188, 188, 188, 188, 185, 183, 181, 182, 183, 182, 184, 186, 188, 189, 188, 187, 186, 188, 188, 188, 187, 184, 180, 177, 175, 175, 180, 186, 189, 188, 185, 183, 182, 187, 185, 181, 178, 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178, 177, 176, 176, 175, 175, 176, 176, 175, 175, 175, 175, 175, 174, 174, 174, 175, 173, 171, 170, 172, 174, 174, 174, 176, 177, 178, 179, 181, 182, 183, 183, 187, 186, 185, 184, 182, 179, 177, 176, 170, 173]\n[185, 184, 183, 184, 184, 182, 179, 179, 182, 186, 184, 183, 182, 180, 179, 179, 179, 179, 184, 184, 183, 182, 180, 178, 176, 175, 178, 177, 177, 176, 177, 179, 180, 181, 178, 177, 175, 174, 173, 173, 173, 174, 174, 174, 173, 172, 172, 173, 174, 175, 176, 175, 175, 175, 175, 175, 176, 177, 178, 177, 175, 174, 174, 174, 175, 176, 175, 175, 175, 175, 176, 176, 176, 176, 176, 174, 171, 171, 172, 174, 174, 173, 175, 175, 176, 178, 179, 179, 180, 180, 183, 183, 183, 182, 182, 181, 180, 180, 179, 179]\n[180, 179, 177, 179, 180, 178, 177, 179, 183, 188, 182, 181, 179, 178, 177, 176, 176, 177, 178, 179, 180, 181, 180, 179, 177, 176, 177, 175, 174, 174, 175, 177, 180, 182, 177, 176, 174, 172, 171, 171, 171, 172, 174, 173, 172, 170, 170, 171, 172, 173, 176, 176, 175, 174, 174, 174, 175, 175, 178, 176, 175, 173, 173, 174, 175, 175, 177, 177, 177, 178, 179, 179, 180, 180, 179, 176, 174, 173, 174, 176, 176, 175, 175, 176, 177, 178, 179, 179, 179, 179, 180, 180, 181, 182, 183, 184, 184, 184, 187, 184]\n[176, 177, 175, 175, 175, 175, 175, 175, 175, 175, 173, 174, 174, 175, 177, 178, 178, 179, 178, 177, 177, 177, 177, 177, 177, 177, 174, 174, 175, 176, 177, 177, 178, 178, 178, 177, 175, 173, 172, 171, 170, 170, 172, 173, 173, 172, 170, 170, 172, 174, 173, 173, 173, 173, 172, 171, 171, 171, 172, 171, 170, 170, 172, 174, 177, 179, 177, 177, 177, 176, 176, 176, 175, 175, 177, 177, 177, 175, 174, 174, 176, 178, 172, 174, 175, 177, 178, 178, 177, 176, 179, 180, 181, 183, 184, 186, 187, 187, 189, 185]\n[175, 175, 175, 175, 175, 175, 175, 175, 175, 175, 175, 175, 176, 176, 176, 176, 176, 176, 178, 178, 178, 177, 176, 176, 176, 175, 175, 175, 175, 175, 176, 176, 176, 176, 175, 174, 173, 171, 169, 169, 168, 168, 167, 168, 169, 169, 168, 168, 169, 171, 173, 172, 171, 170, 169, 169, 169, 169, 170, 169, 168, 168, 169, 172, 175, 176, 175, 175, 174, 174, 174, 173, 173, 173, 175, 175, 176, 174, 173, 173, 176, 178, 174, 175, 176, 177, 178, 177, 176, 176, 177, 177, 178, 179, 180, 181, 182, 183, 183, 181]\n[173, 174, 175, 175, 175, 175, 175, 175, 175, 175, 177, 177, 176, 176, 175, 175, 175, 174, 179, 179, 178, 177, 176, 175, 174, 173, 176, 176, 175, 175, 175, 174, 174, 174, 172, 171, 170, 168, 167, 167, 167, 167, 168, 170, 172, 172, 170, 169, 169, 170, 172, 171, 169, 167, 167, 167, 167, 168, 167, 167, 166, 166, 167, 169, 172, 173, 172, 172, 172, 171, 171, 171, 170, 170, 172, 173, 174, 174, 173, 173, 176, 178, 176, 177, 177, 177, 177, 176, 175, 174, 174, 175, 175, 175, 176, 176, 177, 177, 176, 175]\n[173, 174, 176, 176, 175, 175, 175, 175, 174, 174, 175, 175, 175, 175, 175, 175, 175, 175, 179, 179, 177, 176, 175, 173, 172, 172, 176, 176, 175, 174, 173, 172, 172, 171, 170, 169, 168, 167, 166, 166, 167, 167, 170, 172, 173, 173, 171, 169, 168, 169, 172, 171, 168, 166, 165, 166, 167, 168, 166, 166, 166, 166, 167, 168, 170, 171, 171, 171, 170, 170, 170, 169, 169, 169, 171, 172, 174, 174, 173, 174, 176, 178, 178, 178, 177, 177, 176, 175, 174, 173, 174, 174, 174, 174, 174, 174, 174, 174, 171, 171]\n[175, 175, 176, 176, 176, 175, 175, 174, 174, 174, 173, 173, 174, 174, 175, 176, 177, 177, 178, 178, 177, 175, 174, 173, 171, 171, 175, 175, 174, 173, 172, 171, 170, 169, 169, 169, 168, 167, 167, 168, 168, 168, 166, 167, 169, 169, 168, 168, 169, 170, 170, 169, 168, 167, 166, 167, 168, 168, 167, 167, 167, 167, 168, 169, 170, 170, 171, 171, 171, 170, 170, 169, 169, 169, 170, 172, 174, 175, 174, 174, 176, 178, 178, 177, 176, 175, 174, 173, 172, 172, 175, 175, 174, 174, 174, 173, 173, 173, 169, 169]\n[176, 176, 177, 177, 176, 175, 175, 174, 173, 173, 171, 172, 173, 174, 175, 176, 177, 178, 177, 176, 175, 174, 173, 172, 171, 171, 174, 173, 173, 172, 171, 170, 169, 169, 169, 168, 168, 168, 168, 169, 169, 170, 166, 167, 168, 168, 167, 167, 170, 172, 166, 167, 167, 167, 168, 168, 168, 168, 167, 167, 168, 168, 169, 169, 170, 170, 171, 171, 171, 170, 170, 169, 169, 169, 169, 171, 174, 174, 173, 173, 174, 175, 176, 175, 174, 172, 171, 171, 171, 171, 173, 173, 173, 172, 172, 172, 172, 172, 169, 169]\n[176, 175, 177, 177, 176, 175, 175, 174, 173, 173, 173, 173, 173, 174, 174, 175, 175, 176, 175, 174, 174, 174, 173, 172, 172, 172, 172, 172, 171, 171, 170, 169, 169, 169, 167, 167, 167, 167, 167, 168, 169, 170, 171, 169, 166, 161, 157, 155, 157, 159, 160, 162, 165, 167, 168, 168, 167, 167, 167, 167, 168, 168, 169, 169, 168, 168, 170, 170, 170, 169, 169, 168, 168, 168, 167, 170, 172, 172, 171, 170, 170, 170, 174, 173, 171, 170, 169, 169, 170, 171, 168, 168, 168, 168, 168, 169, 169, 169, 170, 168]\n[175, 175, 177, 177, 176, 175, 175, 174, 173, 173, 175, 175, 174, 174, 174, 174, 173, 173, 173, 173, 173, 173, 173, 173, 173, 172, 171, 171, 170, 170, 170, 169, 169, 169, 166, 166, 166, 166, 167, 168, 169, 170, 171, 167, 159, 149, 140, 135, 134, 135, 156, 159, 163, 166, 168, 168, 166, 165, 166, 166, 167, 168, 168, 168, 167, 167, 169, 169, 169, 168, 168, 167, 167, 167, 166, 168, 170, 170, 168, 167, 166, 167, 172, 171, 170, 168, 168, 169, 170, 170, 163, 164, 164, 164, 165, 165, 166, 166, 170, 168]\n[175, 174, 178, 178, 178, 177, 176, 174, 172, 171, 176, 175, 173, 172, 170, 169, 169, 169, 168, 168, 169, 170, 169, 169, 168, 167, 169, 169, 168, 166, 165, 165, 167, 169, 169, 168, 166, 165, 166, 166, 166, 165, 161, 161, 160, 150, 124, 103, 108, 127, 145, 158, 167, 164, 160, 162, 164, 163, 167, 168, 168, 168, 168, 169, 169, 169, 168, 168, 167, 166, 165, 164, 164, 163, 166, 167, 168, 168, 169, 168, 168, 168, 171, 171, 170, 168, 165, 165, 167, 169, 166, 166, 164, 163, 163, 162, 162, 163, 162, 164]\n[172, 172, 174, 174, 174, 173, 171, 170, 168, 167, 171, 171, 171, 171, 171, 171, 171, 171, 168, 168, 167, 167, 167, 167, 166, 166, 167, 167, 167, 165, 164, 164, 165, 167, 168, 167, 165, 165, 164, 164, 162, 161, 160, 159, 157, 148, 126, 110, 118, 136, 154, 163, 168, 165, 163, 165, 166, 165, 164, 164, 164, 164, 164, 164, 164, 164, 163, 163, 163, 163, 163, 163, 163, 163, 164, 165, 166, 168, 169, 169, 168, 167, 166, 167, 168, 166, 164, 163, 164, 166, 168, 166, 163, 160, 158, 157, 156, 156, 156, 158]\n[170, 169, 170, 170, 170, 170, 170, 169, 168, 167, 165, 166, 167, 167, 166, 165, 163, 162, 158, 157, 156, 154, 154, 154, 155, 156, 156, 156, 156, 155, 155, 154, 154, 154, 157, 158, 159, 160, 160, 159, 157, 156, 159, 158, 158, 151, 136, 125, 135, 152, 160, 163, 163, 160, 160, 164, 165, 163, 164, 164, 164, 164, 164, 164, 164, 163, 163, 163, 162, 162, 162, 162, 162, 161, 161, 163, 165, 167, 167, 166, 164, 163, 161, 162, 164, 163, 160, 157, 156, 156, 158, 156, 152, 148, 146, 145, 145, 146, 146, 148]\n[161, 160, 162, 162, 163, 163, 163, 162, 161, 161, 162, 162, 162, 160, 156, 152, 147, 144, 143, 141, 139, 137, 136, 137, 139, 140, 142, 141, 140, 140, 140, 140, 138, 137, 142, 145, 149, 151, 152, 152, 152, 152, 151, 153, 155, 153, 144, 138, 145, 158, 160, 157, 153, 152, 155, 158, 159, 157, 157, 157, 157, 157, 157, 157, 157, 157, 158, 158, 157, 156, 156, 155, 154, 154, 159, 161, 164, 166, 166, 165, 163, 161, 161, 163, 165, 164, 160, 155, 152, 151, 150, 148, 145, 142, 141, 141, 143, 144, 150, 153]\n[154, 154, 156, 156, 155, 154, 151, 149, 147, 146, 152, 152, 151, 149, 144, 139, 134, 131, 129, 127, 125, 124, 124, 125, 127, 129, 131, 128, 126, 126, 127, 127, 125, 123, 127, 131, 136, 139, 138, 138, 138, 140, 135, 138, 143, 145, 141, 137, 140, 145, 153, 147, 143, 144, 149, 151, 151, 150, 143, 143, 144, 144, 145, 145, 145, 145, 149, 149, 150, 151, 152, 152, 153, 153, 160, 162, 165, 169, 171, 172, 172, 171, 171, 174, 178, 178, 176, 172, 169, 168, 170, 168, 165, 163, 161, 161, 162, 163, 174, 177]\n[163, 163, 164, 163, 161, 158, 154, 150, 146, 144, 139, 139, 139, 138, 136, 134, 131, 130, 124, 124, 123, 123, 124, 125, 127, 129, 129, 125, 120, 119, 121, 123, 121, 119, 120, 125, 129, 130, 128, 127, 129, 132, 132, 136, 141, 144, 143, 140, 138, 137, 146, 142, 140, 145, 150, 150, 150, 151, 151, 151, 152, 153, 154, 156, 156, 157, 159, 160, 163, 166, 170, 173, 175, 176, 172, 174, 177, 181, 185, 188, 190, 191, 188, 192, 197, 200, 200, 199, 198, 198, 207, 205, 202, 199, 196, 194, 192, 191, 194, 196]\n[175, 175, 173, 172, 172, 170, 168, 166, 163, 162, 149, 149, 150, 150, 151, 151, 152, 152, 143, 144, 145, 147, 148, 150, 151, 152, 150, 143, 137, 135, 137, 140, 139, 137, 136, 141, 146, 148, 148, 149, 154, 159, 163, 166, 168, 169, 168, 167, 163, 159, 162, 160, 164, 172, 176, 174, 174, 177, 184, 185, 186, 188, 190, 192, 194, 195, 191, 192, 195, 197, 201, 204, 206, 207, 200, 200, 200, 201, 202, 204, 206, 207, 203, 207, 211, 213, 214, 213, 214, 215, 225, 224, 223, 221, 217, 213, 210, 208, 200, 200]\n[177, 176, 170, 171, 173, 175, 177, 178, 178, 178, 176, 176, 176, 177, 178, 179, 181, 182, 173, 174, 176, 179, 181, 183, 183, 184, 179, 172, 164, 161, 164, 167, 167, 166, 164, 170, 177, 181, 183, 188, 197, 204, 203, 203, 202, 200, 200, 199, 195, 190, 192, 191, 198, 209, 212, 209, 209, 213, 213, 214, 216, 218, 221, 223, 225, 226, 217, 217, 218, 219, 220, 221, 222, 222, 227, 224, 220, 216, 214, 213, 213, 213, 212, 214, 216, 217, 215, 213, 213, 214, 220, 221, 222, 221, 219, 216, 213, 211, 202, 199]\n[181, 178, 177, 178, 179, 177, 177, 183, 195, 204, 202, 199, 196, 196, 201, 207, 212, 215, 201, 203, 207, 212, 216, 218, 220, 220, 212, 206, 198, 194, 194, 196, 196, 195, 199, 199, 199, 200, 203, 209, 216, 221, 226, 224, 223, 224, 225, 224, 219, 215, 212, 212, 214, 219, 226, 229, 227, 224, 226, 227, 230, 233, 235, 233, 229, 226, 227, 217, 213, 217, 220, 219, 221, 227, 228, 226, 226, 227, 226, 220, 215, 213, 219, 219, 218, 214, 211, 210, 214, 217, 221, 222, 222, 221, 217, 211, 204, 200, 194, 196]\n[219, 217, 207, 208, 207, 204, 200, 201, 207, 213, 220, 217, 214, 214, 217, 221, 224, 225, 224, 225, 227, 229, 231, 233, 233, 234, 231, 226, 219, 216, 216, 218, 219, 219, 210, 209, 209, 208, 210, 214, 219, 223, 225, 223, 221, 222, 224, 225, 223, 220, 215, 215, 217, 219, 221, 221, 219, 217, 223, 223, 225, 228, 230, 228, 224, 221, 216, 211, 207, 208, 210, 212, 214, 217, 225, 223, 222, 222, 221, 219, 218, 217, 221, 221, 220, 216, 214, 216, 221, 225, 225, 226, 226, 224, 221, 216, 212, 209, 206, 207]\n[234, 233, 228, 230, 231, 227, 222, 219, 220, 222, 230, 228, 226, 226, 229, 230, 230, 230, 225, 225, 224, 223, 223, 223, 223, 223, 225, 222, 217, 215, 216, 218, 219, 219, 214, 213, 211, 210, 211, 213, 216, 217, 220, 218, 215, 215, 216, 217, 217, 217, 211, 213, 215, 215, 213, 211, 210, 210, 216, 216, 217, 219, 221, 220, 216, 213, 211, 212, 210, 206, 208, 213, 218, 218, 219, 219, 217, 216, 216, 217, 218, 219, 221, 221, 220, 218, 217, 220, 224, 228, 223, 223, 223, 223, 222, 220, 218, 217, 220, 220]\n[222, 222, 224, 227, 230, 230, 227, 224, 222, 222, 221, 221, 221, 224, 227, 228, 227, 226, 225, 224, 222, 220, 218, 218, 219, 220, 221, 219, 217, 216, 216, 218, 219, 220, 212, 210, 208, 207, 208, 210, 211, 211, 216, 214, 211, 209, 208, 209, 210, 210, 207, 211, 214, 214, 211, 209, 210, 212, 214, 213, 213, 214, 215, 214, 211, 209, 214, 217, 213, 205, 204, 212, 219, 221, 214, 216, 216, 213, 212, 214, 215, 214, 216, 216, 217, 217, 217, 217, 218, 219, 216, 216, 216, 216, 216, 217, 218, 218, 217, 216]\n[218, 216, 213, 216, 220, 223, 222, 220, 217, 216, 210, 211, 214, 219, 224, 226, 225, 224, 223, 222, 221, 219, 219, 220, 221, 222, 219, 219, 218, 217, 217, 217, 218, 220, 217, 214, 210, 210, 212, 215, 216, 216, 218, 218, 217, 215, 214, 214, 215, 216, 214, 217, 220, 219, 216, 215, 217, 220, 218, 216, 215, 214, 215, 214, 212, 210, 214, 214, 208, 196, 189, 192, 200, 205, 207, 214, 216, 212, 209, 210, 208, 205, 206, 207, 209, 211, 210, 207, 203, 200, 204, 202, 201, 199, 198, 198, 198, 198, 190, 188]\n[219, 217, 215, 216, 218, 220, 219, 216, 213, 211, 208, 209, 213, 218, 223, 225, 224, 222, 219, 219, 219, 220, 221, 223, 224, 225, 219, 221, 221, 220, 218, 217, 217, 218, 223, 217, 212, 211, 215, 219, 220, 220, 216, 219, 222, 222, 221, 220, 219, 220, 215, 216, 217, 216, 215, 214, 215, 217, 216, 213, 210, 209, 209, 209, 207, 206, 207, 202, 196, 185, 172, 164, 169, 179, 194, 204, 208, 201, 196, 197, 195, 190, 190, 190, 192, 194, 193, 189, 182, 177, 178, 176, 173, 170, 166, 164, 162, 161, 157, 155]\n[219, 219, 222, 222, 221, 220, 219, 216, 213, 211, 208, 208, 210, 213, 216, 216, 214, 212, 214, 215, 217, 220, 222, 223, 224, 225, 222, 224, 225, 224, 219, 216, 216, 217, 212, 205, 197, 195, 198, 203, 206, 205, 199, 204, 209, 210, 206, 200, 196, 194, 188, 187, 187, 189, 192, 195, 195, 195, 196, 193, 189, 187, 187, 187, 186, 185, 184, 177, 176, 174, 159, 140, 142, 156, 172, 183, 186, 176, 171, 174, 174, 170, 169, 167, 166, 166, 166, 164, 158, 154, 150, 150, 148, 147, 145, 143, 141, 140, 141, 139]\n[224, 227, 226, 224, 221, 219, 218, 217, 215, 213, 206, 205, 204, 205, 205, 204, 201, 198, 188, 190, 193, 196, 198, 200, 200, 200, 201, 204, 205, 203, 198, 193, 192, 193, 194, 185, 176, 172, 175, 180, 183, 183, 180, 185, 190, 189, 181, 171, 162, 158, 154, 152, 153, 158, 165, 171, 173, 172, 174, 171, 166, 163, 163, 163, 163, 162, 156, 150, 155, 162, 148, 124, 124, 142, 153, 164, 165, 154, 148, 154, 157, 154, 152, 148, 145, 143, 144, 144, 141, 138, 138, 139, 141, 142, 144, 144, 144, 144, 142, 139]\n[219, 218, 212, 208, 203, 201, 201, 200, 197, 195, 192, 191, 190, 191, 190, 186, 179, 173, 170, 165, 165, 171, 173, 167, 163, 164, 175, 173, 170, 168, 167, 167, 169, 170, 167, 159, 150, 147, 151, 156, 157, 156, 152, 155, 158, 158, 154, 146, 137, 131, 131, 133, 136, 138, 140, 143, 147, 150, 148, 146, 147, 150, 149, 143, 141, 142, 136, 141, 145, 142, 133, 126, 126, 128, 142, 143, 140, 134, 132, 136, 140, 140, 136, 139, 142, 143, 142, 141, 141, 142, 137, 135, 135, 137, 137, 135, 138, 144, 136, 138]\n[189, 188, 179, 174, 168, 165, 165, 166, 165, 163, 159, 158, 158, 159, 160, 158, 153, 149, 147, 144, 145, 150, 150, 145, 142, 143, 156, 154, 151, 149, 148, 148, 149, 150, 148, 143, 138, 136, 137, 139, 139, 137, 143, 144, 146, 146, 143, 137, 131, 127, 127, 129, 130, 130, 129, 130, 132, 134, 137, 135, 136, 138, 137, 132, 130, 131, 129, 134, 138, 134, 127, 123, 124, 128, 139, 141, 137, 131, 130, 134, 137, 137, 141, 144, 147, 147, 145, 143, 141, 141, 138, 134, 132, 132, 130, 129, 134, 140, 139, 140]\n]", "contributor": "Jiankun Yang" }, { "task_id": "NS_PA_SS_06", "query_token_num": 401, "Engineering Domain": "Digital Hardware Design", "prompt": "You are a hardware\u2010design expert. Write synthesizable SystemVerilog for a dot\u2010product module that computes A\u00b7B for two 3\u2010element vectors, according to the following spec:\n\n1. Parameterization \n - Each input element is an 8\u2010bit unsigned word. \n - The output is an 18\u2010bit unsigned word.\n\n2. Ports \n```verilog\nmodule model (\n input logic [7:0] din, // serial input words: a1,a2,a3,b1,b2,b3\n input logic clk, // clock signal\n input logic resetn, // synchronous, active\u2010low reset\n output logic [17:0] dout, // dot product result\n output logic run // asserted for one cycle when dout is valid\n);\n\nBehavior\n\nInput sequencing: On each rising edge of clk while resetn==1, sample din and store it in order a1\u2192a2\u2192a3\u2192b1\u2192b2\u2192b3.\n\nDot\u2010product: After the 6th word (b3) is captured, in the same clock cycle assert run=1 and compute\n dout = a1*b1 + a2*b2 + a3*b3;\n\nas an 18\u2010bit unsigned sum.\n\nOutput timing:\n\nWhen run=1, dout holds the new product.\n\nIn subsequent cycles (until the next 6 inputs), run=0 but dout retains its last value.\n\nReset: On resetn==0, clear all internal registers, set dout=0, and assert run=1 once (since 0\u00b70=0).\n\nImplementation hints\n\nUse a 3\u2010entry shift\u2010register or counter to track which input you\u2019re on.\n\nMultiply and accumulate within one cycle after the 6th sample.\n\nEnsure all operations are synchronous to clk.\n\nPlease produce clean, commented, synthesizable SystemVerilog that meets this specification.```", "contributor": "Nippun Sabharwal, Shreyanka Sinha, Prakhar Agarwal" }, { "task_id": "LX_03", "query_token_num": 882, "Engineering Domain": "Control Design", "prompt": "In vehicle dynamics, the \\emph{quarter\u2013car model} captures the vertical motion of a single wheel assembly and the corresponding section of chassis, using two masses (the sprung mass $M$ and unsprung mass $m$), interconnected by a suspension spring\u2013damper and a tire spring. An \\emph{active suspension} system adds a controllable actuator force $u$ between the sprung and unsprung masses, allowing real\u2011time adjustment of ride stiffness and damping. By rejecting road disturbances $y_R$ and shaping the chassis response, active control can greatly improve both \\emph{ride comfort} and \\emph{road holding}. Here, we linearize about the static equilibrium, normalize all displacements so that the resting positions are zero, and derive a linear time\u2011invariant state\u2013space model suitable for controller design.\n\nYou can find a schematic of an active suspension system in the provided figure. \n\nA state\u2013space model in scientific units is given below, where $v_i = \\dot x_i$. \nThe states $x_i$ have been normalized so that their nominal values are $0$.\n\\[\n\\frac{d}{dt}\n\\begin{bmatrix}\nx_1\\\\\nx_2\\\\\nv_1\\\\\nv_2\n\\end{bmatrix}\n=\n\\begin{bmatrix}\n0 & 0 & 1 & 0\\\\\n0 & 0 & 0 & 1\\\\\n-10 & 10 & -2 & 2\\\\\n60 & -660 & 12 & -12\n\\end{bmatrix}\n\\begin{bmatrix}\nx_1\\\\\nx_2\\\\\nv_1\\\\\nv_2\n\\end{bmatrix}\n+\n\\begin{bmatrix}\n0\\\\\n0\\\\\n3.34\\\\\n-20\n\\end{bmatrix}\nu\n+\n\\begin{bmatrix}\n0\\\\\n0\\\\\n0\\\\\n600\n\\end{bmatrix}\ny_R\n\\]\n\n\\begin{enumerate}\n \\item Perform an open\u2011loop simulation of $x_1$ and $x_2$ for $0 \\le t \\le 20\\,$s, \n with \n \\[\n x_1(0)=0.5\\ \\mathrm{m},\\quad\n x_2(0)=0\\ \\mathrm{m},\\quad\n v_1(0)=v_2(0)=0,\\quad\n u(t)=y_R(t)\\equiv 0.\n \\]\n Determine the values $p_1$ and $p_2$ of the two largest peaks in $x_1(t)$. Also, find the settling time $t_s$ defined as the time after which $|x_1(t)|<\\SI{0.025}{m}$ holds for all subsequent $t$.\n \\item Repeat (1), but let $x_1(0)=\\SI{0}{m}$ and $y_R$ be a square\u2010wave of amplitude $0.2\\,$m \n and fundamental frequency $0.2\\,$Hz. Determine the number of peaks $N$ in $x_1(t)$ within one period, and find the value of the largest peak $p_m$.\n \n \\item Design a state\u2010feedback control law $K=[k1\\ k2\\ k3\\ k4]$ for a comfortable ride, meeting the following requirements:\n \\begin{enumerate}\n \\item The DC gains of $X_1(s)/Y_R(s)$ and $X_2(s)/Y_R(s)$ remain $1$.\n \\item Achieve a critically damped closed\u2010loop response for $X_1(s)/Y_R(s)$.\n \\item Reduce the settling time to approximately half of the open\u2010loop value.\n \\item The car does not bottom out under the conditions of (1). In normalized states, this means that\n \\[\n x_1(t)-x_2(t) > -0.5\\ \\mathrm{m}.\n \\]\n \\end{enumerate}\n\\end{enumerate}", "contributor": "Liujun Xu" }, { "task_id": "YX_02", "query_token_num": 781, "Engineering Domain": "Mechanical Systems", "prompt": "## Task Description\nIn this task, your goal is to produce local maps for a diesel engine calibration. You are provided with two global inputs: engine speed (N) and fuel mass (F), and four local inputs: injection (S), fuel pressure (P), variable geometry turbo rack position (G) and exhaust gas recirculation valve lift (E). Given the defined input ranges and physical constraints, you are required to perform structured sampling of the input space using the specified sampling strategy, ensuring representative and constraint-compliant coverage for subsequent modeling and calibration tasks.\n\n### Task 1\nFirst, for the global inputs: engine speed (N) and fuel mass (F), the maximum value of F changes as the value of N changes. You need to find the functional relationship between them.\nThe following information is given:\n - At N = 1600, F <= 200.\n - At N = 2000, F <= 175.\n - Values between these two breakpoints are linearly interpolated.\nFind the linear relationship between the maximum value of F and the value of N, and express their relationship in the format: F_max = a * N + b, where a, b are parameters.\n\n### Task 2\nAfter Task 1, you need to generate a **15 point Latin Hypercube Sampling (LHS)** design for the global inputs (N, F) based on the following specifications:\n- Global Input Definitions:\n - Engine speed (N):\n - Range: [1600, 2200]\n - Unit: rpm\n - Fuel mass (F):\n - Range: [20, 200]\n - Unit: mg/stroke\n- Physical Constraint:\n - The maximum value of F has a linear relationship with the value of N, which you have gained from Task 1. When N is in the interval [1600, 2000], the sampling points you find need to satisfy this linear relationship. When N is not in the interval [1600, 2000], there are no constraints on F.\n- Requirements:\n - Use the LHS strategy to generate 15 design points.\n - All sampled points must satisfy the constraint on F based on N.\n\n### Task 3\nGiven a global operating point with engine speed N = 1900 rpm, calculate the **normalized speed factor** as: f = (N - 1600) / (2200 - 1600).\nUse this factor f to determine input-dependent variable limits via **linear interpolation**:\n- For the fuel pressure (P) limits:\n - P_range = (1 \u2212 f) * [90, 120] + f * [110, 160]\n- For the variable geometry turbo rack position (G) limits:\n - G_range = (1 \u2212 f) * [0.2, 0.4] + f * [0.6, 0.9]\nThese bounds will be used for local sampling in the next task.\n\n### Task 4\nBased on the result from Task 2 and the given global inputs:\n- Engine speed: N = 1900 rpm\n- Fuel mass: F = 110 mg/stroke\nConstruct a **local design of experiments** using **Latin Hypercube Sampling (LHS)** over the following local inputs:\n- Injection (S):\n - Range: [-9, 3]\n - Unit: deg\n- Fuel pressure (P):\n - Range: P_range computed from Task 2\n - Unit: MPa\n- Variable geometry turbo rack position (G):\n - Range: G_range computed from Task 2\n - Unit: ratio\n- Exhaust gas recirculation valve lift (E):\n - Range: [0.5, 5]\n - Unit: mm\nYour design must contain **30 local samples** that respect the variable-specific bounds defined above.\n", "contributor": "Yaxin Li" }, { "task_id": "XG_12", "query_token_num": 484, "Engineering Domain": "Control Design", "prompt": "## Task Description\nConsider the following plant with a resonance:\n\\[\nG(s) = \\frac{0.5}{s}\\frac{169}{s^2 + 0.26s + 169},\n\\]\nThis plant has a resonance around 13 rad/sec. Assuming the desired loop bandwidth is $ \\omega_{L} = 3 $ rad/sec. An initial loop shaping controller using controller gain and integral boost is given as:\n- gain: $ K_g = \\frac{1}{|G(j\\omega_L)|}$,\n- integral boost: $ K_i(s) = \\frac{\\beta_b s + \\omega_L}{s \\sqrt{\\beta_b^2 + 1}}$ with $ \\beta_b = \\sqrt{10}$.\nAnd the initial loop shaping controller is:\n\\[\nC(s) = K_g \\cdot K_i(s)\n\\]\n\n### Task 1\nYour first task is to obtain the explicit transfer function of the initial loop shaping controller. Please provide the complete transfer function of \\( C(s) \\) as part of your response in the form of numerator and denominator coefficients.\n\n### Task 2\nThe initial design yeilds a unstable closed-loop system since there are additional gain crossings at 11.3 and 14.2 rad/sec. Your task is to build upon the initial controller, add a notch filter to attenuate the resonance. A notch filter with three parameters (\\omega_n, \\alpha_n, f_n) is given as:\n\\[\nK_n(s) = \\frac{s^2 + (f_n \\omega_n \\sqrt{\\alpha_n})s + \\omega_n^2}{s^2 + ((f_n \\omega_n)/(\\sqrt{\\alpha_n}))s + \\omega_n^2}.\n\\]\nNow your goal is to determine the parameters of the notch filter to attenuate the resonance. Here are some information may help you design the notch filter:\n- The resonance frequency is 13 rad/sec.\n- The loop without notch filter has a magnitude of 21 dB near the resonance frequency.\n\n\nYou need to design the notch filter to achieve the following requirements:\n- The closed-loop system is stable.\n- The closed-loop system should have a phase margin of at least 60 degrees.\n- The closed-loop system should have a gain margin of at least 2 dB.\n\n", "contributor": "Xingang Guo" }, { "task_id": "NS_PA_SS_07", "query_token_num": 453, "Engineering Domain": "Digital Hardware Design", "prompt": "You are a hardware\u2010design expert. Write synthesizable Verilog for a simple 1-read/1-write register file (RF) implemented as a multidimensional array of flip-flops, according to the following spec:\n\n1. Architecture \n - The RF has 8 entries, each 8 bits wide. \n - Internally use `reg [7:0] mem [0:7];` or equivalent to model the array of flip-flops. \n\n2. Ports \n```verilog\nmodule model (\n input wire [7:0] din, // data input for write\n input wire [2:0] addr, // address for read or write\n input wire wr, // write-enable\n input wire rd, // read-enable\n input wire clk, // clock\n input wire resetn, // synchronous, active-low reset\n output reg [7:0] dout, // data output for read\n output reg error // error flag for invalid op\n);\nBehavior\n\nReset (resetn == 0):\n\nClear all memory entries (optional) or implicitly treat as \u201cunwritten.\u201d\n\nDrive dout = 0, error = 0.\n\nOne operation per cycle on rising edge of clk:\n\nIf both wr and rd are high \u2192 invalid:\n\nerror = 1, dout = 0.\n\nElse if wr is high (wr == 1 && rd == 0):\n\nWrite din into mem[addr].\n\nerror = 0, dout = 0.\n\nElse if rd is high (rd == 1 && wr == 0):\n\nIf the addressed entry has been written before (or track via a valid bit):\n\ndout = mem[addr], error = 0.\n\nElse (unwritten address):\n\ndout = 0, error = 0.\n\nElse (no operation):\n\ndout = 0, error = 0.\n\nImplementation notes\n\nYou may use a reg valid [0:7]; array to track which entries have been written.\n\nAll logic must be synchronous to clk.\n\nKeep the design simple and fully synthesizable.\n\nProduce clean, commented Verilog that meets this specification.", "contributor": "Nippun Sabharwal, Shreyanka Sinha, Prakhar Agarwal" }, { "task_id": "LX_02", "query_token_num": 645, "Engineering Domain": "Control Design", "prompt": "Magnetic levitation systems suspend a ferromagnetic ball beneath an electromagnet by balancing gravitational and magnetic forces. The fundamental nonlinear dynamics are given by\n\\[\nm\\ddot y=mg-\\frac{kI^2}{y^2},\n\\]\nwhere \\(y(t)\\) is the ball\u2019s vertical displacement and \\(I(t)\\) the coil current. Around an operating point \\((y_0,I_0)\\), a first\u2011order Taylor expansion and appropriate nondimensionalization yield a normalized second\u2011order linear model suitable for controller design. In this task, you are required to analyze that linearized model and then validate the controller on the original nonlinear dynamics.\n\nTo simplify the problem, consider the following equation:\n\\[\n\\ddot y=1-\\frac{u^2}{y^2}.\n\\]\n\n\\begin{enumerate}\n \\item Linearize the nonlinear equation around the operating point $y = 1, u=1$. You need to give $a_{11},a_{12},a_{21},a_{22},b_{11},b_{21}$, where\n \\[\\dot{x}=\\begin{bmatrix}\n a_{11}&a_{12}\\\\\n a_{21}&a_{22}\n \\end{bmatrix}x+\\begin{bmatrix}\n b_{11}\\\\\n b_{21}\n \\end{bmatrix}u.\\]\n \\item Determine a feedback gain $K=(k1\\ k2)$ that places the closed\u2011loop poles at \\(-1\\pm j1\\).\n \\item The ball position $x_1$ can be measured using a photocell, but the velocity $x_2$ is more difficult to obtain. Therefore, suppose the output is $y=x_1$. Design a full-order observer $L = (l1\\ l2)'$ having eigenvalues at $-5, -6$, and use the observer feedback to produce closed-loop eigenvalues at $-1\\pm j1, -5, -6$. \n \\item Simulate your controller for the nonlinear model\n \\[\n \\ddot{y} = 1 -\\frac{u^2}{y^2},\n \\]\n with nominal equilibrium \\(y_0=u_0=1\\). With the initial condition $(x(0),\\dot{x}(0))$ set as $(1,0)$ for the observer, you need to identify whether the following initial conditions $(x(0),\\dot{x}(0))$ for the real system are within the region of asymptotic stability -- the set of initial states from which the closed\u2011loop system converges to the equilibrium. You need to use $1$ as yes and $0$ as no.\n \\begin{enumerate}\n \\item $(2, 2)$\n \\item $(2.5, 0)$\n \\item $(0.8, 0)$\n \\item $(0.9, -1)$\n \\end{enumerate}\n\\end{enumerate}", "contributor": "Liujun Xu" }, { "task_id": "JY_03", "query_token_num": 154, "Engineering Domain": "Signal Processing", "prompt": "You are now working with polarization images. \nGiven the Raw image is shaped 100x100\nyou decided to create the AoLP and DoLP images with the same resolution( 100x100 ) as the original raw frame \nHowever, after you gotten the frames, Degree0, Degree45, Degree90 and Degree135, Degree0 is corrupted, the pattern shown a checker board with alternating zeros.\n\nYou task is the following:\n1, Given the array for Degree0.\n\nDegree0 = [[229, 0, 195, 0, 209, 0, 199, 0, 193, 0, 194, 0, 201, 0, 188, 0, 203, 0, 181, 0, 195, 0, 187, 0, 135, 0, 79, 0, 35, 0, 22, 0, 14, 0, 10, 0, 43, 0, 58, 0, 73, 0, 72, 0, 75, 0, 105, 0, 137, 0], [0, 179, 0, 245, 0, 215, 0, 195, 0, 218, 0, 227, 0, 207, 0, 186, 0, 201, 0, 199, 0, 178, 0, 181, 0, 113, 0, 47, 0, 29, 0, 32, 0, 19, 0, 31, 0, 26, 0, 62, 0, 76, 0, 68, 0, 80, 0, 134, 0, 182], [197, 0, 191, 0, 211, 0, 222, 0, 197, 0, 195, 0, 188, 0, 227, 0, 177, 0, 199, 0, 211, 0, 227, 0, 158, 0, 59, 0, 22, 0, 30, 0, 23, 0, 31, 0, 18, 0, 50, 0, 56, 0, 89, 0, 69, 0, 113, 0, 160, 0], [0, 192, 0, 215, 0, 195, 0, 163, 0, 226, 0, 191, 0, 204, 0, 182, 0, 197, 0, 189, 0, 202, 0, 187, 0, 129, 0, 60, 0, 25, 0, 26, 0, 32, 0, 25, 0, 47, 0, 55, 0, 76, 0, 52, 0, 65, 0, 154, 0, 168], [182, 0, 187, 0, 211, 0, 207, 0, 198, 0, 211, 0, 193, 0, 197, 0, 220, 0, 183, 0, 213, 0, 171, 0, 131, 0, 88, 0, 34, 0, 29, 0, 15, 0, 26, 0, 30, 0, 44, 0, 73, 0, 51, 0, 36, 0, 120, 0, 156, 0], [0, 195, 0, 204, 0, 194, 0, 205, 0, 195, 0, 235, 0, 190, 0, 216, 0, 201, 0, 183, 0, 188, 0, 153, 0, 108, 0, 73, 0, 36, 0, 30, 0, 32, 0, 30, 0, 25, 0, 22, 0, 51, 0, 46, 0, 81, 0, 107, 0, 166], [199, 0, 200, 0, 194, 0, 209, 0, 216, 0, 216, 0, 195, 0, 197, 0, 198, 0, 215, 0, 193, 0, 174, 0, 112, 0, 93, 0, 56, 0, 21, 0, 25, 0, 25, 0, 23, 0, 21, 0, 22, 0, 36, 0, 78, 0, 103, 0, 134, 0], [0, 207, 0, 200, 0, 197, 0, 204, 0, 211, 0, 207, 0, 184, 0, 191, 0, 213, 0, 213, 0, 188, 0, 120, 0, 85, 0, 43, 0, 35, 0, 29, 0, 32, 0, 22, 0, 18, 0, 35, 0, 10, 0, 50, 0, 55, 0, 86, 0, 131], [186, 0, 220, 0, 214, 0, 204, 0, 195, 0, 209, 0, 210, 0, 201, 0, 188, 0, 183, 0, 207, 0, 187, 0, 113, 0, 85, 0, 43, 0, 34, 0, 39, 0, 13, 0, 28, 0, 27, 0, 55, 0, 23, 0, 40, 0, 62, 0, 101, 0], [0, 201, 0, 220, 0, 210, 0, 213, 0, 219, 0, 185, 0, 215, 0, 190, 0, 202, 0, 197, 0, 205, 0, 147, 0, 113, 0, 58, 0, 36, 0, 16, 0, 7, 0, 6, 0, 40, 0, 25, 0, 23, 0, 18, 0, 31, 0, 52, 0, 93], [189, 0, 182, 0, 193, 0, 186, 0, 201, 0, 222, 0, 195, 0, 203, 0, 193, 0, 197, 0, 207, 0, 185, 0, 139, 0, 88, 0, 36, 0, 25, 0, 17, 0, 6, 0, 19, 0, 28, 0, 13, 0, 15, 0, 13, 0, 58, 0, 92, 0], [0, 204, 0, 214, 0, 198, 0, 208, 0, 187, 0, 199, 0, 203, 0, 211, 0, 189, 0, 170, 0, 184, 0, 169, 0, 101, 0, 28, 0, 28, 0, 36, 0, 23, 0, 31, 0, 9, 0, 19, 0, 25, 0, 19, 0, 54, 0, 73, 0, 93], [217, 0, 209, 0, 206, 0, 181, 0, 202, 0, 210, 0, 193, 0, 183, 0, 188, 0, 174, 0, 184, 0, 175, 0, 135, 0, 86, 0, 36, 0, 47, 0, 46, 0, 24, 0, 21, 0, 13, 0, 27, 0, 44, 0, 43, 0, 67, 0, 77, 0], [0, 192, 0, 206, 0, 200, 0, 211, 0, 185, 0, 195, 0, 231, 0, 214, 0, 211, 0, 195, 0, 156, 0, 136, 0, 121, 0, 83, 0, 38, 0, 14, 0, 21, 0, 30, 0, 26, 0, 8, 0, 13, 0, 22, 0, 54, 0, 52, 0, 77], [207, 0, 204, 0, 216, 0, 192, 0, 226, 0, 184, 0, 216, 0, 206, 0, 186, 0, 198, 0, 200, 0, 147, 0, 147, 0, 115, 0, 77, 0, 28, 0, 6, 0, 23, 0, 36, 0, 40, 0, 31, 0, 22, 0, 26, 0, 46, 0, 67, 0], [0, 209, 0, 216, 0, 191, 0, 213, 0, 195, 0, 202, 0, 221, 0, 201, 0, 184, 0, 193, 0, 193, 0, 121, 0, 126, 0, 99, 0, 40, 0, 21, 0, 16, 0, 12, 0, 19, 0, 20, 0, 23, 0, 19, 0, 35, 0, 56, 0, 69], [213, 0, 215, 0, 204, 0, 217, 0, 204, 0, 203, 0, 216, 0, 208, 0, 202, 0, 172, 0, 189, 0, 129, 0, 134, 0, 118, 0, 52, 0, 31, 0, 15, 0, 11, 0, 15, 0, 15, 0, 29, 0, 11, 0, 39, 0, 54, 0, 47, 0], [0, 192, 0, 221, 0, 236, 0, 209, 0, 198, 0, 227, 0, 222, 0, 183, 0, 185, 0, 174, 0, 174, 0, 156, 0, 113, 0, 80, 0, 55, 0, 32, 0, 25, 0, 30, 0, 18, 0, 10, 0, 18, 0, 22, 0, 26, 0, 35, 0, 70], [223, 0, 206, 0, 204, 0, 195, 0, 172, 0, 221, 0, 205, 0, 188, 0, 209, 0, 192, 0, 202, 0, 185, 0, 170, 0, 109, 0, 67, 0, 30, 0, 23, 0, 25, 0, 14, 0, 35, 0, 27, 0, 25, 0, 25, 0, 31, 0, 56, 0], [0, 193, 0, 204, 0, 188, 0, 215, 0, 217, 0, 219, 0, 213, 0, 199, 0, 161, 0, 210, 0, 195, 0, 175, 0, 172, 0, 64, 0, 51, 0, 48, 0, 28, 0, 10, 0, 14, 0, 34, 0, 7, 0, 29, 0, 23, 0, 51, 0, 73], [206, 0, 195, 0, 208, 0, 191, 0, 232, 0, 208, 0, 171, 0, 221, 0, 184, 0, 213, 0, 201, 0, 183, 0, 178, 0, 144, 0, 81, 0, 51, 0, 42, 0, 14, 0, 21, 0, 25, 0, 18, 0, 13, 0, 34, 0, 30, 0, 63, 0], [0, 209, 0, 227, 0, 199, 0, 205, 0, 183, 0, 203, 0, 189, 0, 201, 0, 217, 0, 217, 0, 197, 0, 179, 0, 173, 0, 134, 0, 60, 0, 44, 0, 24, 0, 25, 0, 19, 0, 18, 0, 8, 0, 30, 0, 23, 0, 42, 0, 73], [255, 0, 224, 0, 211, 0, 194, 0, 201, 0, 215, 0, 222, 0, 213, 0, 195, 0, 205, 0, 211, 0, 185, 0, 193, 0, 163, 0, 99, 0, 60, 0, 34, 0, 32, 0, 28, 0, 23, 0, 18, 0, 19, 0, 35, 0, 29, 0, 44, 0], [0, 213, 0, 200, 0, 195, 0, 192, 0, 203, 0, 184, 0, 209, 0, 191, 0, 193, 0, 218, 0, 221, 0, 171, 0, 159, 0, 147, 0, 65, 0, 47, 0, 22, 0, 28, 0, 7, 0, 7, 0, 18, 0, 23, 0, 6, 0, 43, 0, 52], [194, 0, 217, 0, 190, 0, 227, 0, 209, 0, 195, 0, 211, 0, 193, 0, 190, 0, 237, 0, 204, 0, 207, 0, 175, 0, 172, 0, 147, 0, 80, 0, 25, 0, 28, 0, 14, 0, 18, 0, 16, 0, 28, 0, 27, 0, 18, 0, 32, 0], [0, 211, 0, 221, 0, 211, 0, 190, 0, 234, 0, 211, 0, 203, 0, 176, 0, 192, 0, 176, 0, 207, 0, 179, 0, 172, 0, 162, 0, 126, 0, 71, 0, 48, 0, 23, 0, 26, 0, 12, 0, 24, 0, 27, 0, 25, 0, 40, 0, 58], [197, 0, 205, 0, 219, 0, 211, 0, 211, 0, 225, 0, 204, 0, 226, 0, 227, 0, 205, 0, 185, 0, 185, 0, 178, 0, 195, 0, 178, 0, 109, 0, 32, 0, 25, 0, 30, 0, 15, 0, 11, 0, 22, 0, 17, 0, 40, 0, 70, 0], [0, 195, 0, 211, 0, 187, 0, 226, 0, 181, 0, 207, 0, 224, 0, 186, 0, 211, 0, 230, 0, 211, 0, 193, 0, 171, 0, 163, 0, 167, 0, 96, 0, 32, 0, 32, 0, 8, 0, 31, 0, 27, 0, 26, 0, 23, 0, 31, 0, 70], [215, 0, 224, 0, 216, 0, 211, 0, 203, 0, 216, 0, 205, 0, 203, 0, 208, 0, 219, 0, 204, 0, 204, 0, 175, 0, 197, 0, 172, 0, 141, 0, 58, 0, 46, 0, 23, 0, 24, 0, 21, 0, 19, 0, 17, 0, 22, 0, 48, 0], [0, 199, 0, 213, 0, 227, 0, 216, 0, 213, 0, 226, 0, 223, 0, 227, 0, 194, 0, 219, 0, 204, 0, 201, 0, 171, 0, 176, 0, 156, 0, 118, 0, 38, 0, 30, 0, 14, 0, 23, 0, 32, 0, 23, 0, 10, 0, 24, 0, 59], [202, 0, 205, 0, 191, 0, 213, 0, 194, 0, 208, 0, 220, 0, 213, 0, 204, 0, 203, 0, 208, 0, 200, 0, 197, 0, 195, 0, 181, 0, 163, 0, 92, 0, 43, 0, 23, 0, 20, 0, 9, 0, 23, 0, 16, 0, 20, 0, 36, 0], [0, 195, 0, 173, 0, 230, 0, 193, 0, 187, 0, 195, 0, 221, 0, 207, 0, 211, 0, 205, 0, 191, 0, 185, 0, 211, 0, 198, 0, 189, 0, 111, 0, 51, 0, 24, 0, 19, 0, 13, 0, 17, 0, 36, 0, 32, 0, 17, 0, 56], [187, 0, 215, 0, 214, 0, 194, 0, 202, 0, 234, 0, 187, 0, 219, 0, 200, 0, 217, 0, 224, 0, 218, 0, 203, 0, 193, 0, 167, 0, 150, 0, 56, 0, 29, 0, 13, 0, 26, 0, 24, 0, 26, 0, 10, 0, 13, 0, 38, 0], [0, 211, 0, 213, 0, 197, 0, 207, 0, 195, 0, 199, 0, 195, 0, 188, 0, 183, 0, 198, 0, 192, 0, 179, 0, 179, 0, 174, 0, 188, 0, 111, 0, 40, 0, 10, 0, 24, 0, 23, 0, 18, 0, 0, 0, 26, 0, 24, 0, 19], [216, 0, 211, 0, 197, 0, 206, 0, 220, 0, 202, 0, 195, 0, 193, 0, 205, 0, 222, 0, 202, 0, 188, 0, 189, 0, 181, 0, 168, 0, 137, 0, 99, 0, 35, 0, 21, 0, 32, 0, 17, 0, 23, 0, 15, 0, 25, 0, 13, 0], [0, 170, 0, 237, 0, 205, 0, 203, 0, 238, 0, 216, 0, 199, 0, 214, 0, 192, 0, 215, 0, 194, 0, 213, 0, 185, 0, 175, 0, 188, 0, 125, 0, 65, 0, 42, 0, 26, 0, 17, 0, 15, 0, 35, 0, 16, 0, 26, 0, 28], [197, 0, 207, 0, 230, 0, 187, 0, 191, 0, 195, 0, 198, 0, 195, 0, 192, 0, 206, 0, 199, 0, 183, 0, 221, 0, 179, 0, 171, 0, 161, 0, 96, 0, 60, 0, 35, 0, 18, 0, 27, 0, 13, 0, 27, 0, 14, 0, 23, 0], [0, 206, 0, 220, 0, 215, 0, 222, 0, 218, 0, 195, 0, 214, 0, 205, 0, 215, 0, 197, 0, 195, 0, 205, 0, 185, 0, 195, 0, 172, 0, 152, 0, 91, 0, 31, 0, 18, 0, 12, 0, 36, 0, 15, 0, 30, 0, 28, 0, 31], [219, 0, 234, 0, 224, 0, 188, 0, 211, 0, 195, 0, 188, 0, 178, 0, 185, 0, 205, 0, 225, 0, 216, 0, 221, 0, 195, 0, 175, 0, 179, 0, 146, 0, 64, 0, 31, 0, 28, 0, 25, 0, 27, 0, 14, 0, 3, 0, 36, 0], [0, 206, 0, 237, 0, 184, 0, 184, 0, 204, 0, 214, 0, 234, 0, 178, 0, 187, 0, 211, 0, 204, 0, 189, 0, 187, 0, 189, 0, 208, 0, 165, 0, 107, 0, 46, 0, 28, 0, 26, 0, 17, 0, 22, 0, 24, 0, 17, 0, 15], [218, 0, 195, 0, 210, 0, 199, 0, 188, 0, 203, 0, 200, 0, 221, 0, 201, 0, 179, 0, 189, 0, 189, 0, 187, 0, 170, 0, 187, 0, 163, 0, 146, 0, 69, 0, 39, 0, 10, 0, 13, 0, 10, 0, 17, 0, 22, 0, 31, 0], [0, 208, 0, 199, 0, 218, 0, 222, 0, 207, 0, 201, 0, 215, 0, 184, 0, 170, 0, 162, 0, 191, 0, 162, 0, 178, 0, 198, 0, 191, 0, 179, 0, 121, 0, 38, 0, 26, 0, 1, 0, 17, 0, 21, 0, 13, 0, 11, 0, 32], [229, 0, 184, 0, 203, 0, 186, 0, 194, 0, 203, 0, 207, 0, 208, 0, 195, 0, 170, 0, 197, 0, 149, 0, 168, 0, 157, 0, 162, 0, 176, 0, 147, 0, 60, 0, 17, 0, 18, 0, 12, 0, 24, 0, 13, 0, 30, 0, 19, 0], [0, 200, 0, 201, 0, 188, 0, 233, 0, 216, 0, 184, 0, 195, 0, 178, 0, 157, 0, 179, 0, 154, 0, 105, 0, 125, 0, 137, 0, 163, 0, 143, 0, 65, 0, 52, 0, 36, 0, 7, 0, 27, 0, 22, 0, 29, 0, 26, 0, 14], [227, 0, 195, 0, 211, 0, 201, 0, 199, 0, 195, 0, 199, 0, 176, 0, 151, 0, 147, 0, 162, 0, 129, 0, 121, 0, 113, 0, 117, 0, 116, 0, 131, 0, 62, 0, 19, 0, 24, 0, 27, 0, 18, 0, 40, 0, 16, 0, 12, 0], [0, 200, 0, 217, 0, 204, 0, 222, 0, 179, 0, 188, 0, 189, 0, 190, 0, 117, 0, 121, 0, 142, 0, 116, 0, 71, 0, 105, 0, 110, 0, 112, 0, 94, 0, 68, 0, 32, 0, 19, 0, 29, 0, 11, 0, 11, 0, 15, 0, 26], [220, 0, 163, 0, 190, 0, 224, 0, 209, 0, 203, 0, 165, 0, 203, 0, 160, 0, 119, 0, 121, 0, 123, 0, 75, 0, 109, 0, 84, 0, 80, 0, 83, 0, 63, 0, 21, 0, 29, 0, 23, 0, 23, 0, 15, 0, 10, 0, 19, 0], [0, 203, 0, 188, 0, 211, 0, 220, 0, 211, 0, 183, 0, 200, 0, 171, 0, 131, 0, 85, 0, 97, 0, 107, 0, 77, 0, 85, 0, 70, 0, 92, 0, 67, 0, 69, 0, 21, 0, 13, 0, 16, 0, 13, 0, 16, 0, 27, 0, 22], [199, 0, 198, 0, 209, 0, 216, 0, 189, 0, 171, 0, 193, 0, 185, 0, 139, 0, 99, 0, 59, 0, 84, 0, 63, 0, 60, 0, 62, 0, 73, 0, 63, 0, 51, 0, 52, 0, 22, 0, 0, 0, 23, 0, 25, 0, 21, 0, 13, 0], [0, 189, 0, 201, 0, 206, 0, 218, 0, 195, 0, 155, 0, 125, 0, 113, 0, 83, 0, 52, 0, 58, 0, 60, 0, 36, 0, 48, 0, 42, 0, 59, 0, 65, 0, 44, 0, 17, 0, 15, 0, 2, 0, 25, 0, 27, 0, 25, 0, 22]]\n\n2, Design a mathematical kernel that mimics linear interpolation to fill the values that is zero for the Degree0, make sure the center of the kernel is 1\n\n3, the Aolp and DoLP image will also be tested as a metrics to the kernel score \n\n\n\n\n\n", "contributor": "Jiankun Yang" }, { "task_id": "NS_PA_SS_09", "query_token_num": 222, "Engineering Domain": "Digital Hardware Design", "prompt": "You are a hardware\u2010design expert. Write synthesizable SystemVerilog for a parameterized Gray\u2010to\u2010binary converter that maps an N-bit Gray code value to its binary index, according to the following spec:\n\n1. Parameterization \n - parameter WIDTH = 8; \n\n2. Ports \n```verilog\nmodule model #(\n parameter WIDTH = 8\n) (\n input logic [WIDTH-1:0] gray, // N-bit Gray code input\n output logic [WIDTH-1:0] bin // N-bit binary index output\n);\nBehavior\n\nCombinational conversion:\n\nbin[WIDTH-1] = gray[WIDTH-1];\n\nFor i from WIDTH-2 down to 0:\nbin[i] = bin[i+1] ^ gray[i];\n\nNo clock or reset\u2014purely combinational logic.\n\nImplementation notes\n\nYou may use a generate\u2013for loop or bitwise reduction to implement the XOR cascade.\n\nEnsure fully synthesizable, zero-latency logic.\n\nPlease produce clean, commented, synthesizable SystemVerilog that meets this specification.", "contributor": "Nippun Sabharwal, Shreyanka Sinha, Prakhar Agarwal" }, { "task_id": "YX_03", "query_token_num": 2304, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\nIn this task, you should evaluate the detection performance of an S-band radar system operating at 3 GHz. Across 14 tasks, you will calculate key metrics such as available and required SNR, integration gain, fluctuation loss, MTI and CFAR losses, beam and scan-related losses, and the overall effective detectability factor. Results should be expressed in dB or km with proper rounding and error estimation.\n\n\n### Task 1\nGiven an S-band airport surveillance radar operating at the frequency of 3 GHz. The peak transmit power is 0.2 MW, the transmit and receive antenna gain is 34 dB, the pulse duration is 11 microseconds, and the noise figure is 4.1 dB. Assume the radar is required to detect a target with 1 m^2 RCS at the maximum range R_m of 100 km. Assume no losses, that is L = 0 dB. Calculate the available SNR at the required maximum range of 100 km.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n### Task 2\nCompute the required SNR for a single pulse received from a steady target by a square-law detector, assuming the desired probability of detection Pd = 0.9 and the maximum acceptable probability of false alarm Pfa = 1e-6.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n### Task 3\nAssuming Pd = 0.9 and Pfa = 1e-6, calculate the required SNR for a single pulse received from a Swerling 1 fluctuating target.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n### Task 4\nTo lower the detectability factor, we can perform pulse integration. Calculate the required SNR for N = 10 noncoherently integrated pulses received from a Swerling 1 fluctuating target, assuming Pd = 0.9 and Pfa = 1e-6.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n### Task 5\nThe integration gain is the difference between the SNR required to detect a steady target using a single pulse and the SNR required to detect a steady target using N pulses. Given Pd = 0.9 and Pfa = 1e-6, N = 10, calculate the integration gain.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n### Task 6\nThe fluctuation loss is the difference between the SNR required to detect a fluctuating target and the SNR required to detect a steady target. Given Pd = 0.9 and Pfa = 1e-6, using 10 pulses, calculate the fluctuation loss.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n### Task 7\nUsing your result of Task 4 as the minimum required SNR, and the same conditions as in Task 1 (An S-band airport surveillance radar is operating at the frequency of 3 GHz. The peak transmit power is 0.2 MW, the transmit and receive antenna gain is 34 dB, the pulse duration is 11 microseconds, and the noise figure is 4.1 dB. The radar is required to detect a target with 1 m^2 RCS.), evaluate the actual maximum range of the system.\nExpress the result in km, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n\n### Task 8\nPulse radar systems turn off their receivers during the pulse transmission. Thus, the target echoes arriving from the ranges within one pulse length from the radar or within one pulse length around the unambiguous range will be eclipsed by the transmitted pulse resulting in only a fraction of the pulse being received and processed.\nGiven the radar system with the pulse width of 11 microseconds, calcuate the closest range from which a full pulse can be received, Rmin.\nExpress the result in km, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n### Task 9\nEclipsing effect can also be observed for the targets located at or near the multiples of the unambiguous range. Assuming the pulse repetition frequency is 1350 Hz, calculate the unambiguous range of the system.\nExpress the result in km, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n\n### Task 10\nAssume the radar system employs an electronically steered phased array to perform scanning. Using the phased array antenna will cause an increase in the required SNR due to two effects: 1. beam broadening due to the reduced projected array area in the beam direction, and 2. reduction of the effective aperture area of the individual array elements at off-broadside angles. To account for these effects, add the scan sector loss to the detectability factor. Assume that the system scans only in the azimuth dimension and the scan sector spans from \u201360 to 60 degrees. Assume the target is a fluctuating target. Given Pd = 0.9 and Pfa = 1e-6, N = 10, compute the resultant loss.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain four decimal places. Round your result instead of truncating.\n\n\n### Task 11\nMoving target indicator (MTI) is a process of rejecting fixed or slowly moving clutter while passing echoes from targets moving with significant velocities. Typical MTI uses 2, 3, or 4-pulse canceller that implements a high-pass filter to reject echoes with low Doppler shifts. Passing the received signal through the MTI pulse canceller introduces correlation between the noise samples. This in turn reduces the total number of independent noise samples available for integration, resulting in MTI noise correlation loss. Additionally, the MTI canceller significantly suppresses targets with velocities close to the nulls of its frequency response, causing an additional MTI velocity response loss.\nAssume the target is a fluctuating target. Given Pd = 0.9 and Pfa = 1e-6, N = 10. Assuming a 2-pulse canceller is used, calculate these two components of the MTI loss, the MTI noise correlation loss Lmti_a and the MTI velocity response loss Lmti_b.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain four decimal places. Round your result instead of truncating.\n\n### Task 12\nBinary integration is a suboptimal noncoherent integration technique also known as the M-of-N integration. If M out of N received pulses exceed a predetermined threshold, a target is declared to be present. The binary integrator is a relatively simple automatic detector and is less sensitive to the effects of a single large interference pulse that might exist along with the target echoes. Therefore, the binary integrator is more robust when the background noise or clutter is non-Gaussian. Since the binary integration is a suboptimal technique, it results in a binary integration loss compared to optimal noncoherent integration. The optimal value of M is not a sensitive selection and it can be quite different from the optimum without significant penalty resulting in the binary integration loss being lower than 1.4 dB.\nGiven Pd = 0.9 and Pfa = 1e-6. Calculate the binary integration loss when N is 10 and M is set to 6.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain four decimal places. Round your result instead of truncating.\n\n### Task 13\nConstant false alarm rate (CFAR) detector is used to maintain an approximately constant rate of false target detections when the noise or the interference levels vary. Since CFAR averages a finite number of reference cells to estimate the noise level, the estimates are subject to an error which leads to a CFAR loss. CFAR loss is an increase in the SNR required to achieve a desired detection performance using CFAR when the noise levels are unknown compared to a fixed threshold with a known noise level.\nCalculate the CFAR loss assuming that Pfa = 1e-6 and total 120 cells are used for cell-averaging CFAR.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain four decimal places. Round your result instead of truncating.\n\n\n### Task 14\nThe detectability factor reflects the minimum SNR required to detect a target under ideal conditions. However, practical radar systems experience additional signal processing and scanning losses.\nUsing the baseline detectability factor for a steady target with a single pulse from Task 2, and incorporating the following computed components:\n- Integration gain (Task 5)\n- Fluctuation loss (Task 6)\n- Beam shape loss = 1.2338 dB\n- Scan sector loss (Task 10)\n- MTI noise correlation loss and velocity response loss (Task 11)\n- Binary integration loss (Task 12)\n- CFAR loss (Task 13)\nCalculate the effective detectability factor by appropriately adjusting the baseline with gains and adding all losses.\nExpress the result in dB, and please specify the absolute error you believe exists between your result and the standard answer. Retain two decimal places. Round your result instead of truncating.\n\n### Task 15\nBased on the effective detectability factor calculated in Task 14, evaluate whether the radar system described in Task 1 \u2014 an S-band airport surveillance radar operating at 3 GHz with 0.2 MW peak transmit power, 34 dB antenna gain (Tx/Rx), 11 microseconds pulse duration, and a 4.1 dB noise figure \u2014 is capable of detecting a 1 m^2 RCS target at 100 km with Pd = 0.9 and Pfa = 1e-6.\nCompare the available SNR from Task 1 with the required detectability factor from Task 14, and conclude whether the system satisfies the performance requirement.\nIf the system meets the requirement, return 1; if it does not, return 0.\n", "contributor": "Yaxin Li" }, { "task_id": "XG_13", "query_token_num": 273, "Engineering Domain": "Control Design", "prompt": "## Background\nControl systems play a critical role in stabilizing and regulating the behavior of dynamic systems, such as robotic arms and autonomous vehicles. In this task, you will design a proportional-integral-derivative (PID) controller for a mass-spring-damper system. The system is described by the following physical parameters:\n- Mass: $m = 1\\, \\text{kg}$ \n- Damping coefficient: $b = 10\\, \\text{N s/m}$ \n- Spring constant: $k = 20\\, \\text{N/m}$ \n- External force: $F = 1\\, \\text{N}$\nAn illustrative diagram is provided to help visualize the system.\n\n## Task Description\nPlease design a PID controller for the given mass-spring-damper system, such that the closed-loop system satisfies the following performance requirements:\n - **Settling time:** $T_s < 0.2\\, \\text{seconds}$\n - **Overshoot:** $M_p < 5\\%$\n - **Steady-state error:** Zero\n**Note:** You may choose to implement a simplified controller by setting one or more of the PID parameters (i.e., $K_i$ or $K_d$) to zero, effectively designing a PI, PD, or P controller as needed.\n", "contributor": "Xingang Guo" }, { "task_id": "XG_07", "query_token_num": 1361, "Engineering Domain": "Control Design", "prompt": "## Task Description\nIn this task, you are required to design a H-infinity controller for an active suspension system using hinfsyn command in MATLAB in robust control toolbox. Conventional passive suspensions use a spring and damper between the car body and wheel assembly. The spring-damper characteristics are selected to emphasize one of several conflicting objectives such as passenger comfort, road handling, and suspension deflection. Active suspensions allow the designer to balance these objectives using a feedback-controller hydraulic actuator between the chassis and wheel assembly. In this task, we use a quarter-car model of the active suspension system (see in the attached figure). The mass m_b (in kilograms) represents the car chassis (body) and the mass m_w (in kilograms) represents the wheel assembly. The spring k_s and damper b_s represent the passive spring and shock absorber placed between the car body and the wheel assembly. The spring k_t models the compressibility of the pneumatic tire. The variables x_b, x_w, and r (all in meters) are the body travel, wheel travel, and road disturbance, respectively. The force f_s (in kiloNewtons) applied between the body and wheel assembly is controlled by feedback and represents the active component of the suspension system.\n\n### Task 1\nWith the state vector: (x_1, x_2, x_3, x_4) = (x_b, \\dot{x}_b, x_w, \\dot{x}_w), the linearlized state-space model of the quarter-car active suspension system is given by:\n\\begin{equation}\n\\dot{x}_1 &= x_2\n\\dot{x}_2 &= -(1/m_b)(k_s(x_1-x_3)+b_s(x_2-x_4)-10^3f_s)\n\\dot{x}_3 &= x_4\n\\dot{x}_4 &= (1/m_w)(k_s(x_1-x_3)+b_s(x_2-x_4)-k_t(x_3-r)-10^3f_s)\n\\end{equation}\nYour first task is to derive the numerical values of the state space matrices (A, B) using the above equations with the following parameters:\n- m_b = 300 kg\n- m_w = 60 kg\n- k_s = 16000 N/m\n- b_s = 1000 N/m/s\n- k_t = 190000 N/m\n\n### Task 2\nYour second task is to design a H-infinity controller for the active suspension system using hinfsyn command in MATLAB in robust control toolbox. Consider that the state space matrices are given as (A, B, C, D) with A and B defined in Task 1 and C and D defiend as:\nC = [1 0 0 0; 1 0 -1 0; A(2,:)];\nD = [0 0; 0 0; B(2,:)]; \nThe following MATLAB code is given to you as a baseline assuming the correct state space matrices:\n\nqcar = ss(A,B,C,D);\nqcar.StateName = {'body travel (m)';'body vel (m/s)';...\n 'wheel travel (m)';'wheel vel (m/s)'};\nqcar.InputName = {'r';'fs'};\nqcar.OutputName = {'xb';'sd';'ab'};\n% Nominal Actuator dynamics\nActNom = tf(1,[1/60 1]);\nActNom.InputName = 'u';\nActNom.OutputName = 'fs';\n%% Design Setup\nWroad = ss(0.07); \nWroad.u = 'd'; \nWroad.y = 'r';\nWact = 0.8*tf([1 50],[1 500]); \nWact.u = 'u'; \nWact.y = 'e1';\nHandlingTarget = 0.04 * tf([1/8 1],[1/80 1]);\nComfortTarget = 0.4 * tf([1/0.45 1],[1/150 1]);\nbeta = 0.01;\nWsd = beta/HandlingTarget;\nWsd.u = 'sd'; \nWsd.y = 'e3';\nWab = (1-beta)/ ComfortTarget;\nWab.u = 'ab'; \nWab.y = 'e2';\n%% Apply Design using hinfsyn\nsdmeas = sumblk('y1 = sd');\nabmeas = sumblk('y2 = ab');\nICinputs = {'d';'u'};\nICoutputs = {'e1';'e2';'e3';'y1';'y2'};\nqcaric = connect(qcar,ActNom,Wroad,Wact,Wab,Wsd,sdmeas,abmeas,ICinputs,ICoutputs);\nncont = 1; % one control signal, u\nnmeas = 2; % two measurement signals, sd and ab\nK = ss(zeros(ncont,nmeas));\n[K,~,gamma] = hinfsyn(qcaric,nmeas,ncont);\nK.u = {'sd','ab'}; K.y = 'u';\nCL = connect(qcar,ActNom,K,'r',{'xb';'sd';'ab'});\n% Road disturbance\nt = 0:0.0025:1;\nroaddist = zeros(size(t));\nroaddist(1:101) = 0.025*(1-cos(8*pi*t(1:101)));\n% Simulate\np1 = lsim(qcar(:,1),roaddist,t);\ny1 = lsim(CL,roaddist,t);\n% Performance Metrics\nrms_closed = rms(y1(:,1));\npeak_closed = max(abs(y1(:,1)));\nenergy_open = trapz(t, p1(:,1).^2);\nenergy_closed = trapz(t, y1(:,1).^2);\nattenuation_ratio = energy_closed / energy_open;\n\nWith correct A and B matrices, it achieves the following performance:\n- RMS of the body travel: 0.014 m\n- Peak of the body travel: 0.0309 m\n- Energy Attenuation: 57.23%\n\nPlease choose another beta parameter between 0 and 1 in the Design Setup section of the baseline MATLAB code to achieve the following performance requirements:\n - RMS body travel \u2264 0.012m \n - Peak body travel \u2264 0.035m\n - Energy attenuation \u2264 35%", "contributor": "Xingang Guo" }, { "task_id": "XW_02", "query_token_num": 1241, "Engineering Domain": "Operating System Design", "prompt": "## Task Description\nIn this task, you will be provided with a filesystem image. You are required to develop separate programs\u2014each implementing a different filesystem operation (e.g., create, read, update, delete)\u2014to modify the corresponding sections of that image. Your objective is to ensure that each program correctly performs its assigned operation on the intended part of the filesystem image while preserving its overall integrity.\n\nHere is the class definition for your reference:\n\nfrom dataclasses import dataclass, field\nfrom typing import List, Dict, Optional\n\n@dataclass\nclass SuperBlock:\n \"\"\"File system superblock, stores metadata.\"\"\"\n block_size: int # Size of each block (bytes)\n total_blocks: int # Total number of blocks\n inode_count: int # Total number of inodes\n free_block_bitmap: List[bool] # Free block bitmap, True = free\n\n@dataclass\nclass Inode:\n \"\"\"Inode structure, stores file/directory metadata.\"\"\"\n ino: int # Inode number\n is_dir: bool # Whether this inode is a directory\n size: int # File size (bytes)\n direct_blocks: List[int] # List of direct block indices\n # Optional: add indirect block pointers, multi-level indexing, permissions, timestamps, etc.\n\n@dataclass\nclass DirEntry:\n \"\"\"Directory entry: maps a filename to an inode.\"\"\"\n name: str\n inode: int\n\n@dataclass\nclass FileSystemImage:\n \"\"\"Complete file system image structure.\"\"\"\n superblock: SuperBlock\n inodes: Dict[int, Inode] = field(default_factory=dict)\n # Directory tree: inode -> list of entries in that directory; valid only for is_dir=True inodes\n directories: Dict[int, List[DirEntry]] = field(default_factory=dict)\n # Data block storage area: index corresponds to block number, content is bytes\n data_blocks: List[Optional[bytes]] = field(default_factory=list)\n\n def __post_init__(self):\n # Initialize data block storage area\n if not self.data_blocks:\n self.data_blocks = [None] * self.superblock.total_blocks\n\n def allocate_block(self) -> int:\n \"\"\"Allocate a block from the free bitmap and return its index; raise if none available.\"\"\"\n for idx, free in enumerate(self.superblock.free_block_bitmap):\n if free:\n self.superblock.free_block_bitmap[idx] = False\n self.data_blocks[idx] = b'' # Initialize with empty content\n return idx\n raise RuntimeError(\"No free blocks available\")\n\n def free_block(self, block_idx: int):\n \"\"\"Free the specified block index.\"\"\"\n if 0 <= block_idx < self.superblock.total_blocks:\n self.superblock.free_block_bitmap[block_idx] = True\n self.data_blocks[block_idx] = None\n else:\n raise IndexError(\"Block index out of range\")\n\n def create_inode(self, is_dir: bool) -> Inode:\n \"\"\"Create a new inode and return it.\"\"\"\n new_ino = len(self.inodes) + 1\n if new_ino > self.superblock.inode_count:\n raise RuntimeError(\"No free inodes\")\n inode = Inode(\n ino=new_ino,\n is_dir=is_dir,\n size=0,\n direct_blocks=[]\n )\n self.inodes[new_ino] = inode\n if is_dir:\n self.directories[new_ino] = []\n return inode\n\n def add_dir_entry(self, dir_ino: int, name: str, inode: int):\n \"\"\"Add a directory entry to the directory with inode dir_ino.\"\"\"\n if dir_ino not in self.directories:\n raise RuntimeError(\"Not a directory inode\")\n self.directories[dir_ino].append(DirEntry(name=name, inode=inode))\n\n### Task 1\ndef write(fs_img: FileSystemImage, name: str, pos: int, data: str) -> FileSystemImage:\n \"\"\"\n Write the UTF\u20118 encoded bytes of `data` into the file called `name`\n in the given FileSystemImage, starting at byte offset `pos`. Return\n the updated FileSystemImage so that its blocks and inode metadata\n can be inspected for correctness.\n\n Parameters:\n - fs_img: the FileSystemImage instance containing inodes, directories,\n and data blocks.\n - name: an absolute or relative path to the target file within `fs_img`.\n - pos: the byte offset within the file at which to begin writing.\n - data: a Python string whose UTF\u20118 encoding will be written.\n\n Returns:\n - The same FileSystemImage instance (`fs_img`), mutated to reflect the\n writes (updated data_blocks and inode.size).\n\n Behavior:\n 1. If the file `name` does not exist or refers to a directory, raise\n `FileNotFoundError` or `IsADirectoryError` respectively.\n 2. If `pos` is negative or greater than the file\u2019s current size, raise\n `ValueError`.\n 3. Encode `data` as UTF\u20118 bytes.\n 4. If writing beyond the current end of file, extend the file:\n - Allocate new blocks via `fs_img.allocate_block()` as needed.\n - Update the inode\u2019s `direct_blocks` list accordingly.\n 5. Compute which blocks and byte\u2010ranges within them correspond to\n the target file range `[pos, pos + len(bytes))`.\n 6. Overwrite or append bytes in `fs_img.data_blocks[block_idx]` per block.\n 7. Update the inode\u2019s `size` to `max(old_size, pos + len(bytes))`.\n 8. Return the mutated `fs_img` so that test harnesses can inspect\n its `data_blocks` and `inodes` for correctness.\n \"\"\"\n", "contributor": "Licheng Xu, Jinwen Wang" }, { "task_id": "Ziheng_03", "query_token_num": 209, "Engineering Domain": "Control Design", "prompt": "## Task Description\nYou need to design a PID controller for a magnetic levitation system in which an electromagnet holds a steel ball at a desired height. Near the operating point, the nonlinear dynamics can be linearized and modeled by the transfer function:\nG = K / ((tau1*s + 1)*(tau2*s + 1)*(tau3*s + 1));\nwhere:\nK = 1;\ntau1 = 0.5;\ntau2 = 1.0;\ntau3 = 2.0;\n\nDesign a PID controller so that the closed\u2011loop system meets all of the following specifications:\n1. Settling time Ts (to within plus or minus 5 percent) < 5s\n2. Overshoot < 20 percent\n3. Zero steady state error to a unit step input\n4. Gain margin > 10dB\n5. Phase margin > 45 degrees\n\n## Output format\nYou need to give me your Kp, Ki, and Kd in numerical form.\n\n", "contributor": "Ziheng Guo" }, { "task_id": "XG_09", "query_token_num": 780, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\nIn this task, you will use fuzzy logic to process an image for edge detection. An edge is a boundary between two uniform regions. You can detect an edge by comparing the intensity of neighboring pixels. However, because uniform regions are not crisply defined, small intensity differences between two neighboring pixels do not always represent an edge. Instead, the intensity difference might represent a shading effect. The fuzzy logic approach for image processing allows you to use membership functions to define the degree to which a pixel belongs to an edge or a uniform region. Here is a baseline code:\n\n% Import the image.\nIrgb = imread('peppers.png');\n% Convert to 2-D array\nIgray = rgb2gray(Irgb);\n% Convert image to double-precision data\nI = im2double(Igray);\n% Obtain Image gradient\nGx = [-1 1];\nGy = Gx';\nIx = conv2(I,Gx,'same');\nIy = conv2(I,Gy,'same');\n% Define Fuzzy Inference System (FIS) for Edge Detection\nedgeFIS = mamfis('Name','edgeDetection');\nedgeFIS = addInput(edgeFIS,[-1 1],'Name','Ix');\nedgeFIS = addInput(edgeFIS,[-1 1],'Name','Iy');\n% zero-mean Gaussian membership function for each input\nsx = 0.01;\nsy = 0.01;\nedgeFIS = addMF(edgeFIS,'Ix','gaussmf',[sx 0],'Name','zero');\nedgeFIS = addMF(edgeFIS,'Iy','gaussmf',[sy 0],'Name','zero');\n% Specify the intensity of the edge-detected image as an output of edgeFIS\nedgeFIS = addOutput(edgeFIS,[0 1],'Name','Iout');\n% Specify the triangular membership functions, white and black, for Iout\nwa = 0.5;\nwb = 0.5;\nwc = 1;\nba = 0.5;\nbb = 0.5;\nbc = 0.7;\nedgeFIS = addMF(edgeFIS,'Iout','trimf',[wa wb wc],'Name','white');\nedgeFIS = addMF(edgeFIS,'Iout','trimf',[ba bb bc],'Name','black');\n% Specify FIS Rules\nr1 = \"If Ix is zero and Iy is zero then Iout is white\";\nr2 = \"If Ix is not zero or Iy is not zero then Iout is black\";\nedgeFIS = addRule(edgeFIS,[r1 r2]);\nedgeFIS.Rules\n% Evaluate FIS \nIeval = zeros(size(I));\nfor ii = 1:size(I,1)\n Ieval(ii,:) = evalfis(edgeFIS,[(Ix(ii,:));(Iy(ii,:))]');\nend\n\nWe will use three main evaluation metrics to evaluate the edge detection performance:\n1. MSE between the edge detection result and the ground truth edge map\n2. PSNR between the edge detection result and the ground truth edge map\n3. SSIM between the edge detection result and the ground truth edge map\nIn the evaluation, the Canny edge detector is used as the pseudo-ground-truth. The above baselinecode achieves:\nMSE: 0.5958\nPSNR: 2.25 dB\nSSIM: 0.0366\n\nNow your task is to tune the parameters of the membership functions (i.e., sx, sy, wa, wb, wc, ba, bb, bc) to improve the edge detection performance and achieve the following metrics:\nMSE < 0.5\nPSNR > 3 dB\nSSIM > 0.05\n\nThe gray scale image for edge detection is given to you below for your 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"contributor": "Xingang Guo" }, { "task_id": "Yiqi_01", "query_token_num": 4385, "Engineering Domain": "Computer Architecture Design", "prompt": "# Problem Definition of T10 Benchmark\n\nTo compute a matrix multiplication operator on an inter-core connected AI chip, we need you to derive an execution plan using T10's abstraction. For more information about this problem, please refer to \"Background Information of T10 Benchmark\".\n\n**The Computation Task:** \nThe matrix multiplication (MatMul) to be computed is defined as $C[m,n] += A[m,k]*B[k,n]$, where $m = 128$, $k = 5120$, and $n = 15360$. The input and output tensors are all in FP16 format (2 bytes per data element). To find better partitioning plans, you may consider padding this operator along any of its dimensions. However, there will be performance overhead if you pad too much.\n\n**The Hardware:** \nWe use an inter-core connected AI chip called IPU Mk2. An IPU chip has 1,472 cores, and each core executes independent threads in parallel with a private 624KB scratchpad memory, which adds up to a total of 896MB on-chip memory. The IPU cores are interconnected by high-bandwidth low-latency links. Each core can access the scratchpad memory of another core at 5.5GB/s, offering an aggregated inter-core all-to-all bandwidth of $1472 \\times 5.5$ GB/s $\\approx 8$ TB/s [1]. Inside each core, there is a systolic array of shape $16 \\times 16$, which can compute a partition of the MatMul operator at high throughput. If the sub-MatMul to be computed on each core does not have a shape that is a multiple of the systolic array shape, this sub-MatMul must be padded to align with the systolic array shape.\n\n**The Execution Plan:** \nIn this problem, we need you to derive a fast execution plan that computes the above MatMul on an IPU chip. First, this plan should ensure that at any time during execution, the sub-tensor partitions on each core do not overflow the per-core SRAM size. Second, the partition factors in this plan should comply with all constraints defined in T10's background information. Third, this plan should use no more than 1,472 cores. Finally, this plan should try to minimize the total execution time, which is the sum of per-core computation time and inter-core communication time.\n\n**The Output Format:** \nYou should output the execution plan in the following format:\n\n- `F_op`: a list of integers with length 3, which are the operator partition factors on dimensions $m$, $k$, and $n$, respectively.\n- `f_t_A_m`: integer, which is the temporal partition factor of tensor A on dimension $m$.\n- `f_t_A_k`: integer, which is the temporal partition factor of tensor A on dimension $k$.\n- `f_t_B_k`: integer, which is the temporal partition factor of tensor B on dimension $k$.\n- `f_t_B_n`: integer, which is the temporal partition factor of tensor B on dimension $n$.\n- `f_t_C_m`: integer, which is the temporal partition factor of tensor C on dimension $m$.\n- `f_t_C_n`: integer, which is the temporal partition factor of tensor C on dimension $n$.\n\n---\n\n# Background Information of T10 Benchmark\n\n## 1. Inter-core Connected AI Chip\n\nDeep learning accelerators, such as GPUs and TPUs, are widely recognized for their exceptional computing throughput (e.g., hundreds of Tera-FLOPS), making them ideal for handling large-scale models and high-dimensional data in deep learning. Such effectiveness is largely attributed to their massive parallel cores and specialized accelerator units, e.g., TensorCore. However, to saturate the high computing throughput, they usually require a high-throughput memory system, e.g., a large shared memory with multi-hierarchical cache layers in accelerators. Also, an efficient deep learning compiler [7, 8] is necessary to optimize data reuse across the memory hierarchy, ensuring the computing units are fully utilized. This combination of hardware and software design often yields orders of magnitude higher performance than traditional CPUs for critical deep learning operations, including matrix multiplication and convolution.\n\nDespite the success of existing accelerators, the constantly increasing demand for processing large deep-learning models with higher computation throughput presents a significant challenge to the underlying memory system. To address this challenge, the community is exploring a more scalable architecture with fully distributed memory, such as the Graphcore IPU [2], SambaNova SN10 [5], and Cerebras WSE [3]. Rather than relying on shared-memory architecture, they typically associate each computation core with local memory, and connect the cores via a high-bandwidth on-chip network, creating a large aggregated on-chip memory. However, this unique architecture renders previous deep learning compilers designed for shared-memory architectures, which cannot fully leverage the new architecture's scalability, resulting in significant memory waste.\n\nDesigning a deep learning compiler for distributed memory-based accelerators presents several unique challenges:\n1. Due to the absence of global shared memory, it is necessary to partition the operators, along with their input and output tensors, into sub-operators that can operate independently on each core with only local memory access.\n2. As the local memory on each core is mostly on-chip memory, the aggregated memory capacity is considerably smaller than the off-chip memory. Thus, the compiler must effectively utilize the limited memory capacity to support a model size as large as possible, without compromising on computing performance.\n3. Given that there is usually a trade-off between memory consumption and computation performance for each operator, an end-to-end model compilation must consider the trade-offs among all operators, generating a combinatorial optimization space that is infeasible to solve using existing compilers.\n\nIn this problem, we focus on a representative example of the inter-core connected AI chip: the Graphcore Intelligence Processing Unit (IPU) MK2 [2]. An IPU chip has 1,472 cores, and each core executes independent threads in parallel with a private 624KB scratchpad memory, which adds up to a total of 896MB on-chip memory. Compared to the global shared memory architecture, a key distinction is that IPU cores are interconnected by high-bandwidth low-latency links. Each core can access the scratchpad memory of another core at 5.5GB/s, offering an aggregated inter-core all-to-all bandwidth of $1472 \\times 5.5$GB/s $\\approx 8$TB/s [1].\n\n---\n\n## 2. Background of T10\n\nTo eliminate the excessive memory footprint and redundant inter-core communications of VGM, we map the DNN computation to a _compute-shift_ pattern. In each step, each core independently computes a sub-task with data received from its upstream neighbors and shifts the data to its downstream. The feasibility of this approach for general DNNs comes from this observation: most DNN operators can be divided into regular computation tasks, which load and produce consecutive data tiles of the input and output tensors, respectively.\n\n![Figure 1](./images/figure1.png)\nFigure 1 shows an example that maps a MatMul operator to two cores with the compute-shift style execution. \nBoth (b) and (c) are valid compute-shift execution plans, but with different tradeoffs between memory footprint and communication overhead.\n\n**Example: Mapping MatMul to Two Cores**\nWe show an example that maps a matrix multiplication (MatMul) operator to two cores in Figure 1 (a). \n1. **Partitioning:** We first partition the operator along dimension $m$ onto two cores in Figure 1 (b). By default, both cores hold a copy of the weight tensor, which incurs memory capacity overhead. \n2. **Memory Optimization:** To reduce memory footprint, in Figure 1 (c), we further split the weight tensor along dimension $n$ into two parts and place each part on one of the cores. Then, the computation must be conducted in two steps, as each core holds half of the weight tensor and performs half of its computation per step. Between the computation steps, each core circularly shifts its partition to the next core, forming a shift ring of two cores.\n\n**Advantages of Compute-Shift Pattern**\n1. Eliminates the need for a global memory to store shared data, improving memory capacity utilization. \n2. Evenly distributes communication volume across inter-core connections. \n3. Aligns computation with data tile, avoiding redundant communications to many cores.\n\n**Tradeoff Between Memory Footprint and Communication Overhead**\nFor example, both Figure 1 (b) and (c) show valid execution plans:\n- **Plan (b):** Finishes the entire computation in one step without inter-core communication, but has a higher memory footprint. \n- **Plan (c):** Has less memory footprint but incurs more communication overhead.\n\nIn reality, deriving the best tradeoff is challenging due to multi-dimensional DNN operators and thousands of cores on an IPU chip. An efficient compute-shift execution plan may contain numerous nested shift rings along multiple tensor dimensions, composing a massive tradeoff space to search through.\n\n---\n\n## 3. T10's Execution Plan Format\n\n### $r$Tensor: A New Tensor Abstraction\nT10 introduces a distributed tensor abstraction called RotatingTensor ($r$Tensor). $r$Tensor describes how each tensor is partitioned, mapped, and shifted on the interconnected cores (summarized in Table 1).\n\n**Table 1. Terminologies used in T10**\n| **Symbol** | **Name** | **Description** |\n|------------|------------------------------|-------------------------------------------------------------------------------|\n| `f_s^X` | Spatial Partition Factor | Spatially partitions a tensor X into sub-tensors. |\n| `f_t^X` | Temporal Partition Factor | Temporally partitions a sub-tensor of X into sub-tensor partitions. |\n| `F_op` | Operator Partition Factor | Spatially partitions an entire operator into sub-operators. |\n\nFirst, T10 partitions the computation of an operator onto multiple cores. Based on the data dependency, the computation partitioning will imply how each of its input/output tensor is partitioned. This gives a spatial partition factor ($f_s$), which splits a tensor into sub-tensors. Second, each sub-tensor may be required by multiple cores. To share a sub-tensor among them, we specify how the sub-tensor is further partitioned among the cores using a temporal partition factor ($f_t$). $f_t$ also specifies how the partitions of a sub-tensor are circularly shifted among the cores. Altogether, a set of $r$Tensors of an operator defines a compute-shift execution plan. The numerous possible $r$Tensor configurations of an operator generate a huge search space of execution plans.\n\n![Figure 2](./images/figure2.png)\nFigure 2 shows the llustration of rTensor partitioning and rotating.\n\nSpecifically, $f_s$ and $f_t$ are vectors with a length equal to the number of dimensions of a tensor, indicating how the tensor is partitioned along each dimension. For example, in Figure 2 (a), a tensor $T$ of shape $[6,8]$ is partitioned onto 8 cores by a spatial factor $f_s=[2,1]$, forming 2 sub-tensors of shape $[3,8]$. Thus, to share each sub-tensor among 4 cores without incurring high memory footprint, a temporal factor $f_t=[1,2]$ further partitions each sub-tensor into 2 partitions with shape $[3,4]$, as shown in Figure 2 (b). It forms $\\frac{4}{2} = 2$ rotation rings with 2 cores in each, where cores share the sub-tensor by circularly shifting its partitions. In comparison, Figure 2 (c) shows how another $f_t=[1,4]$ splits the same sub-tensor to 4 partitions, on $\\frac{4}{4}=1$ rotation ring with 4 cores.\n\n---\n\n## 3.2. Compute-Shift Execution Plan\n\nUsing the $r$Tensor abstraction, T10 organizes the computation of a general DNN operator into a compute-shift pattern, where the operator's computation and tensors are partitioned to individual cores and their local memories. The entire computation involves multiple compute-shift steps until each tensor has been shifted across all cores. Each compute step is defined as a *sub-task*. In each compute-shift step, each core computes a sub-task and shifts local tensors to its neighbors. We now discuss how T10 partitions DNN operators into compute-shift-based execution plans.\n\n### Operator representation.\nTo represent an operator's computation, T10 uses tensor expression [6], which defines how each output tensor value is computed from the input values. For example, a matrix multiplication of tensors $A$ in shape $[M,K]$ and $B$ in $[K,N]$ into $C$ is defined as\n\n$C[m,n] \\longleftarrow A[m,k]*B[k,n]$,\n\nwhere $m$, $k$, and $n$ are axes to index the elements in each tensor. Equation (1) indicates that any value in $C$ indexed by $m$ and $n$ (i.e., $C[m,n]$) is computed by summing $A[m,k]*B[k,n]$ over all possible indices $k$. T10 supports all common operators, like MatMult and Convolution, from DNN workloads in both inference and training. For a few special cases like Sort, which cannot be represented in tensor expression, T10 uses the implementations from the vendor library.\n\n### Partitioning an operator.\nTo map an operator to interconnected cores, T10 first partitions it into parallel *sub-operators* along all unique axes in its tensor expression, using an *operator partition factor* ($F_{op}$). For example, Equation (1) contains axes $m$, $k$, and $n$, then $F_{op}$ is a vector of three integer factors specifying how the three axes are spatially partitioned. The total number of sub-operators is the product of all elements in $F_{op}$. For example, $F_{op}=[2,1,4]$ for $[m,k,n]$ slices the operator into 8 sub-operators on 8 cores, each computing a $\\lceil\\frac{M}{2},\\frac{K}{1}\\rceil \\times \\lceil\\frac{K}{1},\\frac{N}{4}\\rceil$ sub-matrix multiplication.\n\n### Partitioning $r$Tensors.\nT10 then uses $F_{op}$ to derive the spatial partition factor $f_s$ for each tensor, following the data dependencies in tensor expression. With the same example, for $F_{op}=[2,1,4]$ on $[m,k,n]$, the spatial partition factor for the tensor A is $f_s^A=[2,1]$ for axes $m$ and $k$. Similarly, for tensors B and C, we have $f_s^B=[1,4]$ and $f_s^C=[2,4]$.\n\nIf a tensor's dimensions do not include some axis in $F_{op}$, each of the sliced sub-tensors is required by multiple sub-operators along the missing axis. Thus, once the spatial factor determines the number of cores that will share a sub-tensor, the temporal factor determines how we split the sub-tensor across these cores into rotation ring(s). In the above example, $F_{op}$ partitions the entire operator onto $2 \\times 1 \\times 4 = 8$ cores, and $f_s^B$ spatially partitions tensor B into $1 \\times 4 = 4$ sub-tensors. Thus, each sub-tensor is shared by $P=\\frac{8}{4}=2$ cores. Then, a temporal factor $f_t^B=[2,1]$ further splits each sub-tensor into $2 \\times 1 = 2$ partitions, forming $\\frac{P}{2}=1$ rotation ring.\n\nT10 enforces that the product of elements in $f_t$, or $\\prod f_t$, is a divisor of the number of cores that shares the sub-tensor ($P$), so that the number of rotation rings (i.e., $\\frac{P}{\\prod f_t}$) is an integer. If there is more than one rotation ring, we replicate each sub-tensor $\\frac{P}{\\prod f_t}$ times to ensure that each ring shares one copy of the sub-tensor. While the duplication consumes memory space, it may reduce the number of rotation steps by allowing a larger sub-task on each core at each step, which enables a trade-off between memory usage and communication cost.\n\n![Figure 3](./images/figure3.png)\nFigure 3 shows an example of the rotation of rTensor.\nThe compute-shift executions of the sub-operators need to be aligned.\n\n### Aligning the rotations of $r$Tensors.\nSince a general DNN operator can have various tensor shapes, a naive partitioning plan can easily cause the tensor shifting and the sub-task computing at an unaligned pace. In Figure 3 (a), we still use the MatMult operator in Equation (1) as an example. We partition it into a $2 \\times 4$ grid in Figure 3 (b), with the specified partition factors. Note that both A and B are temporally partitioned along axis $k$, but with different $f_t$ factors.\n\nThe rotating paces of tensors in one operator must be aligned to ensure correct data dependency. In Figure 3 (b), tensors A and B are shifted with different paces along axis $k$. To synchronizes the paces, each core shifts A for 2 times along $k$ for each time B is shifted, and computes a sub-task (i.e., a sub-MatMult) of shape $[\\text{m=1, k=1, n=1}]$ for each time A is shifted. This requires 4 compute steps to finish the sub-operator on this core, where A is shifted after each step and B is shifted every 2 steps.\n\n### Alignment constraints.\nTo ensure that a $r$Tensor configuration can be translated into a valid execution plan, the product of the temporal partition factors of a tensor (i.e., the total number of temporal partitions) should be a factor of the replication number caused by spatial partitioning. Additionally, for different tensors of an operator that share a common dimension, all their temporal factors on this dimension should be aligned. Thus, any pair of temporal factors should be a factor or multiple of each other. This approach allows each tensor or sub-tensor to flow across cores at a different pace, while ensuring that corresponding tensor partitions can meet at the same time step on a specific core. For instance, in the matrix multiplication illustrated in Figure 3(b), tensor A has a temporal factor of 4 along dimension $k$, tensor B has a factor of 2, and these factors along $k$ (i.e., 4 and 2) must be a factor or multiple of each other.\n\n### Sub-operator scheduling.\nWith the above constraints, we can organize an operator's computation into a valid compute-shift execution plan. At each step, each sub-operator computes a sub-task partitioned by $F_{op}$ and the $f_t$ along each axis. Each sub-operator iterates over all its sub-tasks by nested-looping through the axes of this operator. Between sub-tasks, an $r$Tensor is rotated along the currently iterating axis for all its sub-tensors, until all sub-tasks are enumerated.\n\nSpecifically, T10 organizes the computation on each core as nested loops of interleaved compute and shift stages. Each loop corresponds to a temporally partitioned dimension. For example, if there are two dimensions to shift, $m$ and $n$, with $m$ shifting twice and $n$ shifting once, then there are two valid 5-time shift schedules: (1) $m$ is the inner loop, i.e., $\\text{shift}(m) \\times 2 \\rightarrow \\text{shift}(n) \\rightarrow \\text{shift}(m) \\times 2$; and (2) $n$ is the inner loop, i.e., $\\text{shift}(n) \\rightarrow \\text{shift}(m) \\rightarrow \\text{shift}(n) \\rightarrow \\text{shift}(m) \\rightarrow \\text{shift}(n)$. To determine the optimal loop order, T10 designates the dimension belonging to the tensor with the smaller size as the inner loop to reduce the total communication volume, as the inner loop is executed more times. To generate local computations for each core, T10 invokes the corresponding compute function with the partition configuration and the tensor expression.\n\n---\n\n# References\n[1] Zhe Jia, Blake Tillman, Marco Maggioni, and Daniele Paolo Scarpazza. 2019. Dissecting the Graphcore IPU Architecture via Microbenchmarking. \n[2] Simon Knowles. 2021. Graphcore Colossus Mk2 IPU. \n[3] Sean Lie. 2021. Multi-Million Core, Multi-Wafer AI Cluster. \n[4] Yiqi Liu et al. 2024. Scaling Deep Learning Computation over the Inter-Core Connected Intelligence Processor with T10. \n[5] Raghu Prabhakar and Sumti Jairath. 2021. SambaNova SN10 RDU. \n[6] Nicolas Vasilache et al. 2018. Tensor Comprehensions. \n[7] Lianmin Zheng et al. 2020. Ansor. \n[8] Hongyu Zhu et al. 2022. ROLLER. ", "contributor": "Yiqi Liu" }, { "task_id": "KV_02", "query_token_num": 389, "Engineering Domain": "Control Design", "prompt": "## Task Description\n\nYou are designing control parameters for a **Switched Capacitor Battery Balancing System** involving active balancing of three Li-ion battery cells connected in series.\n\nThe system uses:\n- 2 capacitors and 6 bidirectional switches (active balancing architecture)\n- Initial state of charge (SOC) of each cell:\n - Cell 1: 0.70\n - Cell 2: 0.75\n - Cell 3: 0.80\n- PWM switching for UP and DOWN phases:\n - Switching period (Tper) = 0.006 seconds\n - 50% duty cycle\n - 180\u00b0 interleaving\n- CC-CV Battery control block:\n - Maximum voltage vMax = 4.1 V\n - PI controller: Kp = 100, Ki = 10\n- Charge and discharge behavior controlled by relay toggling logic\n\nYou must propose control parameters that allow safe, efficient, and effective balancing.\n\n---\n\n## Your Task\n\nYou are tasked with proposing **four numerical values** that control balancing behavior:\n\n1. `lowest_current`:\n - The **smallest balancing current** (in Amperes) that could reasonably allow balancing progress.\n2. `highest_current`:\n - The **maximum allowable balancing current** (in Amperes) without causing SOC instability.\n3. `on_threshold`:\n - The **SOC level** at which the relay should **stop charging** (start discharging).\n4. `off_threshold`:\n - The **SOC level** at which the relay should **resume charging** after discharge.\n\n---\n\n## Output Format\n\nYou must **only** return the following exact Python dictionary format:\n\n```python\n{\n \"lowest_current\": YOUR_VALUE,\n \"highest_current\": YOUR_VALUE,\n \"on_threshold\": YOUR_VALUE,\n \"off_threshold\": YOUR_VALUE\n}\n", "contributor": "Kojo Vandyck" }, { "task_id": "XW_04", "query_token_num": 1292, "Engineering Domain": "Operating System Design", "prompt": "## Task Description\nIn this task, you will be provided with a filesystem image. You are required to develop a separate program that implements a different filesystem operation (e.g., create, read, update, delete)\u2014to modify the corresponding sections of that image. Your objective is to ensure that the program correctly performs its assigned operation on the intended part of the filesystem image while preserving its overall integrity.\n\nHere is the class definition for your reference:\n\nfrom dataclasses import dataclass, field\nfrom typing import List, Dict, Optional\n\n@dataclass\nclass SuperBlock:\n \"\"\"File system superblock, stores metadata.\"\"\"\n block_size: int # Size of each block (bytes)\n total_blocks: int # Total number of blocks\n inode_count: int # Total number of inodes\n free_block_bitmap: List[bool] # Free block bitmap, True = free\n\n@dataclass\nclass Inode:\n \"\"\"Inode structure, stores file/directory metadata.\"\"\"\n ino: int # Inode number\n is_dir: bool # Whether this inode is a directory\n size: int # File size (bytes)\n direct_blocks: List[int] # List of direct block indices\n # Optional: add indirect block pointers, multi-level indexing, permissions, timestamps, etc.\n\n@dataclass\nclass DirEntry:\n \"\"\"Directory entry: maps a filename to an inode.\"\"\"\n name: str\n inode: int\n\n@dataclass\nclass FileSystemImage:\n \"\"\"Complete file system image structure.\"\"\"\n superblock: SuperBlock\n inodes: Dict[int, Inode] = field(default_factory=dict)\n # Directory tree: inode -> list of entries in that directory; valid only for is_dir=True inodes\n directories: Dict[int, List[DirEntry]] = field(default_factory=dict)\n # Data block storage area: index corresponds to block number, content is bytes\n data_blocks: List[Optional[bytes]] = field(default_factory=list)\n\n def __post_init__(self):\n # Initialize data block storage area\n if not self.data_blocks:\n self.data_blocks = [None] * self.superblock.total_blocks\n\n def allocate_block(self) -> int:\n \"\"\"Allocate a block from the free bitmap and return its index; raise if none available.\"\"\"\n for idx, free in enumerate(self.superblock.free_block_bitmap):\n if free:\n self.superblock.free_block_bitmap[idx] = False\n self.data_blocks[idx] = b'' # Initialize with empty content\n return idx\n raise RuntimeError(\"No free blocks available\")\n\n def free_block(self, block_idx: int):\n \"\"\"Free the specified block index.\"\"\"\n if 0 <= block_idx < self.superblock.total_blocks:\n self.superblock.free_block_bitmap[block_idx] = True\n self.data_blocks[block_idx] = None\n else:\n raise IndexError(\"Block index out of range\")\n\n def create_inode(self, is_dir: bool) -> Inode:\n \"\"\"Create a new inode and return it.\"\"\"\n new_ino = len(self.inodes) + 1\n if new_ino > self.superblock.inode_count:\n raise RuntimeError(\"No free inodes\")\n inode = Inode(\n ino=new_ino,\n is_dir=is_dir,\n size=0,\n direct_blocks=[]\n )\n self.inodes[new_ino] = inode\n if is_dir:\n self.directories[new_ino] = []\n return inode\n\n def add_dir_entry(self, dir_ino: int, name: str, inode: int):\n \"\"\"Add a directory entry to the directory with inode dir_ino.\"\"\"\n if dir_ino not in self.directories:\n raise RuntimeError(\"Not a directory inode\")\n self.directories[dir_ino].append(DirEntry(name=name, inode=inode))\n\n\n### Task\ndef delete(fs_img: FileSystemImage, path: str) -> FileSystemImage:\n \"\"\"\n Delete the file or directory at the given path within the FileSystemImage.\n Return the updated FileSystemImage so that its inodes, directory entries,\n and data blocks can be inspected for correctness.\n\n Parameters:\n - fs_img: the FileSystemImage instance containing inodes, directories,\n and data blocks.\n - path: an absolute or relative path to the file or directory to delete.\n\n Returns:\n - The same FileSystemImage instance (`fs_img`), mutated to reflect the\n removal of the entry and reclamation of resources.\n\n Behavior:\n 1. Split `path` into `parent_path` and `name`:\n e.g. `/a/b/c` \u2192 `parent_path='/a/b'`, `name='c'`.\n 2. Look up `parent_path`:\n - If not found, raise `FileNotFoundError`.\n - If found but not a directory, raise `NotADirectoryError`.\n 3. In the parent directory\u2019s entries, locate an entry whose `name` matches:\n - If none found, raise `FileNotFoundError`.\n - Determine its `inode` number.\n 4. Inspect the target inode:\n - If it is a directory and is **not empty**, raise `OSError(\"Directory not empty\")`.\n - If it is a directory and empty, remove its entry list from `fs_img.directories`.\n - If it is a file, proceed to free its data blocks:\n - For each block index in `inode.direct_blocks`, call `fs_img.free_block(index)`.\n 5. Remove the inode from `fs_img.inodes`.\n 6. Remove the directory entry from the parent\u2019s `fs_img.directories[parent_inode.ino]`.\n 7. Return the mutated `fs_img`.\n\n Exceptions:\n - `FileNotFoundError` if the path or parent directory does not exist.\n - `NotADirectoryError` if the parent exists but is not a directory.\n - `FileExistsError` is **not** used here; instead:\n - `OSError(\"Directory not empty\")` if attempting to delete a non-empty directory.\n \"\"\"\n # Your implementation here\u2026", "contributor": "Licheng Xu, Jinwen Wang" }, { "task_id": "Ziheng_02", "query_token_num": 563, "Engineering Domain": "Robotics", "prompt": "##Task Description\nThe question: Find a set of joint variables that would produce a given tool pose for a 6-DOF robot\n\nFrame 0 is fixed to the base. Frame 1 is fixed to the tool. Set the frame 0 as the reference, for frame 1, the homogeneous transformation matrix M_1in0 is:\n\nM = [ 0.0000 0.0000 1.0000 -8.0000;\n 1.0000 0.0000 0.0000 2.0000;\n 0.0000 1.0000 0.0000 0.0000;\n 0.0000 0.0000 0.0000 1.0000]];\n\n\nThe matrix of spatial screw axes is:\n\nS = [ 0.0000 1.0000 0.0000 0.0000 -1.0000 0.0000;\n 0.0000 0.0000 0.0000 1.0000 0.0000 1.0000;\n 0.0000 0.0000 -1.0000 0.0000 0.0000 0.0000;\n 0.0000 0.0000 2.0000 0.0000 0.0000 0.0000;\n 1.0000 0.0000 -4.0000 0.0000 0.0000 0.0000;\n 0.0000 0.0000 0.0000 -6.0000 0.0000 -8.0000 ];\n\n\nThe goal pose T_1in0 is:\n\nT_1in0 = [ -0.5429 0.5940 0.5937 -9.3919;\n 0.6499 -0.1506 0.7449 -1.8656;\n 0.5319 0.7903 -0.3043 0.6739;\n 0 0 0 1.0000 ];\n\n## Output Format\nFind a set of joint variables \u03b8 that is:\n\ntheta=[theta_1; theta_2; theta_3; theta_4; theta_5; theta_6]\n\nthat would result in the given pose T_1in0.", "contributor": "Ziheng Guo" }, { "task_id": "XG_08", "query_token_num": 730, "Engineering Domain": "Control Design", "prompt": "## Task Description\nIn this task, you will need to build a fuzzy inference system using MATLAB Fuzzy Logic Designer app for a tipping problem. For this problem, the tipping behavior is defined using the following rule:\n1. If the service is poor or the food is rancid, then the tip is cheap.\n2. If the service is good, then the tip is average.\n3. If the service is excellent or the food is delicious, then the tip is generous.\nThe following MATLAB code is given to build the fuzzy inference system with some missing parts:\n\n% create a Mamdani FIS, specifying its name\nfis = mamfis(\"Name\",\"tipper\");\n% add input variables\nfis = addInput(fis,[0 10],\"Name\",\"service\");\nfis = addInput(fis,[0 10],\"Name\",\"food\");\n% add membership function 1\nfis = addMF(fis,\"service\",\"\",,\"Name\",\"poor\");\n% add membership function 2\nfis = addMF(fis,\"service\",\"\",,\"Name\",\"good\");\n% add membership function 3\nfis = addMF(fis,\"service\",\"\",,\"Name\",\"excellent\");\n% add membership function 4\nfis = addMF(fis,\"food\",\"\",,\"Name\",\"rancid\");\n% add membership function 5\nfis = addMF(fis,\"food\",\"\",,\"Name\",\"delicious\");\n% add output variable\nfis = addOutput(fis,[0 30],\"Name\",\"tip\");\n% add membership function 6\nfis = addMF(fis,\"tip\",\"\",,\"Name\",\"cheap\");\n% add membership function 7\nfis = addMF(fis,\"tip\",\"\",,\"Name\",\"average\");\n% add membership function 8\nfis = addMF(fis,\"tip\",\"\",,\"Name\",\"generous\");\n% add rules\nruleList = ;\nfis = addRule(fis,ruleList);\n\n\n### Task 1\nYour first task is to complete the code to build the fuzzy inference system. For membership functions, the corresponding shape is given in the attached image 1 to 8. You need to determine the type of membership function and the parameters using the images. You should choose membership function types among gaussmf, trapmf, and trimf.\n\n### Task 2\nYour second task is to specify the rule list for the fuzzy inference system as a numeric array using the aforementioned rules. \nEach row of the array contains one rule in the following format.\n- Column 1 \u2014 Index of membership function for first input\n- Column 2 \u2014 Index of membership function for second input\n- Column 3 \u2014 Index of membership function for output\n- Column 4 \u2014 Rule weight (from 0 to 1)\n- Column 5 \u2014 Fuzzy operator (1 for AND, 2 for OR)\nTherefore, you should return a 3x5 array for this rule list.\n\n### Task 3\nYour third task is to use the fuzzy inference system to determine the tip for the following inputs:\nInput 1:\n- service = 6\n- food = 6\nInput 2:\n- service = 1\n- food = 2\n", "contributor": "Xingang Guo" }, { "task_id": "XW_03", "query_token_num": 1261, "Engineering Domain": "Operating System Design", "prompt": "## Task Description\nIn this task, you will be provided with a filesystem image. You are required to develop a separate program that implements a filesystem operation (e.g., create, read, update, delete)\u2014to modify the corresponding sections of that image. Your objective is to ensure that each program correctly performs its assigned operation on the intended part of the filesystem image while preserving its overall integrity.\n\nHere is the class definition for your reference:\n\nfrom dataclasses import dataclass, field\nfrom typing import List, Dict, Optional\n\n@dataclass\nclass SuperBlock:\n \"\"\"File system superblock, stores metadata.\"\"\"\n block_size: int # Size of each block (bytes)\n total_blocks: int # Total number of blocks\n inode_count: int # Total number of inodes\n free_block_bitmap: List[bool] # Free block bitmap, True = free\n\n@dataclass\nclass Inode:\n \"\"\"Inode structure, stores file/directory metadata.\"\"\"\n ino: int # Inode number\n is_dir: bool # Whether this inode is a directory\n size: int # File size (bytes)\n direct_blocks: List[int] # List of direct block indices\n # Optional: add indirect block pointers, multi-level indexing, permissions, timestamps, etc.\n\n@dataclass\nclass DirEntry:\n \"\"\"Directory entry: maps a filename to an inode.\"\"\"\n name: str\n inode: int\n\n@dataclass\nclass FileSystemImage:\n \"\"\"Complete file system image structure.\"\"\"\n superblock: SuperBlock\n inodes: Dict[int, Inode] = field(default_factory=dict)\n # Directory tree: inode -> list of entries in that directory; valid only for is_dir=True inodes\n directories: Dict[int, List[DirEntry]] = field(default_factory=dict)\n # Data block storage area: index corresponds to block number, content is bytes\n data_blocks: List[Optional[bytes]] = field(default_factory=list)\n\n def __post_init__(self):\n # Initialize data block storage area\n if not self.data_blocks:\n self.data_blocks = [None] * self.superblock.total_blocks\n\n def allocate_block(self) -> int:\n \"\"\"Allocate a block from the free bitmap and return its index; raise if none available.\"\"\"\n for idx, free in enumerate(self.superblock.free_block_bitmap):\n if free:\n self.superblock.free_block_bitmap[idx] = False\n self.data_blocks[idx] = b'' # Initialize with empty content\n return idx\n raise RuntimeError(\"No free blocks available\")\n\n def free_block(self, block_idx: int):\n \"\"\"Free the specified block index.\"\"\"\n if 0 <= block_idx < self.superblock.total_blocks:\n self.superblock.free_block_bitmap[block_idx] = True\n self.data_blocks[block_idx] = None\n else:\n raise IndexError(\"Block index out of range\")\n\n def create_inode(self, is_dir: bool) -> Inode:\n \"\"\"Create a new inode and return it.\"\"\"\n new_ino = len(self.inodes) + 1\n if new_ino > self.superblock.inode_count:\n raise RuntimeError(\"No free inodes\")\n inode = Inode(\n ino=new_ino,\n is_dir=is_dir,\n size=0,\n direct_blocks=[]\n )\n self.inodes[new_ino] = inode\n if is_dir:\n self.directories[new_ino] = []\n return inode\n\n def add_dir_entry(self, dir_ino: int, name: str, inode: int):\n \"\"\"Add a directory entry to the directory with inode dir_ino.\"\"\"\n if dir_ino not in self.directories:\n raise RuntimeError(\"Not a directory inode\")\n self.directories[dir_ino].append(DirEntry(name=name, inode=inode))\n\n\n\n### Task\ndef create(fs_img: FileSystemImage, path: str, is_dir: bool = False) -> FileSystemImage:\n \"\"\"\n Create a new empty file or directory at the given path within the FileSystemImage.\n Return the updated FileSystemImage so that its inodes and directory entries\n can be inspected for correctness.\n\n Parameters:\n - fs_img: the FileSystemImage instance containing inodes, directories,\n and data blocks.\n - path: an absolute or relative path where the new file or directory\n should be created.\n - is_dir: if True, create a directory; if False, create a regular file.\n\n Returns:\n - The same FileSystemImage instance (`fs_img`), mutated to include the\n new entry\u2019s inode and parent directory mapping.\n\n Behavior:\n 1. Split `path` into `parent_path` and `name`:\n - e.g. `/a/b/c` \u2192 `parent_path='/a/b'`, `name='c'`.\n 2. Look up `parent_path` in `fs_img`:\n - If not found, raise `FileNotFoundError`.\n - If found but not a directory, raise `NotADirectoryError`.\n 3. In the parent directory\u2019s entries, if `name` already exists\n (file or directory), raise `FileExistsError`.\n 4. Allocate a new inode:\n ```python\n new_inode = fs_img.create_inode(is_dir=is_dir)\n ```\n 5. If creating a directory, initialize its child entry list\n (already handled by `create_inode`).\n 6. Add a directory entry in the parent:\n ```python\n fs_img.add_dir_entry(parent_inode.ino, name, new_inode.ino)\n ```\n 7. Return the mutated `fs_img`.\n\n Exceptions:\n - `FileNotFoundError` if the parent path does not exist.\n - `NotADirectoryError` if the parent exists but is not a directory.\n - `FileExistsError` if an entry with the same `name` already exists.\n \"\"\"\n # Your implementation here\u2026", "contributor": "Licheng Xu, Jinwen Wang" }, { "task_id": "XG_01", "query_token_num": 775, "Engineering Domain": "Control Design", "prompt": "In this task, you will use MATLAB\u2019s Robust Control Toolbox, specifically the loopsyn function, to design a stabilizing controller for an aircraft system. \n## Aircraft Model\nThe aircraft is modeled by the following state-space system:\nA = \\begin{bmatrix}\n-2.2567 \\times 10^{-2} & -3.6617 \\times 10^{1} & -1.8897 \\times 10^{1} & -3.2090 \\times 10^{1} & 3.2509 & -7.6257 \\times 10^{-1} \\\\\n9.2572 \\times 10^{-5} & -1.8997 & 9.8312 \\times 10^{-1} & -7.2562 \\times 10^{-4} & -1.7080 \\times 10^{-1} & -4.9652 \\times 10^{-3} \\\\\n1.2338 \\times 10^{-2} & 1.1720 \\times 10^{1} & -2.6316 & 8.7582 \\times 10^{-4} & -3.1604 \\times 10^{1} & 2.2396 \\times 10^{1} \\\\\n0 & 0 & 1.0000 & 0 & 0 & 0 \\\\\n0 & 0 & 0 & 0 & -3.0000 \\times 10^{1} & 0 \\\\\n0 & 0 & 0 & 0 & 0 & -3.0000 \\times 10^{1}\n\\end{bmatrix}\nB = \\begin{bmatrix}\n0 & 0 \\\\\n0 & 0 \\\\\n0 & 0 \\\\\n0 & 0 \\\\\n30 & 0 \\\\\n0 & 30\n\\end{bmatrix}\nC = \\begin{bmatrix}\n0 & 1 & 0 & 0 & 0 & 0 \\\\\n0 & 0 & 0 & 1 & 0 & 0\n\\end{bmatrix}\nD = \\begin{bmatrix}\n0 & 0 \\\\\n0 & 0\n\\end{bmatrix}\n\n## Instructions\n### Step 1: Design a target loop shape\nTo use loopsyn design a stabilizing controller, you will first need to provide a target loop shape. Consider a desired loop shape with:\n- crossover frequency of 8 rad/s\n- has low gain at high frequencies for robustness, and high gain at low frequencies for performance\n- consider the transfer function 8/s as an example of a target loop shape\nYour first task is to specify the transfer function of the desired loop shape by providing its numerator and denominator coefficients.\n### Step 2: Use *loopsyn* to Design a Controller\nUsing the target loop shape, design a stabilizing controller K via loopsyn. Your design must ensure the **closed-loop system achieves at least a 0.05 disk margin** and **has a performance gamma less than 1**. Here gamma is a performance measure of how well the loop shape with proposed controller matches the desired loop shape. Values of gamma near or below 1 indicate that G*K is close to Gd.\nThe loopsyn function requires the following inputs:\n- G: dynamical system to be controlled (this will be the aircraft model)\n- Gd: desired loop shape (this will be determined by the num and den provided in the previous step)\n- alpha: a factor (0 < alpha < 1) to balance between performance and robustness\nThere will be an evaluation step to check if the closed-loop system achieves at least 0.05 disk margin.\n\n", "contributor": "Xingang Guo" }, { "task_id": "ZC_01", "query_token_num": 646, "Engineering Domain": "Control Design", "prompt": "## Task Description\nConsider the following continuous\u2011time uncertain system:\n\\[\n\\dot{x}(t) = \\bigl(A_0 + \\Delta A\\bigr)\\,x(t) + B_1\\,w(t) + B_2\\,u(t),\n\\]\n\\[\nz(t) = C_1\\,x(t) + D_{11}\\,w(t) + D_{12}\\,u(t),\n\\]\n\\[\ny(t) = C_2\\,x(t) + D_{21}\\,w(t) + D_{22}\\,u(t),\n\\]\nwhere \\(x\\in\\mathbb{R}^4\\), \\(u\\in\\mathbb{R}\\), \\(w\\in\\mathbb{R}\\), and \\(z,y\\in\\mathbb{R}\\). The nominal matrices are\n\\[\nA_0 = \\begin{bmatrix}\n0 & 1 & 0 & 0\\\\\n0 & 0 & 1 & 0\\\\\n0 & 0 & 0 & 1\\\\\n-5 & -4 & -3 & -2\n\\end{bmatrix},\\quad\nB_1 = \\begin{bmatrix}0\\\\0\\\\0\\\\1\\end{bmatrix},\\quad\nB_2 = \\begin{bmatrix}0\\\\0\\\\1\\\\0\\end{bmatrix},\n\\]\n\\[\nC_1 = \\begin{bmatrix}1 & 0 & 0 & 0\\end{bmatrix},\\quad\nD_{11} = 0,\\quad\nD_{12} = 0,\n\\]\n\\[\nC_2 = \\begin{bmatrix}0 & 0 & 1 & 0\\end{bmatrix},\\quad\nD_{21} = 0,\\quad\nD_{22} = 0.\n\\]\n\nThe uncertainties are\n\\[\n\\Delta A \\in \\mathrm{Co}\\{\\,0.2\\,I_4,\\;-0.2\\,I_4\\}, \n\\qquad\nw(s) = \\Delta_{\\mathrm{dyn}}(s)\\,z(s),\\;\\|\\Delta_{\\mathrm{dyn}}\\|_\\infty \\le 1.\n\\]\n\n### Task\u00a0\nBy solving a SDP to meet the H-infinity performance, design a static state\u2011feedback gain \\(K\\in\\mathbb{R}^{1\\times 4}\\) such that the closed\u2011loop system satisfies:\n\n1. Robust stability: for all \\(\\Delta A \\in \\mathrm{Co}\\{\\,\\pm0.2\\,I_4\\}\\) and any \\(\\Delta_{\\mathrm{dyn}}\\) with \\(\\|\\Delta_{\\mathrm{dyn}}\\|_\\infty \\le 1\\), the closed\u2011loop matrix is Hurwitz.\n\n2. \\(\\mathcal{H}_\\infty\\) performance: the transfer function \\(T_{zw}(s)\\) satisfies \\(\\|T_{zw}\\|_\\infty < 0.3\\).\n", "contributor": "Zichen Wang" }, { "task_id": "KV_03", "query_token_num": 707, "Engineering Domain": "Control Design", "prompt": "Switched Capacitor Battery Balancing System \u2013 Design Challenge Task\n\nTask Title:\nFill-in-the-Blank System Architecture Inference \u2013 Battery CC-CV Interface\n\nSystem Description:\nThe system balances a 3-cell lithium-ion battery pack using switched-capacitor charge redistribution. The system includes six switches (S1\u2013S6), two capacitors, and a Battery CC-CV block that can both inject and extract current depending on the system\u2019s state-of-charge (SOC). The current flow is dynamically controlled based on SOC feedback, voltage readings, and a relay mechanism to toggle modes. A PI controller regulates behavior during charging and discharging. The goal is to maintain safe and efficient balancing under varying SOC conditions using only local cell information and logic-driven control blocks.\n\nTechnical Specifications:\n- Battery: 3 Li-ion cells in series, each 27 Ah\n- Capacitors: 0.5 F each (2 total)\n- Switches: 6 total; closed resistance = 0.00734 \u03a9, open conductance = 1e-5 S\n- Switching control: 50% duty cycle, Tper = 0.006 s\n- Initial SOCs: Cell 1 = 0.8, Cell 2 = 0.75, Cell 3 = 0.7\n- Battery CC-CV behavior with max voltage = 4.1 V\n- PI Controller: Proportional gain = 100, Integral gain = 10\n- Feedback channels include SOC and voltage monitoring through ZOH blocks\n- Relay logic is used to switch between injecting and withdrawing current\n- Final current output is passed through a control logic layer before being applied to the Battery CC-CV block\n\nDesign Task:\nYou are given a redacted system diagram with 9 missing functional blocks labeled A through J (excluding H, which is not used). Each label corresponds to a required Simulink or logic block that enables correct operation of the system. Your task is to infer and name the correct block for each label based only on your understanding of the system architecture and its operational requirements.\n\nTo assist, here are examples of Simulink or logical block types that may appear somewhere in the system (not in any particular order, and not mapped to any specific label):\n\n- max\n- chargingenabled\n- cellvoltage\n- currentwhencharging\n- currentwhendischarging\n- gain\n- constant\n- relay\n- current output port\n\nYou must **not assume the ordering** or directly match these terms to any label. Instead, you must analyze the described system behavior and infer the correct Simulink block for each missing label. Do not include any explanations, justifications, or descriptions \u2014 only provide the mapping.\n\nExpected Output Format:\nReturn a dictionary in the following format, using strings that correspond to valid Simulink block types or logic expressions (no comments, no extra spaces, no Markdown, no special control characters):\n\n{\n \"A\": \"\",\n \"B\": \"\",\n \"C\": \"\",\n \"D\": \"\",\n \"E\": \"\",\n \"F\": \"\",\n \"G\": \"\",\n \"I\": \"\",\n \"J\": \"\"\n}\n", "contributor": "Kojo Vandyck" }, { "task_id": "AM_03", "query_token_num": 1159, "Engineering Domain": "Robotics", "prompt": "## Task Description\nYour task is to navigate a robot around static obstacles and walking pedestrians. \nThe map is a 30 by 30 grid. The origin, i.e. (x,y) = (0,0), is at the bottom left of the grid.\nx-axis grows to the right and y-axis grows upwards.\n\nThere are three static rectangular obstacles formatted in ((x1, y1), (x2, y2)) that describe the\nbottom left and top right corners of the obstacle box:\n[\n ((5, 0), (7, 15)),\n ((10,20), (20,30)),\n ((15, 5), (30, 10))\n]\n\nThere are pedestrians walking around and their trajectory is \nstored as a list of tuples (t, x, y), where t is number of seconds from 0 to 29, \nand x and y are the coordinates of the bottom left corner in the grid.\nThe pedestrians and robots are both 2 by 2 in size.\nTheir paths are as follows:\n'ped1': [ (0,1,1),\n (1,1,2),\n (2,1,4),\n (3,1,6),\n (4,1,7),\n (5,1,9),\n (6,1,11),\n (7,2,13),\n (8,2,14),\n (9,3,16),\n (10,6,16),\n (11,7,15),\n (12,8,13),\n (13,9,12),\n (14,10,11),\n (15,11,11),\n (16,12,11),\n (17,13,11),\n (18,14,11),\n (19,15,11),\n (20,16,11),\n (21,17,11),\n (22,18,11),\n (23,19,11),\n (24,20,11),\n (25,21,11),\n (26,22,11),\n (27,23,11),\n (28,24,11),\n (29,25,11)\n ], \n'ped2': [ (0,25,28),\n (1,25,28),\n (2,25,26),\n (3,25,24),\n (4,25,22),\n (5,25,20),\n (6,25,18),\n (7,25,16),\n (8,25,14),\n (9,24,12),\n (10,22,12),\n (11,20,12),\n (12,19,12),\n (13,17,12),\n (14,16,12),\n (15,16,12),\n (16,15,13),\n (17,14,15),\n (18,12,16),\n (19,10,16),\n (20,8,16),\n (21,6,16),\n (22,5,16),\n (23,4,16),\n (24,4,17),\n (25,4,18),\n (26,4,19),\n (27,4,20),\n (28,4,21),\n (29,4,22)\n ], \n'ped3': [ (0, 25, 2),\n (1, 24, 2),\n (2, 23, 2),\n (3, 22, 2),\n (4, 21, 2),\n (5, 20, 2),\n (6, 19, 2),\n (7, 18, 2),\n (8, 17, 2),\n (9, 16, 2),\n (10,15,2),\n (11,14,2),\n (12,13,2),\n (13,12,2),\n (14,11,2),\n (15,10,2),\n (16,9,3),\n (17,8,4),\n (18,8,6),\n (19,8,8),\n (20,8,10),\n (21,8,12),\n (22,8,14),\n (23,8,16),\n (24,8,18),\n (25,8,20),\n (26,8,22),\n (27,8,24),\n (28,8,26),\n (29,8,28)\n ]\n\nThe robot must start at (17, 2), and hit goals A and B one after another in any order. \nGoal A is positioned at (5, 20) and Goal B at (25, 24).\n\nYou must provide a list of tuples in (t,x,y) format that is free of collisions from\nboth pedestrians and static rectangular obstacles. \n\nThe speed limit of robot in either x and y direction is 2 between each time step.\nThis means that the robot can move in the x direction 2 steps and y direction 2 steps and be ok.\n\nYou will be evaluated on the following:\n- Starting position at t=0 is correct\n- Hits Goal A at some point in time\n- Hits Goal B at some point in time\n- No collision between robot and static obstacles\n- No collision between robot and walking pedestrians\n- Does not exceed top speed", "contributor": "Asher Mai" }, { "task_id": "YJ_02", "query_token_num": 240, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nIn this task, you are required to perform a topology optimization to design an optimal cantilever beam structure that minimizes the compliance (maximizes stiffness) under a given volume constraint. The beam is fixed on the left edge and subjected to a downward load at the bottom right corner. The design domain is discretized into a uniform rectangular grid, and material is distributed in this domain to achieve the best structural performance.\n\n## Input Parameters\n\n### Material properties\nyoung = 1\npoisson = 0.3\n\n#### Constraints\nEmin = 1e-9\nvolfrac = 0.4\nmove = 1\n\n#### Mesh dimensions\nnelx = 10\nnely = 10\n\n## Task\nUse the input parameters to set up a topology optimization problem for a cantilever beam. Your task is to:\n\n- Simulate the optimization process.\n\n- Ensure that the design adheres to the specified volume fraction.\n\n- Output the final material distribution, y_hat, and report the minimal compliance value, named C_y_hat, obtained after convergence.\n\n- y_hat must be a matrix where each element ranges from 0 to 1 inclusively. \n", "contributor": "Yilan Jiang" }, { "task_id": "YF_01", "query_token_num": 483, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nIn this task, you are required to determine a suitable **thickness (`Th`)** for an L-shaped steel beam, which will be subjected to a horizontal load and evaluated using 3D structural simulation in MATLAB\u2019s PDE Toolbox.\n\nThe L-shaped beam is formed by extruding a 2D profile composed of a horizontal and vertical segment connected by a fillet arc. The extrusion occurs in the z-direction to produce a 3D object.\n\nYou are given the following fixed parameters:\n\n- `Lh = 50` mm (Horizontal length)\n- `Lv = 80` mm (Vertical length)\n- `Rf = 20` mm (Fillet radius)\n- `Height = 50` mm (Extrusion height)\n- External surface traction: `[10, -20, 0]` N/mm\u00b2 applied to Face ID = 5\n- Face ID = 4 is fixed\n- Material properties:\n - Young\u2019s modulus: 21,000 MPa\n - Poisson\u2019s ratio: 0.3\n\nThe beam will be evaluated using a static linear elasticity model. The performance criterion is that the **maximum displacement in the z-direction (`uz`) must be less than 0.1 mm**.\nThe score depends on the ratio of the maximum measured displacement to the allowable threshold. If that ratio falls between seventy percent and ninety percent, the beam earns the full 100 points. If the ratio is below seventy percent, partial credit is awarded in direct proportion to how close it is to seventy-percent (with zero displacement scoring zero and seventy-percent scoring 100). If the ratio lies between ninety percent and one hundred percent, points are deducted in proportion to how far it exceeds ninety percent (dropping from 100 at ninety percent down to zero at the full threshold). Any ratio below zero or above one hundred percent results in a score of zero.\n---\n\n### Task\n\nYour task is to:\n- Propose a structurally sound value for `Th` (thickness of the beam, in mm), you need to numerically compute the Th, not reply with your previous experience.\n- Provide a brief justification for your choice of thickness, considering stiffness, loading, and geometric constraints, you must give the computation process\n\nYou do **not** need to evaluate the displacement yourself. The simulation and evaluation will be done separately.\n", "contributor": "Yufan Zhang" }, { "task_id": "YF_06", "query_token_num": 431, "Engineering Domain": "Structure Design", "prompt": "## Task Description\nIn this task, you are required to determine a suitable thickness t (in mm) for a 3D rectangular steel plate of dimensions 1000\u00d7500\u00d7t mm, loaded by a uniform transverse pressure and with all four side faces fixed. The evaluation will be performed via MATLAB\u2019s PDE Toolbox.\nYou are given the following fixed parameters:\n\nFixed parameters:\nGeometry:\n - Length L=1000 mm\n - Width W=500 mm\n - Thickness t mm (design variable)\n\n- Material properties:\n - Young\u2019s modulus: 210,000 MPa\n - Poisson\u2019s ratio: 0.3\n - Density 7850kg/m^3\n- boundary condition\n All four side faces (the faces at X=0, X=L, Y=0, Y=W) are fixed.\n- loading \n Uniform pressure p= 2 N/mm\u00b2 on the top face (Z=t).\n\nPerformance criterion:\nThe maximum nodal displacement must satisfy \u03b4 max < 0.5 mm\nThe score depends on the ratio of the maximum measured deflection to the allowable threshold. If that ratio falls between seventy percent and ninety percent, the structure earns the full 100 points. If the ratio is below seventy percent, partial credit is awarded in direct proportion to how close it is to seventy-percent (with zero displacement scoring zero and seventy-percent scoring 100). If the ratio lies between ninety percent and one hundred percent, points are deducted in proportion to how far it exceeds ninety percent (dropping from 100 at ninety percent down to zero at the full threshold). Any ratio below zero or above one hundred percent results in a score of zero.\n---\n\n### Task\n\nYour task is to:\n- a numerical value of plate thickness t (in mm) that ensures 1.0 mm under the given load and boundary conditions.\n- justify your choice of t, considering the plate\u2019s bending stiffness, the applied pressure, and the geometric proportions. You need to compute the result\n\nYou do **not** need to evaluate the angle yourself. The simulation and evaluation will be done separately.\n\n", "contributor": "Yufan Zhang" }, { "task_id": "qjlim2_02", "query_token_num": 270, "Engineering Domain": "Signal Processing", "prompt": "## Background\n\nStrip dipole antennas are simple, efficient, and widely used in wireless communication systems for their broad bandwidth and omnidirectional radiation characteristics in the azimuth plane.\n\nIn this task, you are to design a strip dipole antenna that meets the specified performance objectives and constraints outlined below.\n\nThe dipole is centered at the origin and aligned along the x-axis, with its arms extending symmetrically in the \u00b1x directions. The feed point lies at the center of the dipole, located in the x-y plane. The antenna is made of highly conductive material such as copper and is radiating in free space.\n\n## Task Objective and Constraints\n\nYour task is to design a Strip dipole antenna that meets the following specifications:\n\n- Resonant Frequency: 3 GHz (S11 <= \u201310 dB)\n- Bandwidth: >= 100 MHz\n- Gain: >= 2 dBi\n- Space Constraint [ Length \u00d7 Width ]: <= 100 mm \u00d7 100 mm\n\n## Design Inputs\n\nDetermine the optimal design parameters to satisfy the task objectives:\n\n- Length of Metallic Patch in mm: length_mm\n- Width of Metallic Patch in mm: width_mm\n- Confidence of your design: confidence\n\n## Additional Note\n\nThe width of the antenna should generally be at most 1/10 of the length of the antenna.\n\n", "contributor": "Qi Jian Lim\n" }, { "task_id": "YJ_03", "query_token_num": 343, "Engineering Domain": "Structure Design", "prompt": "## Task Description\n\nThis optimisation problem aims to minimise the Mode I stress-intensity factor (SIF) at the crack tip, thereby maximising fatigue-crack-propagation life and enhancing damage tolerance of the structural component. Material is selectively distributed within the design domain so that the resulting layout reduces the SIF while respecting a prescribed material-usage limit.\n\n## Input Parameters\n\n### Material properties\nyoung = 1 # Young\u2019s modulus (normalised)\npoisson = 0.3 # Poisson\u2019s ratio\next_stiff = 0.0 # Stiffness of surrounding \u201cvoid\u201d (external) material\n\n### Constraints\nEmin = 1e-9 # Minimum ersatz stiffness for void elements\nvolfrac = 1.1 # Maximum allowable volume fraction\nmove = 0.25 # Maximum density change per iteration\n\n### Mesh definition\nnelx = 10 # Number of finite-element columns (x-direction)\nnely = int(np.round(nelx/1.25*1.2/2))\ncrack_length= 2 # Initial edge-crack length in elements\n\n## Task\nUse the input parameters to set up a topology optimization problem to minimize the stress-intensity factor. Your task is to:\n\n- Simulate the optimization process.\n\n- Ensure that the design adheres to the specified material properties, constraints, and mesh definitions.\n\n- Output the final material distribution, y_hat, and report the minimal stress-intensity factor, named K_y_hat, obtained after convergence.\n\n- y_hat must be a matrix where each element ranges from 0 to 1 inclusively. \n", "contributor": "Yilan Jiang" }, { "task_id": "DL_02", "query_token_num": 3399, "Engineering Domain": "Computer Architecture Design", "prompt": "# Solid-State Drive Design Task - Parmeter Set with Constraints\n\nIn this problem, you will finalize a set of Solid-State Drive (SSD) designs that meet the performance requirements for a specific workload type. In this problem, you need to identify an optimized parameter set that satisfy the given performance criteria under given constraints (e.g., the capacity constriants need the multiple of several parameters to stay in a given range).\n\n## Background\n\n![fig_ssd_arch](./images/ssdhardware.png)\n\nThe internal architecture of a typical SSD is presented in the above Figure. An SSD consists of five major components: a set of flash memory packages, an SSD controller having embedded processors like ARM, off-chip DRAM (SSD DRAM), flash controllers, and the I/O interface that includes SATA and NVMe protocols. The flash packages are organized in a hierarchical manner. Each SSD has multiple channels, and each channel can process read/write commands independently. Each channel is shared by multiple flash packages. Each package has multiple flash chips. Within each chip, there are multiple planes. Each plane includes multiple flash blocks, and each block has multiple flash pages. The page size varies in different SSDs. When a free flash page is written once, that page is no longer available for future writes until that page is erased. However, erase operation is expensive and performed at block granularity. As each flash block has limited endurance, it is important for blocks to age uniformly (i.e., wear leveling). Modern SSD controllers employ out-of-place write, GC, and wear leveling to overcome these shortcomings and maintain indirections for the address translation in their flash translation layer (FTL).\n\nIn this problem, our aim is to design SSDs that allow developers to customize SSD hardware according to the application needs.\n\n## Task Description\n\nSSD customers typically evaluate SSD performance using key metrics including I/O throughput, average latency and tail latency. In this section, you should optimize the given SSD configuration by tuning only the layout related parameters (\"Overprovisioning_Ratio\", \"Flash_Channel_Count\", \"Chip_No_Per_Channel\", \"Die_No_Per_Chip\", \"Plane_No_Per_Die\",\n \"Block_No_Per_Plane\", \"Page_No_Per_Block\"). You should identify a set of these parameter that satisfy the capacity constraint (The total usable capacity, not considering the over provisioning, should be around 2TB, specifically, 1.7TB - 2.1TB) and reach the performance requirements. If the requirement cannot be reached, please answer \"impossible\" instead of the final parameter value. Please always provide your reasoning.\n\n### Formal Problem Definition\n\nGiven a parameter set $S$ and a workload set $W$, tune the parameters (\"Overprovisioning_Ratio\", \"Flash_Channel_Count\", \"Chip_No_Per_Channel\", \"Die_No_Per_Chip\", \"Plane_No_Per_Die\",\n \"Block_No_Per_Plane\", \"Page_No_Per_Block\") $s \\in S$ that affects the I/O throughput, average latency or both of them for each workload $w \\in W$. Specifically, address the following question:\n\nIf we want to get 20\\% performance improvement on I/O throughput or on average latency comparing to the baseline configuration (see next section), while also satisfy the capacity constraint (The total capacity, not considering the over provisioning, should be around 2TB, specifically, 1.7TB - 2.1TB) how should we tune these parameters? If this is impossible, please answer \"impossible\" instead of providing the number and explain why. Note that the correlation between performance and parameter values are usurally not linear.\n\n### Configuration Set\n\nPlease provide answer for each parameter listed in the table below. The third column of this table listed the baseline configuration (Samsung 983 DCT 1.92TB SSD). We provide typical values for each parameter, the tuned parameter should follow the general trend in the listed parameters (e.g., number of channels should be descrete numbers). \n\nFor convenience of reasoning, we provide all the parameters for the baseline. Please only tune the speciftied parameters (\"Overprovisioning_Ratio\", \"Flash_Channel_Count\", \"Chip_No_Per_Channel\", \"Die_No_Per_Chip\", \"Plane_No_Per_Die\",\n \"Block_No_Per_Plane\", \"Page_No_Per_Block\") and the tuning range is specified in the listed parameters.\n\n| Parameter Name | Description | Baseline |\n|:--------------------------|:----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:-----------|\n| PCIe_Lane_Bandwidth | The PCIe bandwidth per lane in GB/s. Typical values: 0.5, 1.0, 2.0, 4.0, 8.0. | 8.0 |\n| PCIe_Lane_Count | The number of PCIe lanes. Typical values: 1, 2, 4, 8, 16. | 4 |\n| HostInterface_Type | The type of host interface. Typical values: NVME, SATA. | NVME |\n| IO_Queue_Depth | the length of the host-side I/O queue. Typical values: 4, 8, 16, 32, 64, 128, 256. | 16 |\n| Queue_Fetch_Size | The maximum number of requests that can be served in parallel in a queue. Typical values: 4, 8, 16, 32, 64, 128, 256. | 16 |\n| Data_Cache_Capacity | The size of the DRAM Data Cache in bytes. Typical values:100663296, 167772160, 234881024, 301989888, 369098752, 436207616. | 536870912 |\n| Data_Cache_DRAM_Row_Size | The size of the DRAM rows in bytes. values:1024, 2048, 4096, 8192, 16384. | 4096 |\n| Data_Cache_DRAM_Data_Rate | The DRAM data transfer rate in MT/s. Typical values:100, 200, 400, 800, 1600, 2133, 2400, 2666, 3200. | 800 |\n| Data_Cache_DRAM_Data_Burst_Size | The number of bytes that are transferred in one DRAM burst (depends on the number of DRAM chips). Typical values: 1, 2, 4, 8, 16. | 8 |\n| Data_Cache_DRAM_tRCD | The value of the timing parameter tRCD in nanoseconds used to access DRAM in the data cache. Typical values:4, 7, 14, 21, 28 | 9 |\n| Data_Cache_DRAM_tCL | The value of the timing parameter tCL in nanoseconds used to access DRAM in the data cache. Typical values:4, 7, 14, 21, 28 | 9 |\n| Data_Cache_DRAM_tRP | The value of the timing parameter tRP in nanoseconds used to access DRAM in the data cache. Typical values:4, 7, 14, 21, 28 | 9 |\n| Address_Mapping | The logical-to-physical address mapping policy implemented in the Flash Translation Layer (FTL).Typical values: PAGE_LEVEL, HYBRID | PAGE_LEVEL |\n| CMT_Capacity | The size of the SRAM/DRAM space in bytes used to cache the address mapping table (Cached Mapping Table). Typical values: 67108864, 134217728, 201326592, 268435456, 335544320, 402653184, 469762048, 536870912 | 268435456 |\n| Plane_Allocation_Scheme | The scheme for plane allocation priorities (C-Channel, W-Way, D-Die, P-Plane). Typical values: CWDP, CWPD, CDWP, CDPW, CPWD, CPDW, WCDP, WCPD, WDCP, WDPC, WPCD, WPDC, DCWP, DCPW, DWCP, DWPC, DPCW, DPWC, PCWD, PCDW, PWCD, PWDC, PDCW, PDWC | CWDP |\n| Overprovisioning_Ratio | The ratio of reserved storage space with respect to the available flash storage capacity. Typical values:0.126, 0.2, 0.3, 0.4, 0.5 | 0.126 |\n| GC_Exect_Threshold | The threshold for starting Garbage Collection (GC). Typical values: 0.1, 0.15, 0.2, 0.25, 0.3 | 0.05 |\n| GC_Block_Selection_Policy | The GC block selection policy. Typical values: GREEDY, RGA, RANDOM, RANDOM P, RANDOM PP, FIFO | GREEDY |\n| Use_Copyback_for_GC | Whether GC Copyback is enabled. Typical values: true, false | false |\n| Preemptible_GC_Enabled | The toggle to enable pre-emptible GC. Typical values:true, false | true |\n| GC_Hard_Threshold | The threshold to stop pre-emptible GC execution. Typical values:0.1, 0.15, 0.2, 0.25, 0.3 | 1 |\n| Dynamic_Wearleveling_Enabled | The toggle to enable dynamic wear-leveling. Typical values: true, false | true |\n| Static_Wearleveling_Enabled | The toggle to enable static wear-leveling. Typical values: true, false | true |\n| Static_Wearleveling_Threshold | The threshold for starting static wear-leveling. Typical values: 50, 60, 70, 80, 90, 100 | 100 |\n| Preferred_suspend_erase_time_for_read | The reasonable time to suspend an ongoing flash erase operation in favor of a recently-queued read operation. Typical values:100000, 200000, 300000, 400000, 500000 | 100000 |\n| Preferred_suspend_erase_time_for_write | The reasonable time to suspend an ongoing flash erase operation in favor of a recently-queued read operation. Typical values:100000, 200000, 300000, 400000, 500000 | 100000 |\n| Preferred_suspend_write_time_for_read | The reasonable time to suspend an ongoing flash erase operation in favor of a recently-queued program operation. Typical values:100000, 200000, 300000, 400000, 500000 | 100000 |\n| Flash_Channel_Count | The number of flash channels in the SSD back end. Typical values:4,6,8,10,12,14,16,18,20 | 8 |\n| Flash_Channel_Width | The width of each flash channel in byte. Typical values:1, 2, 4, 8 | 8 |\n| Channel_Transfer_Rate | The transfer rate of flash channels in the SSD back end in MT/s. Typical values:100, 200, 333, 800 | 800 |\n| Chip_No_Per_Channel | The number of flash chips attached to each channel in the SSD back end. Typical values:2, 4, 8, 12, 16, 20 | 4 |\n| Flash_Technology | Typical values:TLC, MLC, SLC | MLC |\n| CMD_Suspension_Support | The type of suspend command support by flash chips. Typical values:NONE, PROGRAM, PROGRAM ERASE, ERASE | None |\n| Page_Read_Latency_LSB | The latency of reading LSB bits of flash memory cells in nanoseconds. Typical values:25000, 50000, 59975, 75000, 100000 | 5000 |\n| Page_Read_Latency_CSB | Similar as above. Typical values:0, 25000, 50000, 75000, 100000 | 0 |\n| Page_Read_Latency_MSB | Similar as above. Typical values:25000, 50000, 75000, 100000, 104956 | 10000 |\n| Page_Program_Latency_LSB | Similar as above. Typical values:82062, 250000, 500000, 750000, 1000000 | 30000 |\n| Page_Program_Latency_CSB | Similar as above. Typical values:0, 250000, 500000, 750000, 1000000 | 0 |\n| Page_Program_Latency_MSB | Similar as above. Typical values:250000, 500000, 750000, 1000000, 1250000, 1500000, 1750000, 2000000, 2250000 | 800000 |\n| Block_Erase_Latency | The latency of erasing a flash block in nanoseconds.Typical values:3000000, 3800000 | 1000000 |\n| Block_PE_Cycles_Limit | The PE limit of each flash block. Typical values:10000, 20000, 30000, 40000, 50000 | 10000 |\n| Suspend_Erase_Time | The time taken to suspend an ongoing erase operation in nanoseconds.Typical values:700000, 800000, 900000, 1000000, 1100000 | 700000 |\n| Suspend_Program_Time | The time taken to suspend an ongoing program operation in nanoseconds. Typical values:60000, 70000, 80000, 90000, 100000 | 100000 |\n| Die_No_Per_Chip | The number of dies in each flash chip. Typical values:4,6,8, 10, 12, 14, 16, 18, 20 | 8 |\n| Plane_No_Per_Die | The number of planes in each die. Typical values:2,4,6,8,10 | 2 |\n| Block_No_Per_Plane | The number of flash blocks in each plane. Typical values:512,1024,1364, 2048, 4096, 8192 | 1364 |\n| Page_No_Per_Block | The number of physical pages in each flash block. Typical values:512, 768, 1024, 2048, 4096 | 768 |\n| Page_Capacity | The size of each physical flash page in bytes. Typical values:4096 | 4096 |\n| Page_Metadat_Capacity | The size of the metadata area of each physical flash page in bytes. Typical values:224, 448, 672, 896, 1120 | 448 |\n\n### Target Workload Set\n\nPlease provide answer for each workload mentioned below:\n\n#### Real-world Workloads\n\nThese workloads represents typical storage-intensive application patterns.\n\n| **Workload Category** | **Description** |\n|-----------------------|-----------------|\n| Big Data Analytics | MapReduce workloads running in data centers. |\n| Cloud Storage | Cloud storage workloads running in data centers. |\n| Key-Value Store | YCSB benchmarks are executed against RocksDB. |\n| Maps | Maps workloads running on enterprise servers. |\n| Database | TPCC/TPCH executed against Windows SQL Server. |\n| WebSearch | WebSearch services trace from UMassTraceRepository. |\n| Advertisement | Advertisement workloads running on servers. |\n\n## Response Instruction\n\nYour response should be structured in the following format:\n\nFor each workload, create a workload_result class for the tuning result. In each workload_result, you should specify the parameters based on the values we provided.\n\nPlease strictly follow the format, do not include any other text or comments.\n\n\n\n", "contributor": "Daixuan Li" }, { "task_id": "AM_02", "query_token_num": 938, "Engineering Domain": "Robotics", "prompt": "## Task Description\nYour task is to navigate two robots around static obstacles and walking pedestrians. \nThe map is a 30 by 30 grid. The origin, i.e. (x,y) = (0,0), is at the bottom left of the grid.\nx-axis grows to the right and y-axis grows upwards.\n\nThere are three static obstacles formatted in ((x1, y1), (x2, y2)) that describe the\nbottom left and top right corners of the rectangular obstacles:\n\nTHe four corners that define the static obstacles are:\n[\n ((5, 0), (7, 15)),\n ((10,20), (20,30)),\n ((15, 5), (30, 10))\n]\n\nThere are pedestrians walking around and their trajectory is \nstored as a list of tuples (t, x, y), where t is number of seconds from 0 to 19, \nand x and y are the coordinates of the bottom left corner in the grid.\nThe pedestrians and robots are both 2 by 2 in size.\nTheir paths are as follows:\n'ped1': [ (0,1,1),\n (1,1,2),\n (2,1,4),\n (3,1,6),\n (4,1,7),\n (5,1,9),\n (6,1,11),\n (7,2,13),\n (8,2,14),\n (9,3,16),\n (10,6,16),\n (11,7,15),\n (12,8,13),\n (13,9,12),\n (14,10,11),\n (15,11,10),\n (16,12,9),\n (17,12,8),\n (18,12,7),\n (19,12,6)\n ], \n'ped2': [ (0,25,28),\n (1,25,28),\n (2,25,26),\n (3,25,24),\n (4,25,22),\n (5,25,20),\n (6,25,18),\n (7,25,16),\n (8,25,14),\n (9,24,12),\n (10,22,12),\n (11,20,12),\n (12,19,12),\n (13,17,12),\n (14,16,12),\n (15,16,12),\n (16,15,13),\n (17,14,15),\n (18,12,16),\n (19,10,16)\n ], \n'ped3': [ (0, 25, 2),\n (1, 24, 2),\n (2, 23, 2),\n (3, 22, 2),\n (4, 21, 2),\n (5, 20, 2),\n (6, 19, 2),\n (7, 18, 2),\n (8, 17, 2),\n (9, 16, 2),\n (10,15,2),\n (11,14,2),\n (12,13,2),\n (13,12,2),\n (14,11,2),\n (15,10,2),\n (16,9,3),\n (17,8,4),\n (18,8,6),\n (19,8,8)\n ]\n\nThe start and end positions for the first robot are (17, 2) and (5, 24).\nThe start and end positions for the second robot are (5, 25) and (25, 25).\n\nYou must provide two lists of tuples in (t,x,y) format that is free of collisions from\nboth pedestrians and static rectangular obstacles. \n\nThe speed limit of robot in either x and y direction is 2 between each time step.\nThis means that the robot can move in the x direction 2 steps and y direction 2 steps and be ok.\n\nMake sure you navigate around both the walking pedestrians and static obstacles.\n\nYou will be evaluated on the following for each of the two robots:\n- Starting position at t=0 is correct\n- Ending position at t=19 is correct\n- No collision between robot and static obstacles\n- No collision between robot and walking pedestrians\n- Does not exceed top speed", "contributor": "Asher Mai" }, { "task_id": "YZ_01", "query_token_num": 511, "Engineering Domain": "Signal Processing", "prompt": "## Task Description\nIn this task, you are required to design a multi-stage sample rate converter for an LTE receiver. The converter must reduce various input sample rates (for example, 125, 140, or 150 Msps) down to a lower baseband rate while meeting specific passband and stopband requirements. The converter is implemented as a three-stage filter chain. In the first stage, a Farrow rate converter makes a fine adjustment to the sample rate by a predefined factor. The signal is then processed by two decimating FIR filters in the subsequent stages. Your goal is to determine the appropriate parameters for each stage to satisfy the LTE signal integrity constraints.\n\n### Task 1\nYour first task is to specify the top level parameters given the input rate FsADC = 150 MHz and the output rate FsLTERx = 30.72 MHz. The parameters and their requirements are as follows:\n#### Parameters:\n- Fpass, the passband cutoff frequency that accommodates the maximum possible LTE bandwidth of 10 MHz.\n- Fstop, typically the Nyquist rate $\\frac{FsLTERx}{2}$, can be adjusted if more out-of-band signal rejection is required.\n- Ast, the stopband attenuation in dBs.\n- Ap, the desired passband ripple. \n\n### Task 2\nYour second task is to determine the reduction factors(Factor_1 and Factor_2, both of which are integers greater than one) for the last two decimating FIR filters. First, the Farrow rate converter should be placed as far from the Nyquist bandwidth as possible. Next, verify that the converter meets the LTE requirements by confirming that the Error Vector Magnitude (EVM) remains within acceptable limits. The MATLAB code below calculates the EVM:\n\nresults.floatPointSRCEVM = SRCTestUtils.MeasureEVM(sigInfo,floatResamplerOut,FsLTERx);\ndisp([' floating point SRC RMS EVM: ' num2str(results.floatPointSRCEVM.RMS*100,3) ' %']);\ndisp([' floating point SRC Peak EVM: ' num2str(results.floatPointSRCEVM.Peak*100,3) ' %']);\n\nthe following requirements need to be satisfied:\n- floating point SRC RMS EVM: <= 0.03%\n- floating point SRC Peak EVM: <= 0.07%\n- Factor_2 * FsLTERx - 2 * Fpass: > 0 MHz\n", "contributor": "Yizhou Zhao" }, { "task_id": "XZ_01", "query_token_num": 395, "Engineering Domain": "Robotics", "prompt": "## Task Description\nYou are given a 2D gridmap of a construction site, where each node is represented as a triplet (x, y, 0/1). This map follows the specifications below:\n-The construction site spans an area that is 50 meters wide and 40 meters long.\n-Each grid cell is 1 meter \u00d7 1 meter.\n-The bottom-left corner of the site map corresponds to world coordinates (0, 0).\n-The value 0 or 1 in (x, y, 0/1) represents: A value of 1 denotes an obstacle (construction material, equipment, barricade, etc.), while a 0 indicates traversable space.\n\nA small inspection robot's starting position is at the site entrance (0,0,0), and we set the goal position to the far corner inspection point (49,39,0). Suppose this inspection robot can only navigate on grid nodes (i.e., x and y values are integers). Find the shortest way from the entrance to the inspection point without hitting any obstacles.\nThe construction site contains the following obstacles:\n\n-A vertical wall from (10,5) to (10,35)\n-A horizontal wall from (10,20) to (40,20)\n-A vertical wall from (30,0) to (30,15)\n-A cluster of obstacles in the region from (20,25) to (25,30)\n-Several random obstacles at: (15,10), (25,5), (35,25), (40,30), (45,15)\n\n## Required Results:\n1. The complete path as an ordered list of coordinates from start to goal\n2. The total path length (in meters)\n3. The algorithm used (A*, Dijkstra, etc.)\n4. The number of nodes explored during the search\n5. Whether 4-connected or 8-connected movement was used\n6. Execution time of the algorithm\n\n", "contributor": "Xiayu Zhao\n" }, { "task_id": "qjlim2_04", "query_token_num": 290, "Engineering Domain": "Signal Processing", "prompt": "----------\nBackground\n----------\n\nCylindrical monopole antennas are vertically oriented antennas commonly used for broadband and omnidirectional communication in the azimuth plane. They are typically placed over a large ground plane and function as a half-wave dipole with one arm mirrored by the ground.\n\nIn this task, you are to design a cylindrical monopole antenna that meets the specified performance objectives and constraints outlined below.\n\nThe monopole is centered at the origin and aligned along the z-axis, extending vertically from the ground plane. The antenna is made of a highly conductive material such as copper and radiates in free space. It is mounted on a perfectly conducting square ground plane of size 300\u202fm \u00d7 300\u202fm and is fed using a 70-ohm lumped port at its base.\n\n------------------------------\nTask Objective and Constraints\n------------------------------\n\nYour task is to design a cylindrical monopole antenna that meets the following specifications:\n\nResonant Frequency: 0.487 GHz (S11 \u2264 \u201310 dB)\n\nBandwidth: \u2265 10 MHz\n\nGain: \u2265 0 dBi\n\n-------------\nDesign Inputs\n-------------\n\nDetermine the optimal design parameters to satisfy the task objectives:\n\nHeight of cylindrical monopole in mm: height_mm\n\nRadius of cylindrical monopole in mm: radius_mm\n\nConfidence of your design: confidence\n\n----------------\nAdditional Note\n----------------\n\nThe radius of the antenna should generally be at most 1/20 of the length of the antenna.\n", "contributor": "Qi Jian Lim" }, { "task_id": "TB_05", "query_token_num": 547, "Engineering Domain": "Analog Integrated Circuit Design", "prompt": "## Task\u00a0Description\u00a0(Sizing Only)\nYou are asked to design a Common-Source amplifier topology with a resistive load. The amplifier consists of an NMOS transistor, a load resistor RL, and an ideal voltage source VGS. The goal is to meet the given small-signal and DC specifications using simulation.\n\nThe output should be only the TEMPLATE format provided under, which is a SPICE-format netlist used in Cadence for evaluation. You may only adjust the parameters of NMOS( W1, L1, M1), the parameters of R0 (R0, M0) and V0.\nThe amplifier must meet the following specs under CL = 2 pF and VDD = 1.8 V:\n\nTestbench Configuration\nThe testbench is a unity-gain buffer connection (feedback from output vout to inverting input vin).\n\n\n### Task\u00a01\u00a0\u2014 Device Sizing\n**Process Rule** \nAll MOSFETs must instantiate **exactly** the foundry models \n`tsmc18dP`\u00a0(PMOS) and `tsmc18dN`\u00a0(NMOS). \n\n### Task 2 \u2014 Performance Verification\n\nUsing the provided Cadence/SPECTRE testbench, verify that your OTA design satisfies the following specifications:\n| Parameter | Spec Target |\n|----------------|---------------------|\n| DC Gain | \u22125 V/V \u00b1 2% |\n| 3 dB Bandwidth | \u2265 50 Mrad/s |\n| Output Voltage | 900 mV \u00b1 2% |\n---\n\n###