--- title: Projects summary: List of projects. date: "" reading_time: false # Show estimated reading time? share: false # Show social sharing links? profile: false # Show author profile? comments: false # Show comments? # Optional header image (relative to `static/img/` folder). #header: #caption: "" #image: "" ---
My PhD focuses on understanding the process of horizontal transfer of antimicrobial resistance genes. We know that bacteria can exchange genes encoding antimicrobial resistance between them, however the exact dynamics of this are still unclear. At which rate does this occur? What influences the speed of the process? What is the impact of horizontal transfer on the overall public health consequences of antimicrobial resistance? These are some of the questions I’m trying to answer!
My supervisors are Dr Gwen Knight (LSHTM) and Prof Jodi Lindsay (SGUL), and I am funded by an MRC LID studentship.
My relevant publications for this can be found here.
I have been involved in the COVID-19 response work by the Centre of Mathematical Modelling of Infectious Diseases at LSHTM. Notably, I contributed to the daily maintenance of our data pipeline, and have conducted various analyses on COVID-19 transmission in different settings.
A complete list of the most recent coronavirus work by CMMID can be found here
My relevant publications for this can be found here.
Alongside several colleagues from LSHTM, I contributed to the winning entry for the Data Re-use Prize, a competition launched by the Wellcome Trust in 2018. We combined multiple open-access data sources to inform empiric prescribing of antibiotics around the world.
This work has been published, and can be found here.
As part of my previous studies, I was involved in other research projects:
In 2019 I completed a 3 months placement in the Value Evidence team at GlaxoSmithKline (Wavres, Belgium). During this period, I worked on cost of disease evaluation, cost-effectiveness analysis and fiscal modelling.
Part of my work has been published, see here for details.
In my MSc project, I examined the link between the spatial scale at which we simulate epidemics and the results of such simulations. I focused on influenza in England, and developed a complete dynamic spatial model in R.
For this, I was supervised by Dr David Haw and Prof Steven Riley.
This was my very first project on mathematical modelling, in the final year of my BSc. I modified an existing transmission dynamics model of malaria to visualise the indirect protection provided by insecticide-treated nets against mosquito bites.
I was supervised by Dr Thomas Churcher, to whom I am eternally grateful for introducing me to the field of mathematical modelling!


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In the Resources tool, you can make many kinds of materials available online. Resources can include word processing documents, spreadsheets, slide presentations, links to web sites, and simple text documents that display right on the page.
In Resources, you can post up to 10 items at a time, post items outside of folders, create folders inside other folders, and create HTML documents. You can show or hide an item at any time, and set a start and/or end time for its availability.
Using the Permissions feature, site owners can control which types of users can read, post, revise, and/or delete files in specific folders. Site owners and instructors can make a resource available to anyone by choosing to post it with the "public view" setting checked.
Viewing resources: When you click Resources
in a site's menubar, you will see a list of that site's
resources and folders containing resources. Click a resource's title
to open it. To view the contents of a folder, click the folder icon
next to the folder's name or the name itself to open it, or click the
black arrow next to the folder's name to expand it (i.e., make its
contents visible without opening it).
Sorting resources: You can sort the resources by title, size, resource creator, and last modified date. Site leaders can customize the order in which items appear.
Sharing resources: Each item is available via a URL, which you can share with site participants.
Drag and drop: You can drag and drop files to and from your desktop using WebDAV. For more information, see Uploading files to Drop Box and Resources using WebDAV with Windows XP or Uploading files to Drop Box and Resources using WebDAV with Mac OS X.
Group spaces: Resources can be shared with pre-defined groups, which gives you more control over who has access to resource items.


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Bad to the Bone!
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 Your famous baked beans were a sweet blend of smokey and spicy! My husband and I fought over the last serving). Then we tickled our taste buds with your decadent cheesecake! We are looking forward to having your catering again soon! Thanks again!" ~ Connie V.


--- layout: default title: Support Chicago’s civic tech community — donate to Chi Hack Night description: Chi Hack Night will always be free and accessible to all but we need your help to keep it going! ---
Chi Hack Night NFP is a Nonprofit organization based in Chicago Illinois. We rely on donations from corporate sponsors and individuals like you to keep our events free and accessible to all.
Donate today to keep Chicago's civic technology community growing!
Chi Hack Night is a free, weekly event in Chicago to build, share and learn about civic tech. Our community is at the center of Chicago’s civic technology ecosystem.
We are the place in Chicago where civic tech partnership and innovation happens, resulting in new non-profits like mRelief, citizen advocacy campaigns like My Building Doesn’t Recycle, and government innovation like the City of Chicago’s Clear Water Project.
Chi Hack Night will always be free and accessible to all but we need your help to keep it going!
Chi Hack Night operates on a budget of about $50,000 a year.
For each of our 50 events each year, we provide:
Chi Hack Night NFP is a 501(c)(3) tax-exempt organization.


Following up on Ronald Bradford's Checked your MySQL recovery process recently? post, I wish to add a prequel.
To see whether you have a clear definition of your backup requirements, ask yourself these questions:
- Is there a backup/restore plan?
- Is there a written backup/restore plan?
- How fast do you need to recover a backup? What's the longest downtime you will allow from the point of failure to the point of restored, functional database?
- How much data are you willing to lose in case of crash? A second's worth of data? An hour's worth? A day's worth? None?
- Are you willing to allow that the database becomes read-only when taking the backup? Or completely down?
- Are you willing to take the risk that the backup will not be 100% compatible with the data?
- Is the backup plan known to the management team, or do they just know that "the database has backups"?
The above checklist is by no means complete.
I have a vivid memory of a very good sys admin who failed on the last two points. He had some very sour days when recovering a lost file from tape took much longer than was affordable to some contract.
I found that technical people rarely share the same views as marketing/management. Make sure to consult with the management team; they will have a clearer view on what the company can afford and what it cannot afford.
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TechBook is a github project developed by Cian Gannon and Kevin Barry as part of their coursework in GMIT. This website was devloped as their final year project as part of the Level 8 Software Development course.
Software developement (Level 8) student from GMIT
Software developement (Level 8) student from GMIT
The Swagger UI is an open source project to visually render documentation for an API defined with the OpenAPI (Swagger) Specification.
Swagger UI lets you visualize and interact with the API’s resources without having any of the implementation logic in place, making it easy for back end implementation and client side consumption.
The Swagger UI is an open source project to visually render documentation for an API defined with the OpenAPI (Swagger) Specification.
Swagger UI lets you visualize and interact with the API’s resources without having any of the implementation logic in place, making it easy for back end implementation and client side consumption.
Typedoc is a Typescript documentation tool. It Create api documentations for typescript projects.
TypeDoc is an effective tool for documenting TypeScript projects by annotating functions. TypeDoc can convert this annotated source code and render it into HTML documentation.
The disseration goes over all aspects of the project and the technologies involved in developement.
The dissertation shows the technologies we picked the advantages over others and other research related to the project. The dissertation.
MEAN is a free and open-source JavaScript software stack for building dynamic web sites and web applications.
The MEAN stack is MongoDB, Express.js, AngularJS (or Angular), and Node.js. Because all components of the MEAN stack support programs that are written in JavaScript, MEAN applications can be written in one language for both server-side and client-side execution environments.
Reddit is an American social news aggregation, web content rating, and discussion website. Registered members submit content to the site such as links, text posts, and images, which are then voted up or down by other members.
Reddit API offers an easy and less stenosis way of accessing the user content on Reddit. It offers access to nearly every feature on the site that a typical user has access to.
MongoDB is a cross-platform document-oriented database program. Classified as a NoSQL database program, MongoDB uses JSON-like documents with schemata.
A record in MongoDB is a document, which is a data structure composed of field and value pairs. MongoDB documents are similar to JavaScript Object Notation objects but use a variant called Binary JSON (BSON)
Express.js, or simply Express, is a web application framework for Node.js, released as free and open-source software under the MIT License. It is designed for building web applications and APIs. It has been called the de facto standard server framework for Node.js.
Fast, unopinionated, minimalist web framework for Node.js. Released on the 22nd of May 2010.
Angular 6 is a JavaScript framework for building web applications and apps in JavaScript, html, and TypeScript, which is a superset of JavaScript. Angular provides built-in features for animation, http service, and materials which in turn has features such as auto-complete, navigation, toolbar, menus, etc.
The code is written in TypeScript, which compiles to JavaScript and displays the same in the browser.
Node.js is an open-source, cross-platform JavaScript run-time environment that executes JavaScript code outside of a browser. Node.js lets developers use JavaScript to write command line tools and for server-side scripting—running scripts server-side to produce dynamic web page content.
Node.js represents a "JavaScript everywhere" paradigm, unifying web application development around a single language.
Passport is authentication middleware for Node.js. Extremely flexible and modular, Passport can be unobtrusively dropped in to any Express-based web application. A comprehensive set of strategies support authentication using a username and password, Facebook, Twitter, and more.
Passport.js offers a secure and flexible way of authenticating users through the JWT which acts as a sites 'Passport'.
Hypertext Markup Language is the standard markup language for creating web pages and web applications. With Cascading Style Sheets and JavaScript, it forms a triad of cornerstone technologies for the World Wide Web.
HTML elements are the building blocks of HTML pages. With HTML constructs, images and other objects such as interactive forms may be embedded into the rendered page.
Cascading Style Sheets (CSS) is a style sheet language used for describing the presentation of a document written in a markup language like HTML.[1] CSS is a cornerstone technology of the World Wide Web, alongside HTML and JavaScript.
CSS is designed to enable the separation of presentation and content, including layout, colors, and fonts. Enables multiple web pages to share CSS in a separate .css file


Q. 140. What becomes of men at death? A. The body returns to dust, and the soul goes into the world of spirits.
Q. 141. Will the bodies of the dead be raised to life again? A. Yes; "The trumpet shall sound, and the dead shall be raised."


Class SerializationInfo
Describes a type's member information including the serialized name and whether the name should be transformed using the serializer's name transformation logic.
Inheritance
System.Object
SerializationInfo
Inherited Members
System.Object.Equals(System.Object)
System.Object.Equals(System.Object, System.Object)
System.Object.GetType()
System.Object.MemberwiseClone()
System.Object.ReferenceEquals(System.Object, System.Object)
System.Object.ToString()
Namespace: Manatee.Json.Serialization
Assembly: Manatee.Json.dll
Syntax
public class SerializationInfo
Properties
| Improve this Doc View SourceMemberInfo
Gets the member information. Could be a property or a field.
Declaration
public MemberInfo MemberInfo { get; }
Property Value
| Type | Description |
|---|---|
| System.Reflection.MemberInfo |
SerializationName
Gets the value of the key under which the property should be serialized (the JSON property).
Declaration
public string SerializationName { get; }
Property Value
| Type | Description |
|---|---|
| System.String |
ShouldTransform
Gets whether the name should be transformed by SerializationNameTransform or DeserializationNameTransform.
Declaration
public bool ShouldTransform { get; }
Property Value
| Type | Description |
|---|---|
| System.Boolean |
Methods
| Improve this Doc View SourceEquals(Nullable<Object>)
Determines whether the specified object is equal to the current object.
Declaration
public override bool Equals(object? obj)
Parameters
| Type | Name | Description |
|---|---|---|
| System.Nullable<System.Object> | obj | The object to compare with the current object. |
Returns
| Type | Description |
|---|---|
| System.Boolean | true if the specified object is equal to the current object; otherwise, false. |
GetHashCode()
Serves as the default hash function.
Declaration
public override int GetHashCode()
Returns
| Type | Description |
|---|---|
| System.Int32 | A hash code for the current object. |
Overrides
System.Object.GetHashCode()


{% extends 'vesper/base.html' %} {% block head %}
Deletes the audio files of the specified clips of this archive.
{% include "vesper/clips-specification-message.html" %}After the audio files are deleted, whenever Vesper needs the clips' audio data it will read them from the recordings of which the clips are parts, assuming that the recordings are available. Note that if the recordings are not available, you probably don't want to run this command!
{% include "vesper/command-executes-as-job-message.html" %} {% endblock main %}


DAY6 BATCH2 ASSIGNMENT
Q.1:Create a array containing five objects with properties{name,age,city,salary}
A.Display all the objects in a table.
B.Create a search functionality for name and city.
C.Delete button to delete records.
D.Data is not permanent.


There are a some additional options related to command-line execution.
A more complex circuit might include a RAM component that needs to be loaded with a program in order for the circuit to have anything to do. You can specify a memory image file at the command line, which will be loaded into any RAM component in the circuit before simulation begins. (This does not work when loading the GUI - it is only for command-line execution.)
java -jar logisim-filename.jar cpu.circ -tty table -load mem-image.txt
The order of the parameters is not important (except the table parameter must be immediately after -tty, and the memory image's filename must be immediately after -load). The memory image file should be in Logisim's memory image format.
Logisim searches for RAM recursively, so this will still work if RAM is nested within a subcircuit. There is no way, though, to distinguish different RAM components: Logisim will attempt to load the same file into every RAM that it can find.
In our examples thus far, we've always used -tty table
to indicate that a table of output values should be displayed. You can
customize the behavior in other ways by listing one or more options,
separated by commas. For instance, you might write
-tty table,halt,speed
,
and the program will perform all three behaviors listed below.
(The order in which they are listed does not matter.)
After the simulation ends, a one-line message is displayed explaining why the simulation ended. Error conditions - such as a detected oscillation - are displayed in any case.
If you use speed in conjunction with -tty
,
then after completing the simulation Logisim will display a summary of
how quickly the circuit was simulated, such as:
714 Hz (509 ticks in 712 milliseconds)
Note that displaying information during the simulation makes the simulation go much slower. As just one comparison, the same circuit and image ran at 714 Hz above with just the speed option but 490 Hz with the table option as well.
Shows a tab-delimited table containing statistics about components
used by the top-level main
circuit in the project. The table includes
four columns:
The distinction between Unique
and Recursive
is explained
further under Project menu
section.
If the file uses circuits from a loaded Logisim library, those components are
considered to be black boxes
: The contents of the library's circuits are
not included in the unique and recursive counts.
(This feature can be useful for instructors who assign students to build projects using a subset of Logisim's libraries.)
(as already discussed)
Any TTY components send their output to the display (standard output), and any information typed at the keyboard is sent to all Keyboard components in the circuit. These components are included even if they are nested deeply in the subcircuit hierarchy.
Next: Testing multiple files.


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--- layout: archive title: Zulip Chat Archive permalink: /stream/113488-general/topic/how.20to.20use.20linear.20combination.html ---
variables {k : Type u} {V : Type v} variable [field k] variables [ring k] [module k V] variables {a : k} {b : V} include k variables (x y : V) variable (fvs : finite_dimensional_vector_space k V) def is_in_vecsp (v : V) (fvs : finite_dimensional_vector_space k V) : Prop := v ∈ span {v₁ : V | v₁ ∈ fvs.ordered_basis} lemma add_closed : is_in_vecsp x fvs ∧ is_in_vecsp y fvs → is_in_vecsp (x + y) fvs := begin intro h₀, cases h₀ with le ri, have h₁ : ∃(lc₁ : lc k V), (∀ x∉fvs.ordered_basis, lc₁ x = 0) ∧ x = lc₁.sum (λb a, a • b), from le,
I don't know why for lc₁
in lc₁.sum (λb a, a • b)
, it reports
synthesized type class instance is not definitionally equal to expression inferred by typing rules, synthesized no_zero_divisors.to_has_zero k inferred mul_zero_class.to_has_zero k
Can anyone help me to solve this problem?
Probably not until you give us a MWE (depending only on mathlib and not your own code).
You can use gist or pasteall if it's too long
I think you should not have both field k
and ring k
Yes -- try deleting the variable [field k]
line and see if it works. If it doesn't, then follow Patrick's advice and post some code which will work for everyone, if possible.
Yes, I deleted variable [field k]
. now it works. Thx!
Last updated: Apr 24 2020 at 19:02 UTC


{% extends "base.html" %} {% block title %}Internal Server Error{% endblock %} {% block content_title %}Internal Server Error{% endblock %} {% block content %}
An Error occured. We are not able to process your request.


---
order: 30
title: Adeptus Mechanicus – Skitarii Legion
name: Gryphonne IV Skitarii Legion
forces:
- skitarii-legion
using_the_army_list:
|
The following army list allows you to field an Adeptus Mechanicus army that is based on an Gryphonne IV Skitarii Legion. It can also be used as a stand in
army list for other Skitarii Legions as well.
Gryphonne IV Skitarii Legion formations come in three types: _demi-century_, _ordinatus_ and _support formations_. Each demi-century you include in the army allows you to field any one ordinatus formation and any two support formations. Although you can only take an ordinatus or support formation if you first take a demi-century, they are treated as separate independent formations during a battle and do not have to move around together.
In addition, demi-centuries may be given up to three upgrades. Each type of upgrade can only be taken once by a company. Upgrades are added to the company and are not a separate formation. Ordinatus and support formations may not be given company upgrades (although Ordinatus Minorus formations must be given Battle Titan Weapon Upgrades). Each upgrade that is taken adds to the cost of the demi-century, as shown on the upgrade chart.
Gryphonne IV Skitarii Legion Adeptus Mechanicus armies may be supported by Mechanicus allies. A maximum of up to a third of the points available to the army may be spent on these formations. In addition, certain Mechanicus ally formations may be given Titan upgrades. Which Titan upgrades a formation may be given are listed in the upgrades
column. Titan upgrades are added to the formation and are not a separate formation. Each Titan upgrade that is taken adds to the cost of the formation, as shown on the Titan upgrade chart.
special_rules:
- gryphonne-iv-skitarii-legion-epic-tournament-special-rules
---
Gryphonne IV Skitarii Legion armies have a strategy rating of 2. All Mechanicus ally formations, except for Cataphractii, have an initiative rating of 1+. all other formations have an initiative rating of 2+.
Demi-century Formations
| Formation |
Units |
Cost |
| Sagitarii |
Five Sagitarii units and five Gun Servitor units |
250 points |
| (Replace five Gun Servitor units with three Rapier units) |
(+25 points) |
| Skitarii |
Three Hypaspist units, two Secutor units and five additional Hypaspist or Gun Servator units |
225 points |
| (Replace three Hypaspist units with three Secutor units) |
(+125 points) |
Ordinatus Formations
| (Any one ordinatus formation may be fielded per each demi-century.) |
| Formation |
Units |
Cost |
| Majoris |
One of the following Ordinatus Majoris: |
Mars |
450 points |
| Golgotha |
550 points |
| Armageddon |
500 points |
| Minorus |
Two Ordinatus Minorus |
250 points |
| (Add one Ordinatus Minorus) |
(+100 points) |
Support Formations
| (Any two support formation may be fielded per each demi-century.) |
| Formation |
Units |
Cost |
| Assault Maniple |
Four Colossus Robots |
200 points |
| Avengers |
Two Avenger Strike Fighters |
200 points |
| 0–1 Orbital Support |
Ark Mechanicus Battleship |
200 points |
| Praetorian Maniple |
Five Praetorian Combat Servitor units |
250 points |
| (Add one Ordinatus Minorus) |
(+100 points) |
| Scout Maniple |
Four Crusader Robots |
125 points |
Demi-century Upgrades
| (Up to three demi-century upgrades may be taken once per demi-century.) |
| Formation |
Units |
Cost |
| Chimedons |
Add ten Chimedons |
+175 points |
| Flak |
Add one Hydra |
+50 points |
| 0–1 Magos |
Add one Magos character to a Secutor unit |
+50 points |
| Ordinatus |
Add one Ordinatus Minorus |
+100 points |
Mechanicus Allies
| (Up to a third of the points available may be spent on these formations.) |
| Formation |
Units |
Upgrades |
Cost |
| Cataphractii |
One Macharius Command and two Macharius |
None |
350 points |
| Emperor |
One Imperator or Warmonger Class Titan |
Carapace Multilasers, Sacred Icon, Veteran Princeps |
1250 points |
| Reaver |
One Reaver Class Titan |
All Titan Upgrades |
550 points |
| Warhound |
One Warhound Class Titan |
All Scout Titan Weapons, Veteran Princeps |
275 points |
| Warhound Pack |
Two Warhound Class Titans |
All Scout Titan Weapons, Veteran Princeps |
500 points |
| Warlord |
One Warlord Class Titan |
All Titan Upgrades |
675 points |
Titan Upgrades
Battle Titan Weapons
| (Mount each weapon mount in the formation with one of the following upgrades.) |
| Upgrade |
Cost |
| Apocalypse Missile Launcher |
+25 points each |
| Carapace Landing Pad |
Free |
| Close Combat Weapon |
+25 points each |
| Corvus Assault Pod |
Free |
| Gatling Blaster |
+25 points each |
| Laser Blaster |
+50 points each |
| Laser Burner |
Free |
| Melta Cannon |
+50 points each |
| Plasma Cannon |
+25 points each |
Plasma Destructor
Note: Carapace weapon mounts only.
|
+75 points each |
| Quake Cannon |
+75 points each |
Support Missile
Note: Carapace weapon mounts only.
|
+75 points each |
| Volcano Cannon |
+50 points each |
Scout Titan Weapons
| (Mount each weapon mount in the formation with one of the following upgrades.) |
| Upgrade |
Cost |
| Inferno Gun |
Free |
| Plasma Blastgun |
Free |
| Turbo-Laser Destructor |
+25 points each |
| Vulcan Mega-Bolter |
Free |
Scout and Battle Titan Upgrades
| (Add any of the following upgrades to a unit up to once per formation.) |
| Upgrade |
Cost |
| Carapace Multilasers |
+50 points |
| Sacred Icon |
+50 points |
| Veteran Princeps |
+25 points |
|


{% extends 'academics/base.html' %} {% load static %} {% block content %}
Nepal College of Information Technology – NCIT, established in 2001, runs Pokhara University-affiliated Bachelor’s and Master’s programs – BE, BBA, ME, MSc & MCIS. Our Engineering Degrees are approved by the Nepal Engineering Council. It has produced over a thousand engineers since its establishment.
NCIT, a pioneer private institution providing engineering education in Nepal, is renowned for excellence in teaching & research, while maintaining close and mutually beneficial links with various sectors. The College provides excellent higher education opportunities and nurtures individual talent using an applicable knowledge base that fully supports ongoing social changes and economic advances. The institution is committed to providing quality education in various engineering disciplines keeping in mind emerging professional needs. Our highly qualified and experienced faculty is fully dedicated to their teaching. We have a state-of-the-art infrastructure to foster academic excellence. Moreover, we provide vital non-credit inputs including research & project work, supplementing the regular courses to meet the diverse learning needs of its students and improve their employability.
The College is also an authorized training partner of CISCO, Red Hat, and Microsoft. It provides related- training and conducts preparatory examinations leading to internationally recognized certifications from these renowned institutions. NCIT has MOUs with the Microsoft Innovation Center and many reputed multinational and local companies for internships and training programmers.
NCIT envisions an institutional role for itself beyond academic boundaries. It takes the aspirations and future success of its students as pathway to nation building.


QML Tutorial 3 - States and Transitions
In this chapter, we make this example a little bit more dynamic by introducing states and transitions.
We want our text to move to the bottom of the screen, rotate and become red when clicked.
Here is the QML code:
import QtQuick 2.0 Rectangle { id: page width: 320; height: 480 color: "lightgray" Text { id: helloText text: "Hello world!" y: 30 anchors.horizontalCenter: page.horizontalCenter font.pointSize: 24; font.bold: true MouseArea { id: mouseArea; anchors.fill: parent } states: State { name: "down"; when: mouseArea.pressed == true PropertyChanges { target: helloText; y: 160; rotation: 180; color: "red" } } transitions: Transition { from: ""; to: "down"; reversible: true ParallelAnimation { NumberAnimation { properties: "y,rotation"; duration: 500; easing.type: Easing.InOutQuad } ColorAnimation { duration: 500 } } } } Grid { id: colorPicker x: 4; anchors.bottom: page.bottom; anchors.bottomMargin: 4 rows: 2; columns: 3; spacing: 3 Cell { cellColor: "red"; onClicked: helloText.color = cellColor } Cell { cellColor: "green"; onClicked: helloText.color = cellColor } Cell { cellColor: "blue"; onClicked: helloText.color = cellColor } Cell { cellColor: "yellow"; onClicked: helloText.color = cellColor } Cell { cellColor: "steelblue"; onClicked: helloText.color = cellColor } Cell { cellColor: "black"; onClicked: helloText.color = cellColor } } }
Walkthrough
states: State { name: "down"; when: mouseArea.pressed == true PropertyChanges { target: helloText; y: 160; rotation: 180; color: "red" } }
First, we create a new down state for our text type. This state will be activated when the MouseArea is pressed, and deactivated when it is released.
The down state includes a set of property changes from our implicit default state (the items as they were initially defined in the QML). Specifically, we set the y
property of the text to 160
, the rotation to 180
and the color
to red.
transitions: Transition { from: ""; to: "down"; reversible: true ParallelAnimation { NumberAnimation { properties: "y,rotation"; duration: 500; easing.type: Easing.InOutQuad } ColorAnimation { duration: 500 } } }
Because we don't want the text to appear at the bottom instantly but rather move smoothly, we add a transition between our two states.
from
and to
define the states between which the transition will run. In this case, we want a transition from the default state to our down state.
Because we want the same transition to be run in reverse when changing back from the down state to the default state, we set reversible
to true
. This is equivalent to writing the two transitions separately.
The ParallelAnimation type makes sure that the two types of animations (number and color) start at the same time. We could also run them one after the other by using SequentialAnimation instead.
For more details on states and transitions, see Qt Quick States and the states and transitions example.


class: center, middle .title[Lecture 3: Regression analysis & model fitting] .author[Shane Elipot] .institution[The Rosenstiel School of Marine and Atmospheric Science, University of Miami] .coauthor[] .institution[] .date[] .note[] .footnote[Created with [{Remark.js}](http://remarkjs.com/) using [{Markdown}](https://daringfireball.net/projects/markdown/) + [{MathJax}](https://www.mathjax.org/)] --- exclude: true name: foreword class: left, .toc[[✧](#toc)] ## Foreword --- name: references class: left, .toc[[✧](#toc)] ## References [1] Bendat, J. S., & Piersol, A. G. (2011). *Random data: analysis and measurement procedures* (Vol. 729). John Wiley & Sons. [2] Thomson, R. E., & Emery, W. J. (2014). *Data analysis methods in physical oceanography*. Newnes. [dx.doi.org/10.1016/B978-0-12-387782-6.00003-X](http://dx.doi.org/10.1016/B978-0-12-387782-6.00003-X) [3] Press, W. H. et al. (2007). *Numerical recipes 3rd edition: The art of scientific computing*. Cambridge university press. [4] von Storch, H. and Zwiers, F. W. (1999). *Statistical Analysis in Climate Research*, Cambridge University Press [5] Rawlings, J., Pantula, S. G., and Dickey, D. A. (1998) *Applied Regression Analysis*, A research tool, second edition, Springer [6] Wunsch, C. (2006). Discrete inverse and state estimation problems : with geophysical fluid applications. Cambridge University Press. [7] Fan, J. and Gijbels, I. (1996), *Local Polynomial Modelling and Its Applications*, CRC Press --- name: toc class: left, .toc[[✧](#toc)] # Lecture 3: Outline 1. [Introduction](#introduction) 2. [Linear regression](#regression) 3. [Polynomial interpolation](#polynomial) 4. [Local Polynomial modeling](#localpolynomial) 5. [A note on non linear modeling](#nonlinear) --- name: introduction class: center, middle, .toc[[✧](#toc)] # 1. Introduction --- class: left, .toc[[✧](#toc)] ## Introduction Regression analysis consists in using mathematical expressions (that is modeling, or modelling in the U.K.) to describe to some extent the behavior of a random variable (r.v.) of interest. This variable is called a *dependent variable*. The variables that are thought to provide information about the dependent variable and are incorporated in the model are called *independent variables*. The models used in regression analysis typically involve unknown constants, called *parameters*, which are to be **estimated** from the data. -- The mathematical complexity of the model, and the degree to which it is realistic, depend on how much is known about the process and the purpose of the regression analysis (and the ability and knowledge of the scientist). Most regression models that we will encounter are **linear** in their parameters. If they are not linear, they can often be linearized. Critical thinking should be employed, as **any model can be fitted to (or regressed against) any data**. --- class: left, .toc[[✧](#toc)] ## Example Daily atmospheric CO$_2$ measured at Mauna Loa in Hawaii at an altitude of 3400 m. Data from Dr. Pieter Tans, NOAA/ESRL ([www.esrl.noaa.gov/gmd/ccgg/trends/](http://www.esrl.noaa.gov/gmd/ccgg/trends/)) and Dr. Ralph Keeling, Scripps Institution of Oceanography ([scrippsco2.ucsd.edu](http://scrippsco2.ucsd.edu/)). .center[
] --- class: left, .toc[[✧](#toc)] ## Example Determining the linear trend of this time series is an example of linear regression. Further modeling could include estimating the seasonal cycle of the time series etc. .center[
] --- name: regression class: center, middle, .toc[[✧](#toc)] # 2. Linear regression --- class: left, .toc[[✧](#toc)] ## Simple linear regression We are going to review the simplest linear model involving one independent variable `$x$` and one dependent variable `$y$`. In parallel we will also present the equations for a more general model relating `$y$` to `$p$` dependent variables `$x_1,x_2,\ldots,x_p$`. Matlab uses notation that ressemble the matrix formulas for the general (multivariate) linear model. -- As an example, we will see that the *least squares* solution of the linear model is `$$ \widehat{\boldsymbol{\beta}} = (\mathbf{X}^\mathrm{T}\mathbf{X})^{-1}\mathbf{X}^\mathrm{T}\mathbf{Y} $$` which in Matlab can be written ```ruby B = (X'*X)^-1*X'*Y; ``` but is better coded as ```ruby B = (X'*X)\X'*Y; ``` --- class: left, .toc[[✧](#toc)] ## Simple linear regression Previously, when examining a set of observations `$Y_i$` of `$y$`, we assumed that the expectation, or true mean, was constant, i.e. `$E[Y_i] = \mu_y$`. -- We know consider the case when the mean is a function of another variable, as an example time. Linear regressions can consist in estimating the trend and the seasonal cycle of your time series. -- .left-column[
In the case of the CO$_2$ record, the mean is clearly not a constant, increasing every year, but also oscillating within each year.] .right-column[
] --- class: left, .toc[[✧](#toc)] ## Simple linear regression The simplest model is that the **true mean or expectation** of `$y$` changes at a constant rate as the value of `$x$` decreases or increases: `$$ E[Y_i] = \beta_0 + \beta_1 X_i, \quad i = 1,\ldots,n $$` where `$\beta_0$` and `$\beta_1$` are the parameters to estimate. .right-column[
] .left-column[
This model is applicable as an example for estimating a linear trend of a time series, or any linear relationship between two r.vs.] --- class: left, .toc[[✧](#toc)] ## Simple linear regression The observations of the dependent variable `$y$` are looked at as individual realizations of the r.vs. `$Y_i$` with populations means `$E[Y_i]$`. The deviation of `$Y_i$` from `$E[Y_i]$` is taken into account by incorporating a random error `$\epsilon_i$` in the linear model `$$ Y_i = \beta_0 + \beta_1 X_i + \epsilon_i $$` -- .right-column[
] .left-column[
The `$\epsilon_i$` are assumed normally independent identically distributed (i.i.d.) r.vs. as `$\sim \mathcal{N}(0,\sigma)$`. Since `$\beta_0,\beta_1$` and `$X_i$` are constant, `$Y_i \sim \mathcal{N}(E[Y_i],\sigma)$`.
In contrast, the observed values of `$X$` are supposed to be free of errors, treated as constants.] --- class: left, .toc[[✧](#toc)] ## General linear model (or multiple regression) The general linear model with `$p$` **independent variables** for observation `$i$` is `$$ Y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \cdots + \beta_p X_{ip} + \epsilon_i $$` There are `$p'=p+1$` parameters to estimate: a constant `$(\beta_0)$` and `$p$` factors `$\beta_1, \ldots,\beta_p$`. In matrix notation, for `$n$` observations, we obtain the *linear system* `$$ \mathbf{Y} = \mathbf{X} \boldsymbol{\beta} + \boldsymbol{\epsilon} $$` `$$ \begin{eqnarray} \begin{bmatrix} Y_1 \\ Y_2 \\ \vdots \\ Y_n\end{bmatrix} &=& \begin{bmatrix} 1 & X_{11} & X_{12} & \cdots & X_{1p}\\ 1 & X_{21} & X_{22} & \cdots & X_{2p}\\ \vdots & \vdots & \vdots & & \vdots\\ 1 & X_{n1} & X_{n2} & \cdots & X_{np}\\ \end{bmatrix} & \begin{bmatrix} \beta_0 \\ \beta_1 \\ \vdots \\ \beta_p \end{bmatrix} + & \begin{bmatrix} \epsilon_1 \\ \epsilon_2 \\ \vdots \\ \epsilon_n \end{bmatrix} \\ (n \times 1) & & (n\times p') & (p' \times 1) & (n \times 1) \\ \end{eqnarray} $$` --- class: left, .toc[[✧](#toc)] ## General linear model `$$ \boldsymbol{\beta} = \begin{bmatrix} \beta_0 \\ \beta_1 \\ \vdots \\ \beta_p \end{bmatrix} $$` Each element `$\beta_j$` is a *partial regression coefficient* that quantifies the change in the dependent variable `$Y_i$` per unit change in the independent variable `$X_{ij}$`, **assuming all other independent variables are held constant**. --- class: left, .toc[[✧](#toc)] ## Simple linear model `$$ Y_i = \beta_0 + \beta_1 X_i + \epsilon_i $$` If the `$\epsilon_i$` were `$0$` and the model were absolutely true, any two pairs of observations `$(X_i,Y_i)$` would be enough to solve for the two unkown parameters `$\beta_0$` and `$\beta_1$`. -- Yet, because of errors, another method is used, called *least squares estimation*, which gives a solution, or estimate `$(\widehat{\beta_0},\widehat{\beta_1})$` that leads to **the smallest possible sum of squared deviations** of the observations `$Y_i$` from the estimates `$\widehat{E[Y_i]}$` of their true means `$E[Y_i]$`. --- class: left, .toc[[✧](#toc)] ## Simple linear model: LS solution Let `$(\widehat{\beta_0},\widehat{\beta_1})$` provide the estimate of the true mean `$$ \widehat{E[Y_i]} = \widehat{\beta_0} + \widehat{\beta_1} X_i \equiv \widehat{{Y}_i} $$` such that the sum of squares of deviations from the mean `$$ SS(Res) = \sum_{i=1}^n (Y_i - \widehat{{Y}_i})^2 = e^2_i $$` is minimized. `$e_i$` is called the $i$-th observed *residual*. --- class: left, .toc[[✧](#toc)] ## General linear model For the general model, in matrix notation, `$$\widehat{\mathbf{Y}}\equiv \mathbf{X}\widehat{\boldsymbol{\beta}}$$` and the residuals are found in the `$(n \times 1)$` vector `$$ \mathbf{e} = \mathbf{Y}-\widehat{\mathbf{Y}} = \mathbf{Y}-\mathbf{X}\widehat{\boldsymbol{\beta}} $$` and the sum of squares of residuals is `$$ SS(Res) = \mathbf{e}^\mathrm{T}\mathbf{e} = (\mathbf{Y}-\widehat{\mathbf{Y}})^\mathrm{T}(\mathbf{Y}-\widehat{\mathbf{Y}}) = (\mathbf{Y}-\mathbf{X}\widehat{\boldsymbol{\beta}})^\mathrm{T}(\mathbf{Y}-\mathbf{X}\widehat{\boldsymbol{\beta}}) $$` which is a minimum because of `$\widehat{\boldsymbol{\beta}}$`. How to find `$\widehat{\boldsymbol{\beta}}$`? --- class: left, .toc[[✧](#toc)] ## Simple linear model The method to find the values `$(\widehat{\beta_0},\widehat{\beta_1})$` that minimize `$SS(Res)$` is classic. You take the derivatives of `$SS(Res)$` with respect to each of the $p+1$ parameters and equate the results to zero. You obtain a system of $p+1$ equations with $p+1$ unkowns. For the simple linear model you obtain the *normal equations* `$$ \begin{eqnarray} &\widehat{\beta_0} n\, &+& \widehat{\beta_1} \sum_i X_i & = & \sum_i Y_i \\ &\widehat{\beta_0} \sum_i X_i\, &+& \widehat{\beta_1} \sum_i X_i^2 & = & \sum_i X_i Y_i\\ \end{eqnarray} $$` which solution is `$$ \begin{eqnarray} \widehat{\beta_1} & = & \frac{\sum_i (X_i - \overline{X})(Y_i - \overline{Y})}{\sum_i(X_i - \overline{X})^2} = \frac{s_{xy}}{s_{xx}} = \frac{s_{xy}}{s^2_{x}}\\ \widehat{\beta_0} & = & \overline{Y} - \widehat{\beta_1} \overline{X}\\ \end{eqnarray} $$` --- class: left, .toc[[✧](#toc)] ## Simple linear model The predicted values from the solution of the linear model are `$$ \widehat{Y_i} = \widehat{\beta_0} + \widehat{\beta_1}X_i = \widehat{E[Y_i]} $$` `$\widehat{Y_i}$` can be interpreted as being **both** the *estimate of the population mean* of `$y$` for a given value of `$x$`, and the *predicted value* value of `$y$` for a future value of `$x$` which is `$X_i$`. .center[
] --- class: left, .toc[[✧](#toc)] ## General linear model For the multiple regression model, the normal equations are obtained `$$ \frac{\partial SS(Res)}{\partial \widehat{\boldsymbol{\beta}}} = 0 \rightarrow \mathbf{X}^\mathrm{T}\mathbf{X}\widehat{\boldsymbol{\beta}} = \mathbf{X}^\mathrm{T}\mathbf{Y} $$` and the least squares (LS) solution is `$$ \widehat{\boldsymbol{\beta}} = (\mathbf{X}^\mathrm{T}\mathbf{X})^{-1}\mathbf{X}^\mathrm{T}\mathbf{Y} $$` The predicted values of `$y$` are `$$ \begin{eqnarray} \widehat{\mathbf{Y}} & = & \mathbf{X}\widehat{\boldsymbol{\beta}} = \mathbf{X}(\mathbf{X}^\mathrm{T}\mathbf{X})^{-1}\mathbf{X}^\mathrm{T}\mathbf{Y}\\ & = & \mathbf{P} \mathbf{Y} \end{eqnarray} $$` with `$\mathbf{P} = \mathbf{X}(\mathbf{X}^\mathrm{T}\mathbf{X})^{-1}\mathbf{X}^\mathrm{T}$` called *the projection matrix*. This last expressions shows that the estimated `$\widehat{Y_i}$` are linear function of **all** the observed values `$Y_i$`. --- class: left, .toc[[✧](#toc)] ## Simple linear model The observations of `$y$` can now be written as the sum of the estimated population mean for a given value of `$x$` and a residual `$$ Y_i = \widehat{Y_i} + e_i $$` The sum of the squares of the observations are `$$ \begin{eqnarray} \sum_i Y_i^2 & = & \sum_i (\widehat{Y_i} + e_i)^2 \\ & = & \sum_i \widehat{Y_i}^2 + \sum_i e^2_i \end{eqnarray} $$` since it can be shown that `$\sum_i 2 \widehat{Y_i}^2 e_i =0$`. The sum of the squares of the observations is the sum of the squares "accounted for" by the model plus the sum of the squares of "unaccounted for". --- class: left, .toc[[✧](#toc)] ## Simple linear model Using `$\overline{Y} = (1/n)\sum_i Y_i$`, the decomposition of the sum of the squares can be used as follows `$$ \begin{eqnarray} \sum_i Y_i^2 - n\overline{Y}^2 & = & \sum_i \widehat{Y_i}^2 - n\overline{Y}^2 &+& \sum_i e^2_i\\ \sum_i (Y_i - \overline{Y})^2 & = & \widehat{\beta_1}^2 \sum_i(X_i-\overline{X})^2 &+& \sum_i e^2_i\\ \end{eqnarray} $$` -- What does this say? [Up to a factor `$1/(n-1)$`] -- It approximately says that: "The total variance from observations" = "variance from the regression" + "variance of the residuals" In the model `$Y_i = \widehat{\beta_1} X_i + \widehat{\beta_0}$`, the *regression part* is `$\widehat{\beta_1} X_i$`. `$\beta_1$` is called the *regression coefficient*. --- class: left, .toc[[✧](#toc)] ## Coefficient of determination From the linear model, we are interested in a quantity called the *coefficient of determination* `$$ R^2 = \frac{\sum_i (Y_i - \overline{Y})^2 - \sum_i e^2_i}{\sum_i (Y_i - \overline{Y})^2} = 1 - \frac{\sum_i e^2_i}{\sum_i (Y_i - \overline{Y})^2} $$` For the simple (univariate) linear model, `$$ \begin{eqnarray} R^2 & = & \frac{\widehat{\beta_1}^2 \sum_i(X_i-\overline{X})^2}{\sum_i (Y_i - \overline{Y})^2} = \frac{ \left(\frac{s_{xy}}{s^2_x}\right)^2 s_x^2}{s_y^2}\\ & = & \frac{s^2_{xy}}{s_x^2 s_y^2} = \left(\frac{s_{xy}}{\sqrt{s_x^2 s_y^2}}\right)^2 = r^2_{xy} \end{eqnarray} $$` `$R^2$` is thus the square of the Pearson's correlation coefficient between $x$ and $y$. --- class: left, .toc[[✧](#toc)] ## Simple linear model `$R^2$` A traditional interpretation of `$R^2$` is that it is a measure of the fraction of variance of the dependent variable `$y$` explained by the independent variable `$x$`. This is why the (square of the) Pearson correlation coefficient is very quickly interpreted as being a measure of the amount of variance explained between two variables. As an example if `$r_{xy} = 0.7$` you will often read someting like "x is able to explain 49% of the variance of y". (Since `$0.7^2=0.49$`) --- class: left, .toc[[✧](#toc)] ## Simple linear model: uncertainties In the model `$Y_i = \beta_0 + \beta_1 X_i + \epsilon_i$` where we assumed that `$\epsilon_i \sim \mathcal{N}(0,\sigma)$`, we did not know the variance `$\sigma^2$`. -- An unbiased **estimate** of `$\sigma^2$` is given by the *residual mean square*: `$$ \widehat{\sigma}^2 = s^2 \equiv \frac{\sum_i e_i^2}{n - (p + 1)} $$` This "mean" value is obtained by dividing the `$SS(Res)$` by the number of degrees of freedom for the residuals which is the number of data points `$(n)$` minus the number of parameters of the model `$(p+1)$`. --- class: left, .toc[[✧](#toc)] ## Simple linear model: uncertainties A number of formulas for the variance of the estimates can be derived and used for calculating CIs: `$$ \begin{eqnarray} \text{Var}[\widehat{\beta_1}] & = & \frac{s^2}{\sum_i (X_i - \overline{X})^2}\\ \text{Var}[\widehat{\beta_0}] & = & \left[ \frac{1}{n} + \frac{\overline{X}^2}{\sum_i (X_i - \overline{X})^2}\right]s^2\\ \text{Var}[\widehat{Y_i}] &=& \left[ \frac{1}{n} + \frac{(X_i - \overline{X})^2}{\sum_i (X_i - \overline{X})^2} \right]s^2\\ \text{Var}[\widehat{Y_0}] &=& \left[1+\frac{1}{n} + \frac{(X_0 - \overline{X})^2}{\sum_i (X_i - \overline{X})^2} \right]s^2\\ \end{eqnarray} $$` -- `$$ H_0: \widehat{\beta}_{1,0},Y_i = m_{1,0,Y_i}\quad \frac{\widehat{\beta_1}-m_1}{\sqrt{\text{Var}[\widehat{\beta_1}]}}, \frac{\widehat{\beta_0}-m_0}{\sqrt{\text{Var}[\widehat{\beta_0}]}}, \frac{\widehat{Y_i}-m_{Y_i}}{\sqrt{\text{Var}[\widehat{Y_i}]}} \sim t(0,n-p-1) $$` --- class: left, .toc[[✧](#toc)] ## General linear model: uncertainties For the general linear model, the formulas are `$$ \begin{eqnarray} \mathbf{P} &=& \mathbf{X}(\mathbf{X}^\mathrm{T}\mathbf{X})^{-1}\mathbf{X}^\mathrm{T}\\ \mathbf{\text{Var}}[\boldsymbol{\widehat{\beta}}] &=& (\mathbf{X}^\mathrm{T}\mathbf{X})^{-1}\sigma^2 \\ \mathbf{\text{Var}[{\widehat{\mathbf{Y}}}]} &=& \mathbf{P}\sigma^2 \\ \mathbf{\text{Var}[{\widehat{\mathbf{Y_0}}}]} &=& \left[ \mathbf{I} + \mathbf{X_0}(\mathbf{X}^\mathrm{T}\mathbf{X})^{-1}\mathbf{X_0}^\mathrm{T}\right]\sigma^2\\ \mathbf{\text{Var}[{{\mathbf{e}}}]} &=& (\mathbf{I}-\mathbf{P})\sigma^2 \\ \widehat{\sigma}^2 = s^2 &=& \mathbf{e}^\mathrm{T} \mathbf{e}/(n-p-1)\\ \end{eqnarray} $$` -- Beware that the expression aboves are matrices. As an example for the simple linear model for which `$p+1 = 2$`: `$$ \mathbf{\text{Var}}[\boldsymbol{\widehat{\beta}}] = \begin{bmatrix} \text{Var}(\widehat{\beta_0}) & \text{Cov}(\widehat{\beta_0},\widehat{\beta_1}) \cr \text{Cov}(\widehat{\beta_1},\widehat{\beta_0}) & \text{Var}(\widehat{\beta_1})\cr \end{bmatrix} $$` this implies that the parameter estimates **covary**. --- class: left, .toc[[✧](#toc)] ## Simple linear model: uncertainties .right-column[
] .left-column[
Note how the CIs for the prediction `$\widehat{Y_0}$` for future values `$X_0$` of `$x$` are larger than the CIs for the prediction of the mean of `$Y_i$`. The variance of the prediction is the variance of estimating the mean plus the variance of the quantity estimated. The CIs are the smallest for `$X_0 = \overline{X}$`. In this case, I generated data and I had prescribed `$\beta_0=0,\beta_1=0.8,\sigma^2=0.04$` ] --- class: left, .toc[[✧](#toc)] ## Linear model by least squares `$$ Y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \cdots + \beta_p X_{ip} + \epsilon_i $$` The method of least squares to find a solution to the general linear model is appropriate when four assumptions are valid: (1) the random errors `$\epsilon_i$` are normally distributed, (2) independent, (3) with zero mean and constant variance `$\sigma^2$`, and (4) the `$X_{ij}$` are observations of the `$p$` independent variables measured without errors. -- If we rely on a large number `$n$` of data, the normal assumption may be invoked because of the CLT. Otherwise, *Maximum Likelihood methods* can be used. As an example see [Elipot et al. (2016)](http://dx.doi.org/10.1002/2016JC011716). -- When the dependent variable observations are normally distributed but do not have the same variances, or errors, the method of *weighted least squares* can be implemented. -- When the independent variables are actually not independent (because they are maybe correlated), the method of *general least squares* can be implemented. See references [[5]](#references) and [[6]](#references). --- class: left, .toc[[✧](#toc)] ## Linear model by weighted least squares Let's assume that the variance of each `$\epsilon_i$` (and thus of each `$Y_i$`) is `$a^2_i\sigma^2$` where `$\sigma$` is a constant. As an example, some observations may have better accuracy than others. .center[
] --- class: left, .toc[[✧](#toc)] ## Linear model by weighted least squares We can consider the following rescaled model, dividing by `$a_i$`: `$$ \frac{Y_i}{a_i} = \frac{1}{a_i}\beta_0 + \beta_1 \frac{X_{i1}}{a_i} + \beta_2 \frac{X_{i2}}{a_i} + \cdots + \beta_p \frac{X_{ip}}{a_i} + \frac{\epsilon_i}{a_i} $$` or `$$ Y^*_i = X^*_{i0}\beta_0 + \beta_1 X^*_{i1} + \beta_2 X^*_{i2} + \cdots + \beta_p X^*_{ip} + \epsilon^*_i $$` Because the variance of the `$\epsilon_i$` is `$a^2_i \sigma^2$`, the variance of the `$\epsilon^*_i$` becomes `$\sigma^2$`. We can now use least squares to regress `$Y^*_i$` on the `$X^*_{ij}$`. --- class: left, .toc[[✧](#toc)] ## Linear model by weighted least squares The principle here is to assign the least amount of weight to the observations with the largest variance, or error. The *weighting matrix* is `$$ \mathbf{W} = \begin{bmatrix} 1/a_1 & 0 & \cdots 0 \\ 0 & 1/a_2 & & 0\\ \vdots & \vdots & \ddots & \vdots\\ 0 & 0 & \cdots & 1/a_n\\ \end{bmatrix} $$` Consider the general linear model equation left-multiplied by `$\mathbf{W}$` `$$ \mathbf{W}\mathbf{Y} = \mathbf{W}\mathbf{X}\boldsymbol{\beta} + \mathbf{W}\boldsymbol{\epsilon} $$` which can be rewritten as `$$ \mathbf{Y}^* = \mathbf{X}^*\boldsymbol{\beta} + \boldsymbol{\epsilon}^* $$` with `$\mathbf{Y}^* = \mathbf{W}\mathbf{Y}$`, etc. --- class: left, .toc[[✧](#toc)] ## Linear model by weighted least squares The weighted least square solution is `$$ \begin{eqnarray} \widehat{\boldsymbol{\beta}} & = & (\mathbf{X}'\mathbf{V}^{-1}\mathbf{X})^{-1}\mathbf{X}'\mathbf{V}^{-1}\mathbf{Y}\\ \mathbf{\text{Var}}[\boldsymbol{\widehat{\beta}}] & = & (\mathbf{X}'\mathbf{V}^{-1}\mathbf{X})^{-1}\sigma^2\\ \mathbf{\text{Var}}[\mathbf{\widehat{Y}}] & = & \mathbf{X}(\mathbf{X}'\mathbf{V}^{-1}\mathbf{X})^{-1}\mathbf{X}'\sigma^2\\ \mathbf{\text{Var}}[\mathbf{e}] & = & [\mathbf{V} - \mathbf{X}(\mathbf{X}'\mathbf{V}^{-1}\mathbf{X})^{-1}\mathbf{X}']\sigma^2\\ \end{eqnarray} $$` with `$$ \mathbf{V}^{-1} = \mathbf{W}'\mathbf{W} = \begin{bmatrix} a^2_1 & 0 & \cdots 0 \\ 0 & a^2_2 & & 0\\ \vdots & \vdots & \ddots & \vdots\\ 0 & 0 & \cdots & a^2_n\\ \end{bmatrix} $$` -- In fact, the weighting matrix can have whatever coefficient you want! Here it is a special case that simplifies the form of the solution. See section 2.4 of reference [[6]](#references). --- name: polynomial class: middle, center, .toc[[✧](#toc)] # 3. Polynomial interpolation --- class: left, .toc[[✧](#toc)] ## Polynomial fitting Fitting a polynomial function of an independent variable `$x$` to a dependent variable `$y$` is a linear regression problem which consists in estimating the coefficients of the polynomial `$$ y = \beta_0 + \beta_1 x + \beta_2 x^2 + \ldots + \beta_k x^k + \ldots $$` -- We will review two general cases. The first case is *global polynomial fitting* where you are fitting a polynomial function that exactly estimate your data, maybe piecewise, in separate intervals. This polynomial is of maximum order of the number of observations minus one and is called an *interpolating polynomial*. -- The second case is called *local polynomial estimation* when you are fitting a polynomial in the vicinity, that is within a window, of a given value of $x$. This polynomial of arbitrary order approximate your data locally and the solution is typically obtained by weighted least squares. -- These two types of methods can be used in general to process your data to either *interpolate* or *grid* your data. --- name: #lagrange class: left, .toc[[✧](#toc)] ## Interpolating polynomial Assume you have `$N$` pairs of observations `$(X_i,Y_i)$` and would like to interpolate `$y$` for given value of `$x$`. There exists *an interpolating polynomial* of order `$N-1$` given by the following *Lagrange formula* `$$ P_{N-1}(x) = \sum\limits_{k=1}^{N} \left( \prod\limits_{\substack{j=1 \\j \neq k}}^N \frac{x-X_j}{X_k-X_j} \right) Y_k $$` which passes through your data points, i.e. `$P_{N-1}(X_i) = Y_i$` --- class: left, .toc[[✧](#toc)] ## Interpolating polynomial Example with `$N = 5$` .center[
] --- class: left, .toc[[✧](#toc)] ## Polynomial fitting Alternatively you can use least squares to fit a polynomial of any order equal to or less than `$N-1$` with the model `$$ Y_i = \beta_0 + \beta_1 X_i + \beta_2 X^2_i + \ldots \beta_{N-1} X^{N-1}_i $$` .center[
] --- class: left, .toc[[✧](#toc)] ## Interpolating polynomial Beware that interpolating polynomial can quickly generate very large oscillations! Same example as before except that the original data point `$X_i = 2$` was moved to `$2.9$`. .center[
] --- class: left, .toc[[✧](#toc)] ## Piecewise linear interpolation A *piecewise linear interpolation*, or simply *linear interpolation* consist in calculating the interpolating polynomial of order 1 over an interval `$[X_k,X_{k+1}]$`, i.e with `$N=2$` points. The [Lagrange formula](#lagrange) gives `$$ P_1(x) = \left(\frac{x-X_{k+1}}{X_k-X_{k+1}}\right)Y_k + \left(\frac{x-X_{k}}{X_{k+1}-X_{k}}\right)Y_{k+1} $$` which can be rearranged to give the *linear interpolant* `$$ L_1(x) = Y_k + (x-X_k)\frac{Y_{k+1}-Y_k}{X_{k+1}-X_k} $$` In Matlab it is implemented by ```ruby yi = interp1(x,y,xi); ``` --- class: left, .toc[[✧](#toc)] ## Piecewise linear interpolation: errors The Lagrange formula gives you an easy way to estimate the interpolation error. If `$\delta_k$` and `$\delta_{k+1}$` are the errors or uncertainties for `$Y_k$` and `$Y_{k+1}$`, since `$$ \begin{eqnarray} P_1(x) = a_k Y_k + a_{k+1} Y_{k+1}\\ \delta P_1(x) = \sqrt{a^2_k\delta_k^2 + a^2_{k+1}\delta_{k+1}^2} \end{eqnarray} $$` .center[
] --- class: left, .toc[[✧](#toc)] ## Hermite polynomial interpolation The issue of large oscillations in interpolating can be reined in by using *Hermite polynomials* which satisfy additional conditions on its derivatives at the data points, `$$ P_n(X_k) = Y_k, \quad P^{(1)}_n(X_k) = d_k $$` where `$d_k$` is to be specified. `$P^{(\nu)}_n$` is the `$\nu$`-th derivative of `$P_n$`. -- A popular Hermite polynomial is the *shape-preserving piecewise cubic Hermite interpolating polynomial* or *shape-preserving pchip*, implemented in Matlab by ```ruby yi = pchip(x,y,xi); ``` --- class: left, .toc[[✧](#toc)] ## pchip example A pchip polynomial is cubic (order 3) and its derivatives `$d_k$`, or slopes, at each data point are zero or the *harmonic means* of consecutive slopes: `$$ \frac{1}{d_k} = \frac{1}{\delta_k} + \frac{1}{\delta_{k-1}} \quad \text{with}\quad \delta_k = \frac{Y_{k+1}-Y_{k}}{X_{k+1}-X_{k}} $$` .center[
] --- class: left, .toc[[✧](#toc)] ## Spline interpolation Another popular interpolation method uses *cubic splines* which are piecewise cubic interpolating polynomials with constraints on the second derivative to be a continuous. It is implemented in Matlab as ```ruby yi = spline(x,y,xi); ``` .center[
] --- class: left, .toc[[✧](#toc)] ## Cubic interpolation Another method using piecewise polynomials of order 3 is called *cubic convolution* and is described in detail in [Keys 1981](http://dx.doi.org/10.1109/TASSP.1981.1163711). This method is accessible in one or higher dimensions in Matlab as ```ruby yi = interpn(x,y,xi,'cubic'); ``` .center[
] --- class: left, .toc[[✧](#toc)] ## Some comments Interpolating polynomials and splines are great sets of tool that allow you to quickly interpolate your data. Splines are not necessarily polynomial of order 3 and can be of greater order. There exists a very large body of litterature dealing with splines. -- We have dealt so far with methods of interpolation in one dimension but these can be easily expanded in two or more dimensions, notably the linear and cubic methods. -- Polynomial interpolation implies that you are exactly recovering your data, i.e `$P(X_i) = Y_i$`. This implies that your data are effectively error free. We now relax this condition and review some principles of local polynomial modeling. --- name: localpolynomial class: middle, center, .toc[[✧](#toc)] # 4. Local Polynomial Modeling --- class: left, .toc[[✧](#toc)] ## Polynomial by least squares We saw earlier that we can use least squares to fit a polynomial of any order equal to or less than your `$N-1$` data points: `$$ Y_i = \beta_0 + \beta_1 X_i + \beta_2 X^2_i + \ldots \beta_{N-1} X^{N-1}_i $$` .center[
] --- class: left, .toc[[✧](#toc)] ## Local polynomial fitting Once again we attempt to estimate the value of a dependent variable `$y$` given a value of the independent value `$x$`. Here we follow closely reference [[7]](#references). The idea is to estimate an arbitrary function `$m(x)$` and its derivative noted `$m^{(1)}(x),m^{(1)}(x),\ldots,m^{(p)}(x)$` with the model `$$ Y_i = m(X_i) + \sigma(X_i) $$` where `$(X_i,Y_i)$` are observations and `$\sigma(X_i)$` is the variance of $Y_i$ at $x = X_i$. -- The function `$m(x)$` is approximated locally by a polynomial of order `$p$` by considering a Taylor expansion in the neighborhood of `$x_0$` as `$$ \begin{eqnarray} m(x) & \approx m(x_0) & + m'(x_0)(x-x_0) + \frac{m''(x_0)}{2!}(x-x_0)^2+\ldots+\frac{m^{(p)}}{p!}(x-x_0)^p\\ & = & \beta_0 + \beta_1 (x-x_0) + \beta_2 (x-x_0)^2 + \ldots + \beta_p (x-x_0)^p\\ \end{eqnarray} $$` --- class: left, .toc[[✧](#toc)] ## Local polynomial fitting The function `$m(x)$` is modeled locally as `$$ m(x) = \sum\limits_{j=0}^p\beta_j(x-x_0)^j. $$` and `$\widehat{m^{(j)}}(x_0) = j!\widehat{\beta_j}$`. The estimates of `$\beta_j$` of this polynomial are obtained for each location of interest `$x_0$` by least squares fitting, minimizing the following expression `$$ \sum\limits_{i=1}^n \{Y_i - \sum\limits_{j=0}^p \beta_j(X_i-x_0)^j\}^2 K_h(X_i - x_0) $$` where `$$ K_h(x) = \frac{1}{h}K\left(\frac{x}{h}\right) $$` `$K$` is called a *kernel function*, acting over a *half-bandwidth* `$h$`. --- class: left, .toc[[✧](#toc)] ## Local polynomial fitting In this example, the unknown function giving `$E[Y_i] = m(X_i)$` is estimated at `$X=x_0$` using an order one polynomial, using data points within the orange window. .center[
] --- class: left, .toc[[✧](#toc)] ## Local polynomial fitting For fitting a polynomial to your data, a number of aspects need to be considered, all covered in many details as an example in reference [[7]](#references): 1. Which order polynomial do you need? Are you trying to estimate the value of your unknown function only, or are you trying to estimate the `$\nu$`-th derivative as well? In this case, it is recommended that `$p-\nu$` be an odd number. 2. What bandwidth `$h$` do you need? It will depends on the *density* of your data, as well as the order of the chosen polynomial. The choice of the bandwidth is a compromise between bias and variance of your estimate. Since you are trying to estimate `$p+1$` parameters by least squares you should have at least that number of points in your window. 3. What shape should the kernel function have? Should it be uniform? Gaussian? Quadratic? A quadratic kernel called the *Epanechnikov kernel* is often recommended (see practical this afternoon!) --- class: left, .toc[[✧](#toc)] ## Local polynomial fitting This figure shows an example of fitting a known function embedded in noise with a known variance. It shows the impact of the bandwidth and polynomial order on the bias and variance of the estimates. .center[
] --- class: left, .toc[[✧](#toc)] ## Local polynomial fitting A simpler *smoother* consists in estimating the function `$m(x)$` as a polynomial of order `$0$`. The equivalent is called the *Nadaraya-Watson kernel estimator* defined as `$$ \widehat{m}_h(x) \equiv \frac{\sum\limits_{j=1}^n K_h(X_j -x) Y_j}{\sum\limits_{j=1}^n K_h(X_j -x)} $$` The typical kernel functions used are the *Gaussian kernel* `$$ K(z) = (\sqrt{2\pi})^{-1} \exp (-z^2/2) $$` and the *symmetric Beta family* `$$ K(z) = \frac{1}{\text{B}(1/2,\gamma+1)}(1-t^2)^\gamma_+, \quad \gamma = 0,1,\ldots, $$` where `$\text{B}(z,w)$` is a complicated function of no interest here. --- name: nonlinear class: middle, center, .toc[[✧](#toc)] # 5. A note on nonlinear fitting --- class: left, .toc[[✧](#toc)] ## Nonlinear fitting What does one do when the function you are trying to fit to your data is non linear in your parameter? -- As an example, you expect that a sinusoid function is a good model to describe the dependency of your dependent variable `$y$` on the independent variable `$x$`, i.e. `$$ y(x) = a\cos(x + \phi) $$` where `$a$` is the amplitude and `$\phi$` is the phase. -- In this case you're in luck because you can use trigonometric identities and write `$$ y(x) = a\cos(\phi)\cos(x) - a\sin(\phi)\sin(x) $$` -- You have *linearized your problem*, and you are now faced with a multiple linear regression problem, estimating `$a\cos(\phi)$` and `$a\sin(\phi)$` as a function of observations of `$y, \cos(x)$` and `$\sin(x)$` (see practical this afternoon). --- class: left, .toc[[✧](#toc)] ## Nonlinear fitting What if you really cannot linearize your problem? -- As an example, it is often useful to model the lagged correlation function `$\rho(\tau)$`, as in [Beal et al. 2015](http://dx.doi.org/10.1175/JPO-D-14-0119.1) .center[
] --- class: left, .toc[[✧](#toc)] ## Nonlinear fitting In this particular case, we assumed that the lagged correlation function for the along-shore component of velocity, as a function of separation distance (lag) was given by `$ \rho_h(r) = e^{-(r/r_h)^2}\cos\left( \frac{\pi r}{2 r_h}\right) $` The goal is here to fit the data for the value of the parameter `$r_h$`, a spatial lengthscale. We apply the same principle of minimization, trying to find the value `$r_h$` minimizing `$$ SS(Res) = \sum_{i=1}^N (\rho_h(r_i) - \rho_i)^2 $$` -- Since the problem cannot be put in linear form, the least square method is not available. Instead you must rely on *nonlinear optimization routines*. As an example, Matlab can apply common algorithms by the function `$\texttt{fminsearch}$`. --- exclude: true name: statistical class: middle, center .toc[[✧](#toc)] # 6. A note on statistical interpolation --- exclude: true class: left, .toc[[✧](#toc)] ## Statistical interpolation --- class: left, .toc[[✧](#toc)] ## Practical session Please download data at the following link: Please download the Matlab code at the following link: Make sure you have installed and tested the free jLab Matlab toolbox from Jonathan Lilly at [www.jmlilly.net/jmlsoft.html](https://www.jmlilly.net/jmlsoft.html) --- exclude: true class: left, .toc[[✧](#toc)] ```ruby plot(t,x) ``` First Header | Second Header ------------ | ------------- Content from cell 1 | Content from cell 2 Content in the first column | Content in the second column ~~this~~


{# TODO: Make this a modularized for loop via Flask whatnots. #}
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random oneliner demo
Here is some body text, put here for the only purpose that the body not be empty.


Memory Tracker helps those who face memory loss/ inability to recall specific events.It is open to everyone. Even those who do not have difficulty with memory loss can still have fun and play this game.
Memory Tracker is valuable because it can potentially be played anywhere that has a phone/laptop/computer and active internet connection. In the future, we plan to have Memory Tracker be available in video format like VR/AR, become an online game, and have a jeopardy spinoff version. We expect this to happen around 6 months.


Witchcraft
Witchcraft
Witchcraft by DevilHS
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Category Original » Futanari (Dickgirls)
Date Submitted
Views 26432
Favorites... 959
Vote Score 691
Category Original » Futanari (Dickgirls)
Date Submitted
Views 26432
Favorites... 959
Vote Score 691
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Media Digital drawing or painting
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Kessandra on August 15, 2019, 8:21:56 AM
Kessandra on
Looks like some beautiful magic is going on.
TrueInsanity on July 28, 2019, 4:34:52 AM
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Kaze26 on July 27, 2019, 5:23:29 AM
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QuarterLife on July 25, 2019, 6:39:08 PM
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DevilHS on July 25, 2019, 10:59:26 PM
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FloridasSonShines on July 25, 2019, 2:47:00 PM
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We are at the end of this semester now, so we are required to make our final projects as our exam. After Talk with Mr.Gerber, I
decided to make a butterfly wich movable wings. I was planning to use arduino with servo to serve as the power to pull the wings
of the butterfly. This design is actually really really challenge. I spent over 15 hours in it, but eventually I finished it!
I felt so satisfied.
I used four different processes in my butterfly projects: Arduino, electric, Computer aid design and lasier cut.
Step1:
I first
found a copy right free image of a butterfly on the website, then I imported it into Corel Draw. In Corel Draw I changed the format
of this butterfly image from jpg. to stl. Then I imported this this stl formatted image to Fusion 360. In Fusion 360
I extruded the butterfly，so now I had a 3D butterfly model.
Step2:
After finished all of these, I found out that toothpick might be good axles for my butterfly. Therefore, I measured the
width of toothpick which is exat 2 mm. Then I designed four gaps which are 2 mm wide on the bottom and top of the wings of
the butterfly. I made the size of my butterfly around a reasonable size which is 5 cm and imported the whole
thing to Corel Draw again in order to laser cut it. Then I downloaded this file
in my flashdrive and went to use laser cut to cut my butterfly. I actually cutted my butterfly several times, because
after I laser cutted this butterfly, I found out it was too small, so then I changed the size of my butterfly to 9 cm. Finally
after several failures, I got my perfectly cutted butterfly and colored it
File of the butterfly
Step3:
After finishing coloring the butterfly, I used glue gun to stick the toothpicks into the gaps and I connected two toothpicks
together for each axle. Then I measured the middle part of the butterfly and designed a small component to connect that part
with the steel stick on the servo. Mr.Gerber actually helped me to decide the material for the connection of butterfly
and servo. We finally chose to use steel stick. After the small component, the servo ,and the steel stick were setted up, I
use the electrics to form an arduino. I connect the arduino with servo on it to the computer and programmed it. Finally I got
my arduino which allowed my servo to move in 180 degrees.
Step4:
I then measured the dimension of the arduino and designed a box for my butterfly by Corel Draw,
because although Arduino is good, it is not good looking. For athestics purpose, I used
laser cutter to cut all 6 pieces of woodboard and formed a box to cover arduino. After this process,
I felt I became the master of laser cutter. I become really skilled about how to use laser cutter.
For the top one of the wood board, because I needed to allow the stick of servo to pass it in
order to connect with the butterfly, I first tried to use electric drill to form a hole on it.
After the help with Mike, I finally got a hole on the top woodboard. Then I spent a lot of time
and energy try to put the steel stick through the hole and connected the stick with servo. I finally
got it. However, after I let the servo move, I found out a horrible truth that the hole is
too small which makes the butterfly stucked there. Then, sadly, I have to redo everything again.
This time I used laser cutter to cut a large hole on the woodboard and I tried over five times
to put stick of servo in a right position in order for it to move properly. Finally, my butterfly
moved smoothly with the stick which pulls it down regularly with the force of servo.
This really challeging project not only helped me to become more skilled at how to use all the machines in WIC, but also taught me a kind of spirit about how to be a good maker. The tips of being a good maker is never giving up. No matter how many times you failed, you should keep trying. There were several moments I actually want to give up when I was making my project, but I told myself that maybe try one more time then I would get it, so I keep going until I made it. I think I am ready for advanced class and I wish next semester I can make more insteresting things.


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Francesco and Jane Bienni, founders and owners of San Francisco's world-class restaurant, have many reasons to celebrate. Cafe Townsend has been a San Francisco favorite for more than 19 years, and their latest restaurant venture, Cafe Isabella, will soon expand to more locations. Their biggest celebration is for their son Steven's recent graduation from New York's highly acclaimed Culinary Institute of America. San Francisco diners should join the Bienni's in their celebration because this graduation means an even better menu selection at Cafe Townsend, as Steven is lending his modern and innovative culinary talents to his father's traditional, Old World kitchen.
Those who have enjoyed Cafe Townsend and its world-class cuisine shouldn't worry - the stellar tableside service, scrumptious regional specials and menu favorites remain. But Steven's latest menu additions are something you don't want to miss.
"What I am doing is using seasonal Italian ingredients and combining them to create dishes with a modern flair that will invigorate our customers", Steven says.
There is a certain je ne sais quoi in the air.


Cross-Validated Covariance Matrix Estimation
Authors: Philippe Boileau, Brian Collica, and Nima Hejazi
cvCovEst
?cvCovEst
implements an efficient cross-validated procedure for covariance matrix estimation, particularly useful in high-dimensional settings. The general methodology allows for cross-validation to be used to data adaptively identify the optimal estimator of the covariance matrix from a prespecified set of candidate estimators. An overview of the framework is provided in the package vignette. For a more detailed description, see Boileau et al. (2021). A suite of plotting and diagnostic tools are also included.
For standard use, install cvCovEst
from CRAN:
install.packages("cvCovEst")
The development version of the package may be installed from GitHub using remotes
:
remotes::install_github("PhilBoileau/cvCovEst")
To illustrate how cvCovEst
may be used to select an optimal covariance matrix estimator via cross-validation, consider the following toy example:
library(MASS)
library(cvCovEst)
set.seed(1584)
# generate a 50x50 covariance matrix with unit variances and off-diagonal
# elements equal to 0.5
Sigma <- matrix(0.5, nrow = 50, ncol = 50) + diag(0.5, nrow = 50)
# sample 50 observations from multivariate normal with mean = 0, var = Sigma
dat <- mvrnorm(n = 50, mu = rep(0, 50), Sigma = Sigma)
# run CV-selector
cv_cov_est_out <- cvCovEst(
dat = dat,
estimators = c(linearShrinkLWEst, denseLinearShrinkEst,
thresholdingEst, poetEst, sampleCovEst),
estimator_params = list(
thresholdingEst = list(gamma = c(0.2, 2)),
poetEst = list(lambda = c(0.1, 0.2), k = c(1L, 2L))
),
cv_loss = cvMatrixFrobeniusLoss,
cv_scheme = "v_fold",
v_folds = 5,
)
# print the table of risk estimates
# NOTE: the estimated covariance matrix is accessible via the `$estimate` slot
cv_cov_est_out$risk_df
#> # A tibble: 9 × 3
#> estimator hyperparameters cv_risk
#> <chr> <chr> <dbl>
#> 1 linearShrinkLWEst hyperparameters = NA 357.
#> 2 poetEst lambda = 0.2, k = 1 369.
#> 3 poetEst lambda = 0.2, k = 2 372.
#> 4 poetEst lambda = 0.1, k = 2 375.
#> 5 poetEst lambda = 0.1, k = 1 376.
#> 6 denseLinearShrinkEst hyperparameters = NA 379.
#> 7 sampleCovEst hyperparameters = NA 379.
#> 8 thresholdingEst gamma = 0.2 384.
#> 9 thresholdingEst gamma = 2 826.
Contributions are very welcome. Interested contributors should consult our contribution guidelines prior to submitting a pull request.
Please cite the following paper when using the cvCovEst
R software package.
@article{cvCovEst2021,
= {10.21105/joss.03273},
doi = {https://doi.org/10.21105/joss.03273},
url = {2021},
year = {The Open Journal},
publisher = {6},
volume = {63},
number = {3273},
pages = {Philippe Boileau and Nima S. Hejazi and Brian Collica and Mark J. van der Laan and Sandrine Dudoit},
author = {cvCovEst: Cross-validated covariance matrix estimator selection and evaluation in `R`},
title = {Journal of Open Source Software}
journal }
When describing or discussing the theory underlying the cvCovEst
method, please cite the pre-print below.
@misc{boileau2021,
={Cross-Validated Loss-Based Covariance Matrix Estimator Selection in High Dimensions},
title={Philippe Boileau and Nima S. Hejazi and Mark J. van der Laan and Sandrine Dudoit},
author={2021},
year={2102.09715},
eprint={arXiv},
archivePrefix={stat.ME}
primaryClass }
© 2020-2021 Philippe Boileau
The contents of this repository are distributed under the MIT license. See file LICENSE.md
for details.


Web based File Manager in PHP, Manage your files efficiently and easily with Tiny File Manager and it is a simple, fast and small file manager with a single file.
It is a powerful-lightweight fully responsive based on Bootstrap 4, you know that it will look great on any device, whether it's a phone, tablet, or desktop the page will behave responsively!
Advanced AJAX multiple file upload with progress bar. Drag & Drop from your local drive directly to browser's window to start upload. Flash free. we used DropzoneJS and Upload files using URL.
A browser based code editor. It is specialized for editing code, and comes with a number of language modes. IDE have syntax highlighting for over 150+ languages, Over 35+ themes with your favorite programming style.


addNoiseToSignal adds noise with mean 'mu' and standard deviation 'sigma' to a synthetic NMR signal Syntax: addNoiseToSignal(time,signal,varargin) Inputs: signal - vector or matrix containing the NMR data mu - mean of the Gaussian noise (generally 0) sigma - standard deviation of the Gaussian noise Outputs: signalN - NMR signal with noise noise - noise vector/matrix Example: [sN,noise] = addNoiseToSignal(signal,0,0.01) Other m-files required: none Subfunctions: none MAT-files required: none See also: Author: see AUTHORS.md email: see AUTHORS.md License: MIT License (at end)
0001 function [signalN,noise] = addNoiseToSignal(signal,mu,sigma) 0002 %addNoiseToSignal adds noise with mean 'mu' and standard deviation 'sigma' to 0003 %a synthetic NMR signal 0004 % 0005 % Syntax: 0006 % addNoiseToSignal(time,signal,varargin) 0007 % 0008 % Inputs: 0009 % signal - vector or matrix containing the NMR data 0010 % mu - mean of the Gaussian noise (generally 0) 0011 % sigma - standard deviation of the Gaussian noise 0012 % 0013 % Outputs: 0014 % signalN - NMR signal with noise 0015 % noise - noise vector/matrix 0016 % 0017 % Example: 0018 % [sN,noise] = addNoiseToSignal(signal,0,0.01) 0019 % 0020 % Other m-files required: 0021 % none 0022 % 0023 % Subfunctions: 0024 % none 0025 % 0026 % MAT-files required: 0027 % none 0028 % 0029 % See also: 0030 % Author: see AUTHORS.md 0031 % email: see AUTHORS.md 0032 % License: MIT License (at end) 0033 0034 %------------- BEGIN CODE -------------- 0035 0036 % generate the noise 0037 noise = mu + (sigma.*randn(size(signal))); 0038 0039 % and the noisy signal 0040 signalN = signal + noise; 0041 0042 return 0043 0044 %------------- END OF CODE -------------- 0045 0046 %% License: 0047 % MIT License 0048 % 0049 % Copyright (c) 2018 Thomas Hiller 0050 % 0051 % Permission is hereby granted, free of charge, to any person obtaining a copy 0052 % of this software and associated documentation files (the "Software"), to deal 0053 % in the Software without restriction, including without limitation the rights 0054 % to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 0055 % copies of the Software, and to permit persons to whom the Software is 0056 % furnished to do so, subject to the following conditions: 0057 % 0058 % The above copyright notice and this permission notice shall be included in all 0059 % copies or substantial portions of the Software. 0060 % 0061 % THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 0062 % IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 0063 % FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 0064 % AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 0065 % LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 0066 % OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 0067 % SOFTWARE.


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One thing I have been wisely warned about is that if prospective employers check out my Github page and my code is not clean, that's an easy no to a potential job candidate. I have several projects done in Javascript (node.js), PHP (Code Igniter), and Python (Django), but I wanted to go back and review those frameworks and see if I could refactor or improve them.
Otherwise, overall I may consider pruning my Github of some of my less interesting early lessons. But to begin, I have to begin another place. I really wanted to get a reading of Clean Code by Roger Martin under my belt, as it's pretty much software developer gospel.
And to begin with Clean Code, I realized I really needed to begin with Java. Having blown up a runthrough of Kent Beck's Test Driven Development last month, I realize that I need to get as comfortable as I can with Java in the Eclipse IDE. To that end, I have purchased a copy of Murach's Java in the Eclipse environment.
A lot of software engineer/software development books work in Java, so it's a language I want to improve upon. I'm also interested in upping my fluency to use a Java frame (I'm thinking Swing) for putting together a software that houses my family's photo albums (more on that later).


What is Apalis?¶
Apalis is a python library for parallel computing. It focuses on enabling parallel computing with little overhead. In Apalis vs Ray we compare Apalis to ray in speed.
Getting started with Apalis¶
Apalis can be installed from PyPI:
pip install apalis
Apalis can send an object into a child process and interact with it through a Handler. To send an object into a parallel process just:
import apalis
import time
class A:
def expensive(self, x):
time.sleep(1)
return x
a = A()
obj = apalis.Handler(a) # Sends the object to a child process.
token = obj.expensive(5) # Sends the task to the object in the child process.
token() # Calling the token yields the result of the operation.
The same can be done with multiple Handlers at once.
es = [apalis.Handler(A()) for _ in range(16)]
tokens = [obj.expensive(5) for obj in objs]
aplais.get(tokens) # Gets the results of the operations.
More examples can be found in this Jupyter Notebook.
Apalis vs Ray¶
Ray is the go-to option for parallel computing in python. It has a lot of functionality build in which makes it a good choice for a variety of projects. The problem is that the functionality comes at the cost of a lot of overhead. This is especially noticeable when parallelizing tasks that take less than 1ms to complete.
In the figure bellow different tasks that take time are parallelized by both Apalis and Ray on a 16 core CPU. The speedup from both methods is plotted against how expensive the task was, to begin with. Apalis is faster than single-threaded for tasks that are slower than 0.04ms while Ray is only better than single-threaded starting from 0.4ms. Note that the longer the task takes the closer to 16 times improvement we come.
The code to generate the image above can be found in this Jupyter Notebook.


Extremely fast HTTP Archive (HAR) validator using JSON Schema.
npm install --only=production --save har-validator
I recommend using an optimized build matching your Node.js environment version, otherwise, the standard require
would work just fine with any version of Node >= v4.0
.
/*
* Node 7
*/
const validate = require('har-validator/lib/node7')
/*
* Node 6
*/
const validate = require('har-validator/lib/node6')
/*
* Node 4 (Default)
*/
var validate = require('har-validator')
Please refer to har-cli
for more info.
Note: as of v2.0.0
this module defaults to Promise based API. For backward comptability with v1.x
an async/callback API is also provided
:copyright: ahmadnassri.com · License: ISC · Github: @ahmadnassri · Twitter: @ahmadnassri


what is WPS-PD?
A short introduction
WPS 1.0.0 specification
what about data types?
idea of presentation directives
WPS-PD elements
conclusion


Notice that the second integration pattern is not fully working as of now...
Here you can find two ways of integrating a navigaton using Angular JS
This is just as a demonstration so the sticky solution does not work for both navigations (you are only ment to have one in a real senario)


Our expert instructors conduct classes literally anywhere. Take a yoga class on mountaintop. Do boot camp on the beach. Go to an abandoned mansion for mat pilates. The options are limitless.


The pack function is used to combine and transform sets of files into a single output. The following options can be used:
pack({ to: 'Build/site.min.js', include: '*.js', exclude: 'debug.js', minify: true });
You can also pass the pack function a string or an array. These are translated into the include option specified above.
The pack function returns an object that exposes a function called 'to'.
The to function attaches options to outputs defined by the preceding call to the pack function. It has two formats:
pack('*.js').to('combined.js');
Passing a string simply attaches a 'to' option to the existing output.
pack('*.js').to({ 'combined.js': { }, 'combined.min.js': { minify: true } });
Passing a hashtable of paths and additional options creates multiple outputs. The additional options are merged with those specified in the call to pack.
This example combines JavaScript files from the Scripts and Libraries folder into two files, one simply combined and the other prepared for production. A template called license is applied to each file.
pack({ include: [ { files: 'Scripts/*.js', recursive: true }, 'Libraries/*.min.js' ], outputTemplate: 'license' }).to({ 'Build/site.js': { }, 'Build/site.min.js': { minify: true, exclude: '*debug.js' } });
This example embeds all panes, infrastructure scripts, additional templates and styles from their respective folders into a set of three files, combined, minified and a special debug mode.
pack({ include: [ T.panes('Panes'), T.scripts('Infrastructure'), T.templates('Templates'), T.styles('Styles') ], recursive: true }).to({ 'Build/site.js': { }, 'Build/site.min.js': { minify: true } 'Build/site.debug.js': { debug: true } });
See the built-in templates reference for more information.


404
The page you are requesting for could not be found. Maybe you were looking for the documentation or the short tutorial.
© 2019 Alexis Luengas
--- permalink: /404.html ---
The page you are requesting for could not be found. Maybe you were looking for the documentation or the short tutorial.


The-Solution,The-Attitude,
1. The-No-Names,The-Secret,The-Anonymous,The-Stealth,The-Agency,The-Practice, design, The-Division,The-Firm,The-Dog,The-Corporation,The-Consortium,The-Multinational,The-Lion,The-Witch,The-Wardrobe,The-Cubicle,The-List, emotions, The-Office,The-Org,The-Snowdens,The-Intelligence,The-Service,
2. The-Order,The-Mechanic,The-Technician,The-Hegels,The-Syndicate,The-Advocate,The-Password,The-Number,The-Above,The-Default,The-Poetry, thoughts, and stuff The-Square,The-Too-Many,The-Painkiller,The-Few,The-Meta,The-Geometric-Shape,
The-Individual,
The-10016


TDL (Time Definition Language) was created within the MoDECS project as a successor of the Giotto language for time triggered deterministic computation. Its hard real-time properties makes it ideal for use in automation and control engineering.
We will present the concepts and a runtime infrastructure for distributed TDL execution (bus scheduling and distributed E-machine). The key concept is transparent distribution, i.e. there is no difference observable between local and distributed excution of modules. A sample case study will be presented as a proof of concept.
The following source code is an example of TDL usage for a basic counter. The application contains one task and has only one mode of operation.
module counter { const z = 0; // a constant for easy initialization actuator int a := z uses set_act; // use external function set_act task inc [wcet = 1ms] { output int o := z; // initialized with 0 at startup uses inc_func(o); // use external function inc_func with parameter o } start mode main [period = 1000ms] { task [1] inc(); actuator [1] a := inc.o; // set actuator with output of task } }
Copyright © 2004 MoDECS Team


NAME
twistd - run Twisted applications (TACs, TAPs)
SYNOPSIS
twistd [options]
DESCRIPTION
Read a twisted.application.service.Application out of a file and run it.
OPTIONS
-n, --nodaemon Don't daemonize (stay in foreground).
- -q, --quiet
- No-op for backwards compatibility.
- -p, --profile <profile output>
- Run the application under the profiler, dumping results to the specified file.
- --profiler <profiler name>
- Specify the profiler to use. Defaults to the 'hotshot' profiler.
- --savestats
- Save the Stats object rather than the text output of the profiler.
- -b, --debug
- Run the application in the Python Debugger (implies --nodaemon option). Sending a SIGINT or SIGUSR2 signal to the process will drop it into the debugger.
- -e, --encrypted <file>
- The specified tap/aos file is encrypted.
- --euid
- Set only effective user-id rather than real user-id. This option has no effect unless the server is running as root, in which case it means not to shed all privileges after binding ports, retaining the option to regain privileges in cases such as spawning processes. Use with caution.
- -o, --no_save
- Do not save shutdown state.
- --originalname
- Behave as though the specified Application has no process name set, and run with the standard process name (the Python binary in most cases).
- -l, --logfile <logfile>
- Log to a specified file, - for stdout (default: twistd.log). The log file will be rotated on SIGUSR1.
- -l, --logger <fully qualified python name>
- A fully-qualified name to a log observer factory to use for the initial log observer. Takes precedence over --logfile and --syslog.
- --pidfile <pidfile>
- Save pid in specified file (default: twistd.pid).
- --chroot <directory>
- Chroot to a supplied directory before running (default: don't chroot). Chrooting is done before changing the current directory.
- -d, --rundir <directory>
- Change to a supplied directory before running (default: .).
- -u, --uid <uid>
- The uid to run as (default: don't change).
- -g, --gid <gid>
- The gid to run as (default: don't change).
- --umask <mask>
- The (octal) file creation mask to apply. (default: 0077 for daemons, no change otherwise).
- -r, --reactor <reactor>
- Choose which reactor to use. See --help-reactors for a list of possibilities.
- --help-reactors
- List the names of possibly available reactors.
- --spew
- Write an extremely verbose log of everything that happens. Useful for debugging freezes or locks in complex code.
- -f, --file <tap file>
- Read the given .tap file (default: twistd.tap).
- -s, --source <tas file>
- Load an Application from the given .tas (AOT Python source) file.
- -y, --python <python file>
- Use the variable
application
from the given Python file. This option overrides -f. This option implies --no_save. - --syslog
- Log to syslog instead of a file.
- --version
- Print version information and exit.
- --prefix <prefix>
- Use the specified prefix when logging to logfile. Default is
twisted
.
Note that if twistd is run as root, the working directory is not searched for Python modules.
SIGNALS
A running twistd accepts SIGINT for a clean shutdown and SIGUSR1 to rotate log files.
AUTHOR
Written by Moshe Zadka, based on twistd's help messages.
REPORTING BUGS
To report a bug, visit http://twistedmatrix.com/trac/wiki/TwistedDevelopment#DevelopmentProcess
COPYRIGHT
Copyright © 2001-2011 Twisted Matrix Laboratories. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.


Note: This version of the keyboard includes a new version of the Lateef font including multiple typefaces. You may find it helpful to uninstall the old version of the Lateef font before installing this package.
This keyboard was developed for keyboarding the Balochi language in the Arabic Script based on the standard Windows Urdu keyboard.


If you have any short comments, please let us know:
If you have any comments, please let us know: You rock!
If you have any comments, please let us know: Dear Francine, They closed the parks this week, so we won’t be able to meet your there. Should we just have dinner? Love, Daddy


Stephen Colbert, the comedian and host of Comedy Central's Colbert Report,
will succeed David Letterman as host of Late Show,
CBS's flagship late-night franchise, when Mr. Letterman retires next year, the network announced Thursday.
Mr. Colbert will sign on for a five-year term as the new Late Show
host, according to the announcement from Leslie Moonves, the president and chief operating officer of CBS, and Nina Tassler, the chairwoman of CBS's entertainment division.
CBS moved quickly to name a successor to Mr. Letterman, the late-night TV fixture who has hosted Late Show
since 1993 and who revealed his plans to retire in a surprise announcement to his audience last week.
Speculation about who might take over from Mr. Letterman, who was also the founding host of NBC's Late Night
franchise, quickly coalesced around Mr. Colbert, who has played a satirically self-obsessed, know-it-all host on The Colbert Report
since its creation in 2005, and before that a similar character on Comedy Central's The Daily Show With Jon Stewart.
Other contenders to replace Mr. Letterman were said to include Craig Ferguson, the host of CBS's Late Late Show,
which follows Mr. Letterman's program; Chelsea Handler, the host of Chelsea Lately
on the E! cable channel; and Neil Patrick Harris, a star of the sitcom How I Met Your Mother,
which concluded its run on CBS this year.
Simply being a guest on David Letterman's show has been a highlight of my career,
Mr. Colbert said in a statement. I never dreamed that I would follow in his footsteps, though everyone in late night follows Dave's lead.
Mr. Moonves said in a statement: Stephen Colbert is one of the most inventive and respected forces on television. David Letterman's legacy and accomplishments are an incredible source of pride for all of us here, and today's announcement speaks to our commitment of upholding what he established for CBS in late night.
Mr. Colbert said he will not stay in character when he takes over Late Show.
The network said specific creative elements, like a producer and a location, would be announced later. Both New York and Los Angeles have been lobbying to become the home of a new Late Show.
Comedy Central said in its own statement that it was proud that the incredibly talented Stephen Colbert has been part of our family for nearly two decades.
The channel added, We look forward to the next eight months of the groundbreaking 'Colbert Report' and wish Stephen the very best.