Apple to launch new 13-inch MacBook Pro in 2020 with new keyboard
by AbdullahApple to launch new 13-inch MacBook Pro in 2020 with new keyboard
5 (100%) 1 vote
Following the introduction of the new 16-inch MacBook Pro, the smaller model is expected to have the same right. A new report released by Digitimes points precisely in that direction.
According to what is advanced, the new 13-inch MacBook Pro will be unveiled in the first half of 2020. Following the line of the 16-inch model, the new notebook should also feature a “scissor” keyboard.
The butterfly keyboards have proved to be a bit of trouble and criticism on the part of the users. In this regard, Apple has returned to “scissor” keyboards with the new 16-inch MacBook Pro and the same path should be followed with the smaller model.
Leading analyst Ming-Chi Kuo predicted that by 2020 all Apple laptops would use a “scissor” keyboard.
The screen size of new 13-inch MacBook Pro may be the same
To the displeasure of some fans, the report now states that Apple will keep the 13.3-inch screen on the next model. After the maneuver made on the model presented last week, the hope was that the technology would incorporate a 14-inch screen into the same 13.3-inch body.
Going back and behind the keyboard of the new MacBook Pro, also the Touch ID and the “ESC” key should be separate from the Touch Bar. That is the same ideology that the American employed in the latest model.
Hardware is also expected to improve
Although the report does not mention it. Apple is more than likely to take the opportunity to introduce new hardware inside this notebook. In fact, the adoption of a 10th generation Intel processor and a base model with larger storage space is expected.


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Preliminary studies
To join university education, the general and special admission requirements for the specialization that the student wishes to join must be met. The Academy gives students the opportunity to study to study some subjects and grants them a qualifying diploma for university admission.
Read moreBachelor's studies
The Swedish International University provides a wide range of academic, social and professional opportunities, during which the student studies a specific subject to obtain a bachelor's degree awarded by the university after completing the prescribed period of study in accordance with the
criteria and conditions for admission specified by the Swedish Ministry of Higher Education and Scientific Research. At the end of the bachelor's study, the student can combine theoretical study with practical practice. This degree provides the student with the skills and knowledge necessary to obtain a specific job or complete postgraduate studies.
The university grants degrees in a number of disciplines, including educational and psychological sciences, sociology, philosophy, law and politics, media, social service, special education, public health and therapeutic nutrition. Under construction.
Duration of study: Bachelor's degree 3 years.
Postgraduate studies
The university offers different programs for obtaining a master's and doctorate degree, including courses and a final thesis at a high level and a high degree, the thesis in most cases takes more than half of the workload.
Distinguished graduate students who demonstrate their abilities in creative and innovative work are accepted, and the student is required to be academically qualified for scientific research and the upcoming specialization. The competition for admission is in light of the general average obtained in the Bachelor’s and Master’s degrees. Acceptance in some
departments requires success in an admission exam and an individual interview. The graduate student receives individual supervision and prepares a thesis that is publicly discussed. Some departments may require that the thesis be part of an ongoing project within the department. Researchers often work as part of an integrated team in the fields of technology, natural sciences and education.
Master's studies
The master's program has been prepared to meet the needs of students who seek to enhance their skills and expand their knowledge in diverse and modern scientific fields that are compatible with the needs of the labor market locally, regionally and internationally. Where integrated programs have been prepared aiming to apply the knowledge gained from the theoretical and
empirical perspectives in order to graduate people capable of working in many environments.
Duration of study: one year / two semesters: one academic year, during which the thesis is also written.
Language of study: Arabic and English (according to branch and specialization)
PhD studies
This study is the highest university degree granted by the university, and it qualifies the student and helps him to make his own theories resulting from his practical experience and previous academic studies. The applicant for a doctoral study is required to fulfill the minimum requirements and to have an acceptable academic qualification with a grade appropriate to the required level. The duration of the thesis is 3 years.
Previous studies: Master's degree.
Language of study: Arabic, English and Swedish (depending on branch and specialty)
Professional studies
Vocational education is of a very practical nature, and gives the student the necessary skills during working life. It is intended for those young people who have completed their basic education, so they can join work or enroll in higher education after completing their vocational education. The university has prepared various programs in various fields that meet the needs of the labor market in various sectors, whether educational,
health, administrative and so on. Which qualifies applicants to assume the tasks of the job and the ability to adapt within the work environment with the constant desire to learn and develop their personal and practical skills for the advancement of the organization or company in which they work. One of the Academy's priorities is to prepare its students for practical life and train them to be experts and specialists, each in their field.
We also seek to provide opportunities for our students to travel to Sweden for the purpose of student exchange, exchange of practical experiences and actual training in Swedish institutions and under the supervision of a group of professors and experts to transfer their practical experiences to students and teach them in all possible ways.
The university grants a professional diploma in some professional disciplines that suit the needs of the international community in general, and some professional disciplines that meet needs in the Arab countries.


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[System.Runtime.InteropServices.DispId(64653)]
public void AfterWrite ()Remarks
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Namespace: Microsoft.Office.Interop.Outlook
Assembly: ORCAUnitTest (in ORCAUnitTest.dll)
Assembly Versions: <IP_ADDRESS>
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[System.Runtime.InteropServices.DispId(64432)]
public void BeforeAttachmentAdd (Attachment Attachment, out bool Cancel)Parameters
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[System.Runtime.InteropServices.DispId(64431)]
public void BeforeAttachmentPreview (Attachment Attachment, out bool Cancel)Parameters
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[System.Runtime.InteropServices.DispId(64427)]
public void BeforeAttachmentRead (Attachment Attachment, out bool Cancel)Parameters
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Assembly: ORCAUnitTest (in ORCAUnitTest.dll)
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[System.Runtime.InteropServices.DispId(61453)]
public void BeforeAttachmentSave (Attachment Attachment, out bool Cancel)Parameters
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[System.Runtime.InteropServices.DispId(64434)]
public void BeforeAttachmentWriteToTempFile (Attachment Attachment, out bool Cancel)Parameters
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[System.Runtime.InteropServices.DispId(64117)]
public void BeforeDelete (object Item, out bool Cancel)Parameters
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[System.Runtime.InteropServices.DispId(64652)]
public void BeforeRead ()Remarks
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Namespace: Microsoft.Office.Interop.Outlook
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[System.Runtime.InteropServices.DispId(61446)]
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Namespace: Microsoft.Office.Interop.Outlook
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[System.Runtime.InteropServices.DispId(61441)]
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[System.Runtime.InteropServices.DispId(64429)]
public void Unload ()Remarks
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Namespace: Microsoft.Office.Interop.Outlook
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The Edge Table Data Structure
The edge table is an
array of pointers to linked lists, as shown in the figure. It has one row for
each scanline, and each element of the array points to a linked list of edges
whose minimum y coordinate lies on that edge. For example, in the figure,
scanline 5 would contain edge CD since CD's minimum y
coordinate lies on scanline 5.
The actual data stored about each edge is implementation dependent, but one
such implementation could be as shown:
Procedure
The above data structure is filled by using a bucket-sort
algorithm, with each scanline representing a bucket. The edges within each
bucket are kept sorted according to increasing x coordinate.
Back to Polygon Scan Conversion
Viren
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viren@cc.gatech.edu


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Marquette Colleges in Marquette, MI Find and compare the best colleges, universities, certificate programs, career training, community colleges and graduate schools in Marquette, MI. http://www.campusexplorer.com/colleges/in/Michigan/68480733/Marquette/
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Gallery
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I got a log file in my inbox earlier this evening. Sometimes, people write an accompanying email describing a problem but this time, I only had the log file. It didn’t take long to see the crash and stack trace in the logs. After a quick investigation, I found that there was a bug when the last sync had been done long enough ago that the last page synched didn’t exist anymore on the receiver. That was an easy fix and I just pushed the release with the bugfix.
Grab the latest build here.
Thanks to the anonymous bug report!


| Course Duration: | 5½ Years |
| Course Type: | Undergraduate Course |
| Eligibility Criteria: | 10+2 passed with PCB subjects |
| Qualification Awarded: | Bachelor’s Degree |
In this article, we will analyze the professional course called BAMS. BAMS stands for Bachelor of Ayurvedic Medicine and Surgery. This is a professional course that 12th Science students belonging to Biology group (Physics, Chemistry and Biology subjects) may pursue. We will check out basic details of the course, syllabus & important subjects, its value in the job market and career prospects.
Ayurveda is a branch of alternative medicine. The term ‘Ayurveda’ stands for Science of life! It is a mode of treatment that is inspired by natural cure for ailments.This science actually originated in India. Its roots can be traced back to the Vedas! BAMS course is designed to train students get familiar with concepts of Ayurveda and make use of them to treat patients.
Ayurveda mostly focuses on natural cures as well as lifestyle changes to cure ailments. The course covers those topics in detail and helps train students to use those very solutions to solve modern day diseases also!
BAMS is a five and a half years long course. The last one year is dedicated towards Internship.
Only 12th Science stream, Biology group students are eligible to apply for this course. In most cases, the minimum marks criteria for admission is 50% marks in the 12th Board examinations.
First of all, getting admission in a BAMS college is relatively easier, when compared to other medicine course like MBBS! When it comes to MBBS seats, the competition is cut throat and there are limited number of Government College seats available
In case of BAMS, the competition is not too high. So, even above average students may get admission in a Government College and thus pursue this medicine course without having to spend much money! Sure, BAMS is not as valuable as MBBS. But please read the next paragraph to get a glimpse of the changing trend!
After completing the five and a half year long course, Graduates may either start practicing or may study further. They may pursue PG courses or may even go for research after graduation.
After BAMS, a number of job opportunities are available in front of Graduates! They may start up own clinic and start private practice. One may even join Private or Government Hospitals also, after graduation.


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Maximizing
Signal Strength for OFDM Inside Buildings
|
Electrical and Computer Engineering
James Cook University, Douglas Campus, Townsville, Queensland,
4814, Australia
Email<EMAIL_ADDRESS><EMAIL_ADDRESS>|
Published: E.
Lawrey, C. J. Kikkert, "Maximising Signal Strength
of OFDM inside buildings", IEEE Transactions on
Microwave Theory and Techniques, Nov 2001, pp. 2131-2136
|
IEEE retains the copyright to this paper, which can be found
at www.ieee.org/copyright/
Abstract
Propagation inside buildings suffer from large shadowing
and high multipath effects. This is a serious problem for
Wireless Local Area Network (WLAN) systems. This paper shows
that shadowing and path loss can be minimized by exploiting
the multipath tolerance of Orthogonal Frequency Division Multiplexing
(OFDM). This can be achieved by using multiple transmission
antennas spread over the area of a WLAN cell. These antennas
act as repeaters, transmitting and receiving the same signal
at the same time. This decreases the average path loss, but
increases the multipath delay spread. Using OFDM allows the
advantage of reduced path loss to be utilized without detrimental
effects of Inter-Symbol Interference (ISI) caused by the increased
delay spread. The reduced path loss allows an increased system
capacity, quality of service or a decrease in intercellular
interference in a cellular WLAN.
Index terms-- Access point repeater, broad-band communications,
indoor radio communication, multipath channels, orthogonal
frequency division multiplexing, wireless LAN.
I. Introduction
Wireless networking is an emerging technology allowing users
the freedom of movement. The aim of wireless local area network
(WLAN) systems is to provide users with a data rate comparable
with wired networks within a limited geographic area. Currently
most WLAN products use direct-sequence spread-spectrum (DSSS)
techniques, based on the IEEE 802.11b Standard, providing
a data rate of 11 Mb/s in the 2.4- GHz industrial-scientific-medical
(ISM) band [1]. The next generation of WLAN systems will be
based on two similar WLAN standards known as: Hiperlan/2 (Europe),
and IEEE802.11a (U.S.) [2]. These support a physical layer
transmission rate of up to 54 Mb/s and use orthogonal frequency-division
multiplexing (OFDM) for the physical layer implementation.
OFDM is a multi-carrier modulation scheme, which has a high
immunity to multipath effects and allows a wide range of carrier
modulation schemes to be used. Hiperlan/2 adaptively changes
the forward error correcting coding rate and the carrier modulation
scheme (BPSK, QPSK, 16 quadrature amplitude modulation (QAM),
64 QAM) allowing the data rate to be maximized based on the
current radio channel characteristics. Using a higher spectral
efficiency modulation scheme, such as 64 QAM, allows the data
rate to be increased, but requires a higher SNR for a fixed
error rate. Thus, minimizing the path loss, allows the SNR
and corresponding data rate to be maximized.
Shadowing can result in numerous regions of the building
having an inadequate coverage, resulting in a poor quality
of service (QOS). This is a significant problem as the QOS
of WLAN systems is very important if they are to replace wired
networking. Shadowing also increases the average path loss
compared with free space, requiring more transmission power,
in order to maintain communications.
Fig. 1, Methods for obtaining spatial diversity.
Access point repeater (APR). Base station (BS). Power splitter/combiner
(PS). (a) Cellular system with four cells controlled by four
BSs, connected with a wired network for hand off between cells.
(b) Single multiple transmission cell using APRs.
High-quality coverage of a building can be obtained by using
a cellular system as shown in Fig. 1(a). Each base station
(BS) forms a cell covering a small area of the building. These
cells operate at different frequencies to prevent interference
between them. The path loss is minimized, as the distance
from the mobile station to the closest BS is minimized. Additionally
if the transmission path to the closest BS is blocked, the
mobile can connect to another cell. However, this type of
implementation can be expensive, due to the requirement of
a number of BSs. Additionally, it requires multiple frequency
bands for cellular implementation and hand offs between cells,
increasing the system complexity. This paper presents a simpler
and cheaper method for obtaining reliable coverage, in an
environment that suffers from shadowing.
II. Spatial Diversity by Multiple Repeat Transmissions
A form of spatial diversity can also be achieved by splitting
the signal from a single central BS and transmitting the same
signal from multiple locations around the building to be covered.
This is shown in Fig. 1(b). Shadowing is reduced because there
are multiple opportunities to receive the signal. Even if
several paths are blocked by walls or buildings, others may
have a reasonable transmission path. Using multiple transmitters
effectively reduces the transmission distance, as the closest
transmitter dominates the signal power.
An example of how spatial diversity maximizes power efficiency
is lighting of a building. If you were trying to illuminate
a typical large building with a single light bulb, the high
opacity of the walls would result in many deep shadowed regions.
The amount of power that would be required, for all parts
of the building to be reasonably bright, would be extremely
high, as shadowed regions would be lit solely from reflections
and gaps in obstructing walls, such as doorways. However,
by using one light per room, the illumination will be much
more even, with minimal shadowing and a reduced total lighting
power. The same is also true for radio signals; thus by using
multiple transmitters spread over the area of a building,
we can reduce the average path loss.
Most communication systems need two-way communications using
a forward and reverse link. Due to the reciprocal nature of
radio propagation, the properties of the reverse link will
be the same as the forward link. Thus, the path loss for the
reverse link can also be minimized by using multiple receive
antennas connected to a single central BS. The receive and
transmit antennas can be combined into one unit, referred
to here as an access point repeater (APR). The use of APRs
can provide a significant improvement with minimal expense.
The problem with using APRs is that the mobile receiver will
see signals from all APR transmitters. The propagation delay
from each transmitter will be different and, thus, will arrive
at the receiver with a different delay. This is equivalent
to receiving the signal distorted by strong multipath. This
causes frequency-selective fading, and an increase in the
delay spread of the transmission, which can result in inter-symbol
interference (ISI). This is particularly a problem for modulation
schemes such as frequency shift keying (FSK), as the maximum
symbol rate is limited by ISI caused by delay spread.
DSSS systems have a high multipath tolerance due to use of
a RAKE receiver [3]. A RAKE receiver uses correlation to resolve
delayed copies of the signal caused by multipath propagation.
These are then aligned in time and combined. This allows the
signals from each of the transmitters to be resolved and combined.
The maximum delay spread that can be tolerated by an IEEE802.11b
DSSS WLAN system, using a 16-tap RAKE receiver, is 125 ns
at 11 Mb/s and 250 ns at 5.5 Mb/s [4]. This level of multipath
tolerance should allow APRs to be spaced out with a maximum
diameter of about 20-35 m, although problems might arise due
to the increased delay spread. This small antenna spacing
means that there would be little advantage in using multiple
APR with an IEEE802.11b system as sufficient coverage can
easily be obtained over 20-35 m with a single transmitter.
OFDM has a higher multipath tolerance than DSSS, and can
transmit using a higher spectral efficiency. Minimizing the
path loss allows the SNR to be increased, provided inter-cellular
interference is low. This improved SNR can be utilized by
adaptively setting the modulation scheme based on the SNR,
allowing the throughput of the system to be increased.
The high multipath tolerance of OFDM is due the low symbol
rate used, and the use of a guard period between symbols.
The guard period is a cyclic extension of each OFDM symbol,
giving protection against ISI, provided it is longer than
the delay spread of the radio channel. Typically, the guard
period is made to be a small fraction of the OFDM symbol time
and, thus, by using a large number of narrow bandwidth carriers,
the delay spread tolerance can be varied to suit the radio
conditions.
Multipath causes frequency-selective fading, which can result
in carriers of the OFDM signal being lost in nulls in the
spectrum. These nulls are typically handled by including forward
error correction to compensate for the lost data. Adding multiple
transmitters will result in an increased delay spread, resulting
in a decrease in the correlation bandwidth of the channel.
This will not cause any detrimental effects on the OFDM transmission,
provided that enough carriers are used.
Indoor propagation normally suffers from a combination of
Rician and Rayleigh fading [5]. Using multiple APRs will increase
the multipath energy, resulting in more areas in the building
suffering from Rayleigh fading. However, this increase in
fading should be more than compensated for by the decreased
path loss due to the multiple APRs. More research is needed
to establish the extent of the additional multipath when using
APRs.
The use of multiple transmitters to obtain improved coverage
was first introduced in the digital audio broadcasting (DAB)
system [6]. DAB uses OFDM with a low symbol rate and a long
guard period. With DAB, it is possible for all transmitters
to use the same frequency and transmit copies of the same
signal, referred to as a single-frequency network (SFN). For
VHF band transmissions, DAB uses 1536 carriers with a the
symbol time of 1 ms, and a guard period of 246 ms, allowing
transmitters to be up 96 km apart in a SFN, before the delay
spread is too large.
Hiperlan/2 has a guard period of 800 ns, which would provide
an effective delay spread protection of up to 250 ns. This
would allow APRs within each cell, to be placed with a maximum
diameter of 40-60 m, which is sufficient for coverage of most
buildings. Additional research is needed to verify this.
III. Implementation of an APR
All APRs within the same cell transmit and receive the same
signal, thus only one BS is needed per cell. For transmission,
the signal generated by a BS is split N ways, where N is the
number of APRs. Coaxial cable or some other medium, such as
optic fibre, is used to deliver the signal to each APR. The
signal then is amplified at the APR to compensate for any
losses in the coax transmission. For reception, the reverse
process is used. Each APR has a low noise amplifier (LNA)
to compensate for losses in the coax, in order to maintain
a low noise figure. The received signals from all APRs are
combined, then demodulated at the BS. Phase differences between
the APRs have little or no effect as they corrected for, in
the OFDM demodulation process.
Fig. 2. Possible implementation of an APR.
Fig 2. shows a simple implementation of an APR, which can
be used when the loss in the coaxial cable is low (< 20 dB).
The master head amplifier operates at the RF frequency and,
thus, no frequency translation is required. A low frequency
control signal can be used to select whether to transmit or
receive. For a full duplex system, the RF switches can be
replaced with diplexers.
In larger systems where the cable losses are too large, the
signal can be transmitted on the cable at an IF frequency.
A common clock reference must be used by all APRs to ensure
frequency synchronization, otherwise frequency errors will
reduce the orthogonality of the OFDM, causing inter-carrier
interference. A suitable out-of-band clock reference must
be transmitted from the base station. This common clock can
then be frequency multiplied using a phase-locked-loop (PLL)
to generate the local oscillator (LO) for the IF-RF mixing.
For such a design, care must be taken to ensure the phase
noise of the clock reference is low and that the clock signal
does not interfere with the received signal.
Another method for distributing high frequency RF signals
is to use optic fiber. The RF signals can be converted to
optical signals and transmitted over long distances with optic
fiber. This type of technology is currently being developed
for use in mobile phone applications as a method for producing
pico-sized cells [7].
IV. Experimental Setup
An experiment was set up to test the effectiveness of using
multiple transmitters (i.e., APR) to minimize shadowing in
an indoor environment. The forward link from the BS to the
mobile stations was tested, by measuring the effective path
loss from fixed transmitters to a mobile receiver. The path
loss from a single transmitter (simulating a single access
point) was compared with the path loss when using two transmitters
(simulating two APRs).
Fig. 3, Path-loss measurement locations in
the ECE building. Lines represent internal walls. The thin
lines are plaster board walls, and the thick ones are concrete
walls.
The path loss was measured at 235 locations on the second
floor of the Electrical and Computer Engineering (ECE) building
at James Cook University, Townsville, Qld., Australia. The
measurement locations and the building layout are shown in
Fig. 3. The internal walls are shown as dark lines. The selection
of the measurement locations, the position of the transmitters,
and the construction of the building can easily influence
the overall path-loss probability distribution. However, the
results presented will be representative of the improvement
that could be expected in a typical building of similar construction
to the one the measurements were taken in.
Fig. 4, Transmitter set up simulating Access
Point Repeaters. The total transmitter power from Tx2a and
Tx2b were matched to the Tx1 power.
The transmitter set up is shown in Fig. 4. Simple monopole
antennas were used and were assumed to have an effective gain
of 0 dBi, including matching losses. The uncertainty in the
gain of the antennas resulted in an absolute error in the
path-loss measurements of approximately 3 dB and a differential
error between the single and dual transmitter measurements
of 1dB. The signal strength at each location was measured
using a spectrum analyzer on a trolley, and converted to path
loss by compensating for transmitter power and receiver gain.
A slightly different frequency was used for the single and
dual transmitters to allow simultaneous measurements of the
path loss. The receiver antenna was placed on a rotating platform
that was turned during the received power measurement. Video
averaging on the spectrum analyzer was used to average the
power over a 0.6 m circular path swept by the antenna. This
was done to remove the effects of frequency selective fading,
and obtain an accurate measure of the path loss. Even though
the path loss was measured using a continuous wave transmission,
the results are still valid for a wide-bandwidth modulation
schemes.
Due to limitations of the equipment available, the measurements
were performed at 1 GHz, rather than 5 GHz. This will tend
to reduce the effects of shadowing, as the opacity of most
materials is lower at lower RF frequencies; thus, we would
expect the effectiveness of using APRs to improve at higher
RF frequencies.
V. Discussion of Measured Results
Fig. 5 shows the path loss for the single transmitter. The
path loss increases rapidly with distance from the transmitter.
The path loss in the bottom left corner of Fig. 5 at location
5 x 5 m has a high path loss of over 100 dB, which is equivalent
to 1 km of free-space loss, even though it is less than 20
m from the transmitter. Fig. 6 shows the path loss when two
transmitters were used. In this case the path loss is lower
and much more even.
Fig. 5, Measured path loss with one transmitter
over the area of the building at 990 MHz. The dark lines are
the internal walls. The X shows the location of the transmitters.
Fig. 6, Measured path loss for two transmitters
at 990 MHz. This simulates two APRs. Note the total transmitter
power is the same as for the one transmitter measurements.
The X shows the location of the transmitters.
Fig. 7 shows the measured and simulated probability distribution
of the path loss. It shows that the measured path loss is
more than 7 dB lower when using two transmitters as compared
with one. This result is to be expected, as the longest distance
to a transmitter was reduced by 1.62 times. The typical path-loss
exponent of an obstructed path within a building is 4 - 6
[8], as compared to a path loss exponent of 2 for free-space
loss. We would therefore, expect the path loss to be reduced
by 8.4 - 12.6 dB for a reduction in distance of 1.6 times.
Since the transmission power is split over two transmitters
this will reduce the received power by 3 dB, thus resulting
in an overall improvement of 5.4 - 9.6 dB. This compares well
with the measured improvement of 7 dB. Even though there are
two transmitters, the received signal power tends to be dominated
by the closest transmitter due to the rapid fall of power
with distance. This is why the improvement in signal power
can be estimated with reasonable accuracy by considering the
reduction in distance to the transmitter.
Figure 7, Path loss probability distribution
within the measured and simulated building.
VI. Reduction in Cellular Interference
At a large distance, multiple APRs appear as a point source
and, thus, the received power is the same as when using a
single access point, where the total transmitted power is
the same. This means that the interference to neighboring
systems is approximately the same regardless of the number
of APRs used for fixed total transmission power. The near-field
path loss can be reduced by 7 dB using two APRs, allowing
the total transmitted power to be reduced by up to 7 dB for
the same SNR. This will reduce the overall interference to
nearby WLAN systems by 7 dB. Further improvements could be
made using a higher number of APRs. Using one APR per room
could potentially decrease the near field path loss by 20-30
dB, allowing a large reduction in external interference with
suitable power control. The reduced interference will allow
a better frequency reuse in a cellular system.
VII. Shadow Modeling
A simplified ray trace path loss model was developed to allow
investigation into the use of multiple APRs. This is similar
to the model used in [9]. The two dimensional (2-D) model
calculates the path loss along radial rays, which are converted
to a fixed rectangular data grid using interpolation. The
rectangular grid allows the signal power from multiple transmitter
sources to the added together.
Fig. 8. Attenuation calculations for a ray
passing through two objects.
The path loss along each ray is found by calculating its
intercept to each object in the environment. The loss through
each object is calculated based on the reflection coefficient
of the object surface and the distance through the object.
Each surface the ray intercepts results in energy being reflected
causing a jump in the accumulated attenuation. As shown in
Fig. 8(a), surface 1 - 4 result in jumps in the cumulated
object loss shown in Fig. 8(b). In this model, the amount
of reflected energy is constant regardless of the angle of
the ray. This reflected energy is not calculated as another
ray, and is ignored to keep the model simple.
In addition to reflected losses, each object absorbs energy
as the ray passes through it. This is calculated as a loss
proportional, in dB, to the distance traveled through the
object medium. The loss along the ray is accumulated as the
ray passes through multiple objects. This loss is then added
to the loss calculated by the standard free-space radio path-loss
equation to obtain the overall attenuation with distance.
The radio path-loss equation is
where PL is the path loss (in decibels), lambda
is the wavelength of the radio signal (in meters), r
is the distance from the transmitter (in meters), and alpha
(a) is the path loss exponent. For free space propagation,
a = 2. The simulation calculates the path loss due
to objects and, thus, ideally, the path-loss exponent used
in the simulation should be 2. However due to the simplicity
of the model, a path loss exponent of 2.65 was found to best
match the measured results.
VIII. Model Verification, Tuning and Limitations
The radio model was compared to the measured results to verify
the model accuracy and to adjust the model parameters to give
realistic results. The material properties of the walls were
measured directly and are show in Table I. These values compare
well with values measured in [9]. The walls were found to
be non homogeneous, caused by wiring, reinforcing, studs,
and near by objects, making accurate measurements difficult.
In the simulation, the material properties of the walls were
optimized to obtain a good match between the simulated and
measured building path loss shown in Fig. 5 and Fig. 6. The
resulting simulation parameters were found to closely match
the direct wall loss measurements, as shown in Table I. Fig.
7 shows the resulting match between the measured and simulated
results. This figure shows the percentage area of the building
(Y-axis), which has a path loss worse than a specified path
loss in the X-axis. For example, 20% of the building has a
path loss of greater than 90dB when using a single transmitter,
where as it is only 3% for two transmitters.
There is a good match between the simulated and measured
results, despite the simplicity of the model. If the wall
loss were considerably higher, then the path loss would have
been dominated by diffraction and multiple reflections, resulting
in a poor accuracy in the path-loss prediction.
IX. Simulated Results
Fig. 9 and Fig. 10 show the simulated path loss for a single
and double transmitter respectively, for the same building
and transmitter location as measured data shown in Fig. 5
and Fig. 6. The probability distribution of the path loss
is shown in Fig. 8. The main difference between the simulated
and measured results is that the simulated results are smoother,
which is the result of the simple environment model.
Figure 9, Simulated path loss for one transmitter
at 990 MHz. The X shows the transmitter location.
Figure 10, Simulated path loss for two transmitters.
The X shows the location of the transmitters.
In addition to simulating one and two transmitters, the path
loss was simulated with four and eight transmitters. The transmitters
were positioned in the simulation to approximately maximize
their effectiveness. Fig. 11 shows the path loss distribution
for all the simulated results. The path loss for the worst
2% of the area of the building was improved by 7 dB when using
two transmitters, 16 dB for four transmitters and 22 dB for
eight transmitters.
Figure 11, Cumulative probability distribution
for simulated results, showing the result for one, two, four
and eight transmitters.
X. Conclusion
Using multiple APRs is a low-cost method that can be used
to reduce shadowing and near-field path loss within a building.
This allows a reduction in intercellular interference with
suitable power control. It was shown experimentally to decrease
the near-field path loss by 7 dB @ 1 GHz within an indoor
environment, using two repeaters as compared with a single
transmitter. Simulated results show that the improvement can
be as much as 20 dB for eight transmitters. Using multiple
APRs will result in an increase in the received multipath,
however OFDM systems, including Hiperlan/2 and IEEE 802.11a,
should be able to tolerate this without detrimental effects.
This tolerance should allow a maximum spacing of 40-60 m between
any two APRs in a Hiperlan/2 cell.
References
[1] B. Crow, I. Widjaja, J. G. Kim, P. Sakai, "IEEE 802.11
wireless local area networks", IEEE Commun. Mag., pp. 116-126,
Sept. 1997.
[2] HiperLAN/2 - The Broadband Radio Transmission Technology
Operating in the 5 GHz Frequency Band, M. Johnsson, (1999),
[Online]. Available: http://www.hiperlan2.com/site/specific/specmain/specwh.htm
[3] U. Grob, A. L. Welti, E. Zollinger, R. Küng, H. Kaufmann,
"Microcellular Direct-Sequence Spread-Spectrum Radio System
Using N-Path RAKE Receiver", IEEE J. Select. Areas Commun.,
vol. 8, pp. 772-779, June 1990.
[4] HFA3863 data sheet (2000), [Online]. Available: http://www.intersil.com/data/FN/FN4/FN4856/FN4856.pdf
[5] R. Bultitude, S. Mahmoud, W. Sullivan, "A Comparison
of Indoor Radio Propagation Characteristics at 910 MHz and
1.75 GHz", IEEE J. Select. Areas Commun., vol. 7, January
1989.
[6] Digital audio broadcasting - Overview and Summary of
the DAB System, [Online]. Available: http://www.worlddab.org/public_documents/eureka_brochure.pdf
[7] C. Lim, A. Nirmalathas, D. Novak, "Dynamic Range Of A
Multi-Section Laser In A Millimetre-Wave Fibre-Wireless Uplink",
in Proc. Asia-Pacific Microwave Conf., Sydney, N.S.W., Australia,
Dec. 2000, pp. 539-543
[8] The Mobile Communications Handbook. Boca Raton, FL: CRC
Press, 1996, pp. 355-369. [9] S. Y. Seidel and T. S. Rappaport,
"914 MHz path loss prediction models for indoor communications
in multifloored buildings", IEEE Trans. Antennas Propagat.,
vol. 40, pp. 207-217, Feb. 1992.
|


Susan Calman (born 1974-11-06[ref]) has appeared in 151 episodes between 2010-2019. Susan Calman on IMDB. Susan Calman on Wikipedia. Susan Calman on Chortle.


OVER 35 MILLION AIRPODS SOLD IN 2018.
First released by Apple™ in December 2016, AirPods took the world by storm with its sleek, wireless form. At a hefty price tag of ~$150, AirPods quickly became a status symbol for wealth and class.
But the AirPods' clean, white exterior hides its true, insidious nature. Frequent users of the headphones have reported experiencing delusions of grandeur, declining social skills, and fear of losing their AirPods case. A subset of these AirPods users exhibit abnormally extreme symptoms, leading many to dub them the Pod Gang.
AirPod Addiction follows the tragic story of a Pod Gang member whose obsession with AirPods and inability to socialize with others eventually leave him powerless and unable to handle reality.


Ploror688.github.io
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Alyle UI contains an optional package that minimizes and optimizes styles created with lyl
.
This is necessary if you have many styles created with lyl
.
Important: Keep in mind that this will change the source files irreversibly, therefore, you should only use it in production.
Install the Alyle UI CLI globally.
To install the CLI, open a terminal/console window and enter the following command:
npm install -g @alyle/ui
or
yarn global add @alyle/ui
Test that Alyle UI CLI is installed by running on the root of your App:
cd My-App
lyl --version
The CLI only works on Angular projects.
It should be noted that this should only be done for production, or when deploying the App, as this will change the source files. For example, you can use this on a CI/CD.
In the root folder of your App run:
lyl src
Questions? Join the chat at Discord.


Sorry, this was meant to be viewed on a desktop computer, in order to export to PDF. Google Chrome is recommended.


{% extends "layout.html" %} {% block content %}
Moin! This is the portal that will help you to access and manage an infrastructure offered within course you are attending!


St Andrew's Hospice campaign aims to light up lives with memories of loved ones at Christmas
All donations go to supporting patients and their families across Lanarkshire
by Ross ThomsonSt Andrew’s Hospice has launched its annual Light Up a Life Christmas initiative ahead of the festive season.
Light Up a Life is a special opportunity to sponsor a light on the Hospice Christmas tree or on the Christmas tree in your local area, in memory or in honour of a loved one.
You can have a handwritten, personalised card delivered to you or sent to a friend or relative to let them know they are in your thoughts.
All donations go to supporting patients and their families across Lanarkshire.
The campaign has once again been generously sponsored by the Mears Group. Barry Duncan, Mears managing director, said: “We are proud to be involved with St Andrew’s Hospice as it plays an important role in caring for the people of Lanarkshire.
“We are also delighted to continue supporting the Hospice by sponsoring the Light Up a Life campaign again.”
Lorna McCafferty, fundraising officer at St Andrew’s Hospice, said: “The Mears Group have been sponsoring our Light Up a Life Campaign since 2012.
“Their continued support is greatly appreciated. Mears’ support, coupled with the generosity of the people of Lanarkshire makes a great difference to the lives of our patients and their families throughout the year.”
You can sponsor a light by visiting www.st-andrews-hospice.com, by completing a form in any St Andrew’s Hospice shop or in the reception of the Hospice in Henderson Street, Airdrie.
This year, Light Up A Life pin badges are also available for £2. The pins can be purchased in the Hospice, from their online shop or by telephoning Lorna McCafferty on 01236 772087.
You can sponsor a light up until noon on Christmas Eve.
Any cards written that day will be posted but you will not receive the card until the Royal Mail resumes deliveries.
The St Andrew’s Hospice Light Up A Life ceremony will take place in the Hospice grounds on Sunday, December 1 from 7pm.


| Name | Creator | Date | Type | Actions |
|---|---|---|---|---|
| {{ event.name }} | {{ event.creator.firstName }} | {{ event.date | date: 'dd/MM/yyyy' }} | {{ event.eventType }} |
| Name | Creator | Date | Type | Actions |
|---|---|---|---|---|
| {{ event.name }} | {{ event.creator.firstName }} | {{ event.date | date: 'dd/MM/yyyy' }} | {{ event.eventType }} |
If you delete this event, everyone will be disappointed. Are you really sure ?


Cloud Vision V1 API - Class Google::Cloud::Vision::V1::OutputConfig (v0.6.4)
Reference documentation and code samples for the Cloud Vision V1 API class Google::Cloud::Vision::V1::OutputConfig.
The desired output location and metadata.
Inherits
- Object
Extended By
- Google::Protobuf::MessageExts::ClassMethods
Includes
- Google::Protobuf::MessageExts
Methods
#batch_size
def batch_size() -> ::Integer
-
(::Integer) — The max number of response protos to put into each output JSON file on
Google Cloud Storage.
The valid range is [1, 100]. If not specified, the default value is 20.
For example, for one pdf file with 100 pages, 100 response protos will be generated. If
batch_size
= 20, then 5 json files each containing 20 response protos will be written under the prefixgcs_destination
.uri
.Currently, batch_size only applies to GcsDestination, with potential future support for other output configurations.
#batch_size=
def batch_size=(value) -> ::Integer
-
value (::Integer) — The max number of response protos to put into each output JSON file on
Google Cloud Storage.
The valid range is [1, 100]. If not specified, the default value is 20.
For example, for one pdf file with 100 pages, 100 response protos will be generated. If
batch_size
= 20, then 5 json files each containing 20 response protos will be written under the prefixgcs_destination
.uri
.Currently, batch_size only applies to GcsDestination, with potential future support for other output configurations.
-
(::Integer) — The max number of response protos to put into each output JSON file on
Google Cloud Storage.
The valid range is [1, 100]. If not specified, the default value is 20.
For example, for one pdf file with 100 pages, 100 response protos will be generated. If
batch_size
= 20, then 5 json files each containing 20 response protos will be written under the prefixgcs_destination
.uri
.Currently, batch_size only applies to GcsDestination, with potential future support for other output configurations.
#gcs_destination
def gcs_destination() -> ::Google::Cloud::Vision::V1::GcsDestination
- (::Google::Cloud::Vision::V1::GcsDestination) — The Google Cloud Storage location to write the output(s) to.
#gcs_destination=
def gcs_destination=(value) -> ::Google::Cloud::Vision::V1::GcsDestination
- value (::Google::Cloud::Vision::V1::GcsDestination) — The Google Cloud Storage location to write the output(s) to.
- (::Google::Cloud::Vision::V1::GcsDestination) — The Google Cloud Storage location to write the output(s) to.


--- layout: post title: "HTML Test Post" ---
This is only a test.
This test file only contains two <p> tags.
<p>


From it's web site: "....with a Swagger-enabled API, you get interactive documentation, client SDK generation and discoverability."
It's easy to integrate Swagger into your ASP.NET Boilerplate based application.
Install Swashbuckle.Core nuget package to your WebApi project (or Web project).
Add configuration code for Swagger into Initialize method of your module. Example:
public class SwaggerIntegrationDemoWebApiModule : AbpModule
{
public override void Initialize()
{
//your other code...
ConfigureSwaggerUi();
}
private void ConfigureSwaggerUi()
{
Configuration.Modules.AbpWebApi().HttpConfiguration
.EnableSwagger(c =>
{
c.SingleApiVersion("v1", "SwaggerIntegrationDemo.WebApi");
c.ResolveConflictingActions(apiDescriptions => apiDescriptions.First());
})
.EnableSwaggerUi();
}
}
See it's own documentation for more configuration options.
That's all. Let's browse /swagger/ui/index:
You can see all Web API Controllers (and also dynamic web api controllers) and test them.


PySOT Dashboard¶
PySOTDashboard is web application for pySOT, a asynchronous parallel optimization toolbox for global deterministic optimization problems. The purpose of this application is to facilitate the user to be able to run the experiment remortly and moniter the results without having to install any of the dependencies on their machines.
The toolbox is hosted on GitHub:
https://github.com/peiyu313/pySOTDashboard
Dependencies¶
Before starting you will need Python 2.7.x. You need to have numpy, scipy, git and pip installed and we recommend installing Anaconda/Miniconda for your desired Python version.
The setup file might not include some of the optional components of pySOT, if you want any of them then you are going to have to install them manually by following the guide here.
Installation¶
Currenty the only way to install the dashboard is by cloning the github repository. Run the following commands in the terminal
git clone https://github.com/peiyu313/pySOTDashboard
cd pySOTDashboard
python setup.py install
Usage¶
pySOTDashboard essentially provides the same features as pySOT as a web application. In order to understand the working of pySOT refer to:
http://pysot.readthedocs.io/
Several pySOT examples can be found at:
https://github.com/dme65/pySOT/tree/master/pySOT/test
Instruction on how to use the web client can be found in the docs.


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| Service Name | Owning Team | Description | Blue Port | Green Port | View Deployments | View History |
|---|---|---|---|---|---|---|
| {{::service.ServiceName}} | {{::service.OwningCluster}} | {{::service.Value.Description}} | {{::service.Value.BluePort}} | {{::service.Value.GreenPort}} |


On the Manage categories page, you can create, update, and delete categories for a marketplace.
Categories can be used for organizing and classifying services on a marketplace. For example, they may group different types of application software, such as word processing, desktop publishing, or spreadsheet software.
As a marketplace owner, you can create any number of categories for your marketplace. Suppliers, brokers, and resellers can assign these categories to the services they publish to the marketplace. Marketplace visitors can use the categories for browsing the service catalog and filtering the services, provided that you have enabled the display of categories. Categories are also taken into consideration by the full-text search feature on the marketplace.
As a marketplace owner, you can decide to use the categories for grouping the services displayed on the marketplace home page. Click here for details.
A category can be provided in all supported languages. For each category, you define a language-independent ID and the actual term to be displayed in each language. If a term for a specific language is not found, the English term is displayed by default. If the English term is not defined either, the language-independent category ID is used.
To create a category:
To update a category:
Updating a category allows you to change the category ID and the terms to be displayed for the category in all supported languages.
The categories are instantly updated. For marketplace visitors, the update takes effect with their next login to the marketplace.
The assignment of a category to a service by a supplier, broker, or reseller is not affected by the update. Usually, you will inform your suppliers, brokers, and resellers when you update a category. They are not notified automatically.
To delete a category:
The category is instantly deleted. Visitors of the marketplace who use the category for filtering the services receive an empty service list. With their next login to the marketplace, the category is no longer provided to them as a filter.
If suppliers, brokers, or resellers had assigned the deleted category to their services, the assignment is removed. The suppliers, brokers, and resellers are notified by email about the deletion.


Non refutation of the law of excluded middle in intuitionistic logic
Sep 17, 2021 00:00 · 668 words · 4 minute read
Intuitionistic logic refers to a system of symbolic logic that differ from classical logic by removing the law of excluded middle (that is \(p \vee \neg p\)) and the double negation elimination (that is \(\neg \neg p \rightarrow p\)).
One of the central theorem that can be proved in intuitionistic logic, that will be our best friend in this post, is the non refutation of the law of excluded middle, which looks something like this:
\[ \neg \neg (A \vee \neg A) \]
Intuitionism focuses of positive construction of proofs, so the theorem shall be read as "Intuitionistic logic does not positively refute the law of excluded middle".
Remembering that \(\neg A\) is defined as \(A \rightarrow \bot\) the theorem is expressed equivalently like
\[ ((A \vee (A \rightarrow \bot)) \rightarrow \bot) \rightarrow \bot \]
In this post we will prove it with two different methods: using natural deduction and using lambda calculus.
Proof using natural deduction
I assume some familiarity with the natural deduction proof style. You can read about it (more than enough to understand this derivation) on Wikipedia.
For typographical purposes I will split up the proof in two parts.
First let's prove that under the assumption \(w\) that \((A \vee (A \rightarrow \bot)) \rightarrow \bot\) the formula \(A\rightarrow \bot\) holds.
\[ \dfrac{\dfrac{\dfrac{\dfrac{}{A \: \text{true}}u}{A \vee (A \rightarrow \bot)\: \text{true}} \vee _I \qquad \dfrac{}{(A \vee (A \rightarrow \bot)) \rightarrow \bot \: \text{true}}w}{\bot \: \text{true}} \rightarrow _E}{A \rightarrow \bot \: \text{true}}\rightarrow _I ^u \]
In this proof we have discharged the hypothesis \(u\) but not \(w\). I will call this proof \(P^w\) to indicate that there is the non-discharged assumption \(w\).
Now let's complete the proof.
\[ \dfrac{\dfrac{\dfrac{\dfrac{P^w}{A \rightarrow \bot \: \text{true}}}{A \vee (A \rightarrow \bot)\: \text{true}} \vee _I \qquad \dfrac{}{(A \vee (A \rightarrow \bot)) \rightarrow \bot \: \text{true}}w}{\bot \: \text{true}} \rightarrow _E}{((A \vee (A \rightarrow \bot)) \rightarrow \bot)\rightarrow \bot\: \text{true}} \rightarrow _I ^w \]
And with that we have proven the theorem!
Notice that we have actually used the assumption \(w\) two times. This might seem strange at first, but it is allowed because the two assuptions are taken in the same subproof "above" the discharge.
Proof using lambda calculus
By the virtue of the Curry-Howard correspondence, we can try to find a lambda tem that has type
\[ ((A \vee (A \rightarrow \bot)) \rightarrow \bot) \rightarrow \bot \]
and we would have our proof. Lambda terms like this are sometimes called proof terms.  We could check this by hand, but that would require a lot of work. What we can instead do is try to import it into Haskell and let the typechecker do the hard work.
import Data.Void
thm :: ((Either a (a -> Void)) -> Void) -> Void
thm f = f (Right (\a -> f (Left a)))
or, more elegantly
thm f = f (Right (f . Left))
This indeed typechecks, so that is also a proof of our theorem!
Consequences
Even though the law of excluded middle does not hold in intuitionistic logic, it holds in this "double negated form". Now recall that, while in intuitionistic logic it is not valid that \(\neg \neg p \rightarrow p\), a very similar theorem holds:
\[ p \rightarrow \neg \neg p \]
Intuitively this means that everithing that is provable in intuitionistic logic is then provable in this double negated form, so in some sense all the theorems that are of the form \(\neg \neg p\) are all the theorems \(p\) that hold in intuitionistic logic, plus the law of excluded middle. The double negated form is then stronger than the "normal" form.
This central idea is formalized in the double negation translation, in particular in the Glivenko's theorem, that states that
If \(p\) is a propositional formula, \(p\) is a classical tautology iff \(\neg \neg p\) is an intuitionistic tautology
This results has been further extended to first-order logic.


Remember the difference between a boss and a leader. A boss says, Go! A leader says, Let's go!
Scholarship is to be created not by compulsion, but by awakening a pure interest in knowledge.
Education is the passport to the future, for tomorrow belongs to those who prepare for it today


{% extends "application_projects/project_detail.html" %} {% load i18n approval_tools static %} {% block admin_actions %}
{% trans "This project is missing the following documents" %}:
{% trans "This will move the project into contracting and notify the compliance team." %}
{% trans "This cannot be undone." %}
{% trans "Approve" as approve %} {% include 'funds/includes/delegated_form_base.html' with form=add_approval_form value=approve %}{% trans "You confirm that the uploaded contract is acceptable for commencing the project." %}
{% trans "This cannot be undone." %}
{% trans "Confirm" as confirm %} {% include 'funds/includes/delegated_form_base.html' with form=approve_contract_form value=confirm %}


The HRMD intends to capture the relationship between somatic non-coding mutations and cancer. We enter data cancer using NCI Thesaurus identifiers, and some commonly encountered diseases are listed here for convenience (See https://ncit.nci.nih.gov/ncitbrowser/).
| Name | NCI Thesaurus Code |
| Melanoma | C3224 |
| Skin Basal Cell Carcinoma | C2921 |
| Skin Squamous Cell Carcinoma | C4819 |
| Small Cell Lung Carcinoma | C4917 |


This is an area used for configuring the new game while the continued game will using that game's configuration. Try to consult with your partner using the Go Talk Area about how you wish to play the game. When you reach an agreement, anyone of you can submit the result. Be sure that the configuration is for the submitting part while the other part is just the reversed result.


This post summarizes the paper “Szemer'edi’s Regularity Lemma Revisited” by Terence Tao. The paper is published on arXiv.
Draft
Szemeredi Regularity Lemma states that for dense graphs, we can specify an error rate \( 0 < \epsilon < 1 \) such that the graph can be partitioned into $O{\eps}(1)$ parts. Among these partitions, the edges behaves almost randomly. Such partition is called $\eps-$regular.
In this paper, the author views Szemeredi Regularity Lemma from the information theoric perspective. Such point of view not only clarifies the Regularity Lemma, but also allows applications of other techniques (information theory, ergodic theory) to proving and improving the regularity lemma.
Regularity Lemma is a building stone to the Szemeredi Theorem. The theorem states that in a positive density subset of natural numbers, there exists an arbitarily large arithmetic progression. This results relates strongly to the ergodic theory.
Instead of studying dense graph, in this paper, the author uses graphs and bi-paritite graphs as an analogue to random variables. Suppose there are two random variables $x_1$ and $x_2$ mapping from the vertices space ($V_1$ and $V_2$) to some probability measurement.
There is a recent paper from Cambridge (probably sumitted to ICML 2019) that connect ergodic theory with machine learning. It was published on arXiv with the title “The Theory and Algorithm of Ergodic Inference”.
(Dec 26 – paused)
1. Introduction
Main ideas and contributions
-
Starting from a skewed stacked RNN architecture, the authors proposed a novel RNN where each hidden unit is parameterized by a high rank tensor (≥2).
The image above compares a three hidden layers (depth L = 3) skewed recurrent neural network with the proposed model. The tRNN model here has only one hidden layer, but its hidden units are parameterized by a P-by-M matrix rather than a single vector. Furthermore, the interaction between hidden units are captured by the convolution operation (defined later) to take advantages of the tensor representation. According to the authors, the first dimension of the hidden units is “locally connected” in order to share parameters, while the second dimension is “fully connected” for global interaction. This idea will be clearer when we discuss the convolution. In general, the construction of a hidden unit output is computed as following ( is the convolution operator):
Note that the actual output at is computed using the last tensor (in this case it is a vector) of the hidden tensor . As in the figure above, is computed from - the last layer of the hidden unit . Also, the implicit depth P = L = 3 leads us to the same computation.
-
The paper introduces cross-layer convolution and memory cell convolution (for the LSTM extension). The explanation to the convolution is presented in the second section. Note that in this post, I moved the time notation to the top of each symbol when it’s convenient so that the subscript contains only indexing variables (e.g. becomes ).
-
The 2D-tRNN model is further extended to LSTM and higher order tensors (3D).
This extension to LSTM is pretty straight-forward as each gate is computed using the convolution operator in lieu of the standard matrix multiplication. For the higher order tensors extension, the concatenated tensor is constructed by appending the projection (multiplied with weights, added with bias) of to one corner of the hidden unit tensor. This can be understood as going down the tensor dimension-wise, when you reach a 2D matrix with row size of M, append to it. In the same way, is generated with the opposite corner.
Dissecting convolution
It took me sometime to fully grasp the author’s idea . Despite that “sometime”, my understanding can be captured in a single image (and now I feel silly). In the case of 2D hidden units, the operation and the dimensionality of each tensor is:
In here, is the activation tensor. represents the concatenation of a hidden unit’s rank-2 tensor output (matrix) and the input vector from the layer above it (in this case, it is the input vector ). From the skewed sRNN figure above, the concatenation is pretty clear: is pointed to by and , hence the tensor used in computing and will be the concatenation between and . The same principle applies for the tRNN. The convolution kernel consists of weight and bias . is a rank-3 tensor of K filters, each filters has input channels and output channels. In this paper, the authors noted that they let for simplicity. The detail of the convolution is given in the supplementary document:
It might sound obvious, but it is easier for me to think of the indices as “selector”. For example, is the element of tensor that is selected by . Usually, the “selector” is lowercase and the total number of element in a dimension is uppercase. In the figure below, I circled in red the “selectors”.
It might helps with a kind of story. The matrix is what we need to compute for the next time step. We set out to compute each element of this matrix. is given by the convolution operator defined in the formula above. In the figure, the gray small box represents . The two selector and control the center of the convolution in and which output channel to pick in respectively. For example, if and where want to computer at , then for each slice of , the 5 columns associated with will be picked out. Next, on , there are also 5 rows selected. Since , the index of these row vectors are (centered at ). These 5 pairs of vectors are indexed by . Sum of the dot products of the pairs is . Note that the authors use zero-padding to keep the shape of output same as the input. In the case of memory cell convolution, the values used in padding are the border values to avoid interference with the memory values.
Evaluations
The authors uses three main tasks to demonstrate the effectiveness of their proposed model:
-
Algorithmic tasks consist of learning to sum two 15-digit numbers and learning to repeat the input sequence.
Sum two 15-digit integers || Repeat the input Input : --2545-9542------- || Input : -hiworld---------- Output: -----------12087-- || Output: --------hiworld---
The advantage of the proposed model (3D-tLSTM with Channel Normalization) is that it requires much less training samples to reach more than 99 percent accuracy compared with Stacked LSTM and Grid LSTM. However, there are no mention to the training time or other modification of tLSTM. Furthermore, the best performing models have 7 and 10 layers depth. There are not much explanation for these hyper-parameters. The 7-layer requires less training samples than the 10-layer in addition task, but the 10-layer in turn requires much less samples in memorization. I expected the 7-layer model requires less samples in both tasks.
-
MNIST classification tasks consist of normal MNIST and randomized pixel sequence called pMNIST. In these tasks, the pixels of an hand-written digit image are fed into the neural nets as a sequence. In this task, I do not see any advantage of using tLSMT compared with state-of-the-art methods such as DilatedGRU.
-
Wikipedia language modeling task deal with next-character prediction on the Hutter Prize Wikipedia dataset. Similar to the aforementioned MNIST tasks, there are no clear win for tLSTM compared with Large FS-LSTM-4 method (in term of both BPC and number of parameters).
Why tensors?
It is true that we can design a “vector” recurrent neural net that works in the same way as the proposed tRNN here. After all, the variables is stored in arrays on our computer. However, tensors represent a concrete way to think about a “block of numbers”, and more importantly, we can define and argue about convolution easily with it. Let’s take image data as an example. The image below shows the popular 2D convolution operation. Tensor representation gives us a concrete way to think about color channels and its corresponding channels in each convolution kernel. Furthermore, notice that we “scan” each convolution channel in the intensity dimension (on the matrices) but not the color dimension. As such, the weights in the intensity dimension are shared. Similarly, in recurrent neural networks, the tensor hidden unit in some sense enables a more abstract representation and allow weight sharing.
Conclusion
This paper proposes a nice way to increase the structural depth of a recurrent neural network model. Instead of parameterizing hidden units with vectors, tRNN modeled hidden units as tensors for more efficient weight sharing and implicit depth. Such approach greatly reduces the number of parameters in a recurrent neural network while maintaining the depth. tRNN model is also extended to use LSTM module and higher order (3D) tensor for better performance and data abstraction. The effectiveness of tLSTM is demonstrated on three different tasks in which tLSTM achieve state-of-the-art performance with some improvement on number of parameters (minor) and required number of training samples. On the other hand, while the proposed model might improve running time and number of parameters, there was no discussion on the training time and training complexity of tLSTM. It would be interesting to implement the 2D and 3D models to understand the benefit of tLSTM better.
In this post, I wrote about my understanding and commented on the paper “Wider and Deeper, Cheaper and Faster: Tensorized LSTMs for Sequence Learning” by Zhen He, Shaobing Gao, Liang Xiao, Daxue Liu, Hangen He, and David Barber. I left out some details such as Channel Normalization or the constraints on . These minor optimization tricks can be found on the paper. After this post, I plan to implement this technique to see if it is suitable for my current work. In particular, I would like to see if the training cost can potentially be reduced for a stacked LSTM approach to model product names.


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pluginify
steal.build.pluginify(moduleId, opts)
Parameters
-
moduleId
{Object}
The moduleId of the plugin to be built.
-
opts
{Object}
An object map of the following optional configuration properties:
{Object}
The moduleId of the plugin to be built.
{Object}
An object map of the following optional configuration properties:
steal.build.pluginify(moduleId, options)
builds a 'steal-less' version of a module. It can called programatically in JavaScript like:Basic examples can be called from the command line like: