This document discusses methods for accelerating Google's PageRank algorithm. It provides background on how PageRank works and the problem of computing the PageRank vector. It then summarizes several methods studied, including the power method, solving a linear system, Langville and Meyer's algorithm, and the Iterative Aggregation/Disaggregation method. Testing showed that applying a row and column reordering to the power method matrix based on decreasing node degree reduced iteration counts and runtimes the most compared to other methods. Future work is proposed to further optimize PageRank computation.
Aurelian Isar - Decoherence And Transition From Quantum To Classical In Open ...SEENET-MTP
Lecture by Prof. Dr. Aurelian Isar (Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania) on October 20, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
Aurelian Isar - Decoherence And Transition From Quantum To Classical In Open ...SEENET-MTP
Lecture by Prof. Dr. Aurelian Isar (Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania) on October 20, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
Extreme‐Scale Parallel Symmetric Eigensolver for Very Small‐Size Matrices Usi...Takahiro Katagiri
We have developed a parallel eigensolver for very small-size matrices. Unlike conventional solvers, our design policy focusses on nature of non-blocking computations and reduced communications. A communication-avoiding approach for Householder pivot vectors is used to implement part of Householder inverse transformation. In addition to that, we implement some techniques for reducing communications by using non-blocking communications in tridiagonalization part. Performance of the solver with full nodes in the Fujitsu FX10 (76,800 cores) is also presented.
Linear Machine Learning Models with L2 Regularization and Kernel TricksFengtao Wu
The slides are the course project presentation for INFSCI 2915 Machine Learning Foundations course. The presentation reviewed and summarized how the L2 regularization techniques are applied in the linear machine models including linear regression, logistic regression, support vector machine and perceptron learning algorithm. Also the presentation reviewed the quadratic programming problem and took SVM model as an example to illustrate the relation between primal and dual problem. At last, the presentation reviewed the general conclusion which is the representer theorem, and connected the kernel tricks to the L2 regularized linear models.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
The present study concerns the feedback stabilisation of the unstable equilibria of a two-dimensional nonlinear pool-boiling system with essentially heterogeneous temperature distributions in the
fluid-heater interface. Regulation of such equilibria has great potential for application in, for instance, micro-electronics cooling. Here, as a first step, stabilisation of these equilibria is considered. To this end a control law is implemented that regulates the heat supply to the heater as a function of the Fourier-Chebyshev modes of its internal temperature distribution. These
modes are intimately related to the physical eigenmodes of the system and thus admit robust and efficient regulation on the basis of the natural composition of the temperature field. Key to this modal-control strategy and its application for controller design are two equivalent and interchangeable PDE and state-space forms of the linearised pool-boiling model. Derivation of these forms is a central theme of this study. Performance of modal controllers thus designed is demonstrated and analysed by simulations of the nonlinear closed-loop system.
Extreme‐Scale Parallel Symmetric Eigensolver for Very Small‐Size Matrices Usi...Takahiro Katagiri
We have developed a parallel eigensolver for very small-size matrices. Unlike conventional solvers, our design policy focusses on nature of non-blocking computations and reduced communications. A communication-avoiding approach for Householder pivot vectors is used to implement part of Householder inverse transformation. In addition to that, we implement some techniques for reducing communications by using non-blocking communications in tridiagonalization part. Performance of the solver with full nodes in the Fujitsu FX10 (76,800 cores) is also presented.
Linear Machine Learning Models with L2 Regularization and Kernel TricksFengtao Wu
The slides are the course project presentation for INFSCI 2915 Machine Learning Foundations course. The presentation reviewed and summarized how the L2 regularization techniques are applied in the linear machine models including linear regression, logistic regression, support vector machine and perceptron learning algorithm. Also the presentation reviewed the quadratic programming problem and took SVM model as an example to illustrate the relation between primal and dual problem. At last, the presentation reviewed the general conclusion which is the representer theorem, and connected the kernel tricks to the L2 regularized linear models.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
The present study concerns the feedback stabilisation of the unstable equilibria of a two-dimensional nonlinear pool-boiling system with essentially heterogeneous temperature distributions in the
fluid-heater interface. Regulation of such equilibria has great potential for application in, for instance, micro-electronics cooling. Here, as a first step, stabilisation of these equilibria is considered. To this end a control law is implemented that regulates the heat supply to the heater as a function of the Fourier-Chebyshev modes of its internal temperature distribution. These
modes are intimately related to the physical eigenmodes of the system and thus admit robust and efficient regulation on the basis of the natural composition of the temperature field. Key to this modal-control strategy and its application for controller design are two equivalent and interchangeable PDE and state-space forms of the linearised pool-boiling model. Derivation of these forms is a central theme of this study. Performance of modal controllers thus designed is demonstrated and analysed by simulations of the nonlinear closed-loop system.
In deze presentatie ziet u welke resultaten organisaties behalen door middel van pre employment screening. Elke jaar fraudeert personeel voor drie miljard euro. Preventie is het key word om dit tegen te gaan. Screen vooraf uw personeel. Met een recidive getal van 75% is het anders wachten op het moment waarop uw organisatie slachtoffer wordt. www.diis.nl
Delivering Micro-Credentials in Technical and Vocational Education and TrainingAG2 Design
Explore how micro-credentials are transforming Technical and Vocational Education and Training (TVET) with this comprehensive slide deck. Discover what micro-credentials are, their importance in TVET, the advantages they offer, and the insights from industry experts. Additionally, learn about the top software applications available for creating and managing micro-credentials. This presentation also includes valuable resources and a discussion on the future of these specialised certifications.
For more detailed information on delivering micro-credentials in TVET, visit this https://tvettrainer.com/delivering-micro-credentials-in-tvet/
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
2. Background
When a search query is entered in Google, the
relevant results are returned to the user in an
order that Google predetermines.
This order is determined by each web page’s
PageRank value.
Google’s system of ranking web pages has made
it the most widely used search engine available.
The PageRank vector is a stochastic vector that
gives a numerical value (0<val<1) to each web
page.
To compute this vector, Google uses a matrix
denoting links between web pages.
3. Background
Main ideas:
Web pages with the highest number of inlinks
should receive the highest rank.
The rank of a page P is to be determined by
adding the (weighted) ranks of all the pages
linking to P.
4. Background
Problem: Compute a PageRank vector that
contains an meaningful rank of every web
page
rk 1 ( Q ) T
rk ( Pi ) vk rk ( P1 ) rk ( P2 ) rk ( Pn )
Q BP Q
i
1
if there is a link
T T
v k
v k 1
H; H ij Pi
0 if no link
5. Power Method
The PageRank vector is the dominant
eigenvector of the matrix H…after modification
Google currently uses the Power Method to
compute this eigenvector. However, H is often
not suitable for convergence.
T T
Power Method: vk vk 1 H
not stochastic
typically, H is
not irreducible
6. Creating a usable matrix
T T
G (H au ) (1 ) eu
w here 0 1
e is a vector of ones and u (for the moment)
is an arbitrary probabilistic vector.
7. Using the Power Method
T T
vk 1
vk G
T T T T
vk H v k ua (1 )u
|| 2
||
The rate of convergence is: , where
1
|| 1 ||
is the
2
dominant eigenvalue and is the aptly
named subdominant eigenvalue
11. IAD Algorithm
Form the matrix
A
Find the stationary vectorT
w T
w1 c
T
vk T
w1
cu 2
T T
vk 1
vk G
If vk 1
T
vk
T
, then stop. Otherwise,
u2 (vk 1 ) y / (vk 1 ) y
1
12. New Ideas:
The Linear System In IAD
T
G 11 G 12 e
w1 c T T
T
w1 c
u 2 G 21
u 2 G 22 e
T
w1 ( I G 11 ) T
cu 2 G 21
1T G 12 e
w c (1 2 T G 22 e )
u 2 T G 21 e
cu
13. New Ideas: Finding
c
and 1
w
T T
1. S olve (I
G 11 ) w1
cG 21 u 2
T
w1 G 12 e
2. Let c
T
u 2 G 21 e
3. C ontinue until
w1
w1 (old )
14. Functional Codes
Power Method
We duplicated Google’s formulation of the power
method in order to have a base time with which to
compare our results
A basic linear solver
We used Gauss-Seidel method to solve the very basic
linear system: H ) u T
T
x (I
We also experimented with reordering by row degree
before solving the aforementioned system.
Langville & Meyer’s Linear System Algorithm
Used as another time benchmark against our
algorithms
15. Functional Codes (cont’d)
IAD - using power method to find w1
We used the power method to find the dominant
eigenvector of the aggregated matrix A. The
rescaling constant, c, is merely the last entry of
the dominant eigenvector
IAD – using a linear system to find w1
We found the dominant eigenvector as discussed
earlier, using some new reorderings
16. And now… The Winner!
Power Method with
preconditioning
Applying a row and
column reordering
by decreasing
degree almost
always reduces the
number of iterations
required to
converge.
17. Why this works…
1. The power method converges faster as the
magnitude of the subdominant eigenvalue
decreases
2. Tugrul Dayar found that partitioning a matrix
in such a way that its off-diagonal blocks are
close to 0, forces the dominant eigenvalue of
the iteration matrix closer to 0. This is
somehow related to the subdominant
eigenvalue of the coefficient matrix in power
method.
20. Some Comparisons
Calif Stan CNR Stan Berk EU
Sample Size 87 57 66 69 58
Interval Size 100 5000 5000 10000 15000
Mean Time
Pwr/Reorder 1.6334 2.2081 2.1136 1.4801 2.2410
STD Time
Pwr/Reorder 0.6000 0.3210 0.1634 0.2397 0.2823
Mean Iter
Pwr/Reorder 2.0880 4.3903 4.3856 3.7297 4.4752
STD Iter
Pwr/Reorder 0.9067 0.7636 0.7732 0.6795 0.6085
Favorable 100.00% 98.25% 100.00% 100.00% 100.00%
21.
22. Future Research
Test with more advanced numerical algorithms for
linear systems (Krylov subspaces methods and
preconditioners, i.e. GMRES, BICG, ILU, etc.)
Test with other reorderings for all methods
Test with larger matrices (find a supercomputer
that works)
Attempt a theoretical proof of the decrease in the
magnitude of the subdominant eigenvalue as
result of reorderings.
Convert codes to low level languages (C++, etc.)
Decode MATLAB’s spy
23. Langville & Meyer’s Algorithm
H 11 H 12
H
0 0
1 1 T
1 (I H 11 ) (I H 11 ) H 12 v2
(I H)
0 I
T T 1 T 1 T
x v1 ( I H 11 ) v1 ( I H 11 ) H 12 v2
T T
x1 ( I H 11 ) v1
T T T
x2 x1 H 12 v2
24. Theorem: Perron-Frobenius
If is a non-negative irreducible matrix, then
A n xn
p ( A ) is a positive eigenvalue of
A
There is a positive eigenvectorv associated p ( A )
with)
p( A
has algebraic and geometric multiplicity
1
25. The Power Method: Two
Assumptions
The complete set of eigenvectors v n
v1
are linearly independent
For each eigenvector there exists
eigenvalues such that
1 2
n