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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2018, Volume 21, Number 1, Pages 23–45
DOI: https://doi.org/10.15372/SJNM20180102 (Mi sjvm666) 		 
This article is cited in 7 scientific papers (total in 7 papers)

About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines

A. Gasnikovab, P. Dvurechenskybc, M. Zhukovskiiad, S. Kime, S. Plaunovf, D. Smirnovf, F. Noskova

a Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, 141700, Russia
b Institute for Information Transmission Problems RAS, 19, build. 1 Bolshoy Karetny per., Moscow, 127051, Russia
c Weierstrass Institute for Applied Analysis and Stochastics, 39 Mohrenstr., Berlin, 10117, Germany
d "Yandex", 16 Lev Tolstoy str., Moscow, 119034, Russia
e National Research University Higher School of Economics, 20 Myasnitskaya str., Moscow, 101000, Russia
f State Budget Educational Institution Physics and Mathematical "School 2007", 9, build. 1 Gorchakova str., Moscow, 117042, Russia
Full-text PDF (1087 kB) Citations (7)
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DOI: https://doi.org/10.15372/SJNM20180102
Abstract: In the second part of this paper, we consider the Buckley–Osthus model for the formation of a webgraph. For the networks generated according to this model, we numerically calculate the PageRank vector. We show that the components of this vector are distributed according to the power law. We also discuss the computational aspects of this model with respect to different numerical methods for the calculation of the PageRank vector, presented in the first part of the paper. Finally, we describe a general model for the web-page ranking and some approaches to solve the optimization problem arising when learning this model.
Key words: Markov chain, ergodic theorem, multinomial distribution, measure concentration, maximum likelihood estimate, Google problem, gradient descent, automatic differentiation, power law distribution.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation МК-1806.2017.9
Russian Science Foundation 14-50-00150
Received: 07.03.2017
Revised: 16.06.2017
English version:
Numerical Analysis and Applications, 2018, Volume 11, Issue 1, Pages 16–32
DOI: https://doi.org/10.1134/S1995423918010032
Bibliographic databases:
Document Type: Article
UDC: 519.853.62
Language: Russian
Citation: A. Gasnikov, P. Dvurechensky, M. Zhukovskii, S. Kim, S. Plaunov, D. Smirnov, F. Noskov, “About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines”, Sib. Zh. Vychisl. Mat., 21:1 (2018), 23–45; Num. Anal. Appl., 11:1 (2018), 16–32
Citation in format AMSBIB
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\paper About the power law of the PageRank vector distribution. Part~2. Backley--Osthus model, power law verification for this model and setup of real search engines
\jour Sib. Zh. Vychisl. Mat.
\yr 2018
\vol 21
\issue 1
\pages 23--45
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\crossref{https://doi.org/10.15372/SJNM20180102}
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\transl
\jour Num. Anal. Appl.
\yr 2018
\vol 11
\issue 1
\pages 16--32
\crossref{https://doi.org/10.1134/S1995423918010032}
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    Cycle of papers
    This publication is cited in the following 7 articles:
    1. Pavel Dvurechensky, Alexander Gasnikov, Alexander Tyurin, Vladimir Zholobov, Springer Proceedings in Mathematics & Statistics, 425, Foundations of Modern Statistics, 2023, 511  crossref
    2. Marina Danilova, Pavel Dvurechensky, Alexander Gasnikov, Eduard Gorbunov, Sergey Guminov, Dmitry Kamzolov, Innokentiy Shibaev, Springer Optimization and Its Applications, 191, High-Dimensional Optimization and Probability, 2022, 79  crossref
    3. Eduard Gorbunov, Pavel Dvurechensky, Alexander Gasnikov, “An Accelerated Method for Derivative-Free Smooth Stochastic Convex Optimization”, SIAM J. Optim., 32:2 (2022), 1210  crossref
    4. P. Dvurechensky, E. Gorbunov, A. Gasnikov, “An accelerated directional derivative method for smooth stochastic convex optimization”, Eur. J. Oper. Res., 290:2 (2021), 601–621  crossref  mathscinet  isi  scopus
    5. Mikhail Koshelev, “New lower bound on the modularity of Johnson graphs”, Moscow J. Comb. Number Th., 10:1 (2021), 77  crossref
    6. Nikita Derevyanko, Mikhail Koshelev, Andrei Raigorodskii, Trends in Mathematics, 14, Extended Abstracts EuroComb 2021, 2021, 221  crossref
    7. K. Kovalenko, “On the independence number and the chromatic number of generalized preferential attachment models”, Discret Appl. Math., 285 (2020), 301–306  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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