Publications
Applications of Random Walks for the Analysis of Graphs, Musical Compositions, and Language Phylogeny
Volchenkov D (2011)
In: Random Walks: Principles, Processes and Applications. Skogseid A, Fasano V (Eds.); 1st ed. 1. Hauppauge, New York: Nova Science Publishers, Inc.: 1 - 65.
Book Chapter
|
In Press
|
English
Authors:
Volchenkov, Dimitry
Editors:
Skogseid, A.
;
Fasano, V.
Department:
Fakultät für Physik
Center of Excellence - Cognitive Interaction Technology CITEC
AG Mathematische Physik
Alternative Title:
Chap. 16
Link:
http://pub.uni-bielefeld.de/publication/2092673
Introduction to Random Walks on Graphs and Databases
Volchenkov D, Blanchard P (2011)
Springer Series in Synergetics, 10. Berlin, Heidelberg: Springer. 1st ed.
Book
|
Published
|
English
Authors:
Volchenkov, Dimitry
;
Blanchard, Philippe
Department:
Center of Excellence - Cognitive Interaction Technology CITEC
AG Mathematische Physik
Link:
http://pub.uni-bielefeld.de/publication/1997310
Malagasy Dialects and the Peopling of Madagascar
Serva M, Petroni F, Volchenkov D, Wichmann S (2012)
Journal of the Royal Society Interface 9(66): 54 - 67.
Journal Article
|
Published
|
English
Authors:
Serva, Maurizio
;
Petroni, Filippo
;
Volchenkov, Dimitry
;
Wichmann, Søren
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Link:
http://pub.uni-bielefeld.de/publication/2092675
Random Walks and Flights over Connected Graphs and Complex Network
Volchenkov D (2011)
Communications in Nonlinear Science and Numerical Simulation 16(1): 21 - 55.
Journal Article
|
Published
|
English
Authors:
Volchenkov, Dimitry
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Keywords:
Random walks ;
Levy flights ;
Electrical ;
networks ;
Graph theory ;
Complex networks
Link:
http://pub.uni-bielefeld.de/publication/1930163
The phylogeny of Malagasy dialects
Volchenkov D, Petroni F, Serva M, Wichmann S, Holman E, Blanchard P (2010)
Text Processing and Cognitive Technologies 19: 253 - 256.
Journal Article
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Published
|
English
Authors:
Volchenkov, Dimitry
;
Petroni, Filippo
;
Serva, Maurizio
;
Wichmann, Søren
;
Holman, Eric
;
Blanchard, Philippe
Department:
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
AG Mathematische Physik
Link:
http://pub.uni-bielefeld.de/publication/2092680
Markov chains or the game of structure and chance. From Complex Networks, to Language Evolution, to Musical Compositions
Blanchard P, Dawin JR, Volchenkov D (2010)
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 184(1): 1 - 82.
Journal Article
|
Published
|
English
Authors:
Blanchard, Philippe
;
Dawin, J. R.
;
Volchenkov, Dimitry
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Abstract:
Markov chains provide us with a powerful tool for studying the structure of graphs and databases in details. We review the method of generalized inverses for Markov chains and apply it for the analysis of urban structures, evolution of languages, and musical compositions. We also discuss a generalization of L,vy flights over large complex networks and study the interplay between the nonlinearity of diffusion process and the topological structure of the network.
Link:
http://pub.uni-bielefeld.de/publication/1794633
Fair and biased random walks on undirected graphs and related entropies
Volchenkov D, Blanchard P (2011)
In: Towards an Information Theory of Complex Networks. Dehmer M, Emmert-Streib F, Mehler A (Eds.); : Statistical Methods and Applications. Boston, Basel: Birkhäuser.
Book Chapter
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Published
|
English
Authors:
Volchenkov, Dimitry
;
Blanchard, Philippe
Editors:
Dehmer, M.
;
Emmert-Streib, F.
;
Mehler, A.
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Alternative Title:
Chapter 13
Link:
http://pub.uni-bielefeld.de/publication/1997352
Probabilistic embedding of discrete sets as continuous metric spaces
Blanchard P, Volchenkov D (2009)
Stochastics: An International Journal of Probability and Stochastic Processes 81(3-4): 259 - 268.
Journal Article
|
Published
|
English
Authors:
Blanchard, Philippe
;
Volchenkov, Dimitry
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Abstract:
Any symmetric affinity function w : V x V -> R+ defined on a discrete set V induces Euclidean space structure on V. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a metric topological space. We have calculated the visual representations of the probabilistic locus for a chain, a polyhedron and a finite 2D lattice.
Keywords:
random walk ;
probabilistic analogue ;
Euclidean space
Link:
http://pub.uni-bielefeld.de/publication/1794448
Markov Chain Analysis of Electricity Distribution Networks
Volchenkov D (2010)
In: Advances in Energy Research. Acosta MJ (Ed.); Advances in Energy Research. 6. Hauppauge, New York: NOVA Science Publishers, Inc.
Book Chapter
|
Published
|
English
Authors:
Volchenkov, Dimitry
Editors:
Acosta, Morena J.
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Alternative Title:
Chapter 10
Link:
http://pub.uni-bielefeld.de/publication/2018690
Mathematical Analysis of Urban Spatial Networks
Blanchard P, Volchenkov D (2008)
Understanding Complex Systems, 1. Berlin, Heidelberg: Springer.
Book
|
Published
|
English
Authors:
Blanchard, Philippe
;
Volchenkov, Dimitry
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Link:
http://pub.uni-bielefeld.de/publication/1997336
Markov chain methods for analyzing urban networks
Volchenkov D, Blanchard P (2008)
Journal of Statistical Physics 132(6): 1051 - 1069.
Journal Article
|
Published
|
English
Authors:
Volchenkov, Dimitry
;
Blanchard, Philippe
Department:
AG Mathematische Physik
Fakultät für Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Abstract:
Complex transport networks abstracted as graphs (undirected, directed, or multi-component) can be effectively analyzed by random walks (or diffusions). We have unified many concepts into one framework and studied in details the structural and spectral properties of spatial graphs for five compact urban patterns.
Keywords:
traffic equilibrium ;
complex networks ;
random walks
Link:
http://pub.uni-bielefeld.de/publication/1586584
Intelligibility and first passage times in complex urban networks
Blanchard P, Volchenkov D (2008)
Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences 464(2096): 2153 - 2167.
Journal Article
|
Published
|
English
Authors:
Blanchard, Philippe
;
Volchenkov, Dimitry
Department:
AG Mathematische Physik
Fakultät für Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Abstract:
Topology of urban environments can be represented by means of graphs. We explore the graph representations of several compact urban patterns by random walks. The expected time of recurrence and the expected first passage time to a node scales apparently linearly in all urban patterns we have studied. In space syntax theory, a positive relation between the local property of a node (qualified by connectivity or by the recurrence time) and the global property of the node (estimated in our approach by the first passage time to it) is known as intelligibility. Our approach, based on random walks, allows us to extend the notion of intelligibility onto the entire domain of complex networks and graph theory.
Keywords:
space syntax ;
random walks ;
first passage times ;
recurrence times
Link:
http://pub.uni-bielefeld.de/publication/1587324
Scaling and universality in city space syntax: Between Zipf and Matthew
Volchenkov D, Blanchard P (2008)
Physica A 387(10): 2353 - 2364.
Journal Article
|
Published
|
English
Authors:
Volchenkov, Dimitry
;
Blanchard, Philippe
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Abstract:
We report about the universality of rank-integration distributions of open spaces in city space syntax similar to the famous rank-size distributions of cities (Zipf's law). We also demonstrate that the degree of choice an open space represents for other spaces directly linked to it in a city follows a power-law statistic. Universal statistical behavior of space syntax measures uncovers the universality of the city creation mechanism. We suggest that the observed universality may help to establish the international definition of a city as a specific land use pattern. (c) 2007 Elsevier B.V. All rights reserved.
Keywords:
complex networks ;
city space syntax
Link:
http://pub.uni-bielefeld.de/publication/1592151
Analysis of urban complex networks
Volchenkov D (2008)
In: Condensed Matter Physics. 112. INST CONDENSED MATTER PHYSICS NATL ACAD SCIENCES UKRAINE: 331 - 340.
Conference Proceeding/Paper
|
Published
|
English
Authors:
Volchenkov, Dimitry
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Abstract:
We analyze the dual graph representation of urban textures by the methods of complex network theory and spectral graph theory. We present the empirical diagrams of distributions of the nearest and far-away neighbors in the several European compact urban patterns and the spectra of normalized Laplace operator defined on their dual graphs.
Keywords:
complex networks ;
urban studies
Link:
http://pub.uni-bielefeld.de/publication/1587197
Exploring Urban Environments By Random Walks
Blanchard P, Volchenkov D (2008)
In: Stochastic and quantum dynamics of biomolecular systems. Bernido CC, Capo-Bernido MV (Eds.); 1. Melville, New York: Springer: 183 - 203.
Book Chapter
|
Published
|
English
Authors:
Blanchard, Philippe
;
Volchenkov, Dimitry
Editors:
Bernido, C. C.
;
Capo-Bernido, M. V.
Department:
AG Mathematische Physik
Center of Excellence - Cognitive Interaction Technology CITEC
Fakultät für Physik
Link:
http://pub.uni-bielefeld.de/publication/1997314
Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics
Volchenkov D, Blanchard P (2007)
PHYSICAL REVIEW E 75(2): 6104 - 6118.
Journal Article
|
Published
|
English
Authors:
Volchenkov, Dimitry
;
Blanchard, Philippe
Department:
AG Mathematische Physik
Fakultät für Physik
Abstract:
Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an informationlike parameter which plays the role of an individual fingerprint of Genius loci. Global structural properties of a city can be characterized by the thermodynamic parameters calculated in the random walk problem.
Link:
http://pub.uni-bielefeld.de/publication/1595273
Nonlinear diffusion through large complex networks containing regular subgraphs
Volchenkov D, Blanchard P (2007)
JOURNAL OF STATISTICAL PHYSICS 127(4): 677 - 697.
Journal Article
|
Published
|
English
Authors:
Volchenkov, Dimitry
;
Blanchard, Philippe
Department:
AG Mathematische Physik
Fakultät für Physik
Abstract:
Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is Brownian for the rest of the nodes. Transport within a supernode is affected by the finite size effects vanishing as N -> infinity. For the even dimensions of space, d = 2, 4, 6,..., the finite size effects break down the perturbation theory at small scales and can be regularized by using the heat-kernel expansion.
Keywords:
genealogical trees ;
diffusion ;
structures and organization in complex systems ;
networks and
Link:
http://pub.uni-bielefeld.de/publication/1594903