Central Library

Fractional dynamics on networks and lattices / (Record no. 69062)

000 -LEADER
fixed length control field 05708cam a2200625Ii 4500
001 - CONTROL NUMBER
control field on1096435591
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20220711203514.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 190412s2019 enka ob 001 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9781119608165
-- (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 1119608163
-- (electronic bk.)
029 1# - (OCLC)
OCLC library identifier AU@
System control number 000065306467
029 1# - (OCLC)
OCLC library identifier CHNEW
System control number 001050896
029 1# - (OCLC)
OCLC library identifier CHVBK
System control number 567422496
082 04 - CLASSIFICATION NUMBER
Call Number 519.2/33
100 1# - AUTHOR NAME
Author Michelitsch, Thomas,
245 10 - TITLE STATEMENT
Title Fractional dynamics on networks and lattices /
300 ## - PHYSICAL DESCRIPTION
Number of Pages 1 online resource :
490 1# - SERIES STATEMENT
Series statement Mechanical engineering and solid mechanics series
505 8# - FORMATTED CONTENTS NOTE
Remark 2 Cover; Half-Title Page; Title Page; Copyright Page; Contents; Preface; PART 1. Dynamics on General Networks; 1. Characterization of Networks: the Laplacian Matrix and its Functions; 1.1. Introduction; 1.2. Graph theory and networks; 1.2.1. Basic graph theory; 1.2.2. Networks; 1.3. Spectral properties of the Laplacian matrix; 1.3.1. Laplacian matrix; 1.3.2. General properties of the Laplacian eigenvalues and eigenvectors; 1.3.3. Spectra of some typical graphs; 1.4. Functions that preserve the Laplacian structure; 1.4.1. Function g(L) and general conditions
505 8# - FORMATTED CONTENTS NOTE
Remark 2 1.4.2. Non-negative symmetric matrices1.4.3. Completely monotonic functions; 1.5. General properties of g(L); 1.5.1. Diagonal elements (generalized degree); 1.5.2. Functions g(L) for regular graphs; 1.5.3. Locality and non-locality of g(L) in the limit of large networks; 1.6. Appendix: Laplacian eigenvalues for interacting cycles; 2. The Fractional Laplacian of Networks; 2.1. Introduction; 2.2. General properties of the fractional Laplacian; 2.3. Fractional Laplacian for regular graphs; 2.4. Fractional Laplacian and type (i) and type (ii) functions
505 8# - FORMATTED CONTENTS NOTE
Remark 2 2.5. Appendix: Some basic properties of measures3. Markovian Random Walks on Undirected Networks; 3.1. Introduction; 3.2. Ergodic Markov chains and random walks on graphs; 3.2.1. Characterization of networks: the Laplacian matrix; 3.2.2. Characterization of random walks on networks: Ergodic Markov chains; 3.2.3. The fundamental theorem of Markov chains; 3.2.4. The ergodic hypothesis and theorem; 3.2.5. Strong law of large numbers; 3.2.6. Analysis of the spectral properties of the transition matrix; 3.3. Appendix: further spectral properties of the transition matrix
505 8# - FORMATTED CONTENTS NOTE
Remark 2 3.4. Appendix: Markov chains and bipartite networks3.4.1. Unique overall probability in bipartite networks; 3.4.2. Eigenvalue structure of the transition matrix for normal walks in bipartite graphs; 4. Random Walks with Long-range Steps on Networks; 4.1. Introduction; 4.2. Random walk strategies and; 4.2.1. Fractional Laplacian; 4.2.2. Logarithmic functions of the Laplacian; 4.2.3. Exponential functions of the Laplacian; 4.3. Lévy flights on networks; 4.4. Transition matrix for types (i) and (ii) Laplacian functions; 4.5. Global characterization of random walk strategies
520 ## - SUMMARY, ETC.
Summary, etc This book analyzes stochastic processes on networks and regular structures such as lattices by employing the Markovian random walk approach. Part 1 is devoted to the study of local and non-local random walks. It shows how non-local random walk strategies can be defined by functions of the Laplacian matrix that maintain the stochasticity of the transition probabilities. A major result is that only two types of functions are admissible: type (i) functions generate asymptotically local walks with the emergence of Brownian motion, whereas type (ii) functions generate asymptotically scale-free non-local "fractional" walks with the emergence of LEvy flights. In Part 2, fractional dynamics and LEvy flight behavior are analyzed thoroughly, and a generalization of POlya's classical recurrence theorem is developed for fractional walks. The authors analyze primary fractional walk characteristics such as the mean occupation time, the mean first passage time, the fractal scaling of the set of distinct nodes visited, etc. The results show the improved search capacities of fractional dynamics on networks.
650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1
General subdivision Applied.
650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1
General subdivision Probability & Statistics
-- General.
700 1# - AUTHOR 2
Author 2 Pérez Riascos, Alejandro,
700 1# - AUTHOR 2
Author 2 Collet, Bernard,
700 1# - AUTHOR 2
Author 2 Nowakowski, Andrzej,
700 1# - AUTHOR 2
Author 2 Nicolleau, F. C. G. A.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier https://doi.org/10.1002/9781119608165
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type eBooks
264 #1 -
-- London :
-- ISTE Ltd. ;
-- Hoboken :
-- John Wiley & Sons, Inc.,
-- 2019.
336 ## -
-- text
-- txt
-- rdacontent
337 ## -
-- computer
-- c
-- rdamedia
338 ## -
-- online resource
-- cr
-- rdacarrier
588 0# -
-- Online resource; title from PDF title page (EBSCO, viewed April 15, 2019).
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Markov processes.
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Random walks (Mathematics)
650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1
-- MATHEMATICS
650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1
-- MATHEMATICS
650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Markov processes.
-- (OCoLC)fst01010347
650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Random walks (Mathematics)
-- (OCoLC)fst01089818
994 ## -
-- 92
-- DG1

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