000			05708cam a2200625Ii 4500
001			on1096435591
003			OCoLC
005			20220711203514.0
006			m o d
007			cr cnu|||unuuu
008			190412s2019 enka ob 001 0 eng d
040			_aN$T _beng _erda _epn _cN$T _dEBLCP _dN$T _dDG1 _dRECBK _dUKAHL _dOCLCF _dOCLCQ _dYDX
020			_a9781119608165 _q(electronic bk.)
020			_a1119608163 _q(electronic bk.)
020			_z9781786301581
029	1		_aAU@ _b000065306467
029	1		_aCHNEW _b001050896
029	1		_aCHVBK _b567422496
035			_a(OCoLC)1096435591
050		4	_aQA274.73
072		7	_aMAT _x003000 _2bisacsh
072		7	_aMAT _x029000 _2bisacsh
082	0	4	_a519.2/33 _223
049			_aMAIN
100	1		_aMichelitsch, Thomas, _eauthor. _98308
245	1	0	_aFractional dynamics on networks and lattices / _cThomas Michelitsch, Alejandro Pérez Riascos, Bernard Collet, Andrzej Nowakowski, Franck Nicolleau.
264		1	_aLondon : _bISTE Ltd. ; _aHoboken : _bJohn Wiley & Sons, Inc., _c2019.
300			_a1 online resource : _billustrations
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMechanical engineering and solid mechanics series
588	0		_aOnline resource; title from PDF title page (EBSCO, viewed April 15, 2019).
504			_aIncludes bibliographical references and index.
505	8		_aCover; 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		_a1.4.2. 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		_a2.5. 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		_a3.4. 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			_aThis 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		0	_aMarkov processes. _98309
650		0	_aRandom walks (Mathematics) _98310
650		7	_aMATHEMATICS _xApplied. _2bisacsh _95811
650		7	_aMATHEMATICS _xProbability & Statistics _xGeneral. _2bisacsh _95812
650		7	_aMarkov processes. _2fast _0(OCoLC)fst01010347 _98309
650		7	_aRandom walks (Mathematics) _2fast _0(OCoLC)fst01089818 _98310
655		4	_aElectronic books. _93294
700	1		_aPérez Riascos, Alejandro, _eauthor. _98311
700	1		_aCollet, Bernard, _eauthor. _98312
700	1		_aNowakowski, Andrzej, _eauthor. _98313
700	1		_aNicolleau, F. C. G. A. _q(Frank C. G. A.), _eauthor. _98314
830		0	_aMechanical engineering and solid mechanics series. _97010
856	4	0	_uhttps://doi.org/10.1002/9781119608165 _zWiley Online Library
942			_cEBK
994			_a92 _bDG1
999			_c69062 _d69062