when coherent stochastic resonance appears we consider a system driven by a combination of gaussian white noise and a periodic signal it is demonstrated when the mean exit time for this system necessarily exhibits a minimum as a function of the frequency of the periodic bias and gives rise to the phenomenon known as coherent stochastic resonance this reasoning begins by calculating an exact expression for the mean exit time of a system driven by noise and a telegraph signal and showing that no resonancelike behavior arises this unexpected result lets us identify the sufficient conditions for resonance to appear the origin of coherent stochastic resonance lies in the different behavior of low frequency and high frequency periodic signals

on a class of rational p adic dynamical systems in this paper we investigate the behavior of trajectories of one class of rational p adic dynamical systems in complex p adic field cp we studied siegel disks and attractors of such dynamical systems we found the basin of the attractor of the system it is proved that such dynamical systems are not ergodic on a unit sphere with respect to the haar measure

first passage time problems and resonant behavior on a fluctuating lattice abstract we study the mean residence time of a random walker on a line segment of a lattice which randomly switches between two states in each of the states only motions in a one way direction are allowed when the particle can leave the line segment through both of its ends the residence time is a monotonous increasing function of the switching rate and does not depend on the initial state of the lattice nevertheless if one of the boundaries of the segment is reflecting it goes through a minimum for a given value of the flipping rate showing a resonancelike behavior the results are compared with previous studies of first passage time problems in time dependent fields

anti modularity and anti community detecting in complex networks abstract many networks of interest in sciences and social research can be divided naturally into anti communities the problem of detecting and characterizing such anti community structure has attracted recent attention in this paper we first define the anti modularity as a quantitative measure of anti community partitioning on a network we also theoretically and empirically show the reliability of anti modularity as a measurement of the quality of an anti community partitioning a label propagation algorithm lpad for anti community detection is proposed experimental results on synthetic and real world networks show that our algorithm lpad can obtain higher quality anti community partitioning than other methods

subgraph centrality in complex networks we introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network smaller subgraphs are given more weight than larger ones which makes this measure appropriate for characterizing network motifs we show that the subgraph centrality c s i can be obtained mathematically from the spectra of the adjacency matrix of the network this measure is better able to discriminate the nodes of a network than alternate measures such as degree closeness betweenness and eigenvector centralities we study eight real world networks for which c s i displays useful and desirable properties such as clear ranking of nodes and scale free characteristics compared with the number of links per node the ranking introduced by c s i for the nodes in the protein interaction network of s cereviciae is more highly correlated with the lethality of individual proteins removed from the proteome

perturbation results for the estrada index in weighted networks the logarithm of the estrada index has been proposed recently as a spectral measure to character efficiently the robustness of complex networks in this paper we explore the estrada index in weighted networks and develop various perturbation results based on spectral graph theory it is shown that the robustness of a network may be enhanced even when some edge weights are reduced this is of particular theoretical and practical significance to network design and optimization

boundary problems for diffusion in a fluctuating potential abstract using a newly developed formalism adapted for diffusion in the presence of partially absorbing boundaries we treat the overdamped motion of a particle in a fluctuating potential and in a restricted space the potential is assumed to be linear with a slope switching between two possible values the switching process is taken as the standard markov alternating process we first construct the free dynamics propagator no boundaries which controls the evolution of the joint probability for both the particle s position and the state of the potential secondly at a given spatial point we affix a two channel boundary a given channel absorbs the trajectories arriving at the boundary with the potential in a given state we demonstrate the asymmetry of the filling process for the individual channels and we discuss their asymptotic occupation depending on the mean switching frequency finally we study the motion in a domain restricted by two boundaries of the above two channel type and the corresponding first passage time the simple problem setting allows for an explicit analysis of the correlation between the particle s motion and the potential switching process

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

gaussianization of the spectra of graphs and networks theory and applications abstract matrix functions of the adjacency matrix are very useful for understanding important structural properties of graphs and networks such as communicability node centrality bipartivity and many more they are also intimately related to the solution of differential equations describing dynamical processes on graphs and networks here we propose a new matrix function based on the gaussianization of the adjacency matrix of a graph this function gives more weight to a selected reference eigenvalue ref which may be located in any region of the graph spectra we show here that this matrix function can be derived from physical models that consider the interactions between nearest and next nearest neighbors in the graph we first obtain a few mathematical results for the trace of this matrix function when ref 1 h 1 for simple graphs as well as for random graphs we also provide a combinatorial interpretation of this index in terms of subgraphs in the graph and in terms of the competition pressure among agents in a complex system finally we apply this index to the study of magnetic properties of molecules emerging due to spin interactions as well as to studying the temporal evolution of the international trade network in the period 1992 2002 in both cases we give a clear phenomenological interpretation of the processes described

an increasing sequence of lower bounds for the estrada index of graphs and matrices abstract let g be a graph on n vertices and 1 2 n its eigenvalues the estrada index of g is defined as e e g i 1 n e i in this work we use an increasing sequence converging to the 1 to obtain an increasing sequence of lower bounds for e e g in addition we generalize this succession for the estrada index of an arbitrary symmetric nonnegative matrix

a note on new bounds for the estrada index abstract let g be a graph on n vertices and 1 2 n their eigenvalues the estrada index of g is defined as e e g i 1 n e i in this paper we obtain new upper and lower bounds on the estrada index of a given graph considering numerical inequalities present in the literature

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

coherent stochastic resonance in a sextic double well potential abstract we study the response of a stochastic system described by the one dimensional fokker planck equation with a sextic double well potential u 6 x c 4 x 4 c 6 x 6 to a weak sinusoidal periodic signal two types of boundary conditions have been investigated i absorbing boundary conditions and ii natural boundary conditions the unperturbed propagators are calculated by the eigenfunction expansion method we find that for case i the mean survival time shows the coherent stochastic resonance and for case ii the signal to noise ratio exhibits the stochastic resonance the results are compared with those of the bistable quartic double well potential u 4 x 1 2 x 2 1 4 x 4

p adic 2 1 rational dynamical systems abstract we study the dynamics of an arbitrary 2 1 rational function f x x 2 a x b c x d on the field c p of complex p adic numbers we show that the p adic dynamical system generated by f has a very rich behavior siegel disks may either coincide or be disjoint for different fixed points of the dynamical system also we find the basin of the attractor of the system varying the parameters it is proven that there are periodic trajectories for some values of the parameters there are trajectories which go arbitrary far from fixed points

on the estrada index conjecture abstract let g be a simple graph of order n with m edges let the adjacency spectrum be 1 2 n 1 n of g where 1 2 n 1 n the estrada index of a graph g is ee g i 1 n e i in j a pena i gutman j rada estimating the estrada index linear algebra appl 427 2007 70 76 pena et al posed a conjecture that the star s n has maximum estrada index for any tree of order n and the path p n has minimum estrada index for any tree of order n or any connected graph of order n in this paper we have proved that the star has maximum estrada index for any tree also we obtain that the path has minimum estrada index for any connected graph with m 1 8 n 4 or m n 2 6 moreover we give better lower bound on estrada index for any connected graph

spectral measures of bipartivity in complex networks we introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity it is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks trophic interactions in food webs construction principles in metabolic networks or communities in social networks

ultradiffusion the relaxation of hierarchical systems the authors show that the dynamics of relaxation in hierarchical structures leads to an anomalous decay process which they term ultradiffusion using renormalisation group techniques they explicitly calculate the behaviour of the autocorrelation function in a one dimensional hierarchical system and show its universal power law decay as a function of temperature the authors also demonstrate analytically the emergence of a hierarchy of time scales this phenomenon is relevant to systems ranging from macromolecules to computing structures

communicability in complex networks we propose a new measure of the communicability of a complex network which is a broad generalization of the concept of the shortest path according to the new measure most of the real world networks display the largest communicability between the most connected popular nodes of the network assortative communicability there are also several networks with the disassortative communicability where the most popular nodes communicate very poorly to each other using this information we classify a diverse set of real world complex systems into a small number of universality classes based on their structure dynamic correlation in addition the new communicability measure is able to distinguish finer structures of networks such as communities into which a network is divided a community is unambiguously defined here as a set of nodes displaying larger communicability among them than to the rest of the nodes in the network

on network bipartivity systems with two types of agents with a preference for heterophilous interaction produces networks that are more or less close to bipartite we propose two measures quantifying the notion of bipartivity the two measures one well known and natural but computationally intractable one computationally less complex but also less intuitive are examined on model networks that continuously interpolates between bipartite graphs and graphs with many odd circuits we find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity and thus conclude that the measures are quite relevant we also measure and discuss the values of our bipartivity measures for empirical social networks constructed from professional collaborations internet communities and field surveys here we find as expected that networks arising from romantic online interaction have high and professional collaboration networks have low bipartivity values in some other cases probably due to low average degree of the network the bipartivity measures cannot distinguish between romantic and friendship oriented interaction

on metric structure of ultrametric spaces in our work we have reconsidered the old problem of diffusion at the boundary of an ultrametric tree from a number theoretic point of view namely we use the modular functions in particular the dedekind function to construct the continuous analogue of the cayley tree isometrically embedded in the poincare upper half plane later we work with this continuous cayley tree as with a standard function of a complex variable in the framework of our approach the results of ogielsky and stein on dynamics in ultrametric spaces are reproduced semi analytically or semi numerically the speculation on the new geometrical interpretation of replica n 0 limit is proposed

on the chaotic behavior of a generalized logistic p adic dynamical system abstract in the paper we describe basin of attraction p adic dynamical system g x a x 2 x 1 moreover we also describe the siegel discs of the system since the structure of the orbits of the system is related to the geometry of the p adic siegel discs

on maximum estrada indices of k trees abstract the estrada index of a graph g is defined as ee g i 1 n e i where 1 2 n are the eigenvalues of the adjacency matrix of g let t n k be the set of the k trees of order n in this paper we characterize the graphs among t n k having the first resp the second largest estrada index

moments of the first passage time under external driving a general theory is derived for the moments of the first passage time of a one dimensional markov process in the presence of a weak time dependent forcing the linear corrections to the moments can be expressed by quadratures of the potential and of the time dependent probability density of the unperturbed system or equivalently by its laplace transform if none of the latter functions is known the derived formulas may still be useful for specific cases including a slow driving or a driving with power at only small or large times in the second part of the paper explicit expressions for the mean and variance of the first passage time are derived for the cases of a linear or a parabolic potential and an exponentially decaying driving force the analytical results are found to be in excellent agreement with computer simulations of the respective first passage processes the particular examples furthermore demonstrate that already the effect of a simple exponential driving can be fairly involved implying a nontrivial nonmonotonic behavior of mean and variance as functions of the driving s time scale

graph animals subgraph sampling and motif search in large networks we generalize a sampling algorithm for lattice animals connected clusters on a regular lattice to a monte carlo algorithm for graph animals i e connected subgraphs in arbitrary networks as with the algorithm in n kashtan et al bioinformatics 20 1746 2004 it provides a weighted sample but the computation of the weights is much faster linear in the size of subgraphs instead of superexponential this allows subgraphs with up to ten or more nodes to be sampled with very high statistics from arbitrarily large networks using this together with a heuristic algorithm for rapidly classifying isomorphic graphs we present results for two protein interaction networks obtained using the tandem affinity purification tap method one of escherichia coli with 230 nodes and 695 links and one for yeast saccharomyces cerevisiae with roughly ten times more nodes and links we find in both cases that most connected subgraphs are strong motifs z scores 10 or antimotifs z scores 10 when the null model is the ensemble of networks with fixed degree sequence strong differences appear between the two networks with dominant motifs in e coli being nearly bipartite graphs and having many pairs of nodes that connect to the same neighbors while dominant motifs in yeast tend towards completeness or contain large cliques we also explore a number of methods that do not rely on measurements of z scores or comparisons with null models for instance we discuss the influence of specific complexes like the 26s proteasome in yeast where a small number of complexes dominate the k cores with large k and have a decisive effect on the strongest motifs with 6 8 nodes we also present zipf plots of counts versus rank they show broad distributions that are not power laws in contrast to the case when disconnected subgraphs are included

a transition in a noisy linear system driven by a periodic signal we consider a one dimension linear random walk between two trapping points in which the transition probabilities vary periodically in time an earlier analysis of this system showed that the mean time to trapping of a particle in this system exhibits a minimum when considered as a function of frequency in this note we show that this parameter makes a transition in behavior from a monotonic decrease with increasing amplitude of the periodic term to a monotonic increase with this parameter depending on the frequency a physical argument is suggested to explain this behavior confirmation of this crossover can also be derived from a diffusion model

replica symmetry breaking related to a general ultrametric space iii the case of general measure we study replica symmetry breaking related to a general ultrametric space in the case of general measure

topological evolution in dense granular materials a complex networks perspective abstract one of the great challenges in the science of complex materials materials capable of emergent behavior such as self organized pattern formation is deciphering their inherent structural design principles as they deform in response to external loads we have been exploring the efficacy of techniques from complex networks to the study of dense granular materials as a means to i uncover such design principles and ii identify suitable metrics that quantify the evolution of structure during deformation herein we characterize the developing network structure and loss of connectivity in a quasistatically deforming granular medium from the perspective of complex networks attention is paid to the evolution of the contact and contact force networks at the local or mesoscopic level i e a particle and its immediate neighbors as well as the macroscopic level we explore network motifs and other topological properties at these multiple length scales in an attempt to find that which best correlates with the constitutive properties of nonaffine deformation and dissipation spatially and with respect to strain key processes or rearrangement events that cause loss of connectivity within the material domain e g microbanding and force chain buckling are investigated network statistics of these processes previously shown to be major sources of energy dissipation and nonaffine deformation are then tied to corresponding trends observed in the evolving macroscopic network it is shown that consideration of the unweighted contact network alone is insufficient to tie dissipation to loss of material connectivity

coherent stochastic resonance in one dimensional diffusion with one reflecting and one absorbing boundaries it is shown that the single step periodic signal periodic telegraph signal can not produce coherent stochastic resonance for diffusion on a segment with one absorbing and one reflecting end points while the multi step periodic signal does the general features of this process are exihibited the resonant frequency is found to decrease and the mean first passage time at resonant frequency increases linearly as we increase the length of the medium the cycle variable is shown to be the proper argument to express the first passage probability at resonance a formula for first passage probability at resonance is derived in terms of two universal functions which clearly isolates its dependence on the length of the medium

the efficient determination of the percolation threshold by a frontier generating walk in a gradient the frontier in gradient percolation is generated directly by a type of self avoiding random walk the existence of the gradient permits one to generate an infinite walk on a computer of finite memory from this walk the percolation threshold pc for a two dimensional lattice can be determined with apparently maximum efficiency for a naive monte carlo calculation or n 12 for a square lattice the value pc 0 592745 or 0 000002 is found for a simulation of n 2 6 1011 total steps occupied and blocked perimeter sites the power of the method is verified on the kagome site percolation case

subordination on ultrametric spaces using the formalism of continuous time random walks ctrw the authors discuss particle diffusion on ultrametric spaces ums for broad waiting time distributions psi t approximately t alpha 1 the temporal alpha and the energetic gamma parameters combine multiplicatively subordinate i e s t the mean number of ums sites visited follows a s t approximately talpha gamma law this mirrors previous findings for ctrw on fractals

extremal graphs for estrada indices abstract let g be a simple undirected connected graph the signless laplacian estrada laplacian estrada and estrada indices of a graph g is the sum of the exponentials of the signless laplacian eigenvalues laplacian eigenvalues and eigenvalues of g respectively the present work derives an upper bound for the estrada index of a graph as a function of its chromatic number in the family of graphs whose color classes have order not less than a fixed positive integer the graphs for which the upper bound is tight is obtained additionally an upper bound for the estrada index of the complement of a graph in the previous family of graphs with two color classes is given a nordhaus gaddum type inequality for the laplacian estrada index when g is a bipartite graph with color classes of order not less than 2 is presented moreover a sharp upper bound for the estrada index of the line graph and for the signless laplacian index of a graph in terms of connectivity is obtained

dependence centrality similarity measuring the diversity of profession levels of interests abstract to understand the relations between developers and software we study a collaborative coding platform from the perspective of networks including follower networks dependence networks and developer project bipartite networks through the analyzing of degree distribution pagerank and degree dependent nearest neighbors centrality we find that the degree distributions of all networks have a power law form except the out degree distributions of dependence networks the nearest neighbors centrality is negatively correlated with degree for developers but fluctuates around the average for projects in order to measure the diversity of profession levels of interests a new index called dependence centrality similarity is proposed and the correlation between dependence centrality similarity and degree is investigated the result shows an obvious negative correlations between dependence centrality similarity and degree

p adic models of ultrametric diffusion constrained by hierarchical energy landscapes we demonstrate that the p adic analysis is a natural basis for the construction of a wide variety of models of ultrametric diffusion constrained by hierarchical energy landscapes a general analytical description in terms of the p adic analysis is given for a class of models two exactly solvable examples i e the ultrametric diffusion constrained by the linear energy landscape and the ultrametric diffusion with a reaction sink are considered we show that such models can be applied to both the relaxation in complex systems and the rate processes coupled to rearrangement of the complex surrounding

random hierarchical matrices spectral properties and relation to polymers on disordered trees we study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non invariant symmetric transition matrices of the parisi type subjected to locally constant randomization using the explicit expression for eigenvalues of such matrices we compute the spectral density for the gaussian distribution of matrix elements we also compute the averaged survival probability sp having sense of the probability to find a system in the initial state by time t using the similarity between the averaged sp for locally constant randomized parisi matrices and the partition function of directed polymers on disordered trees we show that for times t tcr where tcr is some critical time a lacunary structure of the ultrametric space occurs with the probability 1 const t this means that the escape from some bounded areas of the ultrametric space of states is locked and the kinetics is confined in these areas for infinitely long time the explosion of the interest to the statistical properties of ensembles of random matrices around 1950s has been motivated in first turn by a series of physical problems in nuclear physics later the physical applications of the random matrix theory rmt were extended to mesoscopics and statistical physics one can mention recent works 1 2 which deal with physical applications of the eigenvalue statistics of ensembles of random matrices the typical problems of rmt concern the evaluation of the averaged spectral density as well as distributions of level spacings under the supposition that all matrix elements are independent randomly distributed entries which take values in some specific ensemble 3 despite the standard rmt can be applied to a wide range of physical phenomena rmt in its basic form does not cover a particular class of hierarchical complex systems important for glasses real networks and proteins the description of such complex systems deals with the concept of hierarchical organization of energy landscapes 4 5 a complex system is assumed to have a large number of metastable states corresponding to local minima in the potential energy landscape with respect to the transition rates the minima are suggested to be clustered in hierarchically nested basins of minima i e larger basins consist of smaller basins each of these consists of even smaller ones etc the basins of local energy minima are separated by a hierarchically arranged set of barriers large basins are separated by high barriers and smaller basins within each larger one are separated by lower barriers since the transitions between the basins are determined by the passages over the highest barriers separating them the transitions between any two local minima obey the strong triangle inequality for ultrametric distances hence the hierarchy of basins possesses the ultrametric geometry which has the natural visualization by the uniform p adic i e p 1 branching cayley tree

chaotic hamiltonian systems survival probability we consider the dynamical system described by the area preserving standard mapping it is known for this system that p t the normalized number of recurrences staying in some given domain of the phase space at time t so called survival probability has the power law asymptotics p t ensuremath sim t ensuremath ensuremath nu we present new semiphenomenological arguments which enable us to map the dynamical system near the chaos border onto the effective ultrametric diffusion on the boundary of a treelike space with hierarchically organized transition rates in the framework of our approach we have estimated the exponent ensuremath nu as ensuremath nu text ln text 2 text ln 1 r g ensuremath approx 1 44 where r g sqrt 5 ensuremath 1 2 is the critical rotation number

on extremal bipartite unicyclic graphs abstract let u n be the set of connected bipartite unicyclic graphs with n vertices here we consider the extremal graphs in u n with respect to both the estrada index of themselves and the kirchhoff index of their complements we find that the first two and the last one unicyclic graphs in u n according to these two orderings are coincident

replica symmetry breaking related to a general ultrametric space i replica matrices and functionals abstract a family of replica matrices related to general ultrametric spaces is introduced these matrices generalize the known parisi matrices some functionals of the replica approach are computed

returnability in complex directed networks digraphs the concept of returnability is proposed for complex directed networks digraphs it can be seen as a generalization of the concept of reciprocity two measures of the returnability are introduced we establish closed formulas for the calculation of the returnability measures which are also related to the digraph spectrum the two measures are calculated for simple examples of digraphs as well as for real world complex directed networks and are compared with the reciprocity

p adic description of characteristic relaxation in complex systems this work is a further development of an approach to the description of relaxation processes in complex systems on the basis of the p adic analysis we show that three types of relaxation fitted into the kohlrausch williams watts law the power decay law and the logarithmic decay law are similar random processes inherently these processes are ultrametric and are described by the p adic master equation the physical meaning of this equation is explained in terms of a random walk constrained by a hierarchical energy landscape we also discuss relations between the relaxation kinetics and the energy landscapes

complex networks and economics abstract as the first step toward a study of complex networks in economics we consider business networks categorized into bipartite networks through empirical study we show the possibility that business networks will fall into the scale free category to have an idea about the clustering coefficient and the averaged path length for bipartite networks we perform a one mode reduction we calculate the quantities for networks constructed by banks and companies before after a merger among banks and quantitatively show that the merger among banks increases the cliquishness of companies and decreases the typical separation between two companies

spectral centrality measures in complex networks complex networks are characterized by heterogeneous distributions of the degree of nodes which produce a large diversification of the roles of the nodes within the network several centrality measures have been introduced to rank nodes based on their topological importance within a graph here we review and compare centrality measures based on spectral properties of graph matrices we shall focus on pagerank pr eigenvector centrality ev and the hub and authority scores of the hits algorithm we derive simple relations between the measures and the in degree of the nodes in some limits we also compare the rankings obtained with different centrality measures

asymptotical behavior of one class of p adic singular fourier integrals abstract we study the asymptotical behavior of the p adic singular fourier integrals j m t f m x p x t x f f m t t p t q p where f m d q p is a quasi associated homogeneous distribution generalized function of degree x x p 1 1 x and order m x 1 x and p x are a multiplicative a normed multiplicative and an additive characters of the field q p of p adic numbers respectively d q p is a test function m 0 1 2 c if re 0 the constructed asymptotics constitute a p adic version of the well known erdelyi lemma theorems which give asymptotic expansions of singular fourier integrals are the abelian type theorems in contrast to the real case all constructed asymptotics have the stabilization property

on maximum estrada indices of bipartite graphs with some given parameters abstract the estrada index of a graph g is defined as e e g i 1 n e i where 1 2 n are the eigenvalues of the adjacency matrix of g in this paper we characterize the unique bipartite graph with maximum estrada index among bipartite graphs with given matching number and given vertex connectivity edge connectivity respectively

nonlocal operators parabolic type equations and ultrametric random walks in this article we introduce a new type of nonlocal operators and study the cauchy problem for certain parabolic type pseudodifferential equations naturally associated to these operators some of these equations are the p adic master equations of certain models of complex systems introduced by avetisov v a and bikulov a kh on the ultrametricity of the fluctuation dynamicmobility of protein molecules proc steklov inst math 265 1 75 81 2009 tr mat inst steklova 265 82 89 2009 izbrannye voprosy matematicheskoy fiziki i p adicheskogo analiza in russian avetisov v a bikulov a kh and zubarev a p first passage time distribution and the number of returns for ultrametric random walks j phys a 42 8 085003 2009 avetisov v a bikulov a kh and osipov v a p adic models of ultrametric diffusion in the conformational dynamics of macromolecules proc steklov inst math 245 2 48 57 2004 tr mat inst steklova 245 55 64 2004 izbrannye voprosy matematicheskoy fiziki i p adicheskogo analiza in russian avetisov v a bikulov a kh and osipov v a p adic description of characteristic relaxation in complex systems j phys a 36 15 4239 4246 2003 avetisov v a bikulov a h kozyrev s v and osipov v a p adic models of ultrametric diffusion constrained by hierarchical energy landscapes j phys a 35 2 177 189 2002 avetisov v a bikulov a kh and kozyrev s v description of logarithmic relaxation by a model of a hierarchical random walk dokl akad nauk 368 2 164 167 1999 in russian the fundamental solutions of these parabolic type equations are transition functions of random walks on the n dimensional vector space over the field of p adic numbers we study some properties of these random walks including the first passage time

nonconventional stochastic resonance it is argued on the basis of linear response theory lrt that new types of stochastic resonance sr are to be anticipated in diverse systems quite different from the one most commonly studied to date which has a static double well potential and is driven by a net force equal to the sum of periodic and stochastic terms on this basis three new nonconventional forms of sr are predicted sought found and investigated both theoretically and by analogue electronic experiment a in monostable systems b in bistable systems with periodically modulated noise and c in a system with coexisting periodic attractors in each case it is shown that lrt can provide a good quantitative description of the experimental results for sufficiently weak driving fields it is concluded that sr is a much more general phenomenon than has hitherto been appreciated

applications of estrada indices and energy to a family of compound graphs abstract to track the gradual change of the adjacency matrix of a simple graph g into the signless laplacian matrix v nikiforov in 35 suggested the study of the convex linear combination a adjacency matrix a g d g 1 a g for 0 1 where a g and d g are the adjacency and the diagonal vertex degrees matrices of g respectively taking this definition as an idea the next matrix was considered for a b r the matrix a a b defined by a a b g a d g b a g extends the previous adjacency matrix this matrix is designated the a b adjacency matrix of g both adjacency matrices are examples of universal matrices already studied by w haemers in this paper we study the a b adjacency spectra for a family of compound graphs formed by disjoint balanced trees whose roots are identified to the vertices of a given graph in consequence new families of cospectral adjacency laplacian and signless laplacian graphs new hypoenergetic graphs graphs whose energy is less than its vertex number and new explicit formulae for estrada signless laplacian estrada and laplacian estrada indices of graphs were obtained moreover sharp upper bounds of the above indices for caterpillars in terms of length of the path and of the maximum number of its pendant vertices are given

stochastic resonance and symmetry breaking in a one dimensional system we derive and discuss properties of an exact solution for the average time for trapping of a brownian particle driven by a random asymmetric but unbiased telegraph signal the particle moves along a line segment terminated by either two traps or a trap and a reflecting point numerical results suggest that stochastic resonance defined as a nonmonotonic behavior of the mean trapping time is absent in the first case but present in the second this generalizes a result obtained earlier by doering and gadoua phys rev lett 69 2318 1992 and implies that symmetry breaking alone does not necessarily create stochastic resonance

approximating spectral sums of large scale matrices using stochastic chebyshev approximations computation of the trace of a matrix function plays an important role in many scientific computing applications including applications in machine learning computational physics e g lattice qua

a stochastic p adic model of the capillary flow in porous random medium abstract we develop the p adic model of propagation of fluids e g oil or water in capillary networks in a porous random medium the hierarchic structure of a system of capillaries is mathematically modeled by endowing trees of capillaries with the structure of an ultrametric space considerations are restricted to the case of idealized networks represented by homogeneous p trees with p branches leaving each vertex where p 1 is a prime number such trees are realized as the fields of p adic numbers we introduce and study an inhomogeneous markov process describing the penetration of fluid into a porous random medium

spectral properties of unimodular lattice triangulations random unimodular lattice triangulations have been recently used as an embedded random graph model which exhibit a crossover behavior between an ordered large world and a disordered small world behavior using the ergodic pachner flips that transform such triangulations into another and an energy functional that corresponds to the degree distribution variance markov chain monte carlo simulations can be applied to study these graphs here we consider the spectra of the adjacency and the laplacian matrix as well as the algebraic connectivity and the spectral radius power law dependencies on the system size can clearly be identified and compared to analytical solutions for periodic ground states for random triangulations we find a qualitative agreement of the spectral properties with well known random graph models in the microcanonical ensemble analytical approximations agree with numerical simulations in the canonical ensemble a crossover behavior can be found for the algebraic connectivity and the spectral radius thus combining large world and small world behavior in one model the considered spectral properties can be applied to transport problems on triangulation graphs and the crossover behavior allows a tuning of important transport quantities

pseudo differential operators with semi quasielliptic symbols over p adic fields abstract in this article we study pseudo differential operators with a semi quasielliptic symbols which are extensions of operators of the form f d x f 1 f x p f where 0 is a function of lizorkin type and f denotes the fourier transform and f x f k c k x k q p 1 n where f is a quasielliptic polynomial of degree d and each c k x is a function from q p n into q p satisfying c k x l we determine the function spaces where the equations f d x u v have solutions we introduce the space of infinitely pseudo differentiable functions with respect to a semi quasielliptic operator by using these spaces we show the existence of a regularization effect for certain parabolic equations over p adics

stability of synchronized states in networks of phase oscillators the stability of synchronized states frequency locked states in networks of phase oscillators is investigated for several network topologies it is shown that for some topologies there is more than one stable synchronized state according to the sign of coupling strength between oscillators it is also shown that in some cases the synchronized state corresponds to zero order parameter

first passage time statistics for diffusion processes with an external random force we present exact equations and expressions for the first passage time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous markov noise we prove that the mean first passage time for this system does not show any resonantlike behavior textcopyright 1996 the american physical society

on maximum estrada indices of graphs with given parameters abstract for a graph g with eigenvalues 1 2 n its estrada index is defined as ee g i 1 n e i we determine the unique graphs with maximum estrada indices among graphs with given number of cut vertices connectivity and edge connectivity respectively

topological structural classes of complex networks we use theoretical principles to study how complex networks are topologically organized at large scale using spectral graph theory we predict the existence of four different topological structural classes of networks these classes correspond respectively to highly homogenous networks lacking structural bottlenecks networks organized into highly interconnected modules with low inter community connectivity networks with a highly connected central core surrounded by a sparser periphery and networks displaying a combination of highly connected groups quasicliques and groups of nodes partitioned into disjoint subsets quasibipartites here we show by means of the spectral scaling method that these classes really exist in real world ecological biological informational technological and social networks we show that neither of three network growth mechanisms random with uniform distribution preferential attachment and random with the same degree sequence as real network is able to reproduce the four structural classes of complex networks these models reproduce two of the network classes as a function of the average degree but completely fail in reproducing the other two classes of networks

zeta functions for analytic mappings log principalization of ideals and newton polyhedra in this paper we provide a geometric description of the possi ble poles of the igusa local zeta function z s f associated to an analytic mapping f f1 fl u k n k l and a locally constant function with support in u in terms of a log principalizaton of the k x ideal if f1 fl typically our new method provides a much shorter list of possible poles compared with the previous methods we determine the largest real part of the poles of the igusa zeta function and then as a corollary we ob tain an asymptotic estimation for the number of solutions of an arbitrary sys tem of polynomial congruences in terms of the log canonical threshold of the subscheme given by if we associate to an analytic mapping f f1 fl a newton polyhedron f and a new notion of non degeneracy with respect to f the novelty of this notion resides in the fact that it depends on one newton polyhedron and khovanskii s non degeneracy notion depends on the newton polyhedra of f1 fl by constructing a log principalization we give an explicit list for the possible poles of z s f l 1 in the case in which f is non degenerate with respect to f

nondegenerate ultrametric diffusion the general non degenerate p adic operators of ultrametric diffusion are introduced bases of eigenvectors for the introduced operators are constructed and the corresponding eigenvalues are computed the long time relaxation behavior of the ultrametric diffusion generated by the introduced operators are investigated

reaction diffusion equations on complex networks and turing patterns via p adic analysis abstract nakao and mikhailov proposed using continuous models mean field models to study reaction diffusion systems on networks and the corresponding turing patterns this work aims to show that p adic analysis is the natural tool to carry out this program this is possible due to the fact that the discrete laplacian attached to a network turns out to be a particular case of a p adic laplacian by embedding the graph attached to the system into the field of p adic numbers we construct a continuous p adic version of a reaction diffusion system on a network the existence and uniqueness of the cauchy problems for these systems are established we show that turing criteria for the p adic continuous reaction diffusion system remain essentially the same as in the classical case however the properties of the emergent patterns are very different the classical turing patterns consisting of alternating domains do not occur in the p adic continuous case instead of this several domains clusters occur multistability that is coexistence of a number of different patterns with the same parameter values occurs clustering and multistability have been observed in the computer simulations of large reaction diffusion systems on networks such behavior can be naturally explained in the p adic continuous model in a rigorous mathematical way but not in the original discrete model

the estrada index of evolving graphs abstract the estrada index of a simple graph g with adjacency matrix a is defined as ee g trace e a it can be used in a range of fields as an efficient measuring tool an evolving graph g 1 g 2 g n is a time ordered sequence of graphs over a fixed set of vertices by using the natural definition of a walk on the evolving graph that respects the arrow of time we extend the static estrada index to accommodate this promising dynamic setting we find that although asymmetry is raised intrinsically by time s arrow the dynamic estrada index is order invariant we establish some lower and upper bounds for the dynamic estrada index in terms of the numbers of vertices and edges illustrative examples are worked out to demonstrate the computations involved

estimating the estrada index abstract let g be a graph on n vertices and let 1 2 n be its eigenvalues the estrada index of g is a recently introduced graph invariant defined as ee i 1 n e i we establish lower and upper bounds for ee in terms of the number of vertices and number of edges also some inequalities between ee and the energy of g are obtained

first passage time distribution and the number of returns for ultrametric random walks in this paper we consider a homogeneous markov process t on an ultrametric space qp with distribution density f x t x qp t r satisfying the equation usually called the ultrametric diffusion equation we construct and examine a random variable that has the meaning the first passage times also we obtain a formula for the mean number of returns on the interval 0 t and give its asymptotic estimates for large t

replica symmetry breaking related to a general ultrametric space ii rsb solutions and the n 0 limit we study the replica symmetry breaking related to a general ultrametric space ii in particular the rsb solutions and the n to0 limit

how the quasispecies evolution depends on the topology of the genome space abstract we compared the properties of the error threshold transition in quasispecies evolution for three different topologies of the genome space they are a hypercube b rugged landscape modelled by an ultrametric space and c holey landscape modelled by bethe lattice in all studied topologies the phase transition exists we calculated the critical exponents in all the cases for the critical exponent corresponding to appropriately defined susceptibility we found super universal value

the estrada index of unicyclic graphs abstract the estrada index of a graph g is defined as ee g i 1 n e i where 1 2 n are the eigenvalues of g we determine the unique unicyclic graph with maximum estrada index the unique bipartite unicyclic graph with maximum estrada index and the unique bipartite unicyclic graph of a given bipartition with maximum estrada index we also show that only two graphs are possible to be the unicyclic graph s with minimum estrada index