vector quantization of speech and speech like waveforms an algorithm for the design of vector quantizers that are locally optimum in the sense of minimizing an average quantitative distortion measure is used to design 1 and 2 bit sample vector quantizers for both real sampled speech and a simulated speech like auto regressive random process both weighted and unweighted squared error distortion measures are considered several comparisons are made and discussed based on the average distortions of the vector quantization schemes the results for the simulated speech are compared to mathematical performance bounds from information theory to provide an indication of how nearly globally optimal vector quantization is for such highly correlated sources a comparison of the results for the real speech and the simulated speech provides a quantitative measure of the accuracy of such models and hence of the applicability of information theory bounds and code designs based on probabilistic models the signal to quantization noise ratios of vector quantizers designed to minimize squared error distortion are compared to those of several popular speech waveform coding systems of similar rates

synchronization in weighted scale free networks with degree degree correlation abstract we study synchronization phenomena in scale free networks of asymmetrically coupled dynamical systems featuring degree degree correlation in the topology of the connection wiring we show that when the interaction is dominant from the high degree to the low degree or from the low degree to the high degree nodes synchronization is enhanced for assortative or disassortative degree degree correlations

revisiting node based sir models in complex networks with degree correlations abstract in this paper we consider two growing networks which will lead to the degree degree correlations between two nearest neighbors in the network when the network grows to some certain size we introduce an sir like disease such as pandemic influenza h1n1 09 to the population due to its rapid spread the population size changes slowly and thus the disease spreads on correlated networks with approximately fixed size to predict the disease evolution on correlated networks we first review two node based sir models incorporating degree correlations and an edge based sir model without considering degree correlation and then compare the predictions of these models with stochastic sir simulations respectively we find that the edge based model even without considering degree correlations agrees much better than the node based models incorporating degree correlations with stochastic sir simulations in many respects moreover simulation results show that for networks with positive correlation the edge based model provides a better upper bound of the cumulative incidence than the node based sir models whereas for networks with negative correlation it provides a lower bound of the cumulative incidence

langevin approach for the dynamics of the contact process on annealed scale free networks we study the dynamics of the contact process one of the simplest nonequilibrium stochastic processes taking place on a scale free network we consider the network topology as annealed i e all links are rewired at each microscopic time step so that no dynamical correlation can build up this is a practical implementation of the absence of correlations assumed by mean field approaches we present a detailed analysis of the contact process in terms of a langevin equation including explicitly the effects of stochastic fluctuations in the number of particles in finite networks this allows us to determine analytically the survival time for spreading experiments and the density of active sites in surviving runs the fluctuations in the topological structure induce anomalous scaling effects with respect to the system size when the degree distribution has a hard upper bound when the upper bound is soft the presence of outliers with huge connectivity perturbs the picture even more inducing an apparent shift of the critical point in light of these findings recent theoretical and numerical results in the literature are critically reviewed

identifying important nodes by adaptive leaderrank abstract spreading process is a common phenomenon in complex networks identifying important nodes in complex networks is of great significance in real world applications based on the spreading process on networks a lot of measures have been proposed to evaluate the importance of nodes however most of the existing measures are appropriate to static networks which are fragile to topological perturbations many real world complex networks are dynamic rather than static meaning that the nodes and edges of such networks may change with time which challenge numerous existing centrality measures based on a new weighted mechanism and the newly proposed h index and leaderrank lr this paper introduces a variant of the lr measure called adaptive leaderrank alr which is a new member of the lr family simulations on six real world networks reveal that the new measure can well balance between prediction accuracy and robustness more interestingly the new measure can better adapt to the adjustment or local perturbations of network topologies as compared with the existing measures by discussing the detailed properties of the measures from the lr family we illustrate that the alr has its competitive advantages over the other measures the proposed algorithm enriches the measures to understand complex networks and may have potential applications in social networks and biological systems

dynamical analysis of a iwsr rumor spreading model with considering the self growth mechanism and indiscernible degree abstract propagation of rumor as one of the most important aspects of spreading dynamics on networks which is often accompanied by the self growth of individuals and indiscernible degree of events and the analysis of this phenomenon can help us to better understand the information dissemination in the social network here with the wiseman supplemented to the classical ignorant spreader stifler i s r rumor spreading model a modified ignorant wiseman spreader stifler i w s r model is established with self growth mechanism by considering indiscernible degree of events by mean field equations of i w s r model the spreading threshold c is calculated to describe the theory of steady state dynamics of the rumor spreading numerical simulation is performed to assess the influence of self growth of individual and indiscernible degree of events on dynamic spreading process the results show that when the spreading rate is smaller than the threshold c the rumor will not spread in the population the stronger the self growth ability of the individual is the smaller the range of rumor will be the higher the indiscernible degree of events is the greater influence of the rumor these obtained findings in the present study could not only elaborate our understandings of spreading dynamics in network but also provide us with an insight to develop effective strategies of inhibiting rumor propagation

effect of degree correlations on networked traffic dynamics abstract in order to enhance the transport capacity of scale free networks we study the relation between the degree correlation and the transport capacity of the network we calculate the degree degree correlation coefficient the maximal betweenness and the critical value of the generating rate r c traffic congestion occurs for r r c numerical experiments indicate that both assortative mixing and disassortative mixing can enhance the transport capacity we also reveal how the network structure affects the transport capacity assortative disassortative mixing changes distributions of nodes betweennesses and as a result the traffic decreases through nodes with the highest degree while it increases through the initially idle nodes

epidemic spreading in correlated complex networks we study a dynamical model of epidemic spreading on complex networks in which there are explicit correlations among the node s connectivities for the case of markovian complex networks showing only correlations between pairs of nodes we find an epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix that gives the average number of links which from a node with connectivity k go to nodes with connectivity k ensuremath numerical simulations on a correlated growing network model provide support for our conclusions

predicting epidemic threshold of correlated networks a comparison of methods abstract being able to theoretically predict the outbreak threshold of an epidemic is essential in disease control real world correlated networks are ubiquitous and their topological structure strongly affects the prediction accuracy of present day theoretical methods quantifying their accuracy and fitness in predicting outbreak thresholds of correlated networks is thus essential we use a susceptible infected removed sir model to examine four widely used theoretical methods the heterogeneous mean field h m f quenched mean field q m f dynamical message passing d m p and connectivity matrix c m methods to predict the outbreak threshold of a correlated network the potential topological structure of correlated network impacts on prediction accuracy of these four methods we emphasize that the quantitative changes of degree correlation degree distribution exponent and network size strongly affect the outbreak of sir spreading dynamics and compare the simulation results with the theoretical ones obtained from these four methods the extensive experiments in synthetic networks show that a the increasing degree correlation coefficients reduce outbreak threshold and suppress outbreak size b the increasing degree distribution exponents raise outbreak threshold but suppress outbreak size c the increasing network sizes decrease outbreak threshold but do not affect outbreak size d as for four theoretical methods c m and d m p are more likely to precisely predict outbreak threshold because they to some extent incorporate network topology with dynamical correlations the experimental results in 50 real world networks also prove the above conclusions

optimizing the controllability of arbitrary networks with genetic algorithm abstract recently as the controllability of complex networks attracts much attention how to optimize networks controllability has become a common and urgent problem in this paper we develop an efficient genetic algorithm oriented optimization tool to optimize the controllability of arbitrary networks consisting of both state nodes and control nodes under popov belevitch hautus rank condition the experimental results on a number of benchmark networks show the effectiveness of this method and the evolution of network topology is captured furthermore we explore how network structure affects its controllability and find that the sparser a network is the more control nodes are needed to control it and the larger the differences between node degrees the more control nodes are needed to achieve the full control our framework provides an alternative to controllability optimization and can be applied to arbitrary networks without any limitations

epidemic threshold and immunization on generalized networks abstract the susceptible infected susceptible sis model is widely adopted in the studies of epidemic dynamics when it is applied on contact networks these networks mostly consist of nodes connected by undirected and unweighted edges following certain statistical properties whereas in this article we consider the threshold and immunization problem for the sis model on generalized networks that may contain different kinds of nodes and edges which are very possible in the real situation we proved that an epidemic will become extinct if and only if the spectral radius of the corresponding parameterized adjacent matrix pam is smaller than 1 based on this result we can evaluate the efficiency of immune strategies and take several prevailing ones as examples in addition we also develop methods that can precisely find the optimal immune strategies for networks with the given pam

quasistationary analysis of the contact process on annealed scale free networks we present an analysis of the quasistationary qs state of the contact process cp on annealed scale free networks using a mapping of the cp dynamics in a one step process and analyzing numerically and analytically the corresponding master equation the relevant qs quantities determined via the master equation exhibit an excellent agreement with direct qs stochastic simulations of the cp the high accuracy of the resulting data allows a probe of the strong corrections to scaling present in both the critical and supercritical regions corrections that mask the correct finite size scaling obtained analytically by applying an exact heterogeneous mean field approach our results represent a promising starting point for a deeper understanding of the contact process and absorbing phase transitions on real quenched complex networks

correlations in complex networks under attack for any initially correlated network after any kind of attack where either nodes or edges are removed we obtain general expressions for the degree degree probability matrix and degree distribution we show that the proposed analytical approach predicts the correct topological changes after the attack by comparing the evolution of the assortativity coefficient for different attack strategies and intensities in theory and simulations we find that it is possible to turn an initially assortative network into a disassortative one and vice versa by fine tuning removal of either nodes or edges for an initially uncorrelated network on the other hand we discover that only a targeted edge removal attack can induce such correlations

voter models on weighted networks we study the dynamics of the voter and moran processes running on top of complex network substrates where each edge has a weight depending on the degree of the nodes it connects for each elementary dynamical step the first node is chosen at random and the second is selected with probability proportional to the weight of the connecting edge we present a heterogeneous mean field approach allowing to identify conservation laws and to calculate exit probabilities along with consensus times in the specific case when the weight is given by the product of nodes degree raised to a power we derive a rich phase diagram with the consensus time exhibiting various scaling laws depending on and on the exponent of the degree distribution numerical simulations give very good agreement for small values of an additional analytical treatment heterogeneous pair approximation improves the agreement with numerics but the theoretical understanding of the behavior in the limit of large remains an open challenge

the multivariable servomechanism problem for positive lti systems in this technical note we study the servomechanism problem for positive open loop stable lti systems under constant tracking signals and constant disturbances in particular we show that in general the mimo servomechanism problem for positive systems is not solvable but is solvable for various classes of mimo systems and for the class of siso systems in which the disturbances are small compared to the tracking signal in particular we give existence results as to what subclass of reference and disturbance signals can be considered for the case when either the mathematical model of the plant is known or unknown and we provide the controller structure that solves the problem for the case of measurable or unmeasurable disturbance signals

maximal planar networks with large clustering coefficient and power law degree distribution in this article we propose a simple rule that generates scale free networks with very large clustering coefficient and very small average distance these networks are called random apollonian networks rans as they can be considered as a variation of apollonian networks we obtain the analytic results of power law exponent ensuremath gamma 3 and clustering coefficient c frac 46 3 ensuremath 36 phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex frac 3 2 ensuremath approx 0 74 which agree with the simulation results very well we prove that the increasing tendency of average distance of rans is a little slower than the logarithm of the number of nodes in rans since most real life networks are both scale free and small world networks rans may perform well in mimicking the reality the rans possess hierarchical structure as c k ensuremath sim k ensuremath 1 that are in accord with the observations of many real life networks in addition we prove that rans are maximal planar networks which are of particular practicability for layout of printed circuits and so on the percolation and epidemic spreading process are also studied and the comparisons between rans and barab asi albert ba as well as newman watts nw networks are shown we find that when the network order n the total number of nodes is relatively small as n ensuremath sim 10 4 the performance of rans under intentional attack is not sensitive to n while that of ba networks is much affected by n and the diseases spread slower in rans than ba networks in the early stage of the suseptible infected process indicating that the large clustering coefficient may slow the spreading velocity especially in the outbreaks

percolation on correlated networks we reconsider the problem of percolation on an equilibrium random network with degree degree correlations between nearest neighboring vertices focusing on critical singularities at a percolation threshold we obtain criteria for degree degree correlations to be irrelevant for critical singularities we present examples of networks in which assortative and disassortative mixing leads to unusual percolation properties and new critical exponents

mean field analysis of the q voter model on networks we present a detailed investigation of the behavior of the nonlinear q voter model for opinion dynamics at the mean field level we derive analytically for any value of the number q of agents involved in the elementary update the phase diagram the exit probability and the consensus time at the transition point the mean field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks we finally discuss the case of random regular networks and compare analytical results with simulations

mean field level analysis of epidemics in directed networks the susceptible infected removed spreading model in a directed graph is studied the mean field level rate equations are built with the degree degree connectivity correlation element and the in out degree distribution and the outbreak threshold is obtained analytically it is determined by the combination of connectivity probability and the degree distribution furthermore the methods of calculating the degree degree correlations in directed networks are presented the numerical results of the discrete epidemic processes in networks verify our analyses

resilience to damage of graphs with degree correlations the existence or nonexistence of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking in this work we investigate the problems of site and bond percolation on graphs with degree correlations and their connection with spreading phenomena we obtain some general expressions that allow the computation of the transition thresholds or their bounds using these results we study the effects of assortative and disassortative correlations on the resilience to damage of networks

equitable random graphs random graph models have played a dominant role in the theoretical study of networked systems the poisson random graph of erd s and renyi in particular as well as the so called configuration model have served as the starting point for numerous calculations in this paper we describe another large class of random graph models which we call equitable random graphs and which are flexible enough to represent networks with diverse degree distributions and many nontrivial types of structure including community structure bipartite structure degree correlations stratification and others yet are exactly solvable for a wide range of properties in the limit of large graph size including percolation properties complete spectral density and the behavior of homogeneous dynamical systems such as coupled oscillators or epidemic models

high prevalence regimes in the pair quenched mean field theory for the susceptible infected susceptible model on networks reckoning of pairwise dynamical correlations significantly improves the accuracy of mean field theories and plays an important role in the investigation of dynamical processes in complex networks in this work we perform a nonperturbative numerical analysis of the quenched mean field theory qmf and the inclusion of dynamical correlations by means of the pair quenched mean field pqmf theory for the susceptible infected susceptible model on synthetic and real networks we show that the pqmf considerably outperforms the standard qmf theory on synthetic networks of distinct levels of heterogeneity and degree correlations providing extremely accurate predictions when the system is not too close to the epidemic threshold while the qmf theory deviates substantially from simulations for networks with a degree exponent 2 5 the scenario for real networks is more complicated still with pqmf significantly outperforming the qmf theory however despite its high accuracy for most investigated networks in a few cases pqmf deviations from simulations are not negligible we found correlations between accuracy and average shortest path while other basic network metrics seem to be uncorrelated with the theory accuracy our results show the viability of the pqmf theory to investigate the high prevalence regimes of recurrent state epidemic processes in networks a regime of high applicability

observability transitions in correlated networks yang wang and motter phys rev lett 109 258701 2012 analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable the size of the connected components comprising the observable nodes is a major concern of the model we analyze this model in random heterogeneous networks with degree correlation with numerical simulations and analytical arguments based on generating functions we find that negative degree correlation makes networks more observable this result holds true both when the sensors are placed on nodes one by one in a random order and when hubs preferentially receive the sensors finally we numerically optimize networks with a fixed degree sequence with respect to the size of the largest observable component optimized networks have negative degree correlation induced by the resulting hub repulsive structure the largest hubs are rarely connected to each other in contrast to the rich club phenomenon of networks

block source coding theory for asymptotically mean stationary sources several properties of operational and information theoretic distortion rate functions and of mutual information rate are developed for asymptotically mean stationary ams processes with standard alphabets and used to prove a block source coding theorem for ergodic ams sources in the development we prove an ergodic decomposition of the mutual information rate of ams sources we show that the operational distortion rate function of an ams source equals that of its stationary mean and we provide a new and direct proof of the equality of the ergodic and stationary process distortion rate functions the latter result yields a proof of the block source coding theorem not requiring the nedoma decomposition and complicated code construction used by gallager and berger

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

link space formalism for network analysis we introduce the link space formalism for analyzing network models with degree degree correlations the formalism is based on a statistical description of the fraction of links l i j connecting nodes of degrees i and j to demonstrate its use we apply the framework to some pedagogical network models namely random attachment barab asi albert preferential attachment and the classical erd ifmmode mbox h o else h o fi s and r enyi random graph for these three models the link space matrix can be solved analytically we apply the formalism to a simple one parameter growing network model whose numerical solution exemplifies the effect of degree degree correlations for the resulting degree distribution we also employ the formalism to derive the degree distributions of two very simple network decay models more specifically that of random link deletion and random node deletion the formalism allows detailed analysis of the correlations within networks and we also employ it to derive the form of a perfectly nonassortative network for arbitrary degree distribution

measuring mixing patterns in complex networks by spearman rank correlation coefficient abstract in this paper we utilize spearman rank correlation coefficient to measure mixing patterns in complex networks compared with the widely used pearson coefficient spearman coefficient is rank based nonparametric and size independent thus it is more effective to assess linking patterns of diverse networks especially for large size networks we demonstrate this point by testing a variety of empirical and artificial networks moreover we show that normalized spearman ranks of stubs are subject to an interesting linear rule where the correlation coefficient is just the spearman coefficient this compelling linear relationship allows us to directly produce networks with any prescribed spearman coefficient our method apparently has an edge over the well known uncorrelated configuration model

correlations in scale free networks tomography and percolation we discuss three related models of scale free networks with the same degree distribution but different correlation properties starting from the barabasi albert construction based on growth and preferential attachment we discuss two other networks emerging when randomizing it with respect to links or nodes we point out that the barabasi albert model displays dissortative behavior with respect to the nodes degrees while the node randomized network shows assortative mixing these kinds of correlations are visualized by discussing the shell structure of the networks around an arbitrary node in spite of different correlation behaviors all three constructions exhibit similar percolation properties this result for percolation is also detected for a network with finite second moment and its corresponding randomized models

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

computational complexity arising from degree correlations in networks we apply a bethe peierls approach to statistical mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices using the nondeterministic polynomial time hard optimization problem of finding minimal vertex covers on these graphs we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks this results in a higher complexity of the network in a computational sense simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization

robustness and fragility of the susceptible infected susceptible epidemic models on complex networks we analyze two alterations of the standard susceptible infected susceptible sis dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree all models have the same epidemic thresholds in mean field theories but depending on the network properties simulations yield a dual scenario in which the epidemic thresholds of the modified sis models can be either dramatically altered or remain unchanged in comparison with the standard dynamics for uncorrelated synthetic networks having a power law degree distribution with exponent 5 2 differences are more remarkable for 3 where a finite threshold is found in the modified models in contrast with the vanishing threshold of the original one this duality is elucidated in terms of epidemic lifespan on star graphs we verify that the activation of the modified sis models is triggered in the innermost component of the network given by a k core decomposition for 3 the activation in the modified dynamics is collective involving essentially the whole network while it is triggered by hubs in the standard sis the duality also appears in the finite size scaling of the critical quantities where mean field behaviors are observed for the modified but not for the original dynamics our results feed the discussions about the most proper conceptions of epidemic models to describe real systems and the choices of the most suitable theoretical approaches to deal with these models

measuring degree degree association in networks the pearson correlation coefficient is commonly used for quantifying the global level of degree degree association in complex networks here we use a probabilistic representation of the underlying network structure for assessing the applicability of different association measures to heavy tailed degree distributions theoretical arguments together with our numerical study indicate that pearson s coefficient often depends on the size of networks with equal association structure impeding a systematic comparison of real world networks in contrast kendall gibbons ensuremath tau b is a considerably more robust measure of the degree degree association

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

a metapopulation model for the population dynamics of anopheles mosquito a reactiondiffusion model for the dynamics of anopheles mosquito in a network is designed a fixed point theorem is used to establish the existence uniqueness of a nontrivial equilibrium a threshold parameter is computed sensitivity analysis of parameters and variables are given the monotone operator theory is used to prove the gas of trivial and positive equilibriums assessment of mosquito dispersal patch heterogeneity on the dynamics of mosquito is given a more robust assessment of malaria control will come from a better understanding of the distribution and connectivity of breeding and blood feeding sites spatial heterogeneity of mosquito resources such as hosts and breeding sites affects mosquito dispersal behavior this paper analyzes and simulates the spreading of anopheles mosquito on a complex metapopulation that is networks of populations connected by migratory flows whose configurations are described in terms of connectivity distribution of nodes patches and the conditional probabilities of connections between nodes we examine the impacts of vector dispersal on the persistence and extinction of a mosquito population in both homogeneous and heterogeneous landscapes for uncorrelated networks in a homogeneous landscape we derive an explicit formula of the basic offspring number r0 m using the theory of monotone operators we obtain sufficient conditions for the global asymptotic stability of equilibria precisely the value 1 of the basic offspring number is a forward bifurcation for the dynamics of anopheles mosquito with the trivial mosquito free equilibrium point being globally asymptotically stable gas when r0 m 1 and one stable nontrivial mosquito persistent equilibrium point being born with well determined basins of attraction when r0 m 1 theoretical results are numerically supported and the impact of the migration of mosquitoes are discussed through global sensitivity analysis and numerical simulations

infection dynamics on scale free networks we discuss properties of infection processes on scale free networks relating them to the node connectivity distribution that characterizes the network considering the epidemiologically important case of a disease that confers permanent immunity upon recovery we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual s degree of connectivity within the population as in an earlier study r pastor satorras and a vesipignani phys rev lett 86 3200 2001 phys rev e 63 006117 2001 for an infection that did not confer immunity upon recovery the epidemic process in contrast with many traditional epidemiological models does not exhibit threshold behavior and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale free network finally we discuss effects that arise from finite population sizes showing that networks of finite size do exhibit threshold effects infections cannot spread for arbitrarily low transmission probabilities

source coding for average rate and average distortion new variable length coding theorems although variable length codes are known to be an efficient class of codes in noiseless coding little is known about these codes for sources subjected to a fidelity constraint variable length source coding theorems with a fidelity criterion are proved and variable length coding is shown to be applicable to sources without any regularity requirements such as stationarity also unlike fixed length coding it is shown that the convergence of average performances to the distortion rate function does not depend on the sample path properties of the source

on universal coding for classes of composite and remote sources with memory corresp weakly minimax universal codes for composite sources whose channel analog has asymptotically decreasing input memory and anticipation adima are examined in particular weak universal codes of all rates with respect to an arbitrary distortion measure are shown to exist for adima composite sources when the switch processes belong to a bar d compact class these results are immediately applicable to universal coding for classes of remote sources

rate equation approach for correlations in growing network models we propose a rate equation approach to compute two vertex correlations in scale free growing network models based on the preferential attachment mechanism the formalism based on previous work of szabo et al fphys rev e 67 056102 s2002dg for the clustering spectrum measuring three vertex correlations is based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k with an appropriate boundary condition we study the properties of both two and three vertex correlations for linear preferential attachment models and also for a model yielding a large clustering coefficient the expressions obtained are checked by means of extensive numerical simulations the rate equation proposed can be generalized to more sophisticated growing network models and also extended to deal with related correlation measures as an example we consider the case of a recently proposed model of weighted networks for which we are able to compute a weighted two vertex correlation function taking into account the strength of the interactions between connected vertices

coarse grained monte carlo simulations of the phase transition of the potts model on weighted networks developing an effective coarse grained cg approach is a promising way for studying dynamics on large size networks in the present work we have proposed a strength based cg s cg method to study critical phenomena of the potts model on weighted complex networks by merging nodes with close strengths together the original network is reduced to a cg network with much smaller size on which the cg hamiltonian can be well defined in particular we make an error analysis and show that our s cg approach satisfies the condition of statistical consistency which demands that the equilibrium probability distribution of the cg model matches that of the microscopic counterpart extensive numerical simulations are performed on scale free networks and random networks without or with strength correlation showing that this s cg approach works very well in reproducing the phase diagrams fluctuations and finite size effects of the microscopic model while the d cg approach proposed in our recent work phys rev e 82 011107 2010 does not

phase transition of the susceptible infected susceptible dynamics on time varying configuration model networks we present a degree based theoretical framework to study the susceptible infected susceptible sis dynamics on time varying rewired configuration model networks using this framework on a given degree distribution we provide a detailed analysis of the stationary state using the rewiring rate to explore the whole range of the time variation of the structure relative to that of the sis process this analysis is suitable for the characterization of the phase transition and leads to three main contributions 1 we obtain a self consistent expression for the absorbing state threshold able to capture both collective and hub activation 2 we recover the predictions of a number of existing approaches as limiting cases of our analysis providing thereby a unifying point of view for the sis dynamics on random networks 3 we obtain bounds for the critical exponents of a number of quantities in the stationary state this allows us to reinterpret the concept of hub dominated phase transition within our framework it appears as a heterogeneous critical phenomenon observables for different degree classes have a different scaling with the infection rate this phenomenon is followed by the successive activation of the degree classes beyond the epidemic threshold

correlations in random apollonian network abstract in this paper by both simulations and theoretical predictions we study two and three node or degree correlations in random apollonian network ran which have small world and scale free topologies using the rate equation approach under the assumption of continuous degree we first give the analytical solution for two node correlations expressed by average nearest neighbor degree annd then we revisit the degree distribution of ran using rate equation method and get the exact connection distribution based on which we derive a more accurate result for mean clustering coefficient as an average quantity of three degree correlations than the one previously reported analytical results reveal that annd has no correlations with respect to degree while clustering coefficient is dependent on degree showing a power law behavior as c k k 1 the obtained expressions are successfully contrasted with extensive numerical simulations

slow dynamics and rare region effects in the contact process on weighted tree networks we show that generic slow dynamics can occur in the contact process on complex networks with a tree like structure and a superimposed weight pattern in the absence of additional nontopological sources of quenched disorder the slow dynamics is induced by rare region effects occurring on correlated subspaces of vertices connected by large weight edges and manifests in the form of a smeared phase transition we conjecture that more sophisticated network motifs could be able to induce griffiths phases as a consequence of purely topological disorder

tuning clustering in random networks with arbitrary degree distributions we present a generator of random networks where both the degree dependent clustering coefficient and the degree distribution are tunable following the same philosophy as in the configuration model the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori the algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs the procedure unveils an universal relation among clustering and degree degree correlations for all networks where the level of assortativity establishes an upper limit to the level of clustering maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior correlation measures in real networks are seen to observe this structural bound

revising the simple measures of assortativity in complex networks we find that traditional statistics for measuring degree mixing are strongly affected by superrich nodes to counteract and measure the effect of superrich nodes we propose a paradigm to quantify the mixing pattern of a real network in which different mixing patterns may appear among low degree nodes and among high degree nodes this paradigm and the simple revised measure uncover the true complex degree mixing patterns of complex networks with superrich nodes the alternate method indicates that some networks show a false disassortative mixing induced by superrich nodes and have no tendency to be genuinely disassortative our results also show that the previously observed fragility of scale free networks is actually greatly exacerbated by the presence of even a very small number of superrich nodes

epidemic spreading with nonlinear infectivity in weighted scale free networks abstract in this paper we investigate the epidemic spreading for the sir model in weighted scale free networks with the nonlinear infectivity and weighted transmission rate concretely we introduce the infectivity exponent and the weight exponent into the epidemic system then examine the impact of and on the epidemic spreading we show that one can adjust the values of and to rebuild a nonzero finite epidemic threshold furthermore we also find the infectivity exponent has a stronger effect not only on the epidemic threshold but also on the epidemic prevalence in addition it is also interesting to see that the absence of the epidemic threshold appears not very dejected since the prevalence grows much more slowly as the transmission rate increases

topology and correlations in structured scale free networks we study a recently introduced class of scale free networks showing a high clustering coefficient and nontrivial connectivity correlations we find that the connectivity probability distribution strongly depends on the fine details of the model we solve exactly the case of low average connectivity providing also exact expressions for the clustering and degree correlation functions the model also exhibits a lack of small world properties in the whole parameter range we discuss the physical properties of these networks in the light of the present detailed analysis

are randomly grown graphs really random we analyze a minimal model of a growing network at each time step a new vertex is added then with probability ensuremath delta two vertices are chosen uniformly at random and joined by an undirected edge this process is repeated for t time steps in the limit of large t the resulting graph displays surprisingly rich characteristics in particular a giant component emerges in an infinite order phase transition at ensuremath delta 1 8 at the transition the average component size jumps discontinuously but remains finite in contrast a static random graph with the same degree distribution exhibits a second order phase transition at ensuremath delta 1 4 and the average component size diverges there these dramatic differences between grown and static random graphs stem from a positive correlation between the degrees of connected vertices in the grown graph older vertices tend to have higher degree and to link with other high degree vertices merely by virtue of their age we conclude that grown graphs however randomly they are constructed are fundamentally different from their static random graph counterparts

fluctuation driven dynamics of the internet topology we study the dynamics of the internet topology based on empirical data on the level of the autonomous systems it is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important features of the internet dynamics the network s overall growth can be described approximately by a single characteristic degree growth rate g eff approximately 0 016 and the fluctuation strength sigma eff approximately 0 14 together with the vertex growth rate alpha approximately 0 029 a stochastic model which incorporates these values and an adaptation rule newly introduced reproduces several features of the real internet topology such as the correlations between the degrees of different vertices

class of correlated random networks with hidden variables we study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices we find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices the expressions obtained are checked by means of numerical simulations in a particular example the general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure we also present an extension of the class to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

novel fake news spreading model with similarity on pso based networks abstract this paper proposes a fake news spreading model with similarity taken into account assuming that the similarity between individuals can affect the transmission rate simulations show that the similarity of two connected nodes and the product of their degrees are positively correlated when the network temperature is small and the similarity of two connected nodes decreases as the product of their degrees increases thus the transmission rate can be expressed as the function of their degrees in the proposed model the theoretic analysis demonstrates the critical threshold is related to both the influence coefficient and the similarity function simulation results show a smaller influence coefficient leads to a larger critical threshold and smaller final density of stiflers

interfaces and the edge percolation map of random directed networks the traditional node percolation map of directed networks is reanalyzed in terms of edges in the percolated phase edges can mainly organize into five distinct giant connected components interfaces bridging the communication of nodes in the strongly connected component and those in the in and out components formal equations for the relative sizes in the number of edges of these giant structures are derived for arbitrary joint degree distributions in the presence of local and two point correlations the uncorrelated null model is fully solved analytically and compared against simulations finding an excellent agreement interfaces and their particular conformations giving place from hairy ball percolation landscapes to bottleneck straits could bring new light to the discussion of how a structure is interwoven with functionality in flow networks

asymptotically mean stationary channels a necessary and sufficient condition for a source to satisfy the ergodic theorem and the shannon mcmillan theorem the two basic mathematical tools of the shannon theory is that it be asymptotically mean stationary ams a channel is defined here to be ams if whenever an ams input source is connected to the channel the resulting input output process is ams we develop several characterizations and properties of ams channels that resemble those of ams sources as an application we show that these ideas are useful in characterizing composite sources and in particular that there exist sources that exhibit distinct short term and long term stationarity properties thus locally stationary or quasi stationary processes such as those used to model speech waveforms may also be stationary in addition some preliminary results on coding for ams channels are presented

susceptible infected susceptible model a comparison of n intertwined and heterogeneous mean field approximations we introduce the susceptible infected susceptible sis spreading model which is taken as a benchmark for the comparison between the n intertwined approximation and the pastor satorras and vespignani heterogeneous mean field hmf approximation of the sis model the n intertwined approximation the hmf approximation and the sis spreading model are compared for different graph types we focus on the epidemic threshold and the steady state fraction of infected nodes in networks with different degree distributions overall the n intertwined approximation is superior to the hmf approximation the n intertwined approximation is exactly the same as the hmf approximation in regular graphs however for some special graph types such as the square lattice graph and the path graph the two mean field approximations are both very different from the sis spreading model

mean field diffusive dynamics on weighted networks diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks here we introduce a general formalism that allows to easily write down mean field equations for any diffusive dynamics on weighted networks we also propose the concept of annealed weighted networks in which such equations become exact we show the validity of our approach addressing the problem of the random walk process pointing out a strong departure of the behavior observed in quenched real scale free networks from the mean field predictions additionally we show how to employ our formalism for more complex dynamics our work sheds light on mean field theory on weighted networks and on its range of validity and warns about the reliability of mean field results for complex dynamics

generalized percolation in random directed networks we develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges that is edges pointing in both directions simultaneously these two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena equations for the percolation threshold and the sizes of the giant components are derived in the most general case we also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions

epidemic threshold for the sirs model on the networks abstract we study the phase transition from the persistence phase to the extinction phase for the sirs susceptible infected refractory susceptible model of diseases spreading on the networks we derive an analytical expression for the probability of the descendants to reinfect their ancestors we find that in the case of the recovery time r is larger than the infection time i the infection will flow directionally from the ancestors to descendants however the descendants will be unable to reinfect their ancestors during the time of their illness this behavior leads us to deduce that if the infection rate is high enough so that any infected node on the network infects all its neighbors during its infection time then the sirs model on the network evolves to extinction state where all the nodes on the network become susceptible moreover we assert that in order to the disease spreads frequently throughout the nodes of the networks the loops on the network are necessary which means the clustering coefficient will play an important role in this model hence unlike the other models such as sis model and sir model the sirs model has two critical thresholds which separate the persistence phase from the extinction phase when i r i e for fixed values of i and r there are two critical points for infection rate 1 and 2 where epidemic persists in between of those two points we confirm those results numerically with the simulation of a regular one dimensional sirs system and small world network