degree dispersion increases the rate of rare events in population networks there is great interest in predicting rare and extreme events in complex systems and in particular understanding the role of network topology in facilitating such events in this letter we show that degree dispersion the fact that the number of local connections in networks varies broadly increases the probability of large rare fluctuations in population networks generically we perform explicit calculations for two canonical and distinct classes of rare events network extinction and switching when the distance to threshold is held constant and hence stochastic effects are fairly compared among networks we show that there is a universal exponential increase in the rate of rare events proportional to the variance of a network s degree distribution over its mean squared

generalized voterlike model on activity driven networks with attractiveness we study the behavior of a generalized consensus dynamics on a temporal network of interactions the activity driven network with attractiveness in this temporal network model agents are endowed with an intrinsic activity a ruling the rate at which they generate connections and an intrinsic attractiveness b modulating the rate at which they receive connections the consensus dynamics considered is a mixed voter and moran dynamics each agent either in state 0 or 1 modifies his or her state when connecting with a peer thus an active agent copies his or her state from the peer with probability p or imposes his or her state to him or her with the complementary probability 1 ensuremath p applying a heterogeneous mean field approach we derive a differential equation for the average density of voters with activity a and attractiveness b in state 1 which we use to evaluate the average time to reach consensus and the exit probability defined as the probability that a single agent with activity a and attractiveness b eventually imposes his or her state to a pool of initially unanimous population in the opposite state we study a number of particular cases finding an excellent agreement with numerical simulations of the model interestingly we observe a symmetry between voter and moran dynamics in pure activity driven networks and their static integrated counterparts that exemplifies the strong differences that a time varying network can impose on dynamical processes

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

unified index to quantifying heterogeneity of complex networks abstract although recent studies have revealed that degree heterogeneity of a complex network has significant impact on the network performance and function a unified definition of the heterogeneity of a network with any degree distribution is absent in this paper we define a heterogeneity index 0 h 1 to quantify the degree heterogeneity of any given network we analytically show the existence of an upper bound of h 0 5 for exponential networks thus explain why exponential networks are homogeneous on the other hand we also analytically show that the heterogeneity index of an infinite power law network is between 1 and 0 5 if and only if its degree exponent is between 2 and 2 5 we further show that for any power law network with a degree exponent greater than 2 5 there always exists an exponential network such that both networks have the same heterogeneity index this may help to explain why 2 5 is a critical degree exponent for some dynamic behaviors on power law networks

fast fixation with a generic network structure we investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics spatially structured wright fisher models ecology hubbell type models linguistics the utterance selection model and opinion dynamics the voter model as special cases these models all have absorbing states of fixation where all the nodes are in the same state earlier studies of these models showed that the mean time when this occurs can be made to grow as different powers of the network size by varying the degree distribution of the network here we demonstrate that this effect can also arise if one varies the asymmetry of the copying dynamics while holding the degree distribution constant in particular we show that the mean time to fixation can be accelerated even on homogeneous networks when certain nodes are very much more likely to be copied from than copied to we further show that there is a complex interplay between degree distribution and asymmetry when they may covary and that the results are robust to correlations in the network or the initial condition

self avoiding walks on scale free networks several kinds of walks on complex networks are currently used to analyze search and navigation in different systems many analytical and computational results are known for random walks on such networks self avoiding walks saw s are expected to be more suitable than unrestricted random walks to explore various kinds of real life networks here we study long range properties of random saw s on scale free networks characterized by a degree distribution p k ensuremath sim k ensuremath ensuremath gamma in the limit of large networks system size n ensuremath rightarrow ensuremath infty the average number s n of saw s starting from a generic site increases as ensuremath mu n with ensuremath mu k 2 k ensuremath 1 for finite n s n is reduced due to the presence of loops in the network which causes the emergence of attrition of the paths for kinetic growth walks the average maximum length l increases as a power of the system size l ensuremath sim n ensuremath alpha with an exponent ensuremath alpha increasing as the parameter ensuremath gamma is raised we discuss the dependence of ensuremath alpha on the minimum allowed degree in the network a similar power law dependence is found for the mean self intersection length of nonreversal random walks simulation results support our approximate analytical calculations

discrete opinion dynamics on networks based on social influence a model of opinion dynamics based on social influence on networks was studied the opinion of each agent can have integer values i 1 2 i and opinion exchanges are restricted to connected agents it was found that for any i 2 and self confidence parameter 0 u 1 when u is a degree independent constant the weighted proportion qi of the population that hold a given opinion i is a martingale and the fraction qi of opinion i will gradually converge to qi the tendency can slow down with the increase of degree assortativity of networks when u is degree dependent qi does not possess the martingale property however qi still converges to it in both cases for a finite network the states of all agents will finally reach consensus further if there exist stubborn persons in the population whose opinions do not change over time it was found that for degree independent constant u both qi and qi will converge to fixed proportions which only depend on the distribution of initial obstinate persons and naturally the final equilibrium state will be the coexistence of diverse opinions held by the stubborn people the analytical results were verified by numerical simulations on barabasi albert ba networks the model highlights the influence of high degree agents on the final consensus or coexistence state and captures some realistic features of the diffusion of opinions in social networks

bosonization techniques on algebraic curves and conformal field theories the bosonization of b c systems is studied with conformal weight on riemann surfaces in which the moduli space is parametrized by the branch points algebraic curves besides being interesting in itself the problem is related to perturbative string theories and to nonfree conformal field theories on the complex plane with the insertion of certain spin fields called the twist fields the method of differentials is proposed which allows a complete treatment of the b c systems on algebraic curves with local abelian monodromy group it can be nevertheless applied also to more general algebraic curves allowing the computation of the green s functions and shedding some light about the structure of the twist fields in the general case the connections between our formalism and the solutions of the riemann monodromy problem used to find out the conformal blocks of conformal field theories are pointed out

evolutionary dynamics on degree heterogeneous graphs the evolution of two species with different fitness is investigated on degree heterogeneous graphs the population evolves either by one individual dying and being replaced by the offspring of a random neighbor voter model dynamics or by an individual giving birth to an offspring that takes over a random neighbor node invasion process dynamics the fixation probability for one species to take over a population of n individuals depends crucially on the dynamics and on the local environment starting with a single fitter mutant at a node of degree k the fixation probability is proportional to k for voter model dynamics and to 1 k for invasion process dynamics

belief propagation algorithm and the ising model on networks with arbitrary distributions of motifs we generalize the belief propagation algorithm to sparse random networks with arbitrary distributions of motifs triangles loops etc each vertex in these networks belongs to a given set of motifs generalization of the configuration model these networks can be treated as sparse uncorrelated hypergraphs in which hyperedges represent motifs here a hypergraph is a generalization of a graph where a hyperedge can connect any number of vertices these uncorrelated hypergraphs are treelike hypertrees which crucially simplifies the problem and allows us to apply the belief propagation algorithm to these loopy networks with arbitrary motifs as natural examples we consider motifs in the form of finite loops and cliques we apply the belief propagation algorithm to the ferromagnetic ising model with pairwise interactions on the resulting random networks and obtain an exact solution of this model we find an exact critical temperature of the ferromagnetic phase transition and demonstrate that with increasing the clustering coefficient and the loop size the critical temperature increases compared to ordinary treelike complex networks however weak clustering does not change the critical behavior qualitatively our solution also gives the birth point of the giant connected component in these loopy networks

braid matrices and structure constants for minimal conformal models using the feigin fuchs representation of minimal conformal models in a form introduced recently by one of us the braid group representation matrices describing the analytic continuation properties of conformal blocks are computed in a suitable normalization their matrix elements are shown to essentially factorize into pairs of boltzmann weights of critical rsos models in a certain limit of the spectral parameter these boltzmann weights are related to quantum groupr matrices by the vertex sos transformation we show that the crossing symmetry of the four point function in left right symmetric models follows from a quantum group relation also called crossing symmetry this observation gives a simple way to evaluate the structure constants

phase transitions in the q voter model with noise on a duplex clique we study a nonlinear q voter model with stochastic noise interpreted in the social context as independence on a duplex network to study the role of the multilevelness in this model we propose three methods of transferring the model from a mono to a multiplex network they take into account two criteria one related to the status of independence local vs global and one related to peer pressure and vs or in order to examine the influence of the presence of more than one level in the social network we perform simulations on a particularly simple multiplex a duplex clique which consists of two fully overlapped complete graphs cliques solving numerically the rate equation and simultaneously conducting monte carlo simulations we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior however qualitative changes in the phase transitions can be observed for only one of the considered rules local and for this rule the phase transition becomes discontinuous for q 5 whereas for a monoplex such behavior is observed for q 6 interestingly only this rule admits construction of realistic variants of the model in line with recent social experiments

biased percolation on scale free networks biased degree dependent percolation was recently shown to provide strategies for turning robust networks fragile and vice versa here we present more detailed results for biased edge percolation on scale free net works we assume a network in which the probability for an edge between nodes i and j to be retained is proportional to kikjwith ki and kj the degrees of the nodes we discuss two methods of network recon struction sequential and simultaneous and investigate their properties by analytical and numerical means the system is examined away from the percolation transition where the size of the giant cluster is obtained and close to the transition where nonuniversal critical exponents are extracted using the generating functions method the theory is found to agree quite well with simulations by presenting an extension of the fortuin kasteleyn construction we find that biased percolation is well described by the q 1 limit of the q state potts model with inhomogeneous couplings

ferromagnetic transition in a simple variant of the ising model on multiplex networks abstract multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks layers here a simple variant of the ising model on multiplex networks with two layers is considered with spins located in the nodes and edges corresponding to ferromagnetic interactions between them critical temperatures for the ferromagnetic transition are evaluated for the layers in the form of random erdos renyi graphs or heterogeneous scale free networks using the mean field approximation and the replica method from the replica symmetric solution both methods require the use of different partial magnetizations associated with different layers of the multiplex network and yield qualitatively similar results if the layers are strongly heterogeneous the critical temperature differs noticeably from that for the ising model on a network being a superposition of the two layers evaluated in the mean field approximation neglecting the effect of the underlying multiplex structure on the correlations between the degrees of nodes the critical temperature evaluated from the replica symmetric solution depends sensitively on the correlations between the degrees of nodes in different layers and shows satisfactory quantitative agreement with that obtained from monte carlo simulations the critical behavior of the magnetization for the model with strongly heterogeneous layers can depend on the distributions of the degrees of nodes and is then determined by the properties of the most heterogeneous layer

finiteness and fluctuations in growing networks we study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks we first determine the exact degree distribution of finite networks by generating function approaches the resulting distributions exhibit an unusual finite size scaling behaviour and they are also sensitive to the initial conditions we argue that fluctuations in the number of nodes of degree k become gaussian for fixed degree as the size of the network diverges we also characterize the fluctuations between different realizations of the network in terms of higher moments of the degree distribution

evolutionary graph theory revisited when is an evolutionary process equivalent to the moran process evolution in finite populations is often modelled using the classical moran process over the last 10 years this methodology has been extended to structured populations using evolutionary graph theory an important question in any such population is whether a rare mutant has a higher or lower chance of fixating the fixation probability than the moran probability i e that from the original moran model which represents an unstructured population as evolutionary graph theory has developed different ways of considering the interactions between individuals through a graph and an associated matrix of weights have been considered as have a number of important dynamics in this paper we revisit the original paper on evolutionary graph theory in light of these extensions to consider these developments in an integrated way in particular we find general criteria for when an evolutionary graph with general weights satisfies the moran probability for the set of six common evolutionary dynamics

effects of strategy migration direction and noise in the evolutionary spatial prisoner s dilemma spatial games are crucial for understanding patterns of cooperation in nature and to some extent society they are known to be more sensitive to local symmetries than e g spin models this paper concerns the evolution of the prisoner s dilemma game on regular lattices with three different types of neighborhoods char22 the von neumann moore and kagom e types we investigate two kinds of dynamics for the players to update their strategies that can be unconditional cooperator or defector depending on the payoff difference an individual can adopt the strategy of a random neighbor a voter model like dynamics vmld or impose its strategy on a random neighbor i e invasion process like dynamics ipld in particular we focus on the effects of noise in combination with the strategy dynamics on the evolution of cooperation we find that vmld compared to ipld better supports the spreading and sustaining of cooperation we see that noise has nontrivial effects on the evolution of cooperation maximum cooperation density can be realized either at a medium noise level in the limit of zero noise or in both these regions the temptation to defect and the local interaction structure determine the outcome especially in the low noise limit the local interaction plays a crucial role in determining the fate of cooperators we elucidate these both by numerical simulations and mean field cluster approximation methods

gauge theory in witten s approach to the generation problem in witten s topological theory of the generation problem gauge groups are identified with thee 8 centraliser of the holonomy group of the internal manifold here we show that this amounts to interpreting gauge groups as generalised symmetry groups of the internal levi civita connection we then give techniques for computing centralisers in exceptional groups taking into account the fact that holonomy groups are frequently disconnected these techniques allow us to deal with compact locally irreducible ricci flat riemannian manifolds of all holonomy types and dimensions

mapping the q voter model from a single chain to complex networks abstract we propose and compare six different ways of mapping the modified q voter model to complex networks considering square lattices barabasi albert watts strogatz and real twitter networks we ask the question if always a particular choice of the group of influence of a fixed size q leads to different behavior at the macroscopic level using monte carlo simulations we show that the answer depends on the relative average path length of the network and for real life topologies the differences between the considered mappings may be negligible

ising models on power law random graphs we study a ferromagnetic ising model on random graphs with a power law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite degree exponent 2 for which the random graph has a tree like structure for this we closely follow the analysis by dembo and montanari ann appl probab 20 2 565 592 2010 which assumes finite variance degrees 3 adapting it when necessary and also simplifying it when possible our results also apply in cases where the degree distribution does not obey a power law

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

nonlinear q voter model we introduce a nonlinear variant of the voter model the q voter model in which q neighbors with possible repetition are consulted for a voter to change opinion if the q neighbors agree the voter takes their opinion if they do not have a unanimous opinion still a voter can flip its state with probability epsilon we solve the model on a fully connected network i e in mean field and compute the exit probability as well as the average time to reach consensus by employing the backward fokker planck formalism and scaling arguments we analyze the results in the perspective of a recently proposed langevin equation aimed at describing generic phase transitions in systems with two z2 symmetric absorbing states in particular by deriving explicitly the coefficients of such a langevin equation as a function of the microscopic flipping probabilities we find that in mean field the q voter model exhibits a disordered phase for high epsilon and an ordered one for low epsilon with three possible ways to go from one to the other i a unique generalized voter like transition ii a series of two consecutive transitions one ising like in which the z2 symmetry is broken and a separate one in the directed percolation class in which the system falls into an absorbing state and iii a series of two transitions including an intermediate regime in which the final state depends on initial conditions this third so far unexplored scenario in which a type of ordering dynamics emerges is rationalized and found to be specific of mean field i e fluctuations are explicitly shown to wash it out in spatially extended systems

synchronization landscapes in small world connected computer networks motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small world networks embedded in one and two dimensions we find that the synchronization landscape corresponding to the progress of the individual processors exhibits kardar parisi zhang like kinetic roughening on regular networks with short range communication links although the processors on average progress at a nonzero rate their spread the width of the synchronization landscape diverges with the number of nodes desynchronized state hindering efficient data management when random communication links are added on top of the one and two dimensional regular networks resulting in a small world network large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system size limit synchronized state in the resulting synchronization scheme the processors make close to uniform progress with a nonzero rate without global intervention we obtain our results by simulating the simulations based on the exact algorithmic rules supported by coarse grained arguments

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

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

asymptotically optimal amplifiers for the moran process abstract we study the moran process as adapted by lieberman hauert and nowak this is a model of an evolving population on a graph or digraph where certain individuals called mutants have fitness r and other individuals called non mutants have fitness 1 we focus on the situation where the mutation is advantageous in the sense that r 1 a family of digraphs is said to be strongly amplifying if the extinction probability tends to 0 when the moran process is run on digraphs in this family the most amplifying known family of digraphs is the family of megastars of galanis et al we show that this family is optimal up to logarithmic factors since every strongly connected n vertex digraph has extinction probability n 1 2 next we show that there is an infinite family of undirected graphs called dense incubators whose extinction probability is o n 1 3 we show that this is optimal up to constant factors finally we introduce sparse incubators for varying edge density and show that the extinction probability of these graphs is o n m where m is the number of edges again we show that this is optimal up to constant factors

group theoretic aspects of the hosotani mechanism if a gauge configuration has a non trivial holonomy group phi in the vacuum then the gauge symmetry is broken to the centraliser of phi in the gauge group this approach to symmetry breaking has found important applications recently here the author studies this mechanism from a general point of view given a compact lie group g and a compact subgroup h he finds conditions for the existence of a group j with h cj centraliser of j studies the uniqueness of j and asks whether j can be represented as the holonomy group of some connection

hosotani breaking of e6 to a subgroup of rank five on multiply connected manifolds it is possible to construct vacuum gauge configurations with nontrivial holonomy groups this is the basis of the hosotani mechanism this naturally suggests a hosotani inverse problem if we wish to break a gauge group g to a subgroup h what are the possible finite holonomy groups having this effect and what can one say about the fundamental groups of the underlying manifolds usually this problem is too difficult to solve but we show that for g e6 and h locally isomorphic to the rank five group su 3 su 2 u 1 u 1 a complete solution is possible it is hoped that the results will aid a search for examples of calabi yau manifolds leading to a low energy gauge group of rank five

understanding the temporal pattern of spreading in heterogeneous networks theory of the mean infection time for a reliable prediction of an epidemic or information spreading pattern in complex systems well defined measures are essential in the susceptible infected model on heterogeneous networks the cluster of infected nodes in the intermediate time regime exhibits too large fluctuation in size to use its mean size as a representative value the cluster size follows quite a broad distribution which is shown to be derived from the variation of the cluster size with the time when a hub node was first infected on the contrary the distribution of the time taken to infect a given number of nodes is well concentrated at its mean suggesting the mean infection time is a better measure we show that the mean infection time can be evaluated by using the scaling behaviors of the boundary area of the infected cluster and use it to find a nonexponential but algebraic spreading phase in the intermediate stage on strongly heterogeneous networks such slow spreading originates in only small degree nodes left susceptible while most hub nodes are already infected in the early exponential spreading stage our results offer a way to detour around large statistical fluctuations and quantify reliably the temporal pattern of spread under structural heterogeneity

voter model on networks and the multivariate beta distribution in elections the vote shares or turnout rates show a strong spatial correlation the logarithmic decay with distance suggests that a two dimensional 2d noisy diffusive equation describes the system based on the study of u s presidential elections data it was determined that the fluctuations of vote shares also exhibit a strong and long range spatial correlation previously it was considered difficult to induce strong and long range spatial correlation of the vote shares without breaking the empirically observed narrow distribution we demonstrate that a voter model on networks shows such a behavior in the model there are many voters in a node who are affected by the agents in the node and by the agents in the linked nodes a multivariate wright fisher diffusion equation for the joint probability density of the vote shares is derived the stationary distribution is a multivariate generalization of the beta distribution in addition we also estimate the equilibrium values and the covariance matrix of the vote shares and obtain a correspondence with a multivariate normal distribution this approach largely simplifies the calibration of the parameters in the modeling of elections

multivalued fields on the complex plane and conformal field theories in this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated these theories are realized in terms of free scalar fields starting from the simpleb c systems and scalar fields on algebraic curves the knizhnik zamolodchikov equations for the conformal blocks can be explicitly solved besides the fact that one obtains in this way an entire class of theories in which the operators obey nonstandard statistics these systems are interesting in exploring the connection between statistics and curved space times at least in the two dimensional case

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

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

flux distribution of metabolic networks close to optimal biomass production we study a statistical model describing the steady state distribution of the fluxes in a metabolic network the resulting model defined on continuous variables can be solved by the cavity method in particular analytical tractability is possible solving the cavity equation over an ensemble of networks with the same degree distribution as a real metabolic network the flux distribution that optimizes production of biomass has a fat tail with a power law exponent independent of the structural properties of the underlying network these results are in complete agreement with the flux balance analysis outcome and in qualitative agreement with the experimental results

deformations of complex structures and conformal field theories on riemann surfaces the role of complex structure deformations in representing the virasoro algebra associated to any conformal field theory on a genus p 1 compact riemann surface is investigated

voter model with non poissonian interevent intervals recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long tail distribution we investigate the effect of such a non poissonian nature of human behavior on dynamics of opinion formation we use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks compared with the exponential distribution of interevent intervals i e the standard voter model the power law distribution of interevent intervals slows down consensus on the ring this is because of the memory effect in the power law case the expected time until the next update event on a link is large if the link has not had an update event for a long time on the complete graph the consensus time in the power law case is close to that in the exponential case regular graphs bridge these two results such that the slowing down of the consensus in the power law case as compared to the exponential case is less pronounced as the degree increases

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

early appraisal of the fixation probability in directed networks in evolutionary dynamics the probability that a mutation spreads through the whole population having arisen from a single individual is known as the fixation probability in general it is not possible to find the fixation probability analytically given the mutant s fitness and the topological constraints that govern the spread of the mutation so one resorts to simulations instead depending on the topology in use a great number of evolutionary steps may be needed in each of the simulation events particularly in those that end with the population containing mutants only we introduce two techniques to accelerate the determination of the fixation probability the first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably this technique is computationally advantageous for some of the so called layered networks the second technique which is not restricted to layered networks consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value and counting that event as having led to a total spread of the mutation for advantageous mutations in large populations and regardless of the network s topology we demonstrate both analytically and by means of simulations that using a threshold of about n r ensuremath 1 1 4 mutants where n is the number of simulation events and r is the ratio of the mutants fitness to that of the remainder of the population leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full fledged simulations we have observed speedups of two orders of magnitude for layered networks with 10 text 000 nodes

commitment versus persuasion in the three party constrained voter model in the framework of the three party constrained voter model where voters of two radical parties a and b interact with centrists c and c we study the competition between a persuasive majority and a committed minority in this model a s and b s are incompatible voters that can convince centrists or be swayed by them here radical voters are more persuasive than centrists whose sub population comprises susceptible agents c and a fraction of centrist zealots c whereas c s may adopt the opinions a and b with respective rates 1 a and 1 b with a b 0 c s are committed individuals that always remain centrists furthermore a and b voters can become susceptible centrists c with a rate 1 the resulting competition between commitment and persuasion is studied in the mean field limit and for a finite population on a complete graph at mean field level there is a continuous transition from a coexistence phase when b whereas all species coexist when a b when c and the initial density of centrists is low one finds lnn when n 1 our analytical findings are corroborated by stochastic simulations

spin models on random graphs with controlled topologies beyond degree constraints we study ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution p k can be chosen arbitrarily but which allows for further fine tuning of the topology via preferential attachment of edges on the basis of an arbitrary function q k k of the degrees of the vertices involved we solve these models using finite connectivity equilibrium replica theory within the replica symmetric ansatz in our ensemble of graphs phase diagrams of the spin system are found to depend no longer only on the chosen degree distribution but also on the choice made for q k k the increased ability to control interaction topology in solvable models beyond prescribing only the degree distribution of the interaction graph enables a more accurate modeling of real world interacting particle systems by spin systems on suitably defined random graphs

fixation time in evolutionary graphs a mean field approach using an analytical method we calculate average conditional fixation time of mutants in a general graph structured population of two types of species the method is based on markov chains and uses a mean field approximation to calculate the corresponding transition matrix analytical results are compared with the results of simulation of the moran process on a number of network structures

voter model dynamics in complex networks role of dimensionality disorder and degree distribution we analyze the ordering dynamics of the voter model in different classes of complex networks we observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks we also find that when there is no ordering in the system the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity the existence of hubs i e highly connected nodes in the network modifies the linear system size scaling law of the survival time the size of an ordered domain is sensitive to the network disorder and the average degree decreasing with both however it seems not to depend on network size and on the heterogeneity of the degree distribution

ising model on networks with an arbitrary distribution of connections we find the exact critical temperature t c of the nearest neighbor ferromagnetic ising model on an equilibrium random graph with an arbitrary degree distribution p k we observe an anomalous behavior of the magnetization magnetic susceptibility and specific heat when p k is fat tailed or loosely speaking when the fourth moment of the distribution diverges in infinite networks when the second moment becomes divergent t c approaches infinity the phase transition is of infinite order and size effect is anomalously strong

analytic treatment of consensus achievement in the single type zealotry voter model abstract we introduce zealots of one opinion in the voter model on a complete graph and examine how they affect consensus achievement using first step analysis for markov chains to obtain an exact solution we find that the mean consensus time scales with the population size n increasing the number of zealots z will decrease the consensus time in a power law fashion for large z the mean magnetization was also analytically obtained and was found to contain an exponential dependence on z the dynamics for the complete graph are qualitatively similar to those obtained in another study for the barabasi albert network in general the existence of zealots serves to hasten consensus except in the case where only a few zealots oppose the vast majority

voter model on the two clique graph i examine the mean consensus time i e exit time of the voter model in the so called two clique graph the two clique graph is composed of two cliques interconnected by some links and considered as a toy model of networks with community structure or multilayer networks i analytically show that as the number of interclique links per node is varied the mean consensus time experiences a crossover between a fast consensus regime i e o n and a slow consensus regime i e o n 2 where n is the number of nodes the fast regime is consistent with the result for homogeneous well mixed graphs such as the complete graph the slow regime appears only when the entire network has o 1 interclique links the present results suggest that the effect of community structure on the consensus time of the voter model is fairly limited

partition function zeros for the ising model on complete graphs and on annealed scale free networks we analyse the partition function of the ising model on graphs of two different types complete graphs wherein all nodes are mutually linked and annealed scale free networks for which the degree distribution decays as p k k we are interested in zeros of the partition function in the cases of complex temperature or complex external field fisher and lee yang zeros respectively for the model on an annealed scale free network we find an integral representation for the partition function which in the case 5 reproduces the zeros for the ising model on a complete graph for 3 5 we derive the dependent angle at which the fisher zeros impact onto the real temperature axis this in turn gives access to the dependent universal values of the critical exponents and critical amplitudes ratios our analysis of the lee yang zeros reveals a difference in their behaviour for the ising model on a complete graph and on an annealed scale free network when 3 5 whereas in the former case the zeros are purely imaginary they have a non zero real part in latter case so that the celebrated lee yang circle theorem is violated

number of cliques in random scale free network ensembles abstract in this paper we calculate the average number of cliques in random scale free networks in the limit of large network size n 1 we consider first the hidden variable ensemble and subsequently the molloy reed ensemble in both cases we find that cliques i e fully connected subgraphs appear also when the average degree is finite this is in contrast to what happens in erdos and renyi graphs in which diverging average degree is required to observe cliques of size c 3 moreover we show that in random scale free networks the clique number i e the size of the largest clique present in the network diverges with the system size

criticality on networks with topology dependent interactions weighted scale free networks with topology dependent interactions are studied it is shown that the possible universality classes of critical behavior which are known to depend on topology can also be explored by tuning the form of the interactions at fixed topology for a model of opinion formation simple mean field and scaling arguments show that a mapping gamma gamma mu 1 mu describes how a shift of the standard exponent gamma of the degree distribution can absorb the effect of degree dependent pair interactions j ij proportional to k i k j mu where k i stands for the degree of vertex i this prediction is verified by extensive numerical investigations using the cavity method and monte carlo simulations the critical temperature of the model is obtained through the bethe peierls approximation and with the replica technique the mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network

statistically consistent coarse grained simulations for critical phenomena in complex networks we propose a degree based coarse graining approach that not just accelerates the evaluation of dynamics on complex networks but also satisfies the consistency conditions for both equilibrium statistical distributions and nonequilibrium dynamical flows for the ising model and susceptible infected susceptible epidemic model we introduce these required conditions explicitly and further prove that they are satisfied by our coarse grained network construction within the annealed network approximation finally we numerically show that the phase transitions and fluctuations on the coarse grained network are all in good agreements with those on the original one

voter models on heterogeneous networks we study simple interacting particle systems on heterogeneous networks including the voter model and the invasion process these are both two state models in which in an update event an individual changes state to agree with a neighbor for the voter model an individual imports its state from a randomly chosen neighbor here the average time t n to reach consensus for a network of n nodes with an uncorrelated degree distribution scales as n ensuremath mu 1 2 ensuremath mu 2 where ensuremath mu k is the k text th moment of the degree distribution quick consensus thus arises on networks with broad degree distributions we also identify the conservation law that characterizes the route by which consensus is reached parallel results are derived for the invasion process in which the state of an agent is exported to a random neighbor we further generalize to biased dynamics in which one state is favored the probability for a single fitter mutant located at a node of degree k to overspread the population char22 the fixation probability char22 is proportional to k for the voter model and to 1 k for the invasion process

operator formalism on the zn symmetric algebraic curves on zn symmetric algebraic curves of any genus the hilbert space of analytic free fields with integer spin is constructed as an application an operator formalism for the b c systems is developed the physical states are expressed in terms of creation and annihilation operators as in the complex plane and the correlation functions are evaluated exploiting simple normal ordering rules the formalism is very suitable for performing explicit calculations on riemann surfaces and moreover it gives some insight into the nature of two dimensional field theories on a manifold it is proven in fact that the b c systems on a zn symmetric algebraic curve are equivalent to a conformal field theory on the complex plane having as primary operators twist fields and free ghosts some consequences of the interplay between topology and statistics are also discussed

fixation and consensus times on a network a unified approach we investigate a set of stochastic models of biodiversity population genetics language evolution and opinion dynamics on a network within a common framework each node has a state 0 x i 1 with interactions specified by strengths m ij for any set of m ij we derive an approximate expression for the mean time to reach fixation or consensus all x i 0 or 1 remarkably in a case relevant to language change this time is independent of the network structure

early fragmentation in the adaptive voter model on directed networks we consider voter dynamics on a directed adaptive network with fixed out degree distribution a transition between an active phase and a fragmented phase is observed this transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out degree distribution however if a significant number of nodes with low out degree is present then fragmentation can occur even far below the estimated critical point due to the formation of self stabilizing structures that nucleate fragmentation this process may be relevant for fragmentation in current political opinion formation processes

bosonic field propagators on algebraic curves in this paper we investigate the theory of massless scalar fields on nondegenerate algebraic curves the propagator is written in terms of the parameters appearing in the polynomial defining the curve this provides an alternative to the language of theta functions the main result is the derivation of a third kind differential normalized in such a way that its periods around the homology cycles are purely imaginary all the physical correlation functions of the scalar fields can be expressed in terms of this object this paper contains a detailed analysis of the techniques necessary to study field theories on algebraic curves a simple expression of the scalar field propagator is found in a particular case in which the algebraic curves have zn internal symmetry and one of the fields is located at a branch point

the internal symmetry group of a connection on a principal fiber bundle with applications to gauge field theories the internal symmetry group of a connection on a principal fiber bundlep is studied it is shown that this group is a smooth proper lie transformation group ofp which ifp is connected is also free moreover this group is shown to be isomorphic to the centralizer of the holonomy group of the connection several examples and applications of these results to gauge field theories are given

quenched central limit theorems for the ising model on random graphs the main goal of the paper is to prove central limit theorems for the magnetization rescaled by sqrt n for the ising model on random graphs with n vertices both random quenched and averaged quenched measures are considered we work in the uniqueness regime beta beta c or beta 0 and b ne 0 where beta is the inverse temperature beta c is the critical inverse temperature and b is the external magnetic field in the random quenched setting our results apply to general tree like random graphs as introduced by dembo montanari and further studied by dommers and the first and third author and our proof follows that of ellis in mathbb z d for the averaged quenched setting we specialize to two particular random graph models namely the 2 regular configuration model and the configuration model with degrees 1 and 2 in these cases our proofs are based on explicit computations relying on the solution of the one dimensional ising models

effects of local population structure in a reaction diffusion model of a contact process on metapopulation networks we investigate the effects of local population structure in reaction diffusion processes representing a contact process cp on metapopulations represented as complex networks considering a model in which the nodes of a large scale network represent local populations defined in terms of a homogeneous graph we show by means of extensive numerical simulations that the critical properties of the reaction diffusion system are independent of the local population structure even when this one is given by a ordered linear chain this independence is confirmed by the perfect matching between numerical critical exponents and the results from a heterogeneous mean field theory suited in principle to describe situations of local homogeneous mixing the analysis of several variations of the reaction diffusion process allows us to conclude the independence from population structure of the critical properties of cp like models on metapopulations and thus of the universality of the reaction diffusion description of this kind of models