promotion of cooperation by payoff noise in a 2 2 game a series of numerical simulations of a 2 ifmmode times else texttimes fi 2 symmetric game on a network examined whether payoff matrix noise promotes cooperation as reported initially by perc new j phys 8 22 2006 agents have no memory they offer cooperation c or defection d we assume that the network is time invariable the effect of payoff matrix noise pmn is measured by a simulated payoff difference between a normal network game and a network game with pmn the effect of pmn appears only when a local strategy adaptation is implemented for example a network game with imitation dynamics the influence of pmn becomes more significant with a larger stochastic deviation and less significant in a larger degree network one reason for pmn s effectiveness is the local strategy adaptation mechanism which helps both the preservation and fixation of c agents and not that the payoff matrix noise makes a dilemma game into a trivial dilemma free game

evolutionary dynamics of spatial games abstract a lattice model of coevolution of strategies for two person 2 2 matrix games is introduced the model allows evolution in an unbounded space of strategies in particular we explore the region of parameter space corresponding to the prisoner s dilemma and classify the types of dynamical and evolutionary behavior that appear for certain restricted strategy spaces we explore the complete space of lattice games

the ehrenfeucht conjecture a algebra framework for its proof abstract we describe an algebraic framework including in particular the affine monoid of a given ring within this framework it is a simple matter to deduce ehrenfeucht s conjecture from hilbert s basis theorem

weighted scale free networks with variable power law exponents abstract we present a weighted scale free network model in which the power law exponents can be controlled by the model parameters the network is generated through the weight driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links the simplicity of the model enables us to derive analytically the various statistical properties such as the distributions of degree strength and weight the degree strength and degree weight relationship and the dependencies of these power law exponents on the model parameters finally we demonstrate that networks of words coauthorship of researchers and collaboration of actor actresses are quantitatively well described by this model

return times of random walk on generalized random graphs random walks are used for modeling various dynamics in for example physical biological and social contexts furthermore their characteristics provide us with useful information on the phase transition and critical phenomena of even broader classes of related stochastic models abundant results are obtained for random walk on simple graphs such as the regular lattices and the cayley trees however random walks and related processes on more complex networks which are often more relevant in the real world are still open issues possibly yielding different characteristics in this paper we investigate the return times of random walks on random graphs with arbitrary vertex degree distributions we analytically derive the distributions of the return times the results are applied to some types of networks and compared with numerical data

selection intensity and risk dominant strategy a two strategy stochastic evolutionary game dynamics in finite population abstract stochastic evolutionary game dynamics with weak selection in finite population has been studied and it has been used to explain the emergence of cooperation in this paper following the previous studies the diffusion approximation of a two strategy stochastic evolutionary game dynamics in finite population that includes a small mutation rate between two strategies is investigated where we assume that these two strategies are both strict nash equilibrium ne our main goal is to partially reveal the effect of selection intensity on the stochastic evolutionary game dynamics through the analysis of potential function of the stationary distribution our main result shows that for all possible situations with that the selection intensity is not zero that includes the strong selection if a strategy is a risk dominant ne then its expected fitness with respect to the stationary distribution must be larger than that of other strategy this result not only extends the previous results but also provides some useful insights for understanding the significance of selection intensity in stochastic evolutionary game dynamics in finite population

maximal partial spreads and translation nets of small deficiency abstract partial t spreads and translation nets of small deficiency are considered meaning s d 1 2 where s is the order and d the deficiency it is proved that almost all such translation nets do in fact come from partial t spreads and some open questions about the nets belonging to maximal partial t spreads are answered some new examples of maximal partial t spreads and of unimbeddable nets of small deficiency are also constructed

cooperation in spatial prisoner s dilemma with two types of players for increasing number of neighbors we study a spatial two strategy cooperation and defection prisoner s dilemma game with two types a and b of players located on the sites of a square lattice the evolution of strategy distribution is governed by iterated strategy adoption from a randomly selected neighbor with a probability depending on the payoff difference and also on the type of the neighbor the strategy adoption probability is reduced by a prefactor w 1 from the players of type b we consider the competition between two opposite effects when increasing the number of neighbors k 4 8 and 24 within a range of the portion of influential players type a the inhomogeneous activity in strategy transfer yields a relevant increase dependent on w in the density of cooperators the noise dependence of this phenomenon is also discussed by evaluating phase diagrams

enhancement of cooperation in prisoner s dilemma game on weighted lattices abstract we introduce the vertex weight into the spatial prisoners dilemma game to investigate the evolution of cooperation each player on a square lattice is assigned to a particular weight followed by three types of distributions which include the exponential power law and uniform ones compared with the traditional version we find that the cooperation level is markedly enhanced under the weighted square lattice for most ranges of b the highest cooperation level can be obtained under the uniform distribution while power law distribution usually leads to the lowest cooperation the distributed weight can produce a heavy heterogeneity among the individuals payoff some cooperators with higher weight will foster the cooperative clusters and even spread the cooperation strategy around the clusters while defectors have no such advantages in addition we still investigate the impact of the amplitude of undulation of weight distribution on the cooperation and the non monotonic behavior about b is observed finally the influence of noise on the cooperation is also studied for these types of distribution of weight to some extent our weighted scheme can characterize the difference or diversity of players which will be beneficial to further understand the role of individuals during the evolution of cooperation

branching annihilating random walk on random regular graphs the branching annihilating random walk is studied on a random graph whose sites have a uniform number of neighbors z the monte carlo simulations in agreement with the generalized mean field analysis indicate that the concentration decreases linearly with the branching rate for z 4 while the coefficient of the linear term becomes zero if z 3 these properties are described by a modified mean field theory taking explicitly into consideration the probability of mutual annihilation of the parent and its offspring particles using the returning features of a single walker on the same graph

mixing protocols in the public goods game if interaction partners in social dilemma games are not selected randomly from the population but are instead determined by a network of contacts it has far reaching consequences for the evolutionary dynamics selecting partners randomly leads to a well mixed population where pattern formation is essentially impossible this rules out important mechanisms that can facilitate cooperation most notably network reciprocity in contrast if interactions are determined by a lattice or a network then the population is said to be structured where cooperators can form compact clusters that protect them from invading defectors between these two extremes however there is ample middle ground that can be brought about by the consideration of temporal networks mobility or other coevolutionary processes the question that we here seek to answer is when does mixing on a lattice actually lead to well mixed conditions to that effect we use the public goods game on a square lattice and we consider nearest neighbor and random mixing with different frequencies as well as a mix of both mixing protocols not surprisingly we find that nearest neighbor mixing requires a higher frequency than random mixing to arrive at the well mixed limit the differences between the two mixing protocols are most expressed at intermediate mixing frequencies whilst at very low and very high mixing frequencies the two almost converge we also find a near universal exponential growth of the average size of cooperator clusters as their fraction increases from zero to one regardless of whether this increase is due to increasing the multiplication factor of the public goods decreasing the frequency of mixing or gradually shifting the mixing from random to nearest neighbors

insight into the so called spatial reciprocity up to now there have been a great number of studies that demonstrate the effect of spatial topology on the promotion of cooperation dynamics namely the so called spatial reciprocity however most researchers probably attribute it to the positive assortment of strategies supported by spatial arrangement in this paper we analyze the time course of cooperation evolution under different evolution rules interestingly a typical evolution process can be divided into two evident periods the enduring end period and the expanding exp period where the former features that cooperators try to endure defectors invasion and the latter shows that perfect c clusters fast expand their area we find that the final cooperation level relies on two key factors the formation of the perfect c cluster at the end of the end period and the expanding fashion of the perfect c cluster during the exp period for deterministic rule the smooth expansion of c cluster boundaries enables cooperators to reach a dominant state whereas the rough boundaries for stochastic rule cannot provide a sufficient beneficial environment for the evolution of cooperation moreover we show that expansion of the perfect c cluster is closely related to the cluster coefficient of interaction topology to some extent we present a viable method for understanding the spatial reciprocity mechanism in nature and hope that it will inspire further studies to resolve social dilemmas

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

evolutionary prisoner s dilemma in random graphs abstract we study an evolutionary version of the spatial prisoner s dilemma game spd where the agents are placed in a random graph for graphs with fixed connectivity we show that for low values of the final density of cooperating agents c depends on the initial conditions however if the graphs have large connectivities c is independent of the initial conditions we characterize the phase diagram of the system using both extensive numerical simulations and analytical computations it is shown that two well defined behaviors are present a nash equilibrium where the final density of cooperating agents c is constant and a non stationary region where c fluctuates in time moreover we study the spd in poisson random graphs and find that the phase diagram previously developed looses its meaning in fact only one regime may be defined this regime is characterized by a non stationary final state where the density of cooperating agents varies in time

what is the real size of a sampled network the case of the internet internet mapping projects generally consist in sampling the network from a limited set of sources by usingtraceroute probes this methodology akin to the merging of spanning trees from the different sources to a set of destinations leads necessarily to a partial incomplete map of the internet accordingly determination of internet topology characteristics from such sampled maps is in part a problem of statistical inference our contribution begins with the observation that the inference of many of the most basic topological quantities including network size and degree characteristics fromtraceroute measurements is in fact a version of the so called species problem in statistics this obse rvation has important implications since species problems are often quite challenging we focus here on the most fundamental example of atraceroute internet species the number of nodes in a network specifica lly

role separating ordering in social dilemmas controlled by topological frustration three is a crowd is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models accordingly social relations within a triangle deserve special attention with this motivation we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice this topology provides an irreconcilable frustration which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game by using different strategy updating protocols we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb like organization which helps to minimize the negative consequence of the topological frustration we relate the emergence of these patterns to the microscopic dynamics of the evolutionary process both by means of mean field approximations and monte carlo simulations for comparison we also consider the same evolutionary dynamics on the square lattice where of course the topological frustration is absent however with the deletion of diagonal links of the triangular lattice we can gradually bridge the gap to the square lattice interestingly in this case the level of cooperation in the system is a direct indicator of the level of topological frustration thus providing a method to determine frustration levels in an arbitrary interaction network

epidemic incidence in correlated complex networks a few years ago watts and strogatz 1 introduced a model able to produce networks with properties of both regu lar lattices and random graphs with small diameter their model soon led to a burst of activity in the field 2 3 further spurred by barabasi and co workers who found that many seemingly diverse systems share several topological proper ties such as a power law behavior in their connectivity dis tributions when represented as networks 4 these complex networks are formed by a set of many elements or nodes that are linked together through edges or links if they in teract directly empirical evidence supports that in notable networks such as metabolic or communication webs the probability p k that any node has k links to other nodes is distributed accordingly to a power law p k k 2g 5 7

existence results for translation nets ii abstract let d be a translation bruck net of order s and degree r with translation group g and let s q 1 q n be the prime power factorization of s we prove that r min q i 1 i 1 n moreover equality can be realized provided that g is the direct sum of elementary abelian groups similar results are obtained for translation s r nets and more generally for groups with large systems of large subgroups as a corollary we considerably strengthen a known result on symmetric translation nets by showing that any translation s s net has parameters of the form s p i p j for some prime p and also necessarily has elementary abelian translation group

the evolutionary public goods game on scale free networks with heterogeneous investment abstract the public goods game pgg is generally considered as a suitable paradigm to explain ubiquitous cooperative behavior in this study we investigated the evolutionary pgg on scale free networks and studied the effect of individual heterogeneity by setting the cooperator x an investment value correlated to its degree as i x n k x j k j where k x is the degree of x j runs over all players and is a tunable parameter it is shown that the cooperation level is remarkably promoted by negative values of whereas it is highly depressed by positive values of moreover the effect of environmental noise has also been investigated our result may sharpen the understanding of cooperation induced by the individual diversity

spatial coherence resonance in excitable media we study the phenomenon of spatial coherence resonance in a two dimensional model of excitable media with fitzhugh nagumo local dynamics in particular we show that there exists an optimal level of additive noise for which an inherent spatial scale of the excitable media is best pronounced we argue that the observed phenomenon occurs due to the existence of a noise robust excursion time that is characteristic for the local dynamics whereby the diffusion constant representing the rate of diffusive spread determines the actual resonant spatial frequency additionally biological implications of presented results in the field of neuroscience are outlined

clique percolation in random networks the notion of k clique percolation in random graphs is introduced where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated for the erdos renyi graph of n vertices we obtain that the percolation transition of k cliques takes place when the probability of two vertices being connected by an edge reaches the threshold p c k k 1 n 1 k 1 at the transition point the scaling of the giant component with n is highly nontrivial and depends on k we discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks

promoting cooperation by local contribution under stochastic win stay lose shift mechanism a b s t r a c t we introduce a stochastic win stay lose shift wsls mechanism into evolutionary prisoner s dilemma on small world networks at each time step after playing with all its immediate neighbors each individual gets a score to evaluate its performance in the game the score is a linear combination of an individual s total payoff i e individual gain from the group and local contribution to its neighbors i e individual donation to the group if one s actual score is not larger than its desired score aspiration it switches current strategy to the opposite one with the probability depending on the difference between the two scores under this stochastic wsls regime we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation we also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score for much low intensity of deterministic switch cooperation is to a large extent independent of learning rate and full cooperation can be reached when relative weight is not less than 0 5 otherwise cooperation level is affected by the value of learning rate besides we find that the cooperation level is not sensitive to the topological parameters to explain these simulation results we provide corresponding analytical results based on mean field approximation and find out that simulationresultsareincloseagreementwiththeanalyticalones ourworkmaybehelpful in understanding the cooperative behavior in social systems based on this stochastic wsls mechanism

partial spreads over zq let p be a prime q pa and g z2nq we consider partial spreads in g i e collections of pairwise disjoint subgroups of order qn it is shown that the maximum size of such a collection is exactly pn 1 the method of proof consists in representing partial spreads in g by invertible n n matrices over zq and in finding a close relation to ordinary partial spreads over zp geometrically partial spreads over zq correspond to homogeneous translation nets

evolutionary prisoner s dilemma game on hierarchical lattices an evolutionary prisoner s dilemma pd game is studied with players located on a hierarchical structure of layered square lattices the players can follow two strategies d defector and c cooperator and their income comes from pd games with the neighbors the adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference monte carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels q and by the temptation to defect according to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low q 4 for larger q however the highest frequency of cooperators occurs in the middle layers the four level hierarchical structure provides the highest average total income for the whole community

scale free networks via attaching to random neighbors abstract preferential attachment is considered one of the key factors in the formation of scale free networks however complete random attachment without a preferential mechanism can also generate scale free networks in nature such as protein interaction networks in cells this article presents a new scale free network model that applies the following general mechanisms i networks expand continuously by the addition of new vertices and ii new vertices attach to random neighbors of random vertices that are already well connected the proposed model does not require global based preferential strategies and utilizes only the random attachment method theoretical analysis and numerical simulation results denote that the proposed model has steady scale free network characteristics and random attachment without a preferential mechanism may generate scale free networks

phase diagrams for an evolutionary prisoner s dilemma game on two dimensional lattices the effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner s dilemma game with players located on the sites of different two dimensional lattices this system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive using monte carlo simulations and the generalized mean field approximations we have determined the phase boundaries critical points separating the two phases on the plane of the temperature noise and temptation to choose defection in the zero temperature limit the cooperation can be sustained only for those connectivity structures where three site clique percolation occurs

the ehrenfeucht conjecture a compactness claim for finitely generated free monoids abstract we survey recent results on the so called ehrenfeucht conjecture which states for each language l over a finite alphabet there exists a finite subset f of l such that for each pair g h of morphisms on the equation g x h x holds for all x in l if and only if holds for all x in f we point out that the conjecture is closely related to the theory of equations in free monoids we also state a suprising consequence of the conjecture if it holds even noneffectively for all dol languages then the hdol sequence equivalence problem is decidable furthermore we give examples of when the conjecture is known to hold in particular we establish it for all binary languages as well as for all languages when attention is restricted to bounded delay morphisms of some fixed delay

cooperation in the noisy case prisoner s dilemma game on two types of regular random graphs we have studied an evolutionary prisoner s dilemma game with players located on two types of random regular graphs with a degree of 4 the analysis is focused on the effects of payoffs and noise temperature on the maintenance of cooperation when varying the noise level and or the highest payoff the system exhibits a second order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive for the random regular graph and bethe lattice the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions although the measure of cooperation is enhanced by the absence of loops in the connectivity structure for low noise the optimal connectivity structure is built up from randomly connected triangles

evolutionary prisoner s dilemma game on a square lattice a simplified prisoner s game is studied on a square lattice when the players interacting with their neighbors can follow two strategies to cooperate c or to defect d unconditionally the players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference using monte carlo simulations and dynamical cluster techniques we study the density c of cooperators in the stationary state this system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect in the limits stackrel ensuremath rightarrow c 0 and 1 we have observed critical transitions belonging to the universality class of directed percolation

a study on some urban bus transport networks abstract in this paper we present the empirical investigation results on the urban bus transport networks btns of four major cities in china in btn nodes are bus stops two nodes are connected by an edge when the stops are serviced by a common bus route the empirical results show that the degree distributions of btns take exponential function forms other two statistical properties of btns are also considered and they are suggested as the distributions of so called the number of stops in a bus route represented by s and the number of bus routes a stop joins by r the distributions of r also show exponential function forms while the distributions of s follow asymmetric unimodal functions to explain these empirical results and attempt to simulate a possible evolution process of btn we introduce a model by which the analytic and numerical result obtained agrees well with the empirical facts finally we also discuss some other possible evolution cases where the degree distribution shows a power law or an interpolation between the power law and the exponential decay

epidemic dynamics behavior in some bus transport networks abstract we abstract bus transport networks btns to complex networks using the space p approach first we select three actual btns in three major cities in china namely beijing shanghai and hangzhou using the sis model we simulate and study the epidemic spreading in the three btns we obtain the density of infected vertices varying with time and the stationary density of infected vertices varying with infection rate second we simulate and study the epidemic spreading in a recently introduced btn evolution model the network properties of which correspond well with those of actual btns third we use mean field theory to analyze the epidemic dynamics behavior of the btn evolution model and obtain the theoretical epidemic threshold of this model the theoretical value agrees well with the simulation results based on the work in this paper we provide the following possible forecasts for epidemic dynamics in actual btns an actual btn should have a finite positive epidemic threshold if the effective infection rate is above this threshold the epidemic spread in the network and the density of infected vertices finally stabilizes in a balanced state below this threshold the number of infected vertices decays exponentially fast and the epidemic cannot spread on a large scale

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

groups with a large number of large disjoint subgroups it is known that if g is a group of order 4n2 and g contains n mutually disjoint subgroups of order 2n then the nonidentity elements of these subgroups form a difference set in g gluck recently discovered a nonabelian example with n 4 and showed it to be the only case with n 4 and g not elementary abelian we show here that the only examples with n 4 are elementary abelian 2 groups

a proof of ehrenfeucht s conjecture abstract ehrenfeucht s conjecture states that each subset s of a finitely generated free monoid has a finite subset t such that if two endomorphisms of the monoid agree on t then they agree on s it is the purpose of this note to verify the conjecture

evolutionary matching pennies game on bipartite regular networks evolutionary games are studied here with two types of players located on a chessboard or on a bipartite random regular graph each player s income comes from matching pennies games played with the four neighbors the players can modify their own strategies according to a myopic strategy update resembling the glauber dynamics for the kinetic ising model this dynamical rule drives the system into a stationary state where the two strategies are present with the same probability without correlations between the nearest neighbors while a weak correlation is induced between the second and the third neighbors in stationary states the deviation from the detailed balance is quantified by the evaluation of entropy production finally our analysis is extended to evolutionary games where the uniform pair interactions are composed of an anticoordination game and a weak matching pennies game this system preserves the ising type order disorder transitions at a critical noise level decreasing with the strength of the matching pennies component for both networks

on evolutionary spatial heterogeneous games abstract how cooperation between self interested individuals evolve is a crucial problem both in biology and in social sciences that is far from being well understood evolutionary game theory is a useful approach to this issue the simplest model to take into account the spatial dimension in evolutionary games is in terms of cellular automata with just a one parameter payoff matrix here the effects of spatial heterogeneities of the environment and or asymmetries in the interactions among the individuals are analysed through different extensions of this model instead of using the same universal payoff matrix bimatrix games in which each cell at site i j has its own different temptation to defect parameter t i j are considered first the case in which these individual payoffs are constant in time is studied second an evolving evolutionary spatial game such that t t i j t i e besides depending on the position evolves by natural selection is used to explore the combination of spatial heterogeneity and natural selection of payoff matrices

evolutionary prisoner s dilemma game on weighted scale free networks this paper investigates the evolutionary prisoner s dilemma on weighted scale free networks the weighted networks are generated by adopting barabscale free network and assigning link weight with wij ki kj simulation results show thatthe cooperationfrequency hasa strongdependence on the value of which isassociated withthe maximalcooperation frequency has been sought out moreover gini coefficient and pareto exponent of the system s wealth distribution are investigated the inequality of wealth distribution is minimized at 1

research on the search ability of brownian particles on networks with an adaptive mechanism abstract in this paper we focus on the search ability of brownian particles with an adaptive mechanism in the adaptive mechanism nodes are allowed to be able to change their own accepting probability according to their congestion states two searching traffic models the static one in which nodes have fixed accepting probability to the incoming particles and the adaptive one in which nodes have adaptive accepting probability to the incoming particles are presented for testing the adaptive mechanism instead of number of hops we use the traveling time which includes not only the number of hops for a particle to jump from the source node to the destination but also the time that the particle stays in the queues of nodes to evaluate the search ability of brownian particles we apply two models to different networks the experiment results show that the adaptive mechanism can decrease the network congestion and the traveling time of the first arriving particle furthermore we investigate the influence of network topologies on the congestion of networks by addressing several main properties degree distribution average path length and clustering coefficient we show the reason why random topologies are more able to deal with congested traffic states than others we also propose an absorption strategy to deal with the additional brownian particles in networks the experiment results on barabasi albert ba scale free networks show that the absorption strategy can increase the probability of a successful search and decrease the average per node particles overhead for our models

cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoner s dilemma games we study an evolutionary prisoner s dilemma game with two layered graphs where the lower layer is the physical infrastructure on which the interactions are taking place and the upper layer represents the connections for the strategy adoption learning mechanism this system is investigated by means of monte carlo simulations and an extended pair approximation method we consider the average density of cooperators in the stationary state for a fixed interaction graph while varying the number of edges in the learning graph according to the monte carlo simulations the cooperation is modified substantially in a way resembling a coherence resonance like behavior when the number of learning edges is increased this behavior is reproduced by the analytical results

statistical analysis of 22 public transport networks in poland public transport systems in 22 polish cities have been analyzed the sizes of these networks range from n 152 to 2881 depending on the assumed definition of network topology the degree distribution can follow a power law or can be described by an exponential function distributions of path lengths in all considered networks are given by asymmetric unimodal functions clustering assortativity and betweenness are studied all considered networks exhibit small world behavior and are hierarchically organized a transition between dissortative small networks n approximately or 500 is observed

packing and covering groups with subgroups abstract we study the problem of covering or packing a finite group with subgroups of a specified order and obtain bounds on the size of such covers and packings our main results provide characterizations of the elementary abelian groups by the existence of large packings or small covers respectively hence large packings and small covers can be thought of as geometric objects they correspond to large partial t spreads and small t covers of a suitable projective space pg d p for some prime p we shall also exhibit some series of examples which show that our bounds are reasonable

coevolutionary games on networks we study agents on a network playing an iterated prisoner s dilemma against their neighbors the resulting spatially extended coevolutionary game exhibits stationary states which are nash equilibria after perturbation of these equilibria avalanches of mutations reestablish a stationary state scale free avalanche distributions are observed that are in accordance with calculations from the nash equilibria and a confined branching process the transition from subcritical to critical avalanche dynamics can be traced to a change in the degeneracy of the cooperative macrostate and is observed for many variants of this game

payoff components and their effects in a spatial three strategy evolutionary social dilemma we study a three strategy spatial evolutionary prisoner s dilemma game with imitation and logit update rules players can follow the always cooperating always defecting or the win stay lose shift wsls strategies and gain their payoff from games with their direct neighbors on a square lattice the friendliness parameter of the wsls strategy characterizing its cooperation probability in the first round tunes the cyclic component of the game determining whether the game can be characterized by a potential we measured and calculated the phase diagrams of the system for a wide range of parameters when the game is a potential game and the logit rule is applied the theoretically predicted phase diagram agrees very well with the simulation results surprisingly this phase diagram can be accurate even in the nonpotential case if there are only two surviving strategies in the stationary state this result harmonizes with the fact that all 2 2 games are potential games for the imitation dynamics we found that the effects of spatiality combined with the presence of two cooperative strategies are so strong that they suppress even substantial changes in the payoff matrix thus the phase diagrams are independent of the cyclic component s intensity at the same time this type of strategy update mechanism supports the formation of cooperative clusters that results in a cooperative society in a wider parameter range compared to the logit dynamics

towards effective payoffs in the prisoner s dilemma game on scale free networks we study the transition towards effective payoffs in the prisoner s dilemma game on scale free networks by introducing a normalization parameter guiding the system from accumulated payoffs to payoffs normalized with the connectivity of each agent we show that during this transition the heterogeneity based ability of scale free networks to facilitate cooperative behavior deteriorates continuously eventually collapsing with the results obtained on regular graphs the strategy donations and adaptation probabilities of agents with different connectivities are studied results reveal that strategies generally spread from agents with larger towards agents with smaller degree however this strategy adoption flow reverses sharply in the fully normalized payoff limit surprisingly cooperators occupy the hubs even if the averaged cooperation level due to partly normalized payoffs is moderate

rock scissors paper game on regular small world networks the spatial rock scissors paper game or cyclic lotka volterra system is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours degree at each site on the square lattice this system exhibits a self organizing pattern with equal concentration of the competing strategies species if the quenched background is constructed by substituting random links for the nearest neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value this transition can also be observed if the standard link is replaced temporarily by a random one with a probability p at each step of iteration above a second threshold value of p the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous absorbing states in this case the results of monte carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one two four and six site clusters

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

scaling and correlations in three bus transport networks of china abstract we report the statistical properties of three bus transport networks btn in three different cities of china these networks are composed of a set of bus lines and stations serviced by these network properties including the degree distribution clustering and average path length are studied in different definitions of network topology we explore scaling laws and correlations that may govern intrinsic features of such networks besides we create a weighted network representation for btn with lines mapped to nodes and number of common stations to weights between lines in such a representation the distributions of degree strength and weight are investigated a linear behavior between strength and degree s k k is also observed

social dilemmas in multistrategy evolutionary potential games the nature of social dilemmas is studied in n strategy evolutionary potential games on a square lattice with nearest neighbor interactions and the logit rule for symmetric games with symmetric payoff matrices there are no dilemmas because of the coincidence of individual and common interests the dilemmas are caused by the antisymmetric parts of the self and cross dependent payoff components if it modifies the preferred nash equilibrium the contentment of players and the emergence of dilemmas in the preferred nash equilibria are illustrated on some two dimensional cross sections of the parameter space