dynamics of latent voters we study the effect of latency on binary choice opinion formation models latency is introduced into the models as an additional dynamic rule after a voter changes its opinion it enters a waiting period of stochastic length where no further changes take place we first focus on the voter model and show that as a result of introducing latency the average magnetization is not conserved and the system is driven toward zero magnetization independently of initial conditions the model is studied analytically in the mean field case and by simulations in one dimension we also address the behavior of the majority rule model with added latency and show that the competition between imitation and latency leads to a rich phenomenology

systems with counterclockwise input output dynamics a new input output property is proposed suitable for the study of positive feedback interconnections both in a linear and nonlinear set up convergence results and small gain theorems are proved as well as criteria for the application of the property to the study of multistability lyapunov like conditions and dissipation inequalities for its detection are also provided

role of noise in population dynamics cycles noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase forgetting quasicycles by converting damped into sustained oscillations this function of noise becomes evident when considering langevin equations whose deterministic part yields only damped oscillations we formulate here a consistent and systematic approach to population dynamics leading to a fokker planck equation and the associate langevin equations in accordance with this conceptual framework founded on stochastic lattice gas models that describe spatially structured predator prey systems langevin equations in the population densities and predator prey pair density are derived in two stages first a birth and death stochastic process in the space of prey and predator numbers and predator prey pair number is obtained by a contraction method that reduces the degrees of freedom second a van kampen expansion in the inverse of system size is then performed to get the fokker planck equation we also study the time correlation function the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence

dynamical model for competing opinions we propose an opinion model based on agents located at the vertices of a regular lattice each agent has an independent opinion among an arbitrary but fixed number of choices and its own degree of conviction the latter changes every time two agents which have different opinions interact with each other the dynamics leads to size distributions of clusters made up of agents which have the same opinion and are located at contiguous spatial positions which follow a power law as long as the range of the interaction between the agents is not too short i e the system self organizes into a critical state short range interactions lead to an exponential cutoff in the size distribution and to spatial correlations which cause agents which have the same opinion to be closely grouped when the diversity of opinions is restricted to two a nonconsensus dynamic is observed with unequal population fractions whereas consensus is reached if the agents are also allowed to interact with those located far from them the individual agents convictions the preestablished interaction range and the locality of the interaction between a pair of agents their neighborhood has no effect on the interaction are the main characteristics which distinguish our model from previous ones

cyclical interactions with alliance specific heterogeneous invasion rates we study a six species lotka volterra type system on different two dimensional lattices when each species has two superior and two inferior partners the invasion rates from predator sites to a randomly chosen neighboring prey site depend on the predator prey pair whereby cyclic symmetries within the two three species defensive alliances are conserved monte carlo simulations reveal an unexpected nonmonotonous dependence of alliance survival on the difference of alliance specific invasion rates this behavior is qualitatively reproduced by a four point mean field approximation the study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences

application of statistical physics to politics abstract the concept and technics of real space renormalization group are applied to study majority rule voting in hierarchical structures it is found that democratic voting can lead to totalitarianism by keeping in power a small minority conditions of this paradox are analyzed and singled out indeed majority rule produces critical thresholds to absolute power values of these thresholds can vary from 50 up to at least 77 the associated underlying mechanism could provide an explanation for both former apparent eternity of communist leaderships and their sudden collapse

majority versus minority dynamics phase transition in an interacting two state spin system we introduce a simple model of opinion dynamics in which binary state agents evolve due to the influence of agents in a local neighborhood in a single update step a fixed size group is defined and all agents in the group adopt the state of the local majority with probability p or that of the local minority with probability 1 p for group size g 3 there is a phase transition at p c 2 3 in all spatial dimensions for p p c the global majority quickly predominates while for p p c the system is driven to a mixed state in which the densities of agents in each state are equal for p p c the average magnetization the difference in the density of agents in the two states is conserved and the system obeys classical voter model dynamics in one dimension and within a kirkwood decoupling scheme the final magnetization in a finite length system has a nontrivial dependence on the initial magnetization for all p not equal p c in agreement with numerical results at p c the exact two spin correlation functions decay algebraically toward the value 1 and the system coarsens as in the classical voter model

coalescing random walks and voter model consensus times on the torus in mathbb z d voter models on z d and on the torus of site n in z d are considered the second ones get trapped with probability 1 as t tends to infinity at all 0 s or all 1 s the asymptotic growth of these trapping times are examined as n tends to infinity this is done with limit thewems for coalescing random walk systems on the torus of side n in z d

continuous opinion model in small world directed networks abstract in the compromise model of continuous opinions proposed by deffuant et al the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other below a given threshold of tolerance in directed networks if agent i is a neighbor of agent j j need not be a neighbor of i in watts strogatz networks we performed simulations to find the averaged number of final opinions f and their distribution as a function of and of the network structural disorder in directed networks f exhibits a rich structure being larger than in undirected networks for higher values of and smaller for lower values of

voting and catalytic processes with inhomogeneities we consider the dynamics of the voter model and of the monomer monomer catalytic process in the presence of many competing inhomogeneities and show through exact calculations and numerical simulations that their presence results in a nontrivial fluctuating steady state whose properties are studied and turn out to specifically depend on the dimensionality of the system the strength of the inhomogeneities and their separating distances in fact in arbitrary dimensions we obtain an exact yet formal expression of the order parameters magnetization and concentration of adsorbed particles in the presence of an arbitrary number n of inhomogeneities zealots in the voter language and formal similarities with suitable electrostatic systems are pointed out in the nontrivial cases n 1 2 we explicitly compute the static and long time properties of the order parameters and therefore capture the generic features of the systems when ng2 the problems are studied through numerical simulations in one spatial dimension we also compute the expressions of the stationary order parameters in the completely disordered case where n is arbitrary large particular attention is paid to the spatial dependence of the stationary order parameters and formal connections with electrostatics

saddles arrows and spirals deterministic trajectories in cyclic competition of four species population dynamics in systems composed of cyclically competing species has been of increasing interest recently here we investigate a system with four or more species using mean field theory we study in detail the trajectories in configuration space of the population fractions we discover a variety of orbits shaped like saddles spirals and straight lines many of their properties are found explicitly most remarkably we identify a collective variable that evolves simply as an exponential q e t where is a function of the reaction rates it provides information on the state of the system for late times as well as for t we discuss implications of these results for the evolution of a finite stochastic system a generalization to an arbitrary number of cyclically competing species yields valuable insights into universal properties of such systems

phase transitions and spatio temporal fluctuations in stochastic lattice lotka volterra models we study the general properties of stochastic two species models for predator prey competition and coexistence with lotka volterra type interactions defined on a d dimensional lattice introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical deterministic mean field picture already within mean field theory however spatial constraints modeling locally limited resources lead to the emergence of a continuous active to absorbing state phase transition field theoretic arguments supported by monte carlo simulation results indicate that this transition which represents an extinction threshold for the predator population is governed by the directed percolation universality class in the active state where predators and prey coexist the classical center singularities with associated population cycles are replaced by either nodes or foci in the vicinity of the stable nodes the system is characterized by essentially stationary localized clusters of predators in a sea of prey near the stable foci however the stochastic lattice lotka volterra system displays complex correlated spatio temporal patterns of competing activity fronts correspondingly the population densities in our numerical simulations turn out to oscillate irregularly in time with amplitudes that tend to zero in the thermodynamic limit yet in finite systems these oscillatory fluctuations are quite persistent and their features are determined by the intrinsic interaction rates rather than the initial conditions we emphasize the robustness of this scenario with respect to various model perturbations

opinion dynamics on an adaptive random network we revisit the classical model for voter dynamics in a two party system with two basic modifications in contrast to the original voter model studied in regular lattices we implement the opinion formation process in a random network of agents in which interactions are no longer restricted by geographical distance in addition we incorporate the rapidly changing nature of the interpersonal relations in the model at each time step agents can update their relationships this update is determined by their own opinion and by their preference to make connections with individuals sharing the same opinion or rather with opponents in this way the network is built in an adaptive manner in the sense that its structure is correlated and evolves with the dynamics of the agents the simplicity of the model allows us to examine several issues analytically we establish criteria to determine whether consensus or polarization will be the outcome of the dynamics and on what time scales these states will be reached in finite systems consensus is typical while in infinite systems a disordered metastable state can emerge and persist for infinitely long time before consensus is reached

cyclic cellular automata and related processes abstract a cyclic cellular automaton is a discrete time process defined on the state space 0 1 n 1 zd starting from a random initial condition at each time step each site looks at its nearest neighbors if the state at site x is i then site x will change state to i 1 mod n if it locates state i 1 mod n among its neighbors otherwise site x will remain in state i cyclic cellular automata have properties akin to cyclic particle systems introduced by bramson and griffeath which are continuous time markov processes on 0 1 n 1 zd with a stochastic evolution rather than a deterministic one in one dimension some clustering results about cyclic cellular automata are presented the analogous problems in the context of cyclic particle systems are still unresolved also we discuss the consequences of these clustering results in the context of one dimensional systems of particles with various interaction mechanisms finally we touch upon the work currently being done on two dimensional cyclic particle systems and cellular automata

a kyp lemma and invariance principle for systems with multiple hysteresis non linearities absolute stability criteria for systems with multiple hysteresis non linearities are given in this paper it is shown that the stability guarantee is achieved with a simple two part test on the linear subsystem if the linear subsystem satis es a particular linear matrix inequality and a simple residue condition then as is proven the non linear system will be asymptotically stable the main stability theorem is developed using a combination of passivity lyapunov and popov stability theories to show that the state describing the linear system dynamics must converge to an equilibrium position of the non linear closed loop system the invariant sets that contain all such possible equilibrium points are described in detail for several common types of hystereses the class of non linearities covered by the analysis is very general and includes multiple slope restricted memoryless non linearities as a special case simple numerical examples are used to demonstrate the e ectiveness of the new analysis in comparison to other recent results and graphically illustrate state asymptotic stability

coexistence versus extinction in the stochastic cyclic lotka volterra model cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity see e g b kerr m a riley m w feldman and b j m bohannan nature 418 171 2002 and b kirkup and m a riley nature 428 412 2004 through analytical methods supported by numerical simulations we address this issue by studying the properties of a paradigmatic non spatial three species stochastic system namely the rock paper scissors or cyclic lotka volterra model while the deterministic approach rate equations predicts the coexistence of the species resulting in regular yet neutrally stable oscillations of the population densities we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction after long enough time two of the three species die out as main findings we provide analytic estimates and numerical computation of the extinction probability at a given time we also discuss the implications of our results for a broad class of competing population systems

absolute stability criteria for multiple slope restricted monotonic nonlinearities absolute stability criteria such as the classical popov criterion guarantee stability for a class of sector bounded nonlinearities although the sector restriction bounds the admissible class of the nonlinearities the local slope of the nonlinearity may be arbitrarily large in this paper the authors derive absolute stability criteria for multiple slope restricted time invariant monotonic nonlinearities like the popov criterion in the single input single output case the authors results provide a simple graphical interpretation involving a straight line in a modified popov plane

nonequilibrium phase transition in a lattice prey predator system abstract we study a lattice model of a prey predator system mean field approximation predicts that the active phase i e one with a finite fraction of preys and predators is a generic phase of this model moreover within this approximation the model exhibits quasi oscillations resembling lotka volterra systems however monte carlo simulations for a one two and three dimensional versions of this model do not support this scenario and predict that at a certain value of some parameter the model enters the absorbing state i e a state where the entire population of predators dies out and the model is invaded by preys simulations for the one dimensional version indicate that the transition into the absorbing state belongs to the directed percolation universality class

effect of external fields in axelrod s model of social dynamics the study of the effects of spatially uniform fields on the steady state properties of axelrod s model has yielded plenty of counterintuitive results here we reexamine the impact of this type of field for a selection of parameters such that the field free steady state of the model is heterogeneous or multicultural analyses of both one and two dimensional versions of axelrod s model indicate that the steady state remains heterogeneous regardless of the value of the field strength turning on the field leads to a discontinuous decrease on the number of cultural domains which we argue is due to the instability of zero field heterogeneous absorbing configurations we find however that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model we argue that the dimensionality has a significant impact on the stability of the field free homogeneous steady state

how to introduce temperature to the 1d sznajd model abstract we investigate the possibility of introducing temperature to the one dimensional sznajd model and propose a natural extension of the original model by including other types of interactions we characterise different kinds of equilibria into which the extended system can evolve we determine the consequences of fulfilling the detailed balance condition and we prove that in some cases it is equivalent to microscopic reversibility we found the equivalence of the model to the standard inflow model with interactions up to next nearest neighbors it is shown that under some constraints there exists a hamiltonian compatible with the dynamics and its form resembles that of the 1d annni model it appears however that the standard approach of constructing temperature from the hamiltonian fails in this situation we propose a simple definition of the temperature like quantity that measures the size of fluctuations in the system at equilibrium the complete list of zero temperature degenerated cases as well as the list of ground states of the derived hamiltonian are provided

stability robustness of a feedback interconnection of systems with negative imaginary frequency response a necessary and sufficient condition expressed simply as the dc loop gain i e the loop gain at zero frequency being less than unity is given in this note to guarantee the internal stability of a feedback interconnection of linear time invariant lti multiple input multiple output systems with negative imaginary frequency response systems with negative imaginary frequency response arise for example when considering transfer functions from force actuators to colocated position sensors and are commonly important in for example lightly damped structures the key result presented here has similar application to the small gain theorem which refers to the stability of feedback interconnections of contractive gain systems and the passivity theorem which refers to the stability of feedback interconnections of positive real or passive systems a complete state space characterization of systems with negative imaginary frequency response is also given in this note and also an example that demonstrates the application of the key result is provided

existence of an upper critical dimension in the majority voter model we study the critical properties of the majority voter model on d dimensional hypercubic lattices in two dimensions the majority voter model belongs to the same universality class as that of the ising model however the critical behaviors of the majority voter model on four dimensions do not exhibit mean field behavior using the monte carlo simulation on d dimensional hypercubic lattices we obtain the critical exponents up to d 7 and find that the upper critical dimension is 6 for the majority voter model we also confirm our results using mean field calculation

multi class support vector machine optimized by inter cluster distance and self adaptive deferential evolution abstract support vector machine svm is a popular tool for machine learning task it has been successfully applied in many fields but the parameter optimization for svm is an ongoing research issue in this paper to tune the parameters of svm one form of inter cluster distance in the feature space is calculated for all the svm classifiers of multi class problems inter cluster distance in the feature space shows the degree the classes are separated a larger inter cluster distance value implies a pair of more separated classes for each classifier the optimal kernel parameter which results in the largest inter cluster distance is found then a new continuous search interval of kernel parameter which covers the optimal kernel parameter of each class pair is determined self adaptive differential evolution algorithm is used to search the optimal parameter combination in the continuous intervals of kernel parameter and penalty parameter at last the proposed method is applied to several real word datasets as well as fault diagnosis for rolling element bearings the results show that it is both effective and computationally efficient for parameter optimization of multi class svm

foundations of not necessarily rational negative imaginary systems theory relations between classes of negative imaginary and positive real systems in this technical note we lay the foundations of a not necessarily rational negative imaginary systems theory and its relations with positive real systems theory in analogy with the theory of positive real functions in our general framework negative imaginary systems are defined in terms of a domain of analyticity of the transfer function and of a sign condition that must be satisfied in such domain in this way we do not require to restrict the attention to systems with a rational transfer function in this work we also define various grades of negative imaginary systems and aim to provide a unitary view of the different notions that have appeared so far in the literature within the framework of positive real and in the more recent theory of negative imaginary systems and to show how these notions are characterized and linked to each other

stability analysis and controller design for lur e system with hysteresis nonlinearities a negative imaginary theory based approach in this paper absolute stability condition is investigated when a hysteresis nonlinearity is connected to a linear subsystem via positive feedback in lur e system framework in particular the non

vortices and strings in a model ecosystem we study the spatial pattern formation in a model ecosystem by the position fixed reaction method this ecosystem contains three biospecies whose competing powers are cyclic it is well known that this system is self organized into a quasistationary state and that the mean field approximation mfa never predicts such a pattern formation recently several authors applied the pair approximation pa and obtained considerable improvements however applying pa to our ecosystem fails to yield such an improvement as revealed by computer simulations the failures of mfa and pa may be attributed to the fact that both approximations neglect a long range correlation thus we introduce the concept of topological defects such as vortices or strings and demonstrate that the dynamics of these defects can at least qualitatively account for the observed pattern formation dynamics

non markov stochastic dynamics of real epidemic process of respiratory infections abstract the study of social networks and especially of stochastic dynamics of diseases spread in human population has recently attracted considerable attention in statistical physics in this work we present a new statistical method of analyzing the spread of epidemic processes of grippe and acute respiratory track infections arti by means of the theory of discrete non markov stochastic processes we use the results of our last theory phys rev e 65 2002 046107 to study statistical memory effects long range correlation and discreteness in real data series describing the epidemic dynamics of human arti infections and grippe we have carried out the comparative analysis of the data of the two infections grippe and arti in one of the industrial districts of kazan one of the largest cities of russia the experimental data are analyzed by the power spectra of the initial time correlation function and the memory functions of junior orders the phase portraits of the four first dynamic variables the three first points of the statistical non markov parameter and the locally averaged kinetic and relaxation parameters the received results give an opportunity to provide a strict quantitative description of regular and stochastic components in epidemic dynamics of social networks taking into account their time discreteness and effects of statistical memory they also allow to reveal the degree of randomness and predictability of the real epidemic process in the specific social network

stability analysis of interconnected systems with mixed negative imaginary and small gain properties in this letter an analytical framework is proposed to examine stability of two stable linear time invariant systems interconnected in positive feedback where the systems have mixed properties of negative imaginary and small gain using the notion of dissipativity the interconnection of systems is guaranteed to be finite gain stable under the condition that the dc loop gain is contractive this work builds on griggs and exploits a new set of frequency dependent triplets that was introduced in above reference to mix two unconditional stability statements i e small gain and passivity unlike the above reference the present work explores the important question of how a conditional stability statement as needed when two negative imaginary systems are connected in a feedback loop can be mixed with an unconditional stability statement as needed when two contractive systems are connected in a feedback loop the usefulness of the proposed analytical framework is demonstrated via a numerical example

coexistence and survival in conservative lotka volterra networks analyzing coexistence and survival scenarios of lotka volterra lv networks in which the total biomass is conserved is of vital importance for the characterization of long term dynamics of ecological communities here we introduce a classification scheme for coexistence scenarios in these conservative lv models and quantify the extinction process by employing the pfaffian of the network s interaction matrix we illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time

clustering in the one dimensional three color cyclic cellular automaton cyclic cellular automaton the author has previously shown that this process fluctuates meaning that each lattice site changes color infinitely often so that there is no final state for the system the focus of the current work is on the clustering properties of this system this paper demonstrates that the one dimensional three color cyclic cellular automaton clusters and the mean cluster size as a function of time t is asymptotic to ct1 2 where c is an explicitly calculable constant the method of proof also allows us to compute asymptotic estimates of the mean interparticle distance for a one dimensional system of particles which undergo deterministic motion and which annihilate upon collision no clustering results are known about the four color process but evidence is presented to suggest that the mean cluster size of such systems grows at a rate different from t1 2

spirals and coarsening patterns in the competition of many species a complex ginzburg landau approach in order to model real ecological systems one has to consider many species that interact in complex ways however most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions the few studies dealing with larger number of species and or more complex interaction schemes are mostly restricted to numerical explorations in this paper we determine starting from the deterministic mean field rate equations for large classes of systems the space of coexistence fixed points at which biodiversity is maximal for systems with a single coexistence fixed point we derive complex ginzburg landau equations that allow to describe space time pattern realized in two space dimensions for selected cases we compare the theoretical predictions with the pattern observed in numerical simulations

vector opinion dynamics in a model for social influence we present numerical simulations of a model of social influence where the opinion of each agent is represented by a binary vector agents adjust their opinions as a result of random encounters whenever the difference between opinions is below a given threshold evolution leads to a steady state which highly depends on the threshold and a convergence parameter of the model we analyze the transition between clustered and homogeneous steady states results of the cases of complete mixing and small world networks are compared

erdos renyi phase transition in the axelrod model on complete graphs the axelrod model has been widely studied since its proposal for social influence and cultural dissemination in particular the community of statistical physics focused on the presence of a phase transition as a function of its two main parameters f and q in this work we show that the axelrod model undergoes a second order phase transition in the limit of f ensuremath rightarrow ensuremath infty on a complete graph this transition is equivalent to the erd ifmmode mbox h o else h o fi s r enyi phase transition in random networks when it is described in terms of the probability of interaction at the initial state which depends on a scaling relation between f and q we also found that this probability plays a key role in sparse topologies by collapsing the transition curves for different values of the parameter f

absolute stability analysis for negative imaginary systems this paper deals with absolute stability of a lur e system with positive feedback where the linear subsystem exhibits negative imaginary frequency response and the nonlinearity connected in feedback is time invariant memoryless and slope restricted the proposed absolute stability criterion requires the linear subsystem to belong to the strongly strict negative imaginary class along with that positive definiteness of a symmetric matrix needs to be ensured where the symmetric matrix is obtained by subtracting the dc gain matrix of the linear subsystem from a strictly positive diagonal matrix with elements indicating the reciprocal of the maximum slope bounds of the nonlinearities the stability criterion is proved using a lur e postnikov type lyapunov function numerical examples are presented to demonstrate the proposed results

interplay between partnership formation and competition in generalized may leonard games in order to better understand the interplay of partnership and competition in population dynamics we study a family of generalized may leonard models with n species these models have a very rich structure characterized by different types of space time patterns interesting partnership formations emerge following the maxim that the enemy of my enemy is my friend in specific cases cyclic dominance within coarsening clusters yields a peculiar coarsening behavior with intriguing pattern formation we classify the different types of dynamics through the analysis of the square of the adjacency matrix the dependence of the population densities on emerging pattern and propagating wave fronts is elucidated through a fourier analysis finally after having identified collaborating teams we study interface fluctuations where we initially populate different parts of the system with different teams

constrained opinion dynamics freezing and slow evolution we study opinion formation in a population of leftists centrists and rightist in an interaction between neighbouring agents a centrist and a leftist can become both centrists or leftists and similarly for a centrist and a rightist while leftists and rightists do not affect each other the evolution is controlled by the initial density of centrists 0 for any spatial dimension the system reaches a centrist consensus with probability 0 while with probability 1 0 the final state is either an extremist consensus or a frozen population of leftists and rightists in one dimension we determine the opinion evolution by mapping the system onto a spin 1 ising model with zero temperature glauber kinetics the approach to the final state is governed by a t long time tail with 2 0 as 0 0 in the one dimensional frozen state the length distribution of single opinion domains has an algebraic small size tail x 2 1 and the average domain length is l2 where l is the length of the system

a negative imaginary lemma and the stability of interconnections of linear negative imaginary systems the note is concerned with linear negative imaginary systems first a previously established negative imaginary lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis this result is achieved by suitably extending the definition of negative imaginary transfer function matrices secondly a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems meanwhile some properties of linear negative imaginary systems are developed finally an undamped flexible structure example is presented to illustrate the theory

stable oscillations of a predator prey probabilistic cellular automaton a mean field approach we analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator prey system the individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the lotka volterra model two levels of mean field approximations are set up the simple approximation is equivalent to an extended patch model a simple metapopulation model with patches colonized by prey patches colonized by predators and empty patches this approximation is capable of describing the limited available space for species occupancy the pair approximation is moreover able to describe two types of coexistence of prey and predators one where population densities are constant in time and another displaying self sustained time oscillations of the population densities the oscillations are associated with limit cycles and arise through a hopf bifurcation they are stable against changes in the initial conditions and in this sense they differ from the lotka volterra cycles which depend on initial conditions in this respect the present model is biologically more realistic than the lotka volterra model

effect of initial concentration and spatial heterogeneity of active agent distribution on opinion dynamics abstract we analyze the effect of spatial heterogeneity in the initial spin distribution on spin dynamics in a three state square lattice divided into spatial cells districts in the spirit of the statistical mechanics of social impact we introduce a dominant influence rule dir according to which in a single update step a chosen node adopts the state determined by the influence of its discussion group formed by the node itself and its neighbors within one or more coordination spheres in contrast to models based on some form of majority rule mr a system governed by the dir is easily trapped in a stable non consensus state if all nodes of the discussion group have the same weight of influence to ensure that a consensus in the dir system is necessarily reached we need to put a stochastic process in the update rule further the stochastic dir model is used as a starting point for understanding the effect of spatial heterogeneity of active agent non zero spin distribution on the exit probabilities initially the positive and negative spins active agents are assigned to some nodes with non uniform spatial distributions while the rest of the nodes remain in the state with spin zero uncommitted voters by varying the relative means and skewness of the initial spin distributions we observe critical behaviors of exit probabilities in finite size systems the critical exponents are obtained by monte carlo simulations the results of numerical simulations are discussed in the context of social dynamics

diffusive clustering in the two dimensional voter model on donne des resultats de simulation et une enquete concernant les resultats connus sur le modele du votant dans trois cas distincts trois ou plusieurs dimensions une dimension et deux dimensions

exit probability in generalised kinetic ising model in this paper we study generalised ising glauber models with inflow of information in one dimension and derive expressions for the exit probability using well established analytical methods the analytical expressions agree very well with the results obtained from numerical simulation only when the interaction is restricted to the nearest neighbor but as the range of interaction is increased the analytical results deviate from simulation results systematically the reasons for the deviation as well as some related open questions are discussed

weighted mahalanobis distance kernels for support vector machines the support vector machine svm has been demonstrated to be a very effective classifier in many applications but its performance is still limited as the data distribution information is underutilized in determining the decision hyperplane most of the existing kernels employed in nonlinear svms measure the similarity between a pair of pattern images based on the euclidean inner product or the euclidean distance of corresponding input patterns which ignores data distribution tendency and makes the svm essentially a ldquolocalrdquo classifier in this paper we provide a step toward a paradigm of kernels by incorporating data specific knowledge into existing kernels we first find the data structure for each class adaptively in the input space via agglomerative hierarchical clustering ahc and then construct the weighted mahalanobis distance wmd kernels using the detected data distribution information in wmd kernels the similarity between two pattern images is determined not only by the mahalanobis distance md between their corresponding input patterns but also by the sizes of the clusters they reside in although wmd kernels are not guaranteed to be positive definite pd or conditionally positive definite cpd satisfactory classification results can still be achieved because regularizers in svms with wmd kernels are empirically positive in pseudo euclidean pe spaces experimental results on both synthetic and real world data sets show the effectiveness of ldquopluggingrdquo data structure into existing kernels

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

brief paper input output stability of systems with backlash the objective of this work is to study the stability of systems with backlash from an input output point of view in the first part an l analysis is addressed this analysis provides not only conditions for boundedness of the loop signals but also results on existence of solutions based on schauder fixed point theorem in the second part the system is studied using an l 2 or conic sector approach the backlash graph is confined into certain conic sector which is shown to be optimum or maximal the conic inequality induces frequencial conditions on the linear part which are further relaxed introducing dynamic multipliers in the third part both l and l 2 techniques are combined reaching a final criterion which results in a popov like stability condition

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

nonequilibrium transitions in complex networks a model of social interaction we analyze the nonequilibrium order disorder transition of axelrod s model of social interaction in several complex networks in a small world network we find a transition between an ordered homogeneous state and a disordered state the transition point is shifted by the degree of spatial disorder of the underlying network the network disorder favoring ordered configurations in random scale free networks the transition is only observed for finite size systems showing system size scaling while in the thermodynamic limit only ordered configurations are always obtained thus in the thermodynamic limit the transition disappears however in structured scale free networks the phase transition between an ordered and a disordered phase is restored

kernel improved support vector machine for semanteme data the computation for the inner production of semanteme data and the support vector machine svm classification of semantic data are very difficult in this paper a novel kernel based semanteme data classification method is proposed and the svm is extended to semantic svm called the semanteme based support vector machine ssvm a new dissimilarity definition and a simple inner production computation method for semanteme data are presented and the parameters for optimization selection in ssvm are also discussed in the proposed algorithm the solving support vector process based on the new inner production computation method remains a quadratic program problem but has a lower computation complexity the ssvm is insensitive to outliers and its classification capability for unbalanced data in actual datasets is analyzed the experimental results demonstrate the average advantage of ssvm over algorithm c4 5 adaptive dissimilarity metric and value difference metric in terms of classification and robust capability indicating that the proposed method has promising performance

synchronization of stochastic oscillations due to long range diffusion we investigate the effect of long range diffusive mixing on stochastic processes taking place on low dimensional catalytic supports as a working example the cyclic lattice lotka volterra llv model is used which is conservative at the mean field level and demonstrates fractal patterns and local oscillations when realized on low dimensional lattice supports we show that the local oscillations are synchronized when a weak long range diffusive process is added to llv and global oscillations of limit cycle type emerge this phenomenon is demonstrated as a nonequilibrium phase transition and takes place when the mixing to reaction rate p order parameter is above a critical point p c the value of the critical point is shown to depend on the kinetic parameters the global oscillations in this case emerge as a result of phase synchronization between local oscillations on sublattices

a negative imaginary lemma without minimality assumptions and robust state feedback synthesis for uncertain negative imaginary systems abstract negative imaginary systems have important engineering applications for example in lightly damped flexible structures with collocated position sensors and force actuators this paper proposes a new negative imaginary lemma for generalized negative imaginary systems where the minimality assumption is relaxed the proposed lemma facilitates both analysis and synthesis for negative imaginary systems invoking this result a systematic robust static state feedback synthesis method is proposed in an lmi framework for systems with strictly negative imaginary uncertainty e g unmodeled spill over dynamics in a lightly damped flexible structure assuming all states are available for state feedback two numerical examples are given to show the usefulness of the proposed results

irreversible growth of binary mixtures on small world networks binary mixtures growing on small world networks under far from equilibrium conditions are studied by means of extensive monte carlo simulations for any positive value of the shortcut fraction of the network p 0 the system undergoes a continuous order disorder phase transition while it is noncritical in the regular lattice limit p 0 using finite size scaling relations the phase diagram is obtained in the thermodynamic limit and the critical exponents are evaluated the small world networks are thus shown to trigger criticality a phenomenon analogous to similar observations reported recently in the investigation of equilibrium systems

fixation in a cyclic lotka volterra model we study a cyclic lotka volterra model of n interacting species populating a d dimensional lattice in the realm of a kirkwood approximation a critical number of species nc d above which the system fixates is determined analytically we find nc d 5 14 23 in dimensionsdd 1 2 3 in remarkably good agreement with simulation results in two dimensions a cyclic variant of the lotka volterra model of interacting populations originally introduced by vito volterra for the description of the struggle for existence among species 1 2 has then appeared in a number of apparently unrelated fields ranging from plasma physics 3 to integrable systems 4 5 recently the cyclic lotka volterra model also known as the cyclic voter model has attracted considerable interest as it was realized that introduction of the spatial structure drastically enriches the dynamics 6 11 namely if species live on a one dimensional 1d lattice a homogeneous initial state evolves into a coarsening mosaic of interacting species this heterogeneous spatial structure spontaneously develops when the number of species is sufficiently small n nc fixation occurs i e the system approaches a frozen state little is known in higher dimensions not even the existence of nc has yet been established theoretically or numerically in simulations on two dimensional 2d lattices with n 6 10 species no sign of fixation has been found and instead a reactive steady state has been observed 6 11 in this letter we investigate the cyclic lotka volterra model in the framework of a kirkwood like approximation this approach predicts a finite nc in all spatial dimensions in the following we shall use the language of the voter model 12 consider the cyclic voter model with n possible opinions each site of a d dimensional cubic lattice is occupied by a voter which has an opinion labelled by with d 1 n voters can change their opinions in a cyclic manner 1 modulo n according to the opinions of their neighbourhood specifically the following sequential dynamics is implemented i we randomly choose a site of opinion say and one of its 2d nearest neighbours of opinion ii if d 1 then the chosen site changes its opinion from to d 1 and iii otherwise opinion does not change we set the timescale so that in unit time each site of the lattice is chosen once on average when nd 2 the cyclic voter model is

the asymptotic stability of nonlinear lur e systems with multiple slope restrictions the authors present the analysis of the asymptotic stability of multiple slope restricted nonlinear lur e systems by providing a lyapunov function they obtain a matrix language criterion in terms of algebraic riccati equations and linear matrix inequalities which are discussed at the point of computational issues additionally they consider the frequency domain interpretation of the result

role of dimensionality in axelrod s model for the dissemination of culture we analyze a model of social interaction in one and two dimensional lattices for a moderate number of features we introduce an order parameter as a function of the overlap between neighboring sites in a one dimensional chain we observe that the dynamics is consistent with a second order transition where the order parameter changes continuously and the average domain diverges at the transition point however in a two dimensional lattice the order parameter is discontinuous at the transition point characteristic of a 4rst order transition between an ordered and a disordered state c

necessary and sufficient conditions on negative imaginariness for interval siso transfer functions and their interconnection this article is concerned with the study of the negative imaginariness of interval transfer functions necessary and sufficient conditions for strictly negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on kharitonov s theorem then certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed finally an example is provided to illustrate the main results of the article

a model for social networks social networks are organized into communities with dense internal connections giving rise to high values of the clustering coefficient in addition these networks have been observed to be assortative i e highly connected vertices tend to connect to other highly connected vertices and have broad degree distributions we present a model for an undirected growing network which reproduces these characteristics with the aim of producing efficiently very large networks to be used as platforms for studying sociodynamic phenomena the communities arise from a mixture of random attachment and implicit preferential attachment the structural properties of the model are studied analytically and numerically using the k clique method for quantifying the communities r 2006 elsevier b v all rights reserved

quadratic optimal synchronization of uncertain chaotic systems abstract this paper investigates the quadratic optimal synchronization of uncertain chaotic systems with parameter mismatch parametric perturbations and external disturbances on both master and slave systems a robust control scheme based on lyapunov stability theory and quadratic optimal control approach is derived to realize chaotic synchronization the sufficient criterion for stability condition is formulated in a linear matrix inequality lmi form the effect of uncertain parameters and external disturbance is suppressed to an h norm constraint an adaptive algorithm is proposed to adjust the uncertain bound in the robust controller avoiding the chattering phenomena the simulation results for synchronization of the chua s circuit system and the lorenz system demonstrate the effectiveness of the proposed scheme

dissimilarity learning for nominal data defining a good distance dissimilarity measure between patterns is of crucial importance in many classification and clustering algorithms while a lot of work has been performed on continuous attributes nominal attributes are more difficult to handle a popular approach is to use the value difference metric vdm to define a real valued distance measure on nominal values however vdm treats the attributes separately and ignores any possible interactions among attributes in this paper we propose the use of adaptive dissimilarity matrices for measuring the dissimilarities between nominal values these matrices are learned via optimizing an error function on the training samples experimental results show that this approach leads to better classification performance moreover it also allows easier interpretation of dis similarity between different nominal values

dynamics of majority rule in two state interacting spin systems we introduce a two state opinion dynamics model where agents evolve by majority rule in each update a group of agents is specified whose members then all adopt the local majority state in the mean field limit where a group consists of randomly selected agents consensus is reached in a time that scales ln n where n is the number of agents on finite dimensional lattices where a group is a contiguous cluster the consensus time fluctuates strongly between realizations and grows as a dimension dependent power of n the upper critical dimension appears to be larger than 4 the final opinion always equals that of the initial majority except in one dimension

impact of initial lattice structures on networks generated by traces of random walks abstract we show that the platform stage of network evolution plays a principal role in the topology of resulting networks generated by short cuts stimulated by the movements of a random walker the mechanism of which tends to produce power law degree distributions to examine the numerical results we have developed a statistical method which relates the power law exponent to random properties of the subgraph developed in the platform stage as a result we find that an important exponent in the network evolution is which characterizes the size of the subgraph in the form v t where v and t denote the number of vertices in the subgraph and the time variable respectively 2d lattices can impose specific limitations on the walker s diffusion which keeps the value of within a moderate range and provides typical properties of complex networks 1d and 3d cases correspond to different ends of the spectrum for with 2d cases in between especially for 2d square lattices a discontinuous change of the network structure is observed which varies according to whether is greater or less than 2 for 1d cases we show that emergence of nearly complete subgraphs is guaranteed by 1 2 although the transient power law is permitted at low increase rates of edges additionally the model exhibits a spontaneous emergence of highly clustered structures regardless of its initial structure

an evolutionary strategy based on partial imitation for solving optimization problems abstract in this work we introduce an evolutionary strategy to solve combinatorial optimization tasks i e problems characterized by a discrete search space in particular we focus on the traveling salesman problem tsp i e a famous problem whose search space grows exponentially increasing the number of cities up to becoming np hard the solutions of the tsp can be codified by arrays of cities and can be evaluated by fitness computed according to a cost function e g the length of a path our method is based on the evolution of an agent population by means of an imitative mechanism we define partial imitation in particular agents receive a random solution and then interacting among themselves may imitate the solutions of agents with a higher fitness since the imitation mechanism is only partial agents copy only one entry randomly chosen of another array i e solution in doing so the population converges towards a shared solution behaving like a spin system undergoing a cooling process i e driven towards an ordered phase we highlight that the adopted partial imitation mechanism allows the population to generate solutions over time before reaching the final equilibrium results of numerical simulations show that our method is able to find in a finite time both optimal and suboptimal solutions depending on the size of the considered search space

exact results for kinetics of catalytic reactions the kinetics of an irreversible catalytic reaction on substrate of arbitrary dimension is examined in the limit of infinitesimal reaction rate reaction controlled limit we solve the dimer dimer surface reaction model or voter model exactly in arbitrary dimension d the density of reactive interfaces is found to exhibit a power law decay for d 2 and a slow logarithmic decay in two dimensions we discuss the relevance of these results for the monomer monomer surface reaction model

effects of noise and confidence thresholds in nominal and metric axelrod dynamics of social influence we study the effects of bounded confidence thresholds and of interaction and external noise on axelrod s model of social influence our study is based on a combination of numerical simulations and an integration of the mean field master equation describing the system in the thermodynamic limit we find that interaction thresholds affect the system only quantitatively but that they do not alter the basic phase structure the known crossover between an ordered and a disordered state in finite systems subject to external noise persists in models with general confidence threshold interaction noise here facilitates the dynamics and reduces relaxation times we also study axelrod systems with metric features and point out similarities and differences compared to models with nominal features

input space versus feature space in kernel based methods this paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector sv kernel functions we first discuss the geometry of feature space in particular we review what is known about the shape of the image of input space under the feature space map and how this influences the capacity of sv methods following this we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel using the example of the class of inhomogeneous polynomial kernels which are often used in sv pattern recognition we then discuss the connection between feature space and input space by dealing with the question of how one can given some vector in feature space find a preimage exact or approximate in input space we describe algorithms to tackle this issue and show their utility in two applications of kernel methods first we use it to reduce the computational complexity of sv decision functions second we combine it with the kernel pca algorithm thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real world data

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

the existence of negative absolute temperatures in axelrod s social influence model abstract we introduce the concept of temperature as an order parameter in the standard axelrod s social influence model it is defined as the relation between suitably defined entropy and energy functions t s e 1 we show that at the critical point where the order disorder transition occurs this absolute temperature changes in sign at this point which corresponds to the transition homogeneous heterogeneous culture the entropy of the system shows a maximum we discuss the relationship between the temperature and other properties of the model in terms of cultural traits