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

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

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

estimates for the norms of products of sines and cosines abstract in this paper we prove asymptotic formulas for the l p norms of p n k 1 n 1 e i k and q n k 1 n 1 e i k these products can be expressed using k 1 n sin k 2 and k 1 n cos k 2 respectively we prove an estimate for p n at a point near where its maximum occurs finally we give an asymptotic formula for the maximum of the fourier coefficients of q n

cluster size entropy in the axelrod model of social influence small world networks and mass media we study the axelrod s cultural adaptation model using the concept of cluster size entropy s c which gives information on the variability of the cultural cluster size present in the system using networks of different topologies from regular to random we find that the critical point of the well known nonequilibrium monocultural multicultural order disorder transition of the axelrod model is given by the maximum of the s c q distributions the width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first or second order by scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait q c and the number f of cultural features in two dimensional regular networks we also analyze the effect of the mass media external field on social systems within the axelrod model in a square network we find a partially ordered phase whose largest cultural cluster is not aligned with the external field in contrast with a recent suggestion that this type of phase cannot be formed in regular networks we draw a q b phase diagram for the axelrod model in regular networks

an item response model for nominal data based on the rising selection ratios criterion complete response vectors of all answer options in multiple choice items can be used to estimate ability the rising selection ratios criterion is necessary for scoring individuals because it implies that estimated ability always increases when the correct alternative is selected this paper introduces the generalized dlt model which assumes rising selection ratios and uses three parameters to describe each incorrect alternative it is shown that the nominal categories and the thissen and steinberg model do not meet the criterion a simulation study on goodness of recovery and an example with real data are also included

a response model for multiple choice items in the mid 1960s samejima initiated the development of item response models that involve separate response functions for all of the alternatives in the multiple choice and likert type formats her work in this area began at the educational testing service and continued during a visit to the l l thurstone psychometric laboratory at the university of north carolina both samejima s 1969 this volume original model for graded item responses and bock s 1972 this volume model for nominal responses were originally intended to produce response functions for all of the alternatives of multiple choice items for various reasons neither model has proved entirely satisfactory for that purpose although both have been applied in other contexts using a combination of ideas suggested by bock 1972 and samejima 1968 1979 a multiple choice model was developed that produces response functions that fit unidimensional multiple choice tests better thissen and steinberg 1984 that model is the subject of this chapter

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

nested logit models for multiple choice item response data nested logit item response models for multiple choice data are presented relative to previous models the new models are suggested to provide a better approximation to multiple choice items where the application of a solution strategy precedes consideration of response options in practice the models also accommodate collapsibility across all distractor categories making it easier to allow decisions about including distractor information to occur on an item by item or application by application basis without altering the statistical form of the correct response curves marginal maximum likelihood estimation algorithms for the models are presented along with simulation and real data analyses

message survival and decision dynamics in a class of reactive complex systems subject to external fields abstract in this study the dynamics of decisions in complex networks subject to external fields are studied within a markov process framework using nonlinear dynamical systems theory a mathematical discrete time model is derived using a set of basic assumptions regarding the convincement mechanisms associated with two competing opinions the model is analyzed with respect to the multiplicity of critical points and the stability of extinction states sufficient conditions for extinction are derived in terms of the convincement probabilities and the maximum eigenvalues of the associated connectivity matrices the influences of exogenous e g mass media based effects on decision behavior are analyzed qualitatively the current analysis predicts i the presence of fixed point multiplicity with a maximum number of four different fixed points multi stability and sensitivity with respect to the process parameters and ii the bounded but significant impact of exogenous perturbations on the decision behavior these predictions were verified using a set of numerical simulations based on a scale free network topology

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

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

effects of the underlying topology on perturbation spreading in the axelrod model for cultural dissemination abstract we study the effects of the underlying topologies on a single feature perturbation imposed to the axelrod model of consensus formation from the numerical simulations we show that there are successive updates which are similar to avalanches in many self organized criticality systems when a perturbation is imposed we find that the distribution of avalanche size satisfies the finite size scaling fss ansatz on two dimensional lattices and random networks however on scale free networks with the degree exponent 3 we show that the avalanche size distribution does not satisfy the fss ansatz the results indicate that the disordered configurations on two dimensional lattices or on random networks are still stable against the perturbation in the limit n network size however on scale free networks with 3 the perturbation always drives the disordered phase into an ordered phase the possible relationship between the properties of phase transition of the axelrod model and the avalanche distribution is also discussed

stochastic bifurcations in the nonlinear parallel ising model we investigate the phase transitions of a nonlinear parallel version of the ising model characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one this model arises in problems of opinion formation the mean field approximation shows chaotic oscillations by changing the couplings or the connectivity the spatial model shows bifurcations in the average magnetization similar to that seen in the mean field approximation induced by the change of the topology after rewiring short range to long range connection as predicted by the small world effect these coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins induced by long range couplings similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution degree of asynchronism of the updating we also examined the effects of inhomogeneity mixing ferromagnetic and antiferromagnetic coupling which induces an unexpected bifurcation diagram with a bubbling behavior as also happens for dilution

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

growth of the sudler product of sines at the golden rotation number abstract we study the growth at the golden rotation number 5 1 2 of the function sequence p n r 1 n 2 sin r this sequence has been variously studied elsewhere as a skew product of sines birkhoff sum q pochhammer symbol on the unit circle and restricted euler function in particular we study the fibonacci decimation of the sequence p n namely the sub sequence q n r 1 f n 2 sin r for fibonacci numbers f n and prove that this renormalisation subsequence converges to a constant from this we show rigorously that the growth of p n is bounded by power laws this provides the theoretical basis to explain recent experimental results reported by knill and tangerman 2011 10

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

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

asymptotic behaviour of the sudler product of sines for quadratic irrationals abstract we study the asymptotic behaviour of the sequence of sine products p n r 1 n 2 sin r for real quadratic irrationals in particular we study the subsequence q n r 1 q n 2 sin r where q n is the nth best approximation denominator of and show that this subsequence converges to a periodic sequence whose period equals that of the continued fraction expansion of this verifies a conjecture recently posed by verschueren and mestel 2016 15

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

estimating difficulty from polytomous categorical data a comprehensive analysis of difficulty for multiple choice items requires information at different levels the test the items and the alternatives this paper introduces a new parameterization of the nominal categories model ncm for analyzing difficulty at these three levels the new parameterization is referred to as the ne ncm and is statistically equivalent to the ncm the ne ncm is applied to a sample of responses from a logical analysis test the results suggest that the individuals execute a self terminated response process that is mostly determined by working memory load

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

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

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

distractor selection ratios a latent variable representation for multiple choice item and option characteristic curves is presented under standard assumptions of conditional independence of item responses and monotonicity of item characteristic curves a criterion for distractors is proposed based on distractor selection ratios a connection is made between the proposed criterion and the theory of individual choice behavior providing new insight the main results allow for the testing of the criterion from observable data without first specifying a parametric form for the characteristic curves a series of examples apply the method

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

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

some standard errors in item response theory the mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for some common situations it is shown that the maximum likelihood estimation of a lower asymptote can wreak havoc with the accuracy of estimation of a location parameter indicating that if one needs to have accurate estimates of location parameters say for purposes of test linking equating or computerized adaptive testing the sample sizes required for acceptable accuracy may be unattainable in most applications it is suggested that other estimation methods be used if the three parameter model is applied in these situations

multicategorical spline model for item response theory additional information contained in incorrect responses calls for a multicategorical rather than a binary analysis of multiple choice data a nonparametric divided by total model for joint maximum likelihood estimation of probability of choice functions for particular responses and of latent ability is proposed the model approximates probability functions by rational splines some illustrative examples of real test data analysis and the results of a monte carlo study are presented

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

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

topological bifurcations in a model society of reasonable contrarians people are often divided into conformists and contrarians the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority in practice however the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion which denotes a social norm such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets we present the opinion dynamics of a society of reasonable contrarian agents the model is a cellular automaton of ising type with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms we introduce the entropy of the collective variable as a way of comparing deterministic mean field and probabilistic simulations bifurcation diagrams in the mean field approximation the model exhibits bifurcations and a chaotic phase interpreted as coherent oscillations of the whole society however in a one dimensional spatial arrangement one observes incoherent oscillations and a constant average in simulations on watts strogatz networks with a small world effect the mean field behavior is recovered with a bifurcation diagram that resembles the mean field one but where the rewiring probability is used as the control parameter similar bifurcation diagrams are found for scale free networks and we are able to compute an effective connectivity for such networks

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

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