rational singularities and almost split sequences the main aim of this paper is to relate almost split sequences to singularity theory by showing that the mckay quiver built from the finite dimen sional representations of a finite subgroup g of gl 2 c where c is the complex numbers is isomorphic to the ar quiver of the reflexive modules of the quotient singularity associated with g over the past decade almost split sequences have been playing an increasingly important role in the representation theories of finite dimensional algebras and classical orders see 5 and 3 8 for basic existence theorems in these contexts while they have been known for some time to exist in higher dimensional situations 3 it has not been at all clear how they related to singularity theory if at all the main aim of this paper is to relate almost split sequences to singularity theory by showing that the mckay quiver built from the fimte dimensional complex represen tations of a finite subgroup g of gl 2 c where c is the complex numbers is isomorphic to the ar quiver of the reflexive modules over the quotient singularity r associated with g as in the case of finite dimensional algebras the ar quiver of reflexive r modules is defined in terms of the almost split sequences of reflexive r modules in the case g c sl 2 c mckay observed that the underlying graph of the mckay quiver with the trivial module removed is isomorphic to the desingulariza tion graph of the associated singularity various explanations of this phenomenon have been given by knorrer gonzalez sprinberg verdier 6 and artin verdier 1 which along the way have established most explicitly in 1 a natural one to one correspondence between the indecomposable reflexive r modules and the nodes of the desingularization graph but why the almost split sequences describe the edge of the desingularization graph still remains to be explained an effort has been made to make this paper as self contained as possible in particular no prior knowledge of almost split sequences is required before describing the contents of the six sections of this paper we fix some notation throughout this paper g is a finite group k an algebraically closed field of characteristic not dividing the order of g and v a two dimensional k representation of g setting s k x y the k algebra of formal power series the two dimen sional representation v gives a linear action of g on s as a group of k algebra automorphisms we denote by s g the skew group ring given by this action

long route to consensus two stage coarsening in a binary choice voting model formation of consensus in binary yes no type of voting is a well defined process however even in presence of clear incentives the dynamics involved can be incredibly complex specifically formations of large groups of similarly opinionated individuals could create a condition of support bubbles or spontaneous polarization that renders consensus virtually unattainable e g the question of the uk exiting the eu there have been earlier attempts in capturing the dynamics of consensus formation in societies through simple z 2 symmetric models hoping to capture the essential dynamics of average behavior of a large number of individuals in a statistical sense however in absence of external noise they tend to reach a frozen state with fragmented and polarized states i e two or more groups of similarly opinionated groups with frozen dynamics here we show in a kinetic exchange opinion model considered on l l square lattices that while such frozen states could be avoided an exponentially slow approach to consensus is manifested specifically the system could either reach consensus in a time that scales as l 2 or a long lived metastable state termed a domain wall state for which formation of consensus takes a time scaling as l 3 6 the latter behavior is comparable to some voterlike models with intermediate states studied previously the late time anomaly in the timescale is reflected in the persistence probability of the model finally the interval of zero crossing of the average opinion i e the time interval over which the average opinion does not change sign is shown to follow a scale free distribution which is compared with that seen in the opinion surveys regarding brexit and associated issues since the late 1970s the issue of minority spreading is also addressed by calculating the exit probability

pair approximation for the noisy threshold q voter model in the standard q voter model a given agent can change its opinion only if there is a full consensus of the opposite opinion within a group of influence of size q a more realistic extension is the threshold q voter where a minimal agreement at least 0 q 0 q opposite opinions is sufficient to flip the central agent s opinion including also the possibility of independent nonconformist choices variants of this model including nonconformist behavior have been previously studied in fully connected networks mean field limit here we investigate its dynamics in random networks particularly while in the mean field case it is irrelevant whether repetitions in the influence group are allowed we show that this is not the case in networks and we study the impact of both cases with or without repetition furthermore the results of computer simulations are compared with the predictions of the pair approximation derived for uncorrelated networks of arbitrary degree distributions

maximal cohen macaulay modules over the cone of an elliptic curve let r k y1 y2 y3 f f y13 y23 y33 where k is an algebraically closed field with chark 3 using atiyah bundle classification over elliptic curves we describe the matrix factorizations of the graded indecomposable reflexive r modules equivalently we describe explicitly the indecomposable bundles over the projective curve v f pk2 using the fact that over the completion r of r every reflexive module is gradable we obtain a description of the maximal cohen macaulay modules over r k y1 y2 y3 f

mean variance optimization of discrete time discounted markov decision processes abstract in this paper we study a mean variance optimization problem in an infinite horizon discrete time discounted markov decision process mdp the objective is to minimize the variance of system rewards with the constraint of mean performance different from most of works in the literature which require the mean performance already achieve optimum we can let the discounted performance equal any constant the difficulty of this problem is caused by the quadratic form of the variance function which makes the variance minimization problem not a standard mdp by proving the decomposable structure of the feasible policy space we transform this constrained variance minimization problem to an equivalent unconstrained mdp under a new discounted criterion and a new reward function the difference of the variances of markov chains under any two feasible policies is quantified by a difference formula based on the variance difference formula a policy iteration algorithm is developed to find the optimal policy we also prove the optimality of deterministic policy over the randomized policy generated in the mean constrained policy space numerical experiments demonstrate the effectiveness of our approach

approximate probabilistic cellular automata for the dynamics of single species populations under discrete logisticlike growth with and without weak allee effects we investigate one dimensional elementary probabilistic cellular automata pca whose dynamics in first order mean field approximation yields discrete logisticlike growth models for a single species unstructured population with nonoverlapping generations beginning with a general six parameter model we find constraints on the transition probabilities of the pca that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof several possible models display a negative cubic term that can be interpreted as a weak allee factor we also investigate the conditions under which a one parameter pca derived from the more general six parameter model can generate valid population growth dynamics numerical simulations illustrate the behavior of some of the pca found

phase transitions in a two parameter model of opinion dynamics with random kinetic exchanges recently a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry breaking transition was reported m lallouache a s chakrabarti a chakraborti and b k chakrabarti phys rev e 82 056112 2010 we generalize the model to incorporate two parameters to represent conviction and to represent the influencing ability of individuals a phase boundary given by 1 2 is obtained separating the symmetric and symmetry broken phases the effect of the influencing term enhances the possibility of reaching a consensus in the society the time scale diverges near the phase boundary in a power law manner the order parameter and the condensate also show power law growth close to the phase boundary albeit with different exponents the exponents in general change along the phase boundary indicating a nonuniversality the relaxation times however become constant with increasing system size near the phase boundary indicating the absence of any diverging length scale consistently the fluctuations remain finite but show strong dependence on the trajectory along which it is estimated

seed size strongly affects cascades on random networks the average avalanche size in the watts model of threshold dynamics on random networks of arbitrary degree distribution is determined analytically existence criteria for global cascades are shown to depend sensitively on the size of the initial seed disturbance the dependence of cascade size upon the mean degree z of the network is known to exhibit several transitions these are typically continuous at low z and discontinuous at high z here it is demonstrated that the low z transition may in fact be discontinuous in certain parameter regimes connections between these results and the zero temperature random field ising model on random graphs are discussed

complex networks effect of subtle changes in nature of randomness abstract in two different classes of network models namely the watts strogatz type and the euclidean type subtle changes have been introduced in the randomness in the watts strogatz type network rewiring has been done in different ways and although the qualitative results remain the same finite differences in the exponents are observed in the euclidean type networks where at least one finite phase transition occurs two models differing in a similar way have been considered the results show a possible shift in one of the phase transition points but no change in the values of the exponents the ws and euclidean type models are equivalent for extreme values of the parameters we compare their behaviour for intermediate values

optimization of markov decision processes under the variance criterion in this paper we study a variance minimization problem in an infinite stage discrete time markov decision process mdp regardless of the mean performance for the markov chain under the variance criterion since the value of the cost function at the current stage will be affected by future actions this problem is not a standard mdp and the traditional mdp theory is not applicable in this paper we convert the variance minimization problem into a standard mdp by introducing a concept called pseudo variance then we derive a variance difference formula that quantifies the difference of variances of markov systems under any two policies with the difference formula the correlation of the variance cost function at different stages can be decoupled through a nonnegative term a necessary condition of the optimal policy is obtained it is also proved that the optimal policy with the minimal variance can be found in the deterministic policy space furthermore we propose an efficient iterative algorithm to reduce the variance of markov systems we prove that this algorithm can converge to a local optimum finally a numerical experiment is conducted to demonstrate the efficiency of our algorithm compared with the gradient based method widely adopted in the literature

border collision period doubling scenario using a one dimensional dynamical system representing a poincare return map for dynamical systems ofthe lorenz type we investigate the border collision period doubling bifurcation scenario in contrast to theclassical period doubling scenario this scenario is formed by a sequence of pairs of bifurcations whereby eachpair consists of a border collision bifurcation and a pitchfork bifurcation the characteristic properties of thisscenario like symmetry breaking and symmetry recovering as well as emergence of coexisting attractors andnoninvariant attractive sets are investigated doi 10 1103 physreve 70 026222 pacs number s 05 45 ac 82 40 bj 95 10 fhi introduction

finite size effects for the ising model on random graphs with varying dilution abstract we investigate the finite size corrections to the equilibrium magnetization of an ising model on a random graph with n nodes and n edges with 1 2 by conveniently rescaling the coupling constant the free energy is made extensive as expected the system displays a phase transition of the mean field type for all the considered values of at the transition temperature of the fully connected curie weiss model finite size corrections are investigated for different values of the parameter using two different approaches a replica based finite n expansion and a cavity method numerical simulations are compared with theoretical predictions the cavity based analysis is shown to agree better with numerics

dynamical influence processes on networks general theory and applications to social contagion we study binary state dynamics on a network where each node acts in response to the average state of its neighborhood by allowing varying amounts of stochasticity in both the network and node responses we find different outcomes in random and deterministic versions of the model in the limit of a large dense network however we show that these dynamics coincide we construct a general mean field theory for random networks and show this predicts that the dynamics on the network is a smoothed version of the average response function dynamics thus the behavior of the system can range from steady state to chaotic depending on the response functions network connectivity and update synchronicity as a specific example we model the competing tendencies of imitation and nonconformity by incorporating an off threshold into standard threshold models of social contagion in this way we attempt to capture important aspects of fashions and societal trends we compare our theory to extensive simulations of this limited imitation contagion model on poisson random graphs finding agreement between the mean field theory and stochastic simulations

shortest paths on systems with power law distributed long range connections we discuss shortest path lengths l r on periodic rings of size l supplemented with an average of pl randomly located long range links whose lengths are distributed according to p l approximately l mu using rescaling arguments and numerical simulation on systems of up to 10 7 sites we show that a characteristic length xi exists such that l r approximately r for r xi for small p we find that the shortest path length satisfies the scaling relation l r mu p xi f mu r xi three regions with different asymptotic behaviors are found respectively a mu 2 where theta s 1 b 1 mu 2 where 0 theta s mu 1 2 and c mu 1 where l r behaves logarithmically i e theta s 0 the characteristic length xi is of the form xi approximately p nu with nu 1 2 mu in region b but depends on l as well in region c a directed model of shortest paths is solved and compared with numerical results

the unreasonable effectiveness of tree based theory for networks with clustering we demonstrate that a tree based theory for various dynamical processes operating on static undirected networks yields extremely accurate results for several networks with high levels of clustering we find that such a theory works well as long as the mean intervertex distance l is sufficiently small that is as long as it is close to the value of l in a random network with negligible clustering and the same degree degree correlations we support this hypothesis numerically using both real world networks from various domains and several classes of synthetic clustered networks we present analytical calculations that further support our claim that tree based theories can be accurate for clustered networks provided that the networks are sufficiently small worlds

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

magnetic order in the ising model with parallel dynamics it is discussed how the equilibrium properties of the ising model are described by an hamiltonian with an antiferromagnetic low temperature behavior if only an heat bath dynamics with the characteristics of a probabilistic cellular automaton is assumed to determine the temporal evolution of the system

lie rinehart cohomology and integrable connections on modules of rank one abstract let k be an algebraically closed field of characteristic 0 let r be a commutative k algebra and let m be a torsion free r module of rank one with a connection we consider the lie rinehart cohomology with values in end r m with its induced connection and give an interpretation of this cohomology in terms of the integrable connections on m when r is an isolated singularity of dimension d 2 we relate the lie rinehart cohomology to the topological cohomology of the link of the singularity and when r is a quasi homogenous hypersurface of dimension two we give a complete computation of the cohomology

two dimensional sir epidemics with long range infection we extend a recent study of susceptible infected removed epidemic processes with long range infection referred to as i in the following from 1 dimensional lattices to lattices in two dimensions as in i we use hashing to simulate very large lattices for which finite size effects can be neglected in spite of the assumed power law p x x 2 for the probability that a site can infect another site a distance vector x apart as in i we present detailed results for the critical case for the supercritical case with 2 and for the supercritical case with 0 2 for the latter we verify the stretched exponential growth of the infected cluster with time predicted by m biskup for 2 we find generic power laws with dependent exponents in the supercritical phase but no kosterlitz thouless kt like critical point as in 1 d instead of diverging exponentially with the distance from the critical point the correlation length increases with an inverse power as in an ordinary critical point finally we study the dependence of the critical exponents on in the regime 0 2 and compare with field theoretic predictions in particular we discuss in detail whether the critical behavior for slightly less than 2 is in the short range universality class as conjectured recently by f linder et al as in i we also consider a modified version of the model where only some of the contacts are long range the others being between nearest neighbors if the number of the latter reaches the percolation threshold the critical behavior is changed but the supercritical behavior stays qualitatively the same

optimal control of ergodic continuous time markov chains with average sample path rewards in this paper we study continuous time markov decision processes with the average sample path reward aspr criterion and possibly unbounded transition and reward rates we propose conditions on the system s primitive data for the existence of epsilon aspr optimal deterministic stationary policies in a class of randomized markov policies satisfying some additional continuity assumptions the proof of this fact is based on the time discretization technique the martingale stability theory and the concept of potential we also provide both policy and value iteration algorithms for computing or at least approximating the epsilon aspr optimal stationary policies we illustrate with examples our main results as well as the difference between the aspr and the average expected reward criteria

phase transition in a coevolving network of conformist and contrarian voters in the coevolving voter model each voter has one of two diametrically opposite opinions and a voter encountering a neighbor with the opposite opinion may either adopt it or rewire the connection to another randomly chosen voter sharing the same opinion as we smoothly change the relative frequency of rewiring compared to that of adoption there occurs a phase transition between an active phase and a frozen phase by performing extensive monte carlo calculations we show that the phase transition is characterized by critical exponents ensuremath beta 0 54 1 and overline ensuremath nu 1 5 1 which differ from the existing mean field type prediction we furthermore extend the model by introducing a contrarian type that tries to have neighbors with the opposite opinion and show that the critical behavior still belongs to the same universality class irrespective of such contrarians fraction

between disorder and order a case study of power law abstract power law is an important feature of phenomena in long memory behaviors zipf ever found power law in the distribution of the word frequencies in physics the terms order and disorder are thermodynamic or statistical physics concepts originally and a lot of research work has focused on self organization of the disorder ingredients of simple physical systems it is interesting what make disorder order transition we devise an experiment based method about random symbolic sequences to research regular pattern between disorder and order the experiment results reveal power law is indeed an important regularity in transition from disorder to order about these results the preliminary study and analysis has been done to explain the reasons

navigation in a small world with local information it is commonly known that there exist short paths between vertices in a network showing the small world effect yet vertices for example the individuals living in society usually are not able to find the shortest paths due to the very serious limit of information to study this issue theoretically here the navigation process of launching messages toward designated targets is investigated on a variant of the one dimensional small world network swn in the network structure considered the probability of a shortcut falling between a pair of nodes is proportional to r alpha where r is the lattice distance between the nodes when alpha 0 it reduces to the swn model with random shortcuts the system shows the dynamic small world effect which is different from the well studied static sw effect we study the effective network diameter the path length as a function of the lattice distance and the dynamics they are controlled by multiple parameters and we use data collapse to show that the parameters are correlated the central finding is that in the one dimensional network studied the dynamic sw effect exists for 0 alpha 2 for each given value of alpha in this region the point where the dynamic sw effect arises is m l approximately 1 where m is the number of useful shortcuts and l is their average reduced effective length

scaling behavior in a proportional voting process we perform a statistical analysis on the proportional elections held in brazil in october 1998 we show that the distribution of votes among candidates for the whole country follows a power law n v ensuremath propto v ensuremath ensuremath alpha with ensuremath alpha 1 00 ifmmode pm else textpm fi 0 02 extending over two orders of magnitude the voting distributions for several states of the federation also display scale invariant behavior with ensuremath alpha ensuremath approx 1 we argue that this particular voting system can be modeled as a typical multiplicative process in which the choice of the candidate is governed by a product of probabilities

effect of the nature of randomness on quenching dynamics of the ising model on complex networks randomness is known to affect the dynamical behavior of many systems to a large extent in this paper we investigate how the nature of randomness affects the dynamics in a zero temperature quench of the ising model on two types of random networks in both networks which are embedded in a one dimensional space the first neighbor connections exist and the average degree is 4 per node in random model a the second neighbor connections are rewired with a probability p while in random model b additional connections between neighbors at a euclidean distance l l 1 are introduced with a probability p l proportionally l we find that for both models the dynamics leads to freezing such that the system gets locked in a disordered state the point at which the disorder of the nonequilibrium steady state is maximum is located the behavior of dynamical quantities such as residual energy order parameter and persistence are discussed and compared overall the behavior of physical quantities are similar although subtle differences are observed due to the difference in the nature of randomness

phase transition of a one dimensional ising model with distance dependent connections the critical behavior of the ising model on a one dimensional network which has long range connections at distances l 1 with the probability theta l approximately l m is studied by using monte carlo simulations through analyzing the ising model on networks with different m values this paper discusses the impact of the global correlation which decays with the increase of m on the phase transition of the ising model adding the analysis of the finite size scaling of the order parameter m it is observed that in the whole range of 0 m 2 a finite temperature transition exists and the critical exponents show consistence with mean field values which indicates a mean field nature of the phase transition

nonconservative kinetic exchange model of opinion dynamics with randomness and bounded confidence the concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values 1 1 the characteristics of the unrestricted model which has one parameter representing conviction undergo drastic changes with the introduction of bounded confidence parametrized by three distinct regions are identified in the phase diagram in the plane and the evidences of a first order phase transition for 0 3 are presented a neutral state with all opinions equal to zero occurs for c1 2 3 independent of while for c 1 c 2 an ordered region is seen to exist where opinions of only one sign prevail at c 2 a transition to a disordered state is observed where individual opinions of both signs coexist and move closer to the extreme values 1 as is increased for confidence level 0 3 the ordered phase exists for a narrow range of only the line 0 is apparently a line of discontinuity and this limit is discussed in some detail

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

the fundamental module of a normal local domain of dimension 2 the fundamental module e of a normal local domain r m of dimension 2 is defined by the nonsplit exact sequence 0 a k a e a m a 0 where k is the canonical module of r we prove that if r is complete with r m c then e is decomposable if and only if r is a cyclic quotient singularity various other properties of fundamental modules will be discussed 0 introduction let r m be a normal local domain of dimension 2 which possesses the canonical module k let c r denote the category of finitely generated reflexive r modules note that a finitely generated r module is an object in c r if and only if it is a maximal cohen macaulay module over r by definition k is a reflexive module of rank 1 and it satisfies extr r m k r m see herzog and kunz 8 for the details we denote the duality with respect to r resp k by resp that is homr r and homr k remark that a finitely generated r module m lies in c r if and only if m m or equivalently m m we make the following definition 0 1 since ext m k ext2r r m k r m there uniquely exists the nonsplit exact sequence 0 k e m 0 which is called the fundamental sequence in 3 in particular the module e appearing in the middle term of this sequence is also unique up to isomorphism we call e the fundamental module of r e is said to be decomposable if there is an isomorphism e a e b where a and b are nontrivial ideals of r otherwise e is indecomposable in this paper we are interested in the properties of the fundamental modules in particular we are mostly concerned with its decomposability in fact we can prove that if r is complete with the residue field c then r has the decomposable fundamental module if and only if r is a cyclic quotient singularity see theorem 2 1 and if this is the case then the ar quiver of r will be easily described in 1 we summarize some elementary properties of fundamental modules in particular we can prove that if r is a hypersurface then the fundamental module of r is isomorphic to the third syzygy of k in 2 our main theorem 2 1 stated above will be proved the reader will notice that the keys of the proof are the first author s theorem 11 theorem 1 1 and the theorem of herzog auslander auslander 3 theorem 4 9 herzog 71 received by the editors june 26 1986 and in revised form july 29 1987 1980 mathematics subject classification 1985 revision primary 13h10 13c13 secondary 14b05 14j17

small world phenomena and the statistics of linear polymers a regular lattice in which the sites can have long range connections at a distance l with a probabilty p l l in addition to the short range nearest neighbour connections shows small world behaviour for 0 c in the most appropriate physical example of such a system namely the linear polymer network the exponent is related to the exponents of the corresponding n vector model in the n 0 limit and its value is less than c still the polymer networks do not show small world behaviour here we show that this is due to a small value constraint on the number q of long range connections per monomer in the network in the general q space we obtain a phase boundary separating regions with and without small world behaviour and show that the polymer network falls marginally in the regular lattice region

hipsters on networks how a minority group of individuals can lead to an antiestablishment majority the spread of opinions memes diseases and alternative facts in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread one feature that can change spreading dynamics substantially is heterogeneous behavior among different types of individuals in a social network in this paper we explore how antiestablishment nodes e g hipsters influence the spreading dynamics of two competing products we consider a model in which spreading follows a deterministic rule for updating node states which indicate which product has been adopted in which an adjustable probability p hip of the nodes in a network are hipsters who choose to adopt the product that they believe is the less popular of the two the remaining nodes are conformists who choose which product to adopt by considering which products their immediate neighbors have adopted we simulate our model on both synthetic and real networks and we show that the hipsters have a major effect on the final fraction of people who adopt each product even when only one of the two products exists at the beginning of the simulations a small fraction of hipsters in a network can still cause the other product to eventually become the more popular one to account for this behavior we construct an approximation for the steady state adoption fractions of the products on k regular trees in the limit of few hipsters additionally our simulations demonstrate that a time delay in the knowledge of the product distribution in a population as compared to immediate knowledge of product adoption among nearest neighbors can have a large effect on the final distribution of product adoptions using a local tree approximation we derive an analytical estimate of the spreading of products and obtain good agreement if a sufficiently small fraction of the population consists of hipsters in all networks we find that either of the two products can become the more popular one at steady state depending on the fraction of hipsters in the network and on the amount of delay in the knowledge of the product distribution our simple model and analysis may help shed light on the road to success for antiestablishment choices in elections as such success and qualitative differences in final outcomes between competing products political candidates and so on can arise rather generically in our model from a small number of antiestablishment individuals and ordinary processes of social influence on normal individuals

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

the noisy voter model under the influence of contrarians abstract the influence of contrarians on the noisy voter model is studied at the mean field level the noisy voter model is a variant of the voter model where agents can adopt two opinions optimistic or pessimistic and can change them by means of an imitation herding and an intrinsic noise mechanisms an ensemble of noisy voters undergoes a finite size phase transition upon increasing the relative importance of the noise to the herding form a bimodal phase where most of the agents share the same opinion to a unimodal phase where almost the same fraction of agent are in opposite states by the inclusion of contrarians we allow for some voters to adopt the opposite opinion of other agents anti herding we first consider the case of only contrarians and show that the only possible steady state is the unimodal one more generally when voters and contrarians are present we show that the bimodal unimodal transition of the noisy voter model prevails only if the number of contrarians in the system is smaller than four and their characteristic rates are small enough for the number of contrarians bigger or equal to four the voters and the contrarians can be seen only in the unimodal phase moreover if the number of voters and contrarians as well as the noise and herding rates are of the same order then the probability functions of the steady state are very well approximated by the gaussian distribution

a mean variance optimization problem for discounted markov decision processes in this paper we consider a mean variance optimization problem for markov decision processes mdps over the set of deterministic stationary policies different from the usual formulation in mdps we aim to obtain the mean variance optimal policy that minimizes the variance over a set of all policies with a given expected reward for continuous time mdps with the discounted criterion and finite state and action spaces we prove that the mean variance optimization problem can be transformed to an equivalent discounted optimization problem using the conditional expectation and markov properties then we show that a mean variance optimal policy and the efficient frontier can be obtained by policy iteration methods with a finite number of iterations we also address related issues such as a mutual fund theorem and illustrate our results with an example

exact solutions for social and biological contagion models on mixed directed and undirected degree correlated random networks we derive analytic expressions for the possibility probability and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed and undirected edges and arbitrary degree degree correlations our work extends previous theoretical developments for the undirected case and we provide numerical support for our findings by investigating an example class of networks for which we are able to obtain closed form expressions

disorder induced phase transition in kinetic models of opinion dynamics abstract we propose a model of continuous opinion dynamics where mutual interactions can be both positive and negative different types of distributions for the interactions all characterized by a single parameter p denoting the fraction of negative interactions are considered results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p p c below which a consensus is reached although the order disorder transition is analogous to a ferromagnetic paramagnetic phase transition with comparable critical exponents the model is characterized by some distinctive features relevant to a social system

mean variance portfolio selection under partial information this paper is concerned with a continuous time mean variance portfolio selection problem in a possibly incomplete market with multiple stocks and a bond only the past price movements of the stocks and the bond are the information available to the investors a separation principle is shown to hold in this setting efficient strategies based on the aforementioned partial information are derived which involve the optimal filter of the stock appreciation rate processes the main methodological contribution of the paper is to employ the particle system representation to develop analytical and numerical approaches in obtaining the filter as well as solving the related backward stochastic differential equation

drift and monotonicity conditions for continuous time controlled markov chains with an average criterion we give conditions for the existence of average optimal policies for continuous time controlled markov chains with a denumerable state space and borel action sets the transition rates are allowed to be unbounded and the reward cost rates may have neither upper nor lower bounds in the spirit of the drift and monotonicity conditions for continuous time markov processes we propose a new set of conditions on the controlled process primitive data under which the existence of optimal deterministic stationary policies in the class of randomized markov policies is proved using the extended generator approach instead of kolmogorov s forward equation used in the previous literature and under which the convergence of a policy iteration method is also shown moreover we use a controlled queueing system to show that all of our conditions are satisfied whereas those in the previous literature fail to hold

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

the susceptible infected recovered model on a euclidean network we consider a susceptible infected recovered sir epidemic model on a euclidean network in one dimension in which nodes at a distance l are connected with probability p l l in addition to nearest neighbors the topology of the network changes as is varied and its effect on the sir model is studied r t the recovered fraction of population up to time t and the total duration of the epidemic are calculated for different values of the infection probabilities q and a threshold behavior is observed for all up to 2 0 above the threshold value q qc the saturation value rsat attains a finite value both rsat and show scaling behavior in a finite system of size n and qc is constant for 0 qc the results are compared to static percolation phenomena and also to mean field results for finite systems discussions on the properties of the euclidean network are made in the light of the present results

opinion formation in kinetic exchange models spontaneous symmetry breaking transition we propose a minimal multiagent model for the collective dynamics of opinion formation in the society by modifying kinetic exchange dynamics studied in the context of income money or wealth distributions in a society this model has an intriguing spontaneous symmetry breaking transition to polarized opinion state starting from nonpolarized opinion state in order to analyze the model we introduce an iterative map version of the model which has very similar statistical characteristics an approximate theoretical analysis of the numerical results is also given based on the iterative map version

percolation in a kinetic opinion exchange model we study the percolation transition of the geometrical clusters in the square lattice lccc model a kinetic opinion exchange model introduced by lallouache chakrabarti chakraborti and chakrabarti phys rev e 82 056112 2010 with the change in conviction and influencing parameter the cluster is comprised of the adjacent sites having an opinion value greater than or equal to a prefixed threshold value of opinion the transition point is different from that obtained for the transition of the order parameter average opinion value found by lallouache et al although the transition point varies with the change in the threshold value of the opinion the critical exponents for the percolation transition obtained from the data collapses of the maximum cluster size the cluster size distribution and the binder cumulant remain the same the exponents are also independent of the values of conviction and influencing parameters indicating the robustness of this transition the exponents do not match any other known percolation exponents e g the static ising dynamic ising and standard percolation this means that the lccc model belongs to a separate universality class

small world networks links with long tailed distributions small world networks swn obtained by randomly adding to a regular structure additional links al are of current interest in this paper we explore based on physical models a new variant of swn in which the probability of realizing an al depends on the chemical distance between the connected sites we assume a power law probability distribution and study random walkers on the network focusing especially on their probability of being at the origin we connect the results to l evy flights which follow from a mean field variant of our model

a probabilistic analysis of bias optimality in unichain markov decision processes focuses on bias optimality in unichain finite state and action space markov decision processes using relative value functions we present methods for evaluating optimal bias this leads to a probabilistic analysis which transforms the original reward problem into a minimum average cost problem the result is an explanation of how and why bias implicitly discounts future rewards

bifurcations in models of a society of reasonable contrarians and conformists we study models of a society composed of a mixture of conformist and reasonable contrarian agents that at any instant hold one of two opinions conformists tend to agree with the average opinion of their neighbors and reasonable contrarians tend to disagree but revert to a conformist behavior in the presence of an overwhelming majority in line with psychological experiments the model is studied in the mean field approximation and on small world and scale free networks in the mean field approximation a large fraction of conformists triggers a polarization of the opinions a pitchfork bifurcation while a majority of reasonable contrarians leads to coherent oscillations with an alternation of period doubling and pitchfork bifurcations up to chaos similar scenarios are obtained by changing the fraction of long range rewiring and the parameter of scale free networks related to the average connectivity

deformations of algebras defined by tilting bundles abstract in this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles we do this in two settings first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal deformation of that scheme and then expanding this result to c equivariant deformations over schemes with a good c action in both these situations the endomorphism algebra of the lifted tilting bundle produces a deformation of the original endomorphism algebra and this is a graded deformation in the c equivariant case we apply our results to rational surface singularities generalising the deformed preprojective algebras of crawley boevey and holland and also to symplectic situations where the deformations produced are related to symplectic reflection algebras

contrarian like behavior and system size stochastic resonance in an opinion spreading model abstract we have recently shown that a stochastic driving in an opinion spreading model has a tremendous impact on the system dynamics spontaneously leading to system s agents which are analogous to galam s contrarians we have analyzed the existence of stochastic resonance phenomena in this social model in the presence of such contrarians we have found that the system does not show conventional stochastic resonance but interestingly it does exhibit system size stochastic resonance

phase transitions in a network with a range dependent connection probability we consider a one dimensional network in which the nodes at euclidean distance l can have long range connections with a probability p l approximately l delta in addition to nearest neighbor connections this system has been shown to exhibit small world behavior for delta 2 above which its behavior is like a regular lattice from the study of the clustering coefficients we show that there is a transition to a random network at delta 1 the finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicates that a continuous phase transition occurs at this point using these results we find that the two transitions occurring in this network can be detected in any dimension by the behavior of a single quantity the average bond length the phase transitions in all dimensions are nontrivial in nature

clusters and the entropy in opinion dynamics on complex networks abstract in this work we investigate a heterogeneous population in the modified hegselmann krause opinion model on complex networks we introduce the shannon information entropy about all relative opinion clusters to characterize the cluster profile in the final configuration independent of network structures there exists the optimal stubbornness of one subpopulation for the largest number of clusters and the highest entropy besides there is the optimal bounded confidence or subpopulation ratio of one subpopulation for the smallest number of clusters and the lowest entropy however network structures affect cluster profiles indeed a large average degree favors consensus for making different networks more similar with complete graphs the network size has limited impact on cluster profiles of heterogeneous populations on scale free networks but has significant effects upon those on small world networks

a note on optimality conditions for continuous time markov decision processes with average cost criterion this note deals with continuous time markov decision processes with a denumerable state space and the average cost criterion the transition rates are allowed to be unbounded and the action set is a borel space we give a new set of conditions under which the existence of optimal stationary policies is ensured by using the optimality inequality our results are illustrated with a controlled queueing model moreover we use an example to show that our conditions do not imply the existence of a solution to the optimality equations in the previous literature

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

multistable binary decision making on networks we propose a simple model for a binary decision making process on a graph motivated by modeling social decision making with cooperative individuals the model is similar to a random field ising model or fiber bundle model but with key differences on heterogeneous networks for many types of disorder and interactions between the nodes we predict discontinuous phase transitions with mean field theory which are largely independent of network structure we show how these phase transitions can also be understood by studying microscopic avalanches and describe how network structure enhances fluctuations in the distribution of avalanches we suggest theoretically the existence of a glassy spectrum of equilibria associated with a typical phase even on infinite graphs so long as the first moment of the degree distribution is finite this behavior implies that the model is robust against noise below a certain scale and also that phase transitions can switch from discontinuous to continuous on networks with too few edges numerical simulations suggest that our theory is accurate

mean variance criteria for finite continuous time markov decision processes this technical note deals with the mean variance problem known as the average variance av minimization problem for finite continuous time markov decision processes we first introduce a so called g condition which is weaker than the well known ergodicity and unichain conditions and sufficient for the finiteness of the av of a policy also we present an example of a policy having infinite av when the g condition is not satisfied under the g condition we prove that the av criterion can be transformed into an equivalent mean or expected average criterion by using a martingale technique and an observation from the canonical form of a transition rate matrix and thus the existence and calculation of an av minimal policy over a class of mean optimal policies are obtained by a policy iteration algorithm in an finite number of iterations as byproduct we obtain some interesting new results about the mean average optimality

phase transitions of extended range probabilistic cellular automata with two absorbing states we study phase transitions in a long range one dimensional cellular automaton with two symmetric absorbing states it includes and extends several other models like the ising and domany kinzel ones it is characterized by competing ferromagnetic linear and antiferromagnetic nonlinear couplings despite its simplicity this model exhibits an extremely rich phase diagram we present numerical results and mean field approximations

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

anticonformity or independence insights from statistical physics the aim of this paper is to examine how different types of social influence introduced on the microscopic individual level manifest on the macroscopic level i e in the society the inspiration for this task came mainly from two sources social psychology that recognize two different types of nonconformity anticonformity and independence and the observation related to the agent based modeling that was verbalized in 2002 by macy and willer that there was a little effort to provide analysis of how results differ depending on the model designs to achieve the goal we propose a generalized model of opinion dynamics that as a special cases reduces to the linear voter model sznajd model q voter model and the majority rule we use the model to examine the differences that appear at the macroscopic level under the influence of two types of nonconformity introduced on the microscopic level we answer the question if the observed differences are universal or model dependent