symmetry and phaselocking in chains of weakly coupled oscillators weakly coupled chains of oscillators with nearest neighbor interactions are analyzed for phaselocked solutions it is shown that the symmetry properties of the coupling affect the qualitative form of the phaselocked solutions and the scaling behavior of the system as the number of oscillators grows without bound it is also shown that qualitative behavior of these solutions depends on whether the coupling is diffusive or i synaptic terms defined in the paper the methods include the demonstration that the equations for phaselocked solutions can be approximated by a singularly perturbed two point continuum boundary value problem that is easier to analyze the issue of convergence of the phaselocked solutions to solutions of the continuum equation is closely related to questions involving numerical entropy in computation schemes for a conservation law an application to the neurophysiology of motor behavior is discussed briefly

intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators a theory of intrinsic fluctuations is developed of a phase ordering parameter for large populations of weakly and uniformly coupled limit cycle oscillators with distributed native frequencies in particular it is shown that the intensity as well as the correlation time of fluctuations exhibit power law divergence at the onset of mutual entrainment with critical exponents which depend on whether the coupling strength approaches the threshold from below or above this peculiar feature is demonstrated by numerical simulations mainly through finite size scaling analyses in the course of exploring its origin we encounter a new concept termed a correlation frequency which provides a natural interpretation of the finite size scaling laws a comment is given on a recent theory by kuramoto and nishikawa to clarify why it contradicts our results

associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise we study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise the memory patterns are assumed to be given by uniformly distributed random numbers on 0 2 ensuremath pi so that the patterns encode the phase differences of the oscillators to derive the macroscopic order parameter equations for the network with an extensive number of stored patterns we introduce an effective transfer function by assuming a fixed point equation of the form of the thouless anderson palmer equation which describes the time averaged output as a function of the effective time averaged local field properties of the networks associated with synchronization phenomena for a discrete symmetric natural frequency distribution with three frequency components are studied based on the order parameter equations and are shown to be in good agreement with the results of numerical simulations two types of retrieval states are found to occur with respect to the degree of synchronization when the size of the width of the natural frequency distribution is changed

scaling behaviour at the onset of mutual entrainment in a population of interacting oscillators scaling behaviour of an order parameter and its fluctuations is numerically investigated at the onset of macroscopic mutual entrainment in a population of interacting self oscillators in particular evidence is presented for the power law divergence of the fluctuations with exponents near 1 8 finite size scaling forms are also proposed and verified

lower critical dimension for populations of oscillators with randomly distributed frequencies a renormalization group analysis it is argued by way of a renormalization group analysis that the lower critical dimension of macroscopic mutual entrainment in a class of populations of oscillators satisfies a certain inequality which is sensitive to the tail of the distribution of native frequencies this result is supported in part by numerical simulations as well as a proof of the absence of long range order in one dimension

fuzzy implicative ideals of bck algebras the notion of fuzzy implicative ideals of bck algebras is introduced the following results are obtained for a bck algebra x and fuzzy ideal of x must be a fuzzy subalgebra of x suppose that and v are fuzzy ideals of x with v and 0 v 0 if is a fuzzy implicative ideal of x the so is v a fuzzy ideal of x is fuzzy implicative if and only if is both fuzzy positive implicative and fuzzy commutative a bck algebra x is implicative resp positive implicative commutative if and only if every fuzzy ideal of x is fuzzy implicative resp fuzzy positive implicative fuzzy commulative also several characterizations of fuzzy implicative ideals are given

phase locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies abstract we study phase locking in a network of coupled nonlinear oscillators with local interactions and random intrinsic frequencies the oscillators are located at the vertices of a graph and interact along the edges they are coupled by sinusoidal functions of the phase differences across the edges and their intrinsic frequencies are independent and identically distributed with finite mean and variance we derive an exact expression for the probability of phase locking in a linear chain of such oscillators and prove that this probability tends to zero as the number of oscillators grows without bound however if the coupling strength increases as the square root of the number of oscillators the probability of phase locking tends to a limiting distribution the kolmogorov smirnov distribution this latter result is obtained by showing that the phase locking problem is equivalent to a discretization of pinned brownian motion the results on chains of oscillators are extended to more general graphs in particular for a hypercubic lattice of any dimension the probability of phase locking tends to zero exponentially fast as the number of oscillators grows without bound we also consider a less stringent type of synchronization characterized by large clusters of oscillators mutually entrained at the same average frequency it is shown that if such clusters exist they necessarily have a sponge like geometry

involutory and invertible fuzzy bck algebras the concept of a fuzzy annihilator in a commutative bck algebra will be introduced and then we investigate some basic properties using this notion we define an involutory resp invertible fuzzy ideal we prove that i every bounded implicative bck algebra is an involutory fuzzy bck algebra and ii every categorical commutative bck algebra is an invertible fuzzy bck algebra let x be an involutory and invertible fuzzy bck algebra and let fi x denote the set of all fuzzy ideals of x we show that iii fi x is a distributive lattice and iv fi x is a quasi boolean algebra

critical phenomena in globally coupled excitable elements critical phenomena in globally coupled excitable elements are studied by focusing on a saddle node bifurcation at the collective level critical exponents that characterize divergent fluctuations of interspike intervals near the bifurcation are calculated theoretically the calculated values appear to be in good agreement with those determined by numerical experiments the relevance of our results to jamming transitions is also mentioned

hamiltonian mean field model effect of network structure on synchronization dynamics the hamiltonian mean field model of coupled inertial hamiltonian rotors is a prototype for conservative dynamics in systems with long range interactions we consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix by studying the linear stability of the incoherent state we find that the transition to synchrony begins when the coupling constant k is inversely proportional to the largest eigenvalue of the adjacency matrix we derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors when k is just beyond the transition to synchronization we find that the degree of synchronization is highly dependent on the network s heterogeneity but that for large k the degree of synchronization is robust to changes in the degree distribution our results are illustrated with numerical simulations on erd os renyi networks and networks with power law degree distributions

fuzzy characteristic subgroups of a group abstract a fuzzy characteristic subgroup of a group is characterized in terms of its level subgroups without any restriction on the order of the underlying group

on fuzzy ideals in bck bci algebras in the present paper we give a procedure by which we generate a fuzzy ideal resp closed fuzzy ideal by a fuzzy set in a bci algebra as applications we prove the set of all the fuzzy ideals in a bci algebra forms a complete lattice called fuzzy ideal lattice the set of all the closed fuzzy ideals in a bci algebra is a modular sublattice of the fuzzy ideal lattice but it is not distributive in general for commutative bck algebras we establish the prime fuzzy ideal theorem in particular we give some characterizations of noether bck bci algebras by fuzzy ideals

fuzzy implicative ideals in bck algebras abstract in this paper we introduce the concept of fuzzy implicative ideals in bck algebras and study some of their properties

field theoretic approach to fluctuation effects in neural networks a well defined stochastic theory for neural activity which permits the calculation of arbitrary statistical moments and equations governing them is a potentially valuable tool for theoretical neuroscience we produce such a theory by analyzing the dynamics of neural activity using field theoretic methods for nonequilibrium statistical processes assuming that neural network activity is markovian we construct the effective spike model which describes both neural fluctuations and response this analysis leads to a systematic expansion of corrections to mean field theory which for the effective spike model is a simple version of the wilson cowan equation we argue that neural activity governed by this model exhibits a dynamical phase transition which is in the universality class of directed percolation more general models which may incorporate refractoriness can exhibit other universality classes such as dynamic isotropic percolation because of the extremely high connectivity in typical networks it is expected that higher order terms in the systematic expansion are small for experimentally accessible measurements and thus consistent with measurements in neocortical slice preparations we expect mean field exponents for the transition we provide a quantitative criterion for the relative magnitude of each term in the systematic expansion analogous to the ginsburg criterion experimental identification of dynamic universality classes in vivo is an outstanding and important question for neuroscience

spontaneous synchronization of coupled oscillator systems with frequency adaptation we study the synchronization of kuramoto oscillators with all to all coupling in the presence of slow noisy frequency adaptation in this paper we develop a new model for oscillators which adapt both their phases and frequencies it is found that this model naturally reproduc es some observed phenomena that are not qualitatively produced by the standard kuramoto model such as long waiting times before the synchronization of clapping audiences by assuming a self consistent steady state solution we find three stability regimes for the coupling constant k separated by critical points k1 and k2 i for k k2 the incoherent state becomes unstable and only the synchronized state exists iii for k1 k2 the average waiting time grows logarithmically with the number of oscillators

a shocking display of synchrony abstract this article explores the kuramoto model describing the synchronization of a population of coupled oscillators two versions of this model are considered a discrete version suitable for a population with a finite number of oscillators and a continuum model found in the limit of an infinite population when the strength of the coupling between the oscillators exceeds a threshold the oscillators partially synchronize we explore the transition in the continuum model which takes the form of a bifurcation of a discrete mode from a continuous spectrum we use numerical methods and perturbation theory to study the patterns of synchronization that form beyond transition and compare with the synchronization predicted by the discrete model there are similarities with instabilities in ideal plasmas and inviscid fluids but these are superficial

globally coupled noisy oscillators with inhomogeneous periodic forcing we study the collective properties of an array of nonlinear noisy oscillators driven by nonidentical periodic signals we consider the case of a globally coupled array of harmonically forced weakly nonlinear oscillators where there is a constant difference between the phases of the forcing signals applied to adjacent oscillators this system is a prototypical model of a nonlinear phased array receiver we derive analytical results for the array output in the limit of a large number of oscillators for the noise free and noisy cases numerical simulations show good agreement with the theoretical analysis

finite size effects of avalanche dynamics we study the avalanche dynamics of a system of globally coupled threshold elements receiving random input the model belongs to the same universality class as the random neighbor version of the olami feder christensen stick slip model a closed expression for avalanche size distributions is derived for arbitrary system sizes n using geometrical arguments in the system s configuration space for finite systems approximate power law behavior is obtained in the nonconservative regime whereas for stackrel ensuremath rightarrow n ensuremath infty critical behavior with an exponent of ensuremath 3 2 is found in the conservative case only we compare these results to the avalanche properties found in networks of integrate and fire neurons and relate the different dynamical regimes to the emergence of synchronization with and without oscillatory components

fuzzy ideals in bci algebras abstract the aim of this paper is to introduce the notions of fuzzy bci positive implicative ideals and fuzzy bci implicative ideals of bci algebras and to investigate their properties we give several characterizations of fuzzy bci positive implicative ideals and fuzzy bci implicative ideals the extension theorems of fuzzy bci positive implicative ideals and fuzzy bci implicative ideals are obtained we discuss the relations among various fuzzy ideals and show that a fuzzy set of a bci algebra is fuzzy bci implicative ideal if and only if is both fuzzy bci positive implicative ideal and fuzzy bci commutative ideal finally we characterize implicative positive implicative bci algebras via fuzzy bci implicative fuzzy bci positive implicative ideals

theoretical analysis for critical fluctuations of relaxation trajectory near a saddle node bifurcation a langevin equation whose deterministic part undergoes a saddle node bifurcation is investigated theoretically it is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle node bifurcation point in the weak noise limit while the final value of the deterministic solution changes discontinuously at the point a systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method in this formulation the critical nature turns out to originate from the neutrality of exiting time from a saddle point the theoretical calculation explains results of numerical simulations

analytic expressions for rate and cv of a type i neuron driven by white gaussian noise we study the one dimensional normal form of a saddle node system under the influence of additive gaussian white noise and a static bias current input parameter a model that can be looked upon as the simplest version of a type i neuron with stochastic input this is in contrast with the numerous studies devoted to the noise driven leaky integrate and fire neuron we focus on the firing rate and coefficient of variation cv of the interspike interval density for which scaling relations with respect to the input parameter and noise intensity are derived quadrature formulas for rate and cv are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model we also show that caution must be used to extend these results to the neuron model with multiplicative gaussian white noise the correspondence between the first passage time statistics for the saddle node model and the neuron model is obtained only in the stratonovich interpretation of the stochastic neuron model while previous results have focused only on the ito interpretation the correct stratonovich interpretation yields cvs that are still relatively high although smaller than in the ito interpretation it also produces certain qualitative differences especially at larger noise intensities our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type i neurons from their firing statistics we also briefly discuss the effect of finite boundaries finite values of threshold and reset on the firing statistics

bayesian kalman filtering with elliptically contoured errors summary the basic recursive equations of the kalman filter for independent normally distributed error sources in both the observation and the system equations are shown to hold for a larger class of distributions it is shown that for error sources following jointly a general elliptical distribution the conditional posterior distribution of the parameters and the one step ahead predictive distribution at every stage t are also elliptical this generalizes some recent results of meinhold singpurwalla for error sources distributed as multivariate student t and some older results of zellner for the linear regression model

robustification of kalman filter models abstract kalman filter models based on the assumption of multivariate gaussian distributions are known to be nonrobust this means that when a large discrepancy arises between the prior distribution and the observed data the posterior distribution becomes an unrealistic compromise between the two in this article we discuss a rationale for how to robustify the kalman filter specifically we develop a model wherein the posterior distribution will revert to the prior when extreme outlying observations are encountered and we point out that this can be achieved by assuming a multivariate distribution with student t marginals to achieve fully robust results of the kind desired it becomes necessary to forsake an exact distribution theory approach and adopt an approximation method involving poly t distributions a recursive mechanism for implementing the multivariate t based kalman filter is described its properties are discussed and the procedure is illustrated by an example

fuzzy commutative ideals of bck algebras abstract in this paper we define and discuss the fuzzy commutative ideals in bck algebras a fuzzy characteristic commutative ideal is characterized in terms of its level commutative ideals

approximate inference in state space models with heavy tailed noise state space models have been successfully applied across a wide range of problems ranging from system control to target tracking and autonomous navigation their ubiquity stems from their modeling flexibility as well as the development of a battery of powerful algorithms for estimating the state variables for multivariate models the gaussian noise assumption is predominant due its convenient computational properties in some cases anyhow this assumption breaks down and no longer holds we propose a novel approach to extending the applicability of this class of models to a wider range of noise distributions without losing the computational advantages of the associated algorithms the estimation methods we develop parallel the kalman filter and thus are readily implemented and inherit the same order of complexity we derive all of the equations and algorithms from first principles in order to validate the performance of our approach we present specific instances of non gaussian state space models and test their performance on experiments with synthetic and real data