violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

energy dissipation and violation of the fluctuation response relation in nonequilibrium langevin systems the fluctuation response relation is a fundamental relation that is applicable to systems near equilibrium on the other hand when a system is driven far from equilibrium this relation is violated in general because the detailed balance condition is not satisfied in nonequilibrium systems even in this case it has been found that for a class of langevin equations there exists an equality between the extent of violation of the fluctuation response relation in the nonequilibrium steady state and the rate of energy dissipation from the system into the environment t harada and s i sasa phys rev lett 95 130602 2005 since this equality involves only experimentally measurable quantities it serves as a proposition to determine experimentally whether the system can be described by a langevin equation furthermore the contribution of each degree of freedom to the rate of energy dissipation can be determined based on this equality in this paper we present a comprehensive description on this equality and provide a detailed derivation for various types of models including many body systems brownian motor models time dependent systems and systems with multiple heat reservoirs

a stochastic version of center manifold theory random dynamical systems arise naturally if the influence of white or real noise on the parameters of a nonlinear determinstic dynamical system is studied in this situation lyapunov exponents attached to the linearized flow replace the real parts of the eigenvalues and describe the stability behavior of the linear system if at least one of them vanishes then it is possible to prove the existence of a stochastic analogue of the deterministic center manifold the asymptotic behavior of the entire system can then be derived from the lower dimensional system restricted to this stochastic center manifold a dynamical characterization of the stochastic center manifold is given and approximation results are proved

simulation of the three dimensional ising model on the creutz cellular automaton abstract the three dimensional ising model is simulated on the creutz cellular automaton the values computed for the critical temperature and the static critical exponents within the framework of the finite size scaling theory are in agreement with their values obtained by different methods

exact transformation of a langevin equation to a fluctuating response equation we demonstrate that a langevin equation that describes the motion of a brownian particle under non equilibrium conditions can be exactly transformed to a special equation that explicitly exhibits the response of the velocity to a time dependent perturbation this transformation is constructed on the basis of an operator formulation originally used in nonlinear perturbation theory for differential equations by extending it to stochastic analysis we find that the expression obtained is useful for the calculation of fundamental quantities of the system and that it provides a physical basis for the decomposition of the forces in the langevin description into effective driving dissipative and random forces in a large scale description

an algorithm for generalized fuzzy binary linear programming problems abstract fuzzy binary linear programming fblp problems are very essential in many fields such as assignment and assembly line balancing problems in operational research multiple projects locations and candidates selection cases in management science as well as representing and reasoning with prepositional knowledge in artificial intelligence although fblp problems play a significant role in human decision environment not very much research has focused on fblp problems this work first proposes a simple means of expressing a triangular fuzzy number as a linear function with an absolute term a method of linearizing absolute terms is also presented the developed goal programming gp model weighted by decision makers dms preference aims to optimize the expected objective function and minimize the sum of possible membership functions deviations after presented a novel way of linearizing product terms the solution algorithm is proposed to generate a crisp trade off promising solution that is also an optimal solution in a certain sense three examples equipment purchasing choice investment project selection and assigning clients to project leaders illustrate that the proposed algorithm can effectively solve generalized fblp problems

derivation of stokes law from kirkwood s formula and the green kubo formula via large deviation theory we study the friction coefficient of a macroscopic sphere in a viscous fluid at low reynolds number first kirkwood s formula for the friction coefficient is reviewed on the basis of the hamiltonian description of particle systems according to this formula the friction coefficient is expressed in terms of the stress correlation on the surface of the macroscopic sphere then with the aid of large deviation theory we relate the surface stress correlation to the stress correlation in the bulk of the fluid where the latter is characterized by the viscosity in the green kubo formula by combining kirkwood s formula and the green kubo formula in large deviation theory we derive stokes law without explicitly employing the hydrodynamic equations

computation of critical exponents for two dimensional ising model on a cellular automaton static critical exponents for the two dimensional ising model are computed on a cellular automaton the analysis of the data within the framework of the finite size scaling theory reproduces their well established values

exact scaling functions for one dimensional stationary kpz growth we determine the stationary two point correlation function of the one dimensional kpz equation through the scaling limit of a solvable microscopic model the polynuclear growth model the equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a riemann hilbert problem related to the painleve ii equation we solve these equations numerically with very high precision and compare our up to numerical rounding exact result with the prediction of colaiori and moore 1 obtained from the mode coupling approximation

possibility versus probability the main objective of this note is to try to indicate that a possibility distribution at least in some applications can be interpreted as a family of probabilities possibly subjective an advantage of the latter interpretation is that subsequent derivations can be made by well proven probabilistic arguments rather than relying on an intuition concerning the properties of possibility distributions which is not well developed multistate reliability theory is given as an example of an area of application where the probabilistic approach seems far superior

the use of a fuzzy decision making method in a large scale computer system choice problem abstract we recently proposed a fuzzy decision making method for multiple objectives problems in an uncertain and ill defined environment this paper presents a real and large scale application of the method the problem is to decide what sort of computer system for research and education should be renewed in the department of computer engineering one member of a renewal committee appears as a decision maker after describing the outline of the fuzzy decision making method the decision analysis process objective hierarchy identification of decision maker s preference structure rating and ranking of alternatives and sensitivity analysis is presented

structurally nonlinear fluttering airfoil in turbulent flow the dynamics and response of a structurally nonlinear two dimensional airfoil in turbulent flow are investigated numerically the solution is analyzed in terms of probability density function pdf response mean square power spectral density and lyapunov exponent both the longitudinal and vertical components of turbulence are considered it is shown that turbulent flow due to its longitudinal component diminishes the stability of the aeroelastic system by advancing the flutter point and decreasing the damping thus confirming results from previous work where only the longitudinal component was modeled furthermore the shift in flutter airspeed is strongly dependent on the random stiffness terms it is also observed that turbulence may advance the airspeed at which the pitch angle marginal pdf changes from uni to bimodal compared with the nonexcited deterministic case whereas the heave transition appears to be postponed this observation is attributed to the nonlinearity considered a cubic stiffness in torsion finally in terms of response mean square the system appears to he more sensitive to the presence of the longitudinal excitation component at pre rather than at postinstability airspeeds

a path integral method for coarse graining noise in stochastic differential equations with multiple time scales abstract we present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales the objective of this method is to derive from the original system a new stochastic differential equation describing the system s evolution on slow time scales for this purpose we start from the corresponding path integral representation of the stochastic system and apply a multi scale expansion to the associated path integral kernel of the corresponding lagrangian as a concrete example we apply this expansion to a system that arises in the study of random dispersion fluctuations in dispersion managed fiber optic communications moreover we show that for this particular example the new path integration method yields the same result at leading order as an asymptotic expansion of the associated fokker planck equation

a note on the operativeness of neyman pearson tests with fuzzy information abstract in a previous paper we have studied the extension of the neyman pearson optimality criterion of testing statistical hypotheses when the available experimental information involves fuzzy imprecision this extension usually becomes unmanageable for small samples nevertheless we will verify that when the sample size is large enough the application of the central limit theorem determines an operative extension

the modularity condition for semi t operators and semi uninorms abstract the aim of this paper is mainly to solve the functional equations given by the modularity condition several years ago the modularity equations for t norms t conorms uninorms and t operators which are commutative and associative have been studied our investigations are motivated by modularity condition for generalizations of these operators by removing associativity or commutativity in this work the following main conclusions are proved 1 a continuous t norm with respect to a continuous semicopula is modular if and only if they are equal the case for a semicopula with respect to a strict t norm is also the same a semicopula with respect to a co semicopula is modular if and only if the semicopula is min and the co semicopula is max the modularity condition does not hold for a co semicopula with respect to a semicopula 2 necessary and sufficient conditions are given for a semi t operator with respect to a semi uninorm a pseudo uninorm with respect to a semi t operator to satisfy the modularity condition equation new solutions to the modularity condition equations of the case 1 are characterized

comment on asymptotic properties of coupled langevin equations the asymptotic behavior of coupled langevin equations in the limit of weak noise is studied by general normal form techniques in the vicinity of a pitchfork bifurcation the non gaussian behavior of the critical variable is established the conditional probability of the noncritical variable around the center manifold is determined it is shown that in certain cases the distribution of this later variable may be non gaussian

additive noise induced turing transitions in spatial systems with application to neural fields and the swift hohenberg equation this work studies the spatio temporal dynamics of a generic integral differential equation subject to additive random fluctuations it introduces a combination of the stochastic center manifold approach for stochastic differential equations and the adiabatic elimination for fokker planck equations and studies analytically the systems stability near turing bifurcations in addition two types of fluctuation are studied namely fluctuations uncorrelated in space and time and global fluctuations which are constant in space but uncorrelated in time we show that the global fluctuations shift the turing bifurcation threshold this shift is proportional to the fluctuation variance applications to a neural field equation and the swift hohenberg equation reveal the shift of the bifurcation to larger control parameters which represents a stabilization of the system all analytical results are confirmed by numerical simulations of the occurring mode equations and the full stochastic integral differential equation to gain some insight into experimental manifestations the sum of uncorrelated and global additive fluctuations is studied numerically and the analytical results on global fluctuations are confirmed qualitatively

a fuzzy decision making method and its application to a company choice problem abstract we propose a fuzzy decision making method for multiobjective decision problems its main features are the use of fuzzy connectives to represent the decision maker s preference structure and fuzzy probability to express imprecise and uncertain outcomes the preference structure is extracted through interaction between the decision maker and a computer the fuzzy connectives adopted here are zimmermann s operation and its two extensions the extended operations describe the preference structure better than the operation the proposed method consists of the following five steps 1 1 identification of the problem 2 2 a questionnaire process 3 3 parameter identification 4 4 evaluations of alternatives 5 5 aggregated rating and ranking of alternatives finally an application of this method to a company choice problem is presented

diffusion over barriers eigenanalysis of the smoluchowski equation for bistable potentials abstract a variational method is used to get the eigenvalues and eigenfunctions of the one dimensional smoluchowski equation for two types of symmetric bistable potential fields the effects of barrier height and width on the rate of escape of particles over the barrier first non zero eigenvalue are evaluated numerically and the results are compared with kramers theory in order to assess its range of application

an extended rule based inference for general decision making problems complex decision making problems are usually modeled in terms of a number of decisive variables that are related hierarchically pieces of evidence are aggregated in a bottom up way to determine the final decision goal for dealing with such problems ishizuka et al 5 6 developed a rule based inference procedure by using fuzzy sets to represent imprecise data and employed the dempster shafer theory to aggregate evidence for structural damage assessment this paper highlights the necessity of applying the rules with all possible consequent clauses in the procedure with the considerations of information quality and quantity when applying the procedure to more general decision making problems the use of such rules can provide high quality information which contains much less ignorance in the resultant information also it can afford more information due to the decrease in total ignorance a simple example with two cases is used to compare the results based on the two different presentations of rules in the inference procedure for illustrating the importance of considering the rules proposed in this paper

asymptotic properties of coupled nonlinear langevin equations in the limit of weak noise i cusp bifurcation we show how a singular perturbation technique based on the introduction of properly scaled variables enables us to derive the asymptotic properties of coupled langevin equations in the limit of weak noise this technique can be applied when the macroscopic steady state is asymptotically or marginally stable in the close vicinity of a cusp bifurcation point a simple prescription for the adiabatic elimination of the fast variable is established the critical variable exhibits amplified non gaussian fluctuations on a slow time scale the properties of the fast variable depend on the nonlinearity of the system under consideration because of its coupling to the critical variable it may exhibit amplified fluctuations of non gaussian nature

a new fuzzy multiple attributive group decision making methodology and its application to propulsion manoeuvring system selection problem in this paper a new fuzzy multiple attribute decision making fmadm method which is suitable for multiple attributive group decision making gdm problems in fuzzy environment is proposed to deal with the problem of ranking and selection of alternatives since the subjectivity imprecision and vagueness in the estimates of a performance rating enter into multiple attribute decision making madm problems fuzzy set theory provides a mathematical framework for modelling vagueness and imprecision in the proposed approach an attribute based aggregation technique for heterogeneous group of experts is employed and used for dealing with fuzzy opinion aggregation for the subjective attributes of the decision problem the propulsion manoeuvring system selection as a real case study is used to demonstrate the versatility and potential of the proposed method for solving fuzzy multiple attributive group decision making problems the proposed method is a generalised model which can be applied to great variety of practical problems encountered in the naval architecture from propulsion manoeuvring system selection to warship requirements definition

noise and bifurcations the influence of while noise on bifurcating dynamical systems is investigated using both fokker planck and functional integral methods noise leads to fuzzy bifurcations where physically relevant quantities become smooth functions of the bifurcation parameters we study dynamical and probabilistic quantities such as invariant measures liapunov exponents correlation functions and exit times the behavior of these quantities near the deterministic bifurcation point changes for distinct values of the control parameter therefore the very concept of bifurcation point becomes meaningless and must be replaced by the notion of bifurcation region

fuzzy rule generation methods for high level computer vision abstract in many decision making systems involving multiple sources the decisions made may be considered as the result of a rule based system in which the decision rules are usually enumerated by experts or generated by a learning process in this paper we discuss the various issues involved in the generation of fuzzy rules automatically from training data for high level computer vision features are treated as linguistic variables that appear in the antecedent clauses of the rules we present methods to generate the corresponding linguistic labels values and their membership functions rules are generated by constructing a minimal approximate fuzzy aggregation network and then training the network using gradient descent methods several examples are given

critical behavior of the two dimensional ising model with next nearest neighbor antiferromagnetic interaction on the creutz cellular automaton the two dimensional ising model with nearest and next nearest neighbor antiferromagnetic interactions of ratio r is simulated on the creutz cellular automaton the values of the critical temperature and the critical exponents for o r are estimated within the framework of the finite size scaling theory the dependence of tc on r agrees with the crossover scaling theory for 1 75 the results for 0 r are compatible with ising critical behavior

bifurcations under weak noise dynamical systems driven by gaussian white noise share some general asymptotic properties in the limit of weak noise which are reminiscent of equilibrium thermodynamics these properties and applications to bifurcating systems are discussed

computationally efficient active rule detection method algorithm and architecture in this paper a new active rule detection algorithm is proposed which is efficiently implemented in dedicated fuzzy processors here its advantages are analytically attested a novel realization architecture is proposed that has higher performance and uses lower hardware resources in comparison to the other reported architectures the structure of the proposed active rule detection unit is scalable in terms of the number of inputs the number of membership functions and their bit widths the proposed architecture is flexible in term of membership function shape as well

the response of glassy systems to random perturbations a bridge between equilibrium and off equilibrium we discuss the response of aging systems with short range interactions to a class of random perturbations although these systems are out of equilibrium the limit value of the free energy at long times is equal to the equilibrium free energy by exploiting this fact we define a new order parameter function and we relate it to the ratio between response and fluctuation which is in principle measurable in an aging experiment for a class of systems possessing stochastic stability we show that this new order parameter function is intimately related to the static order parameter function describing the distribution of overlaps between clustering states the same method is applied to investigate the geometrical organization of pure states we show that the ultrametric organization in the dynamics implies static ultrametricity and we relate these properties to static separability i e the property that the measure of the overlap between pure states is essentially unique our results especially relevant for spin glasses pave the way to an experimental determination of the order parameter function

bifurcations in fluctuating systems the center manifold approach bifurcations in fluctuating dynamical systems are studied using the ideas of center manifold reduction the method provides not only a systematic procedure for the reduction of the system to a small number of variables but also a classification scheme for the different kinds of dynamical behavior possible near bifurcation points the joint probability density factorizes into a stationary gaussian densityp v u in the fast variablesv and a time dependent densityp u f in the slow variablesu describing the dynamics on the center manifoldv v0 u p u t obeys a reduced fokker planck equation that can be written in a normal form by means of local nonlinear transformations both additive and multiplicative white noise are considered as is colored noise the results extend and formalize haken s concept of adiabatic elimination of fast variables

properties of the aggregation operators related with fuzzy relations abstract the problem of information generalization in multicriteria decision making is considered in this paper the information is unified by fuzzy relations and the generalization is realized with the help of aggregation operators some of the most oftenly used operators are presented and their properties depending on the properties of the fuzzy relations which they aggregate are proved the sensitivity of the operators with respect to variations in their arguments is investigated the numerical example deciding the problem of alternatives ranking is given as well

resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations we consider a general method for the macroscale modelling of nonlinear nonautomomous partial differential equations or difference equations our method is able to resolve the complex fluctuations which arise in nonliner nonautonomous systems these fluctuations are not accounted for by popular multiscale averaging procedures and homogenization our method is illustrated with the example of a forced burgers equation coarse grained macroscale spatial discretisations of nonlinear nonautonomous partial differential difference equations are given novel support by centre manifold theory dividing the physical domain into overlapping macroscale elements empowers the approach to resolve significant subgrid microscale structures and interactions between neighbouring elements the crucial aspect of this approach is that centre manifold theory organises the resolution of the detailed subgrid microscale structure interacting via the nonlinear dynamics within and between neighbouring elements the techniques and theory developed here may be applied to soundly discretise on a macroscale many dissipative nonautonomous partial differential difference equations such as the forced burgers equation adopted here as an illustrative example

temporal localization of limit cycles in a noise driven chemical oscillator abstract we study the influence of multiplicative random external perturbation on the selkov model exhibiting limit cycles the dynamics are described by stochastic differential equations the numerically computed ensemble averages of the concentrations exhibit temporal localization of the limit cycles for small amplitudes of the noise the localization time is smaller when the amplitude of the noise is higher to understand this behavior a stochastic complex ginzburg landau equation is derived using normal form transformations on the stochastic evolution equations in the case of weak noise the equations for the radial and the phase components of the amplitude separate and can be solved exactly the solution is used to compute the damping factors which were found to be gaussian we also show that asymptotically the radial part fluctuates near the average value and the phase is found to be a gaussian random variable with time dependent mean and variance and may be responsible for the temporal localization of the limit cycle

an interactive fuzzy programming system abstract an interactive system is introduced which supports a decision maker in solving programming models with crisp or fuzzy constraints and crisp or fuzzy goals one part of the system is the determination of membership functions representing goals to this purpose fuzzy extreme solutions are computed and are presented to the decision maker these and each of the proposed compromise solutions are fuzzy efficient

adiabatic elimination for systems of brownian particles with nonconstant damping coefficients we discuss the problem of eliminating the momentum variable in the phase space langevin equations for a system of brownian particles in two related situations i position dependent damping and ii existence of hydrodynamic interactions we discuss the problems associated with the conventional elimination and we develop an alternative elimination procedure in the lagevin framework which leads to the correct smoluchowski equation we give a heuristic argument on the basis of stochastic differential equations for the smoluchowski limit and establish rigorously the limit for the general case of position dependent friction and diffusion coefficents

the efficacy of fuzzy representations of uncertainty advocates of the theory of fuzzy sets as a system for representing uncertainty have based their case on five basic arguments these are 1 the reality hypothesis which holds that imprecision is an inherent property of the world external to an observer 2 the subjectivity hypothesis which holds that probability is an exclusively objective measure of uncertainty and that therefore subjective uncertainty can only be represented with fuzzy sets 3 the behaviorist hypothesis which claims that uncertainty systems should emulate rather than prescribe human behavior in the face of uncertainty 4 the probability as fiction hypothesis which claims that probability does not comprise a field of study in its own right and 5 the superset hypothesis which holds that fuzzy set theory includes probability as a special case and thus provides a richer uncertainty modeling environment we discuss and criticize all five we then criticize the argument that fuzziness represents a type of uncertainty distinct from probability and also the inordinate complexity of fuzzy methods we present a method for assessing the efficacy of fuzzy representations of uncertainty and apply this method in three examples

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

vagueness and bayesian probability this paper is a response to michael laviolette and john w seaman jr s ibid vol 2 no 1 p 4 1994 position paper the efficacy of fuzzy representations of uncertainty which criticizes fuzzy representations of uncertainty and suggests that bayesian probability can do better the commenter argues that the author s make some misleading comments about bayesian probability and he briefly discusses the problem of giving a satisfactory interpretation of membership functions

comparison of empirical and computed values of fuzzy conjunction abstract the necessity for further experiments such as in 4 for the foundation of fuzzy sets theory is shown generality of the experimental results on fuzzy conjunction in the paper by thole zimmermann and zisno 1979 4 for the other objects and language is verified for other conditions usually the minimum the product and the restricted sum operators are used as an intersection conjunction of fuzzy sets in fuzzy optimization f optimization on the basis of experiments it is shown that these operators are correct for f optimization their correctness is founded on the stability of the extremal point a decision in bellman zadeh s scheme under a positive linear mapping it is shown that these mappings exist between empirical conjunction and considered operators as a statistical result of linear regression analysis

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

spectrum of certain non self adjoint operators and solutions of langevin equations with complex drift as part of a program to evaluate expectations in complex distributions by longterm averages of solutions to langevin equations with complex dirft a simple one dimensional example is examined in some detail the validity and rate of convergence of this scheme depends on the spectrum of an associated non selfadjoint hamiltonian which is found numerically in the regime where the stochastic evaluation should be accurate numerical solution of the langevin equation shows this to be the case

noise induced global asymptotic stability we prove analytically that additive and parametric multiplicative gaussian distributed white noise interpreted in either the it6 or stratonovich formalism induces global asymptotic stability in two prototypical dynamical systems designated as supercritical the landau equation and subcritical respectively in both systems without noise variation of a parameter leads to a switching between a single globally stable steady state and multiple locally stable steady states with additive noise this switching is mirrored in the behavior of the extrema of probability densities at the same value of the parameter however parametric noise causes a noise amplitude dependent shift postponement in the parameter value at which the switching occurs it is shown analytically that the density converges to a dirac delta function when the solution of the fokker planck equation is no longer normalizable

linear response theory in stochastic many body systems revisited abstract the green kubo relation the einstein relation and the fluctuation response relation are representative universal relations among measurable quantities that are valid in the linear response regime we provide pedagogical proofs of these universal relations for stochastic many body systems through these simple proofs we characterize the three relations as follows the green kubo relation is a direct result of the local detailed balance condition the fluctuation response relation represents the dynamic extension of both the green kubo relation and the fluctuation relation in equilibrium statistical mechanics and the einstein relation can be understood by considering thermodynamics we also clarify the interrelationships among the universal relations

consistent spectral predictors for dynamic causal models of steady state responses dynamic causal modelling dcm for steady state responses ssr is a framework for inferring the mechanisms that underlie observed electrophysiological spectra using biologically plausible generative models of neuronal dynamics in this paper we examine the dynamic repertoires of nonlinear conductance based neural population models and propose a generative model of their power spectra our model comprises an ensemble of interconnected excitatory and inhibitory cells where synaptic currents are mediated by fast glutamatergic and gabaergic receptors and slower voltage gated nmda receptors we explore two formulations of how hidden neuronal states depolarisation and conductances interact through their mean and variance mean field model or through their mean alone neural mass model both rest on a nonlinear fokker planck description of population dynamics which can exhibit bifurcations phase transitions we first characterise these phase transitions numerically by varying critical model parameters we elicit both fixed points and quasiperiodic dynamics that reproduce the spectral characteristics 2 100 hz of real electrophysiological data we then introduce a predictor of spectral activity using centre manifold theory and linear stability analysis this predictor is based on sampling the system s jacobian over the orbits of hidden neuronal states this predictor behaves consistently and smoothly in the region of phase transitions which permits the use of gradient descent methods for model inversion we demonstrate this by inverting generative models dcms of ssrs using simulated data that entails phase transitions

noise induced stabilization of bumps in systems with long range spatial coupling the position of a localized region of active neurons a bump has been proposed to encode information for working memory the head direction system and feature selectivity in the visual system stationary bumps are ordinarily stable but including spike frequency adaptation in the neural dynamics causes a stationary bump to become unstable to a moving bump through a supercritical pitchfork bifurcation in bump speed adding spatiotemporal noise to the network supporting the bump can cause the average speed of the bump to decrease to almost zero reversing the effect of the adaptation and restabilizing the bump this restabilizing occurs for noise levels lower than those required to break up the bump the restabilizing can be understood by examining the effects of noise on the normal form of the pitchfork bifurcation where the variable involved in the bifurcation is bump speed this noisy normal form can be further simplified to a persistent random walk in which the probability of changing direction is related to the noise level through an arrhenius type rate the probability density function of position for the continuous time version of this random walk satisfies the telegrapher s equation and the closed form solution of this pde allows us to find expressions for the mean and variance of the average speed of the particle the bump undergoing the random walk this noise induced stabilization is a novel example in which moderate amounts of noise have a beneficial effect on a system specifically stabilizing a spatiotemporal pattern 2001 elsevier science b v all rights reserved

compensatory fuzzy multiple level decision making abstract fuzzy set theory has been shown to be an effective tool to overcome the computational difficulties encountered in solving large multiple level programming problems shih et al 1996 in this paper compensatory operators are introduced for adjusting the decision making process between the different levels and also between the decision makers of the same level after a brief consideration of the bi level and three level systems the large decentralized organizations with both equal and unequal goals are investigated various numerical examples are given to compare the influences of compensation and to illustrate the approaches

geometric framework for phase synchronization in coupled noisy nonlinear systems a geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise we show that the emergence of cooperative behavior through a change of stability via a hopf bifurcation entails the spontaneous appearance of a gauge structure in the system arising from the evolution of the slow dynamics but induced by the fast variables the conditions for the oscillators to be synchronised in phase are obtained the role of weak noise appears to be to drive the system towards a more synchronized behavior our analysis provides a framework to explain recent experimental observations on noise induced phase synchronization in coupled nonlinear systems

additive hybrid networks for fuzzy logic abstract evidence aggregation networks based on multiplicative fuzzy hybrid operators were introduced by krishnapuram and lee they have been used for image segmentation pattern recognition and general multicriteria decision making one of the drawbacks of these networks is that the training is complex and quite time consuming we have recently modified these aggregation networks to implement additive fuzzy hybrid connectives these new networks have similar excellent properties for decision making under uncertainty as do their multiplicative precursors and have the advantage that training is easier since the additive operators are not as complex in form in earlier work trainable neural networks have been used to perform inference in a fuzzy logic system fixed architecture networks of fuzzy operators and standard neural networks have been utilized the additive hybrid operators are extremely flexible and so are excellent candidates for nodes in a network structure for fuzzy logic inference the purpose of this paper is to demonstrate the capability of networks of additive hybrid nodes to learn appropriate functional relationships for fuzzy logic an added advantage of these networks is that they are transparent i e after training the individual nodes can be analyzed as a collection of mini rules

critical exponents of the three dimensional blume capel model on a cellular automaton abstract the static critical exponents of the three dimensional blume capel model which has a tricritical point at d j 2 82 value are estimated for the standard and the cooling algorithms which improved from creutz cellular automaton the analyses of the data using the finite size scaling and power law relations reproduce their well established values in the d j 3 and d j 2 8 parameter region at standard and cooling algorithms respectively for the cooling algorithm at d j 2 8 value of single ion anisotropy parameter the static critical exponents are estimated as 0 31 1 6 0 32 and 0 87 these values are different from 0 31 1 25 0 12 and 0 64 universal values this case indicated that the bc model exhibits an ununiversal critical behavior at the d j 2 8 parameter value near the tricritical point d j 2 82 the simulations were carried out on a simple cubic lattice with periodic boundary conditions

the effect of the increase of linear dimensions on exponents obtained by finite size scaling relations for the six dimensional ising model on the creutz cellular automaton the six dimensional ising model is simulated on the creutz cellular automaton using the finite size lattices with the linear dimension 4

dynamics of the stochastic duffing oscillator in gaussian approximation abstract the previously developed general concept of the gaussian approximation allows the description of the driven stochastic duffing oscillator by ordinary differential equations these equations are analyzed analytically as well as numerically to investigate the modification of simple bifurcations and of the feigenbaum cascade by stochastic forces furthermore the method allows a qualitative discussion of the stochastic system in the deterministic irregular region

multi criteria decision making in german automotive industry using fuzzy logic abstract in recent years fuzzy logic technologies have been widely applied to control applications in engineering where they are now considered an enabling technology for intelligent control systems fuzzy logic expedites the design of complex systems by allowing heuristic control strategies to be formulated by natural language rules rather than mathematical models hence the essence of fuzzy logic is its ability to put engineering expertise right into an algorithm the domain of such a technology is not limited to control engineering it can also be applied to incorporate complex decision making and the analysis of numerical data into non control systems this paper covers such an application realized at mercedes benz in germany for the optimization of the design process of truck components such as gear boxes the maturity of a current component development needs to be evaluated the objective is to reduce the amount of existing data of the development project to a single parameter describing the overall maturity of the design

thermodynamic formula for the cumulant generating function of time averaged current the cumulant generating function of time averaged current is studied from an operational viewpoint specifically for interacting brownian particles under nonequilibrium conditions we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added where the modified system is characterized by a variational principle the formula reminds us of einstein s fluctuation theory in equilibrium statistical mechanics furthermore since the formula leads to the fluctuation dissipation relation when the linear response regime is focused on it is regarded as an extension of the linear response theory to that valid beyond the linear response regime the formula is also related to previously known theories such as the donsker varadhan theory the additivity principle and the least dissipation principle but it is not derived from them examples of its application are presented for a driven brownian particle on a ring subject to a periodic potential

the estimation of a ktc p j p phase diagram for a two dimensional site diluted ising model using a microcanonical algorithm abstract the site diluted ising model has been investigated using an improved microcanonical algorithm from creutz cellular automaton for a microcanonical algorithm the basic problem is to estimate the correct temperatures using average values of the kinetic energy in the simulations of site diluted ising model in this study the average kinetic energy has been re described with an expression dependent on dilution x 1 p the values of the temperature have been calculated using the new expression and the critical temperatures have been estimated from the peaks of specific heat for each value of dilution x the obtained phase transition line k t c p j p is in good agreement with functional prediction for the site diluted ising model the simulations were carried out on a square lattice with periodic boundary conditions

comment on bifurcations in fluctuating systems we prove using normal form techniques in a codimension one bifurcation that the conditional probability of the fast variable conditioned by the slow variables is a gaussian distribution centered in the center manifold

self tuning to the hopf bifurcation in fluctuating systems the problem of self tuning a system to the hopf bifurcation in the presence of noise and periodic external forcing is discussed we find that the response of the system has a non monotonic dependence on the noise strength and displays an amplified response which is more pronounced for weaker signals the observed effect is to be distinguished from stochastic resonance for the feedback we have studied the unforced self tuned hopf oscillator in the presence of fluctuations exhibits sharp peaks in its spectrum the implications of our general results are briefly discussed in the context of sound detection by the inner ear

local methods for constructing stationary distribution functions of systems of stochastic differential langevin type equations noise influence on simple bifurcation the influence is considered of two additive correlated noise effects on a two dimensional quadratic nonlinear system describing the behavior of two hydrodynamic modes using the method of gaussian approximation local characteristics of the distribution function are calculated which are used to construct the global distribution function with the aid of the method of fraction rational approximations it is shown that for a system at whose bifurcation point the asymptotic stability is lost in an expanded space of parameters bifurcation parameter in the absence of noise plus noise parameters there appears an instability zone within which the stationary distribution function does not exist the effect of noise correlation on the stationary characteristics of the system is studied

the test of the finite size scaling relations for the six dimensional ising model on the creutz cellular automaton the six dimensional ising model is simulated on the creutz cellular automaton using the finite size lattices with the linear dimension 4 l 10 the exponents in the finite size scaling relations for the magnetic susceptibility and the order parameter at the infinite lattice critical temperature are computed to be 3 00 12 and 1 47 10 using 6 l 10 respectively which are in very good agreement with the theoretical predictions of and the critical temperature for the infinite lattice is found to be 10 835 5 using 4 l 10 which is also in very good agreement with the precise results the finite size scaling relation for the magnetic susceptibility at the infinite lattice critical temperature is also valid for the maxima of the magnetic susceptibilities of the finite size lattices the finite size scaling plots of the magnetic susceptibility and the order parameter verify the finite size scaling relations about the infinite lattice critical temperature

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

introduction to a new weighting method hierarchy consistency analysis abstract this paper proposes a new methodology hierarchy consistency analysis hca the approach to this methodology was developed owing to the fact that in the analysis of large scale problems a different viewpoint or specific points emphasis will result in different hierarchy structures on the basis of different structures being created the methodology is designed to combine these different structures and estimate their compromised criterion weights so that all different hierarchy structures will have the same aggregated index the hca methodology will thus provide us with a comprehensive framework for solving hierarchy evaluation problems its merits include amongst others providing a simpler method for calculating the weight of criteria providing a consistency index for monitoring dm judgment consistency and delivering more types of hierarchy structure schemata to aid the decision maker in understanding and auditing the performance status of systems

energy dissipation and violation of the fluctuation response relation for harmonic oscillators described by the generalized langevin equation the generalized langevin equation gle satisfied by harmonic oscillators coupled to a heat bath is transformed into an equality between the rate of energy dissipation and an extent of violation of the fluctuation response relation its significance is discussed when the system reaches a stationary state and a single harmonic oscillator s frequency is set to zero the equality reduces to a fluctuation dissipation relation which is slightly different from the usual kubo s formalism

fuzzy mcdm based on ideal and anti ideal concepts this paper presents a novel fuzzy multiple criteria decision making mcdm based on the concepts of ideal and anti ideal points the concepts of fuzzy set theory and hierarchical structure analysis are used to develop a weighted suitability decision matrix to evaluate the weighted suitability of different alternatives versus various criteria the distance of different alternatives versus positive ideal solution and negative ideal solution are then obtained by using the proposed ranking method finally the relative approximation values of various alternatives versus positive ideal solution are ranked to determine the best alternative

escape statistics for systems driven by dichotomous noise i general theory previous results on first passage time statistics for systems driven by dichotomous noise are extended in order to cover the escape from regions including fixed points of the stochastic flow for such regions a treatment splitting the escape through one or the other boundary is required the obtained escape probabilities and mean exit times are relevant for the complete characterization of stochastic systems undergoing bifurcations

decisions and evaluations by hierarchical aggregation of information usually in preparing a decision a hierarchy of criteria for evaluating alternatives can he agreed upon by the decision makers the problem addressed in this paper is the appropriate modelling of such evaluations and their aggregation in order to arrive at a proper overall evaluation function by which the decision alternatives can be ordered easily representing the criteria subjective categories by fuzzy sets it is possible to use aggregation operators as models for the amalgamation of those criteria in the framework of an empirical research project a hierarchy of criteria was developed for the evaluation of credit worthiness of customers 50 credit applications were evaluated by a number of credit managers of banks and their judgement could be appropriately modelled by a four level hierarchy of criteria

computation of correlation functions of the two dimensional ising model abstract the spin spin and energy energy correlation functions of the two dimensional ising model are computer on the creutz cellular automaton from the data for the spin spin correlation functions the values of the critical exponents and are obtained they are in agreement with their theoretical values

fluctuation dissipation relations for markov processes the fluctuation dissipation relation is calculated for stochastic models obeying a master equation with continuous time in the general case of a nonstationary process there appears to be no simple relation between the response and the correlation also if one considers stationary processes the linear response cannot be expressed via time derivatives of the correlation function alone in this case an additional function which has rarely been discussed previously is required this so called asymmetry depends on the two times also relevant for the response and the correlation and it vanishes under equilibrium conditions the asymmetry can be expressed in terms of the propagators and the transition rates of the master equation but it is not related to any physical observable in an obvious way it is found that the behavior of the asymmetry strongly depends on the nature of the dynamical variable considered in the calculation of the correlation and the response if one is concerned with a variable which randomizes with any transition among the states of the system the asymmetry vanishes in most cases this is in contrast to the situation for other classes of variables in particular for trap models of glassy relaxation the fluctuation dissipation ratio strongly depends on the observable and the asymmetry plays a dominant role in the determination of this ratio also if only neutral variables are considered some implications of a nonvanishing asymmetry with regard to the definition of an effective temperature are discussed

a spectrum of compromise aggregation operators for multi attribute decision making in many decision making problems a number of independent attributes or criteria are often used to individually rate an alternative from an agent s local perspective and then these individual ratings are combined to produce an overall assessment now in cases where these individual ratings are not in complete agreement the overall rating should be somewhere in between the extremes that have been suggested however there are many possibilities for the aggregated value given this this paper systematically explores the space of possible compromise operators for such multi attribute decision making problems specifically we axiomatically identify the complete spectrum of such operators in terms of the properties they should satisfy and show the main ones that are widely used namely averaging operators uninorms and nullnorms represent only three of the nine types we identify for each type we then go onto analyse their properties and discuss how specific instances can actually be developed finally to illustrate the richness of our framework we show how a wide range of operators are needed to model the various attitudes that a user may have for aggregation in a given scenario bidding in multi attribute auctions

on the low dimensional modelling of stratonovich stochastic differential equations abstract we develop further ideas on how to construct low dimensional models of stochastic dynamical systems the aim is to derive a consistent and accurate model from the originally high dimensional system this is done with the support of centre manifold theory and techniques aspects of several previous approaches are combined and extended adiabatic elimination has previously been used but centre manifold techniques simplify the noise by removing memory effects and with less algebraic effort than normal forms analysis of associated fokker plank equations replace nonlinearly generated noise processes by their long term equivalent white noise the ideas are developed by examining a simple dynamical system which serves as a prototype of more interesting physical situations