adiabatic small noise fluctuations around anticipated synchronization a perspective from scalar master slave dynamics abstract in this paper we extract and highlight some essential ingredients and properties that characterize the phenomenon of anticipated synchronization when external additive noise sources perturb the master and slave dynamics our results rely on a minimal scalar setup able to exhibit the more fundamental aspects of this phenomenon where the fluctuations around the average dynamics are worked out in a small noise and adiabatic approximations allowing to describe their dynamics through linear delay langevin equations in this context we find necessary conditions that guarantee anticipated synchronization in the mean value fluctuations around this condition are studied through the stationary correlation of the delayed difference between the master and slave dynamics it is shown that external noise properties can be inferred by measuring this object conditions for minimizing the dynamical fluctuations around the anticipated synchronization in mean value are found a detailed analysis of the dependence on the characteristic parameters is presented

fast multiresolution algorithms for solving linear equations a comparative study in g beylkin r coifman and v rokhlin comm pure appl math xliv 1991 pp 141 183 and b engquist s osher and s zhong siam j sci comput 15 1994 pp 755 775 orthonormal wavelet basis and the multiscale analysis they define are used as building blocks in the design of algorithms for the rapid numerical application of a number of linear operators to arbitrary vectors the algorithms may be viewed as a method for converting whenever possible dense matrices to sparse form we use the discrete multiresolution analysis described by harten in j appl numer math 12 1993 pp 153 193 as the building block in the algorithms and compare their performance with the wavelet based ones computationally both techniques give comparable results

min transitivity of fuzzy leftness relationship and its application to decision making abstract we show that the fuzzy leftness relationship left a b between two intervals a and b on a line which we had recently defined for modeling spatial relationships satisfies the min transitivity property the previous definitions of leftness given by krishnapuram et al and miyajima et al do not have this property the min transitivity property plays an important role in fuzzy decision making based on orlovsky s result we give several general schemes for constructing concrete min transitive relations based on our left a b for use in fuzzy decision making

brownian dynamics time averaging and colored noise we propose a method to obtain the equilibrium distribution for positions and velocities of a one dimensional particle via time averaging and laplace transformations we apply it to the case of a damped harmonic oscillator in contact with a thermal bath the present method allows us to treat among other cases a gaussian noise function exponentially correlated in time e g gaussian colored noise we obtain the exact equilibrium solution and study some of its properties

small delay approximation of stochastic delay differential equations delay differential equations evolve in an infinite dimensional phase space in this paper we consider the effect of external fluctuations noise on delay differential equations involving one variable thus leading to univariate stochastic delay differential equations sdde s for small delays a univariate nondelayed stochastic differential equation approximating such a sdde is presented another approximation complementary to the first is also obtained using an average of the sdde s drift term over the delayed dynamical variable which defines a conditional average drift this second approximation is characterized by the fact that the diffusion term is identical to that of the original sdde for small delays our approach yields a steady state probability density and a conditional average drift which are in close agreement with numerical simulations of the original sdde we illustrate this scheme with the delayed linear langevin equation and a stochastic version of the delayed logistic equation the technique can be used with any type of noise and is easily generalized to multiple delays s1063 651x 99 08304 x

group decision making with a fuzzy linguistic majority abstract the determination of solutions in group decision making is considered the point of departure is a collection of individual fuzzy preference relations a solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation as opposed to conventional approaches in which a crisp threshold type majority rule is used we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier e g most much more than 50 etc a calculus of linguistically quantified propositions is applied using the fuzzy majority various solution concepts are derived mainly of the type of core minimax opposition set and consensus winner

fast multiresolution algorithms for matrix vector multiplication in this paper the authors present a class of multiresolution algorithms for fast application of structured dense matrices to arbitrary vectors which includes the fast wavelet transform of beylkin coifman and rokhlin and the multilevel matrix multiplication of brandt and lubrecht in designing these algorithms the authors first apply data compression techniques to the matrix and then show how to compute the desired matrix vector multiplication from the compressed form of the matrix in describing this class special attention is paid to an algorithm that is based on discretization by cell averages as it seems to be suitable for discretization of integral transforms with integrably singular kernels

a study on the action of non gaussian noise on a brownian particle abstract we analytically address the non equilibrium problem of a brownian particle in contact with a thermal reservoir by means of a non gaussian langevin noise term t the presence of noise kurtosis is akin to a second temperature reservoir acting on the system and we exploit its consequences by means of studying a converging exact form for the stationary probability distribution

a fast chebyshev s method for quadratic equations a multiresolution transform corresponding to interpolatory technique is used for fast application of chebyshev s method in designing this algorithm we apply data compression to the linear and the bilinear forms that appear on the method a convergence theorem is performed finally some numerical results are presented

fuzzy sets and decision analysis abstract this survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill defined information fuzzy maut as well as fuzzy outranking methods are reviewed aggregation procedures choice problems and treatment of interactive attributes are covered trends in research and open problems are indicated

passage time statistics in exponential distributed time delay models noisy asymptotic dynamics the stochastic dynamics toward the final attractor in exponential distributed time delay non linear models is presented then the passage time statistic is studied analytically in the small noise approximation the problem is worked out by going to the associated two dimensional system the mean first passage time left langle t e right rangle from the unstable state for this non markovian type of system has been worked out using two different approaches firstly by a rigorous adiabatic markovian approximation in the small mean delay time epsilon lambda 1 secondly by introducing the stochastic path perturbation approach to get a non adiabatic theory for any lambda this first passage time distribution can be written in terms of the important parameters of the models we have compared both approaches and we have found excellent agreement between them in the adiabatic limit in addition using our non adiabatic approach we predict a crossover and a novel behavior for the relaxation scaling time as a function of the delay parameter which for lambda ll 1 goes as left langle t e right rangle sim 1 sqrt lambda

influence of strong noise on the decline and propagation of population in the delayed malthus verhulst model abstract the effects of strong noise on the decline and propagation processes of a population in the malthus verhulst model with time delay are investigated by a stochastic simulation time delays in two different processes are concurrent in ecosystems the simulation results indicate that the stability of the population is enhanced by the decreasing multiplicative noise intensity and the increasing delay time the replacement of old individuals with young ones is accelerated by an increasing multiplicative noise intensity an increasing additive noise intensity and a decreasing delay time an increasing multiplicative noise intensity will drive the population of species to fluctuate more largely

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

the generalized wiener process ii finite systems a class of langevin like equations non markovian processes are studied in the presence of non natural boundary conditions exact results for all cumulants and the corresponding kolmogorov hierarchy of distributions are given in terms of our functional approach we previously reported 1997 j phys a math gen 30 8427 the generalized wiener processes on finite domains are completely characterized for reflecting and periodic boundary conditions some examples are given to show the behaviour of the moments and the probability distributions for different noises the interplay between the boundary conditions and the structure of the noises is also pointed out

non markovian noise the properties of non markovian noises with exponentially correlated memory are discussed considered are dichotomic noise white shot noise gaussian white noise and gaussian colored noise the stationary correlation functions of the non markovian versions of these noises are given by linear combinations of two or three exponential functions colored noises or of the delta function and exponential function white noises the non markovian white noises are well defined only when the kernel of the non markovian master equation contains a nonzero admixture of a markovian term approximate equations governing the probability densities for processes driven by such non markovian noises are derived including non markovian versions of the fokker planck equation and the telegrapher s equation as an example it is shown how the non markovian nature changes the behavior of the driven linear process

managing non homogeneous information in group decision making within the frame of decision aid literature decision making problems with multiple sources of information have drawn the attention of researchers from a wide spectrum of disciplines in decision situations with multiple individuals each one has his own knowledge on the alternatives of the decision problem the use of information assessed in different domains is not a seldom situation this non homogeneous information can be represented as values belonging to domains with different nature as linguistic numerical and interval valued or can be values assessed in label sets with different granularity multi granular linguistic information decision processes for solving these problems are composed by two phases aggregation and exploitation the main problem to deal with non homogeneous contexts is how to aggregate the information assessed in these contexts in this paper taking as base the 2 tuple fuzzy linguistic representation model we shall develop an aggregation process for dealing with non homogeneous contexts in first place we shall develop an aggregation process for combining numerical interval valued and linguistic information afterwards we shall propose different extensions of this process to deal with contexts in which can appear other type of information as intuitionistic fuzzy sets or multi granular linguistic information

free inertial processes driven by gaussian noise probability distributions anomalous diffusion and fractal behavior we study the motion of an unbound particle under the influence of a random force modeled as gaussian colored noise with an arbitrary correlation function we derive exact equations for the joint and marginal probability density functions and find the associated solutions we analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories

nonequilibrium fluctuation dissipation relations for independent random rate processes with dynamical disorder a class of rate processes with dynamical disorder is investigated based on the two following assumptions a the system is composed of a random number of particles or quasiparticles which decay according to a first order kinetic law b the rate coefficient of the process is a random function of time with known stochastic properties the formalism of characteristic functionals is used for the direct computation of the dynamical averages the suggested approach is more general than the other approaches used in the literature it is not limited to a particular type of stochastic process and can be applied to any type of random evolution of the rate coefficient we derive an infinity of exact fluctuation dissipation relations which establish connections among the moments of the survival function and the moments of the number of surviving particles the analysis of these fluctuation dissipation relations leads to the unexpected result that in the thermodynamic limit the fluctuations of the number of partic

stochastic processes with finite correlation time modeling and application to the generalized langevin equation the kangaroo process kp is characterized by various forms of covariance and can serve as a useful model of random noises we discuss properties of that process for the exponential stretched exponential and algebraic power law covariances then we apply the kp as a model of noise in the generalized langevin equation and simulate solutions by a monte carlo method some results appear to be incompatible with requirements of the fluctuation dissipation theorem because probability distributions change when the process is inserted into the equation we demonstrate how one can construct a model of noise free of that difficulty this form of the kp is especially suitable for physical applications

fokker planck description for a linear delayed langevin equation with additive gaussian noise we construct an equivalent probability description of linear multi delay langevin equations subject to additive gaussian white noise by exploiting the time convolutionless transform and a time variable transformation we are able to write a fokker planck equation fpe for the 1 time and for the 2 time probability distributions valid irrespective of the regime of stability of the langevin equations we solve exactly the derived fpes and analyze the aging dynamics by studying analytically the conditional probability distribution we discuss explicitly why the initially conditioned distribution is not sufficient to describe fully out a non markov process as both preparation and observation times have bearing on its dynamics as our analytic procedure can also be applied to linear langevin equations with memory kernels we compare the non markov dynamics of a one delay system with that of a generalized langevin equation with an exponential as well as a power law memory application to a generalization of the green kubo formula is also presented

functional characterization of generalized langevin equations we present an exact functional formalism to deal with linear langevin equations with arbitrary memory kernels and driven by an arbitrary noise structure characterized through its characteristic functional no other hypothesis is assumed over the noise neither do we use the fluctuation dissipation theorem we find that the characteristic functional of the linear process can be expressed in terms of noise functional and the green function of the deterministic memory like dissipative dynamics this yields a procedure for calculating the full kolmogorov hierarchy of the non markov process as examples we have characterized through the 1 time probability a noise induced interplay between the dissipative dynamics and the structure of different noises conditions that lead to non gaussian statistics and distributions with long tails are analysed the introduction of arbitrary fluctuations in fractional langevin equations has also been pointed out

an adaptive version of a fourth order iterative method for quadratic equations a fourth order iterative method for quadratic equations is presented a semilocal convergence theorem is performed a multiresolution transform corresponding to interpolatory technique is used for fast application of the method in designing this algorithm we apply data compression to the linear and the bilinear forms that appear on the method finally some numerical results are studied

some basic remarks on eigenmode expansions of time delay dynamics abstract we describe in elementary terms how eigenmode expansions can be used to deal with differential difference equations as particular applications we present the full analytical solution of linear stochastic time delay systems and the weakly nonlinear analysis of nonlinear differential difference equations in the limit of large time delay our exposition is essentially based on an explicit analytical expression for the linear spectrum in terms of the lambert w function and on the explicit formula for the eigenfunctions of the adjoint equation

multivariate markov processes for stochastic systems with delays application to the stochastic gompertz model with delay using the method of steps we describe stochastic processes with delays in terms of markov diffusion processes thus multivariate langevin equations and fokker planck equations are derived for stochastic delay differential equations natural periodic and reflective boundary conditions are discussed both ito and stratonovich calculus are used in particular our fokker planck approach recovers the generalized delay fokker planck equation proposed by guillouzic et al the results obtained are applied to a model for population growth the gompertz model with delay and multiplicative white noise

on reducible nonlinear time delayed stochastic systems fluctuation dissipation relations transitions to bistability and secondary transitions to non stationarity we show the conditions under which nonlinear time delayed dynamical systems with multiplicative noise sources can be transformed into linear time delayed systems with additive noise sources we show that for such reducible systems analytical expressions for stationary distributions can be obtained we demonstrate that fluctuation dissipation relations of reducible systems become trivial and we show that reducible systems may exhibit delay and noise induced transitions to bistability and secondary transitions to non stationarity our general findings are exemplified for three models a gompertz model a hongler model and a model involving a 1 x 2 noise amplitude

characteristic functional approach to multiplicative fractal noise with application to environmental fluctuations in nonlinear chemical systems far from equilibrium a temporal analog of anderson localization abstract we compute the characteristic functional of a nonlinear transformation of a set of random variables the equation is applied to the study of fractal stochastic processes with multiplicative noise for illustration we investigate two types of chemical systems subjected to environmental fluctuations we analyze the interaction between the intrinsic chemical fluctuations and environmental noise and evaluate the stochastic properties of the system in the presence of multiplicative noise for an autocatalytic reaction subjected to external noise and with gaussian and generally non markovian multiplicative external noise the averaged joint probability density of concentrations displays long tails of the negative power law type which are independent of the detailed properties of the noise we also study the influence of multiplicative noise on a nonlinear chemical system with a stable limit cycle in the presence of multiplicative noise the limit cycle collapses and the average trajectory in the composition space becomes a spiral this effect is a temporal analog of anderson localization we evaluate the damping factors and localization times for different types of noise ranging from noise with infinite memory static disorder and noise with long memory dynamic disorder with fractal noise to markovian noise dynamic disorder with short memory

the generalized ornstein uhlenbeck process langevin like equations have been studied in the presence of arbitrary noise the characteristic functional of the generalized langevin process has been built up exact results for all cumulants are given particular stress has been put on the campbell dichotomous and radioactive decay noises transient relaxation susceptibility and diffusion constants for different noisy media have been sketched in order to exemplify the theory the generalized ornstein uhlenbeck and wiener processes have been completely characterized the generalized kubo oscillator has been worked out and all its 1 time moments have been calculated for different noise structures

exact dynamics of stochastic linear delayed systems application to spatiotemporal coordination of comoving agents delayed dynamics result from finite transmission speeds of a signal in the form of energy mass or information in stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic oscillatory and unstable evolution despite the vast literature quantifying this rich behavior is limited by a lack of explicit analytic studies of high dimensional stochastic delay systems here we fill this gap for systems governed by a linear langevin equation of any number of delays and spatial dimensions with additive gaussian noise by exploiting laplace transforms we are able to derive an exact time dependent analytic solution of the langevin equation by using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables as an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment we propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay we highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and or in their spatial separation we also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay

theoretical analysis of destabilization resonances in time delayed stochastic second order dynamical systems and some implications for human motor control a linear stochastic delay differential equation of second order is studied that can be regarded as a kramers model with time delay an analytical expression for the stationary probability density is derived in terms of a gaussian distribution in particular the variance as a function of the time delay is computed analytically for several parameter regimes strikingly in the parameter regime close to the parameter regime in which the deterministic system exhibits hopf bifurcations we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks these peaks are interpreted as delay induced destabilization resonances arising from oscillatory ghost instabilities on the basis of the obtained theoretical findings reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided 2006 the american physical society

fokker planck perspective on stochastic delay systems exact solutions and data analysis of biological systems stochastic delay systems with additive noise are examined from the perspective of fokker planck equations for a linear system the exact stationary probability density is derived by means of a delay fokker planck equation we show how to determine the delay equation of the linear system from experimental data and corroborate a fundamental result previously obtained by kuchler and mensch we also propose a method to derive delay equations of nonlinear systems from experimental data to this end the theory of multivariate fokker planck equations is used the applicability of this method is demonstrated for stochastic models describing tracking and pointing movements of humans

integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations abstract the purpose of this paper is to study a fuzzy multipurpose decision making problem where the information about the alternatives provided by the experts can be of a diverse nature the information can be represented by means of preference orderings utility functions and fuzzy preference relations and our objective is to establish a general model which cover all possible representations firstly we must make the information uniform using fuzzy preference relations as uniform preference context secondly we present some selection processes for multiple preference relations based on the concept of fuzzy majority fuzzy majority is represented by a fuzzy quantifier and applied in the aggregation by means of an owa operator whose weights are calculated by the fuzzy quantifier we use two quantifier guided choice degrees of alternatives a dominance degree used to quantify the dominance that one alternative has over all the others in a fuzzy majority sense and a non dominance degree that generalises orlovski s non dominated alternative concept the application of the two above choice degrees can be carried out according to two different selection processes a sequential selection process and a conjunction selection process

oscillatory correlation of delayed random walks we investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence delayed random walk the characteristic feature of such a model is the oscillatory behavior of its correlation function we investigate a model whose transient and stationary oscillatory behavior is analytically tractable the correspondence of the model with a langevin equation with delay is also considered

theory of second and higher order stochastic processes this paper presents a general approach to linear stochastic processes driven by various random noises mathematically such processes are described by linear stochastic differential equations of arbitrary order the simplest non trivial example is ddot x r t where r t is not a gaussian white noise the stochastic process is discretized into n time steps all possible realizations are summed up and the continuum limit is taken this procedure often yields closed form formulas for the joint probability distributions completely worked out examples include all gaussian random forces and a large class of markovian non gaussian forces this approach is also useful for deriving fokker planck equations for the probability distribution functions this is worked out for gaussian noises and for the markovian dichotomous noise

functional characterization of linear delay langevin equations we present an exact functional characterization of linear delay langevin equations driven by any noise structure defined through its characteristic functional this method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise general properties of the transient dissipative dynamics are analyzed the corresponding interplay with a color gaussian noise is presented as a full application of our functional method we study a model for population growth with non gaussian fluctuations the gompertz model driven by multiplicative white shot noise

multiresolution standard form of a matrix we present a new method to compress matrices based on interpolatory multiresolution the matrices so compressed allow all kinds of algebraic operations including matrix matrix multiplication we illustrate through examples the performance of the compressed matrices we call the form devised here standard in contrast to the nonstandard form introduced by harten and yad shalom in previous papers because they are the interpolatory multiresolution equivalent to the standard and nonstandard wavelet forms respectively

delayed stochastic systems noise and time delay are two elements that are associated with many natural systems and often they are sources of complex behaviors understanding of this complexity is yet to be explored particularly when both elements are present as a step to gain insight into such complexity for a system with both noise and delay we investigate such delayed stochastic systems both in dynamical and probabilistic perspectives a langevin equation with delay and a random walk model whose transition probability depends on a fixed time interval past delayed random walk model are the subjects of in depth focus as well as considering relations between these two types of models we derive an approximate fokker planck equation for delayed stochastic systems and compare its solution with numerical results

on fuzzy strict preference indifference and incomparability relations abstract the existence of fuzzy models for strict preference indifference and incomparability satisfying all classical properties is established a particular class of such models is completely described

generalized langevin equations anomalous diffusion and probability distributions we study the motion of a particle governed by a generalized langevin equation we show that when no fluctuation dissipation relation holds the long time behavior of the particle may be from stationary to superdiffusive along with subdiffusive and diffusive when the random force is gaussian we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions s1063 651x 96 10706 6

effects of time delay on transient behavior of a time delayed metastable system subjected to cross correlated noises abstract the effects of time delay on the transient properties of a time delayed metastable system subjected to cross correlated noises are studied by means of a stochastic simulation method it is found that i both additive noise and multiplicative noise can produce the noise enhanced stability nes effect ii the time delay induces critical behavior on the nes i e there is a critical value of the delay time c 1 2 2 above which the time delay increases the stability of the system enhanced by the additive noise and below which the nes effect induced by the additive noise disappears iii there exists another critical value of the delay time c 2 3 0 above which the time delay increases the stability of the system enhanced by the multiplicative noise and below which the time delay decreases it

delay fokker planck equations novikov s theorem and boltzmann distributions as small delay approximations we study time delayed stochastic systems that can be described by means of so called delay fokker planck equations using novikov s theorem we first show that the theory of delay fokker planck equations is on an equal footing with the theory of ordinary fokker planck equations subsequently we derive stationary distributions in the case of small time delays in the case of additive noise systems these distributions can be cast into the form of boltzmann distributions involving effective potential functions

stationary distributions of stochastic processes described by a linear neutral delay differential equation stationary distributions of processes are derived that involve a time delay and are defined by a linear stochastic neutral delay differential equation the distributions are gaussian distributions the variances of the gaussian distributions are either monotonically increasing or decreasing functions of the time delays the variances become infinite when fixed points of corresponding deterministic processes become unstable

delay and memory like langevin equations abstract by using an exact functional formalism we characterize general stationary properties of linear memory like langevin equations including the case of delay equations driven by arbitrary noises spectral properties and stationary distributions are analyzed in detail

stationary solutions of linear stochastic delay differential equations applications to biological systems recently k uchler and mensch stochastics stochastics rep 40 23 1992 derived exact stationary probability densities for linear stochastic delay differential equations this paper presents an alternative derivation of these solutions by means of the fokker planck approach introduced by guillouzic phys rev e 59 3970 1999 61 4906 2000 applications of this approach which is argued to have greater generality are discussed in the context of stochastic models for population growth and tracking movements

delay fokker planck equations perturbation theory and data analysis for nonlinear stochastic systems with time delays we study nonlinear stochastic systems with time delayed feedback using the concept of delay fokker planck equations introduced by guillouzic l heureux and longtin we derive an analytical expression for stationary distributions using first order perturbation theory we demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data in addition we show that the fokker planck perspective for stochastic systems with time delays is consistent with the so called extended phase space approach to time delayed systems