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

generic features of the fluctuation dissipation relation in coarsening systems the integrated response function in phase ordering systems with scalar vector conserved and nonconserved order parameter is studied at various space dimensionalities assuming scaling of the aging contribution ensuremath chi ag t t w t w ensuremath a ensuremath chi stackrel ifmmode hat else fi ensuremath chi t t w we obtain by numerical simulations and analytical arguments the phenomenological formula describing the dimensionality dependence of a ensuremath chi in all cases considered the primary result is that a ensuremath chi vanishes continuously as d approaches the lower critical dimensionality d l this implies that i the existence of a nontrivial fluctuation dissipation relation and ii the failure of the connection between statics and dynamics are generic features of phase ordering at d l

schur recursions error formulas and convergence of rational estimators for stationary stochastic sequences an exact and approximate realization theory for estimation and model filters of second order stationary stochastic sequences is presented the properties of j lossless matrices as a unifying framework are used necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a j lossless system are deduced an extension of the so called schur algorithm yields an approximate j lossless realization based on partial past information about the process the geometric properties of such partial realizations and their convergence are studied finally connections with the nevanlinna pick problem are made and how the techniques presented constitute a generalization of many aspects of the levinson szego theory of partial realizations is shown as a consequence generalized recursive formulas for reproducing kernels and christoffel darboux formulas are obtained in this paper the scalar case is considered the matrix case will be considered in a separate publication

large deviations condensation and giant response in a statistical system we study the probability distribution p of the sum of a large number of non identically distributed random variables n m condensation of fluctuations the phenomenon whereby one of such variables provides a macroscopic contribution to the global probability is discussed and interpreted by analogy with phase transitions in statistical mechanics a general expression for p is derived and its sensitivity to the details of the distribution of a single n m is worked out these general results are verified by the analytical and numerical solution of some specific examples

on a rational approximation problem in the real hardy space h 2 1 introduction the problem of finding a rational approximation to a holomorphic function in a domain 52 often arises in practice let us give an example from system theory which has first motivated our work l system theory is concerned with the study of physical systems that can be described by a relation between inputs and outputs when considering discrete time systems it is a convention to denote by u z cksko ukzmk uker

orthogonal rational functions with real coefficients and semiseparable matrices when one wants to use orthogonal rational functions orfs in system identification or control theory it is important to be able to avoid complex calculations in this paper we study orfs whose numerator and denominator polynomial have real coefficients these orfs with real coefficients rorfs appear when the poles and the interpolation points appear in complex conjugate pairs which is a natural condition further we deduce that there is a strong connection between rorfs and semiseparable matrices

slow relaxation in the large n model for phase ordering the basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large n model through the exact separation of the order parameter into the sum of thermal and condensation components the aging contribution in the response function x a g t t w is found to ohey a pattern of behavior under variation of dimensionality qualitatively similar to the one observed in ising systems there exists a critical dimensionality d 4 above which x a g t t w is proportional to the defect density d t while for d 4 it vanishes more slowly than d t and at d 2 does not vanish as in the ising case this behavior can be understood in terms of the dependence on dimensionality of the interplay between the defect density and the effective response associated to a single defect

componentwise decomposition of some lattice valued fuzzy integrals lattice valued fuzzy measures are lattice valued set functions which assign the bottom element of the lattice to the empty set the top element of the lattice to the entire universe and satisfy the property of monotonicity if the lattice is complete then a lattice valued fuzzy integral of sugeno type with similar properties such as the sugeno integral in its original form can be introduced in a natural way the main result of the paper is a componentwise decomposition theorem of an l valued fuzzy integral to its l valued fuzzy integrals components where l is a complete lattice with negation and l a b a email protected l a email protected is organized as a complete lattice too this result is useful to obtain the properties of l valued fuzzy integrals from the properties of l valued fuzzy integrals and to calculate in a simple way the values of some integrals from the values of the components the important case l 0 1 when l becomes the lattice of the intuitionistic fuzzy values is distinctly discussed an idea of application to synthetic evaluation of objects is also suggested

scaling in the aging dynamics of the site diluted ising model we study numerically the phase ordering kinetics of the two dimensional site diluted ising model the data can be interpreted in a framework motivated by renormalization group concepts apart from the usual fixed point of the nondiluted system there exist two disorder fixed points characterized by logarithmic and power law growth of the ordered domains this structure gives rise to a rich scaling behavior with an interesting crossover due to the competition between fixed points and violation of superuniversality

on approximation of stable linear dynamical systems using laguerre and kautz functions approximation of stable linear dynamical systems by means of so called laguerre and kautz functions which are the laplace transforms of a class of orthonormal exponentials is studied since the impulse response of a stable finite dimensional linear dynamical system can be represented by a sum of exponentials times polynomials it seems reasonable to use basis functions of the same type assuming that the transfer function of a system is bounded and analytic outside a given disc it is shown that laguerre basis functions are optimal in a mini max sense this result is extended to the two parameter kautz functions which can have complex poles while the poles of laguerre functions are restricted to the real axis by conformai mapping techniques the two parameter kautz approximation problem is recast as two laguerre approximation problems thus the well developed theory of laguerre functions can be applied to analyze kautz approximations unilateral shifts are used to further develop the connection between laguerre functions and kautz functions results on 2 and approximation using kautz models are given furthermore the weighted l2 kautz approximation problem is shown to be equivalent to solving a block toeplitz matrix equation

on sugeno integral as an aggregation function the sugeno integral for a given fuzzy measure is studied under the viewpoint of aggregation in particular we give some equivalent expressions of it we also give an axiomatic characterization of the class of all the sugeno integrals some particular subclasses such as the weighted maximum and minimum functions are investigated as well

on the identification of quasiprimary scaling operators in local scale invariance the relationship between physical observables defined in lattice models and the associated quasi primary scaling operators of the underlying field theory is revisited in the context of local scale invariance we argue that this relationship is only defined up to a time dependent amplitude and derive the corresponding generalizations of predictions for two time response and correlation functions applications to non equilibrium critical dynamics of several systems with a fully disordered initial state and vanishing initial magnetization including the glauber ising model the frederikson andersen model and the ising spin glass are discussed the critical contact process and the parity conserving non equilibrium kinetic ising model are also considered

entropy barriers and slow relaxation in some random walk models we study the zero temperature limit of a simple model of slow relaxation without energy barriers proposed by ritort 1995 as well as two other closely related models with a much faster relaxation these models can be mapped onto random walk problems which allows for their analytic study we analyse in particular a specific aspect of the former model namely the existence of a bias leading to entropy barriers and to a very slow relaxation

spin bond and global fluctuation dissipation relations in the non equilibrium spherical ferromagnet we study the out of equilibrium dynamics of the spherical ferromagnet after a quench to its critical temperature we calculate correlation and response functions for spin observables which probe length scales much larger than the lattice spacing but smaller than the system size and find that the asymptotic fluctuation dissipation ratio fdr x is the same as for local observables this is consistent with our earlier results for the ising model in dimension d 1 and d 2 we also check that bond observables both local and long range give the same asymptotic fdr in the second part of the paper the analysis is extended to global observables which probe correlations among all n spins here non gaussian fluctuations arising from the spherical constraint need to be accounted for and we develop a systematic expansion in to do this applying this to the global bond observable i e the energy we find that non gaussian corrections change its fdr to a nontrivial value which we calculate exactly for all dimensions d 2 finally we consider quenches from magnetized initial states here even the fdr for the global spin observable i e the magnetization is nontrivial it differs from the one for unmagnetized states even in d 4 signalling the appearance of a distinct dynamical universality class of magnetized critical coarsening for lower d the fdr is irrational even to first order in 4 d and d 2 the latter in contrast to recent results for the transverse fdr in the n vector model

orthogonal rational functions for system identification numerical aspects recently there has been a growing interest in the use of orthogonal rational functions orfs in system identification there are many advantages over more classical techniques probably due to a known explicit expression for the basis functions when the orthogonality weight is uniformly equal to 1 the so called malmquist basis the attention has been on the development of methods using this basis however for some discrete identification problems this choice of the orthogonality weight may still lead to serious numerical problems due to the ill conditioning of the linear system of equations to be solved in this note we give an algorithm based on a more general system of orf to overcome the numerical problem and which allows for a fast order update of the estimate

correlation functions and fluctuation dissipation relation in driven phase ordering systems an exactly solvable model the dynamics of a phase ordering system with non conserved order parameter under a plain shear flow with rate is solved analytically in the large n limit a phase transition is observed at a critical temperature tc after a quench from a high temperature equilibrium state to a lower temperature t a non equilibrium stationary state is entered when t tc while aging dynamics characterizes the phases with t tc two time quantities are computed and the off equilibrium generalization of the fluctuation dissipation theorem is provided

ageing in one dimensional coagulation diffusion processes and the fredrickson andersen model we analyse the ageing dynamics of the one dimensional fredrickson andersen fa model in the nonequilibrium regime following a low temperature quench relaxation then effectively proceeds via diffusion limited pair coagulation dlpc of mobility excitations by employing a familiar stochastic similarity transformation we map exact results from the free fermion case of diffusion limited pair annihilation to dlpc crucially we are able to adapt the mapping technique to averages involving multiple time quantities this relies on knowledge of the explicit form of the evolution operators involved exact results are obtained for two time correlation and response functions in the free fermion dlpc process the corresponding long time scaling forms apply to a wider class of dlpc processes including the fa model we are thus able to exactly characterize the violations of the fluctuation dissipation theorem fdt in the ageing regime of the fa model we find nontrivial scaling forms for the fluctuation dissipation ratio fdr x x tw t but with a negative asymptotic value x 3 6 16 3 307 while this prevents a thermodynamic interpretation in terms of an effective temperature it is a direct consequence of probing fdt with observables that couple to activated dynamics the existence of negative fdrs should therefore be a widespread feature in non mean field systems

nonlinear susceptibilities of spherical models the static and dynamic susceptibilities for a general class of mean field random orthogonal spherical spin glass models are studied we show how the static and dynamical properties of the linear and nonlinear susceptibilities depend on the behaviour of the density of states of the two body interaction matrix in the neighbourhood of the largest eigenvalue our results are compared with experimental results and also with those of the droplet theory of spin glasses

algorithms for model reduction of large dynamical systems three algorithms for the model reduction of large scale continuous time time invariant linear dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described they rely on low rank approximations to the controllability and observability gramians which can efficiently be computed by adi based iterative low rank methods the first two model reduction methods are closely related to the well known square root method and schur method which are balanced truncation techniques the third method is a heuristic balancing free technique the performance of the model reduction algorithms is studied in numerical experiments

an interpolation algorithm for orthogonal rational functions let a 1 2 be a sequence of numbers on the extended real line r r and a positive bounded borel measure with support in a subset of r we introduce rational functions n with poles 1 n that are orthogonal with respect to if all poles are at infinity we recover the polynomial situation it is well known that under certain conditions on the location of the poles the system n is regular such that the orthogonal functions satisfy a three term recurrence relation similar to the one for orthogonal polynomials to compute the recurrence coefficients one can use explicit formulas involving inner products we present a theoretical alternative to these explicit formulas that uses certain interpolation properties of the riesz herglotz nevanlinna transform of the measure error bounds are derived and some examples serve as illustration

h sub spl infin model reduction with application to flexible systems in this note h sub spl infin model reduction of continuous time linear systems is revisited the main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem the quality of the proposed suboptimal solution is assessed through comparisons performed via simulation with the already classical balanced truncation method leading to the conclusion that the proposed method performs significantly better finally the proposed method is applied to the determination of a reduced order model of a flexible bar

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

kovacs effect and fluctuation dissipation relations in 1d kinetically constrained models strong and fragile glass relaxation behaviours are obtained simply changing the constraints of the kinetically constrained ising chain from symmetric to purely asymmetric we study the out of equilibrium dynamics of these two models focusing on the kovacs effect and the fluctuation dissipation fd relations the kovacs or memory effect commonly observed in structural glasses is present for both constraints but enhanced with the asymmetric ones most surprisingly the related fd relations satisfy the fd theorem in both cases this result strongly differs from the simple quenching procedure where the asymmetric model presents strong deviations from the fd theorem

edwards measure and the steady state regime of a model with kinetic constraints under tapping we study the tapping dynamics of a one dimensional ising model with symmetric kinetic constraints we define and test a variant of the edwards hypothesis that one may build a thermodynamics for the steady state by using a flat measure over the metastable states with several macroscopic quantities fixed various types of tapping are compared and the accuracy of this measure becomes quickly excellent when the number of quantities fixed on average increases independent of the way the system is excited we attribute the validity of the naive flat measure at weak tapping to the spatial separation of density defects

crossover in growth law and violation of superuniversality in the random field ising model we study the nonconserved phase ordering dynamics of the d 2 3 random field ising model quenched to below the critical temperature motivated by the puzzling results of previous work in two and three dimensions reporting a crossover from power law to logarithmic growth together with superuniversal behavior of the correlation function we have undertaken a careful investigation of both the domain growth law and the autocorrelation function our main results are as follows we confirm the crossover to asymptotic logarithmic behavior in the growth law but at variance with previous findings we find the exponent in the preasymptotic power law to be disorder dependent rather than being that of the pure system furthermore we find that the autocorrelation function does not display superuniversal behavior this restores consistency with previous results for the d 1 system and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random bond ising model

model reduction of discrete time systems through linear matrix inequalities in this paper model reduction of discrete time linear systems is revisited the main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem the quality of the proposed suboptimal solution is assessed through comparisons performed via simulation with the already classical balanced truncation method the results lead to the conclusion that the proposed method performs equivalently when the h 2 norm of the reduction error is considered and significantly better when the h norm is considered instead

model order reduction of mimo bilinear systems by multi order arnoldi method abstract in this paper we present a time domain model order reduction method for multi input multi output mimo bilinear systems by general orthogonal polynomials the proposed method is based on a multi order arnoldi algorithm applied to construct the projection matrix the resulting reduced model can match a desired number of expansion coefficient terms of the original system the approximate error estimate of the reduced model is given and we also briefly discuss the stability preservation of the reduced model in some cases additionally in combination with krylov subspace methods we propose a two sided projection method to generate reduced models which capture properties of the original system in the time and frequency domain simultaneously the effectiveness of the proposed methods is demonstrated by two numerical examples

an algorithmic method for the simplification of linear dynamic scalar systems a comprehensive method is proposed for obtaining reduced order models of a scalar linear time invariant system described by the transfer function g s the method is a viable alternative to the pade approximation technique for model order reduction it approximates the differential operations d i g s dsi proportional to the time moments by the divided difference equivalents and finally leads to linear equations in the unknown coefficients of the reduced model r s it is shown that a parameter governs the stability and the low frequency matching quality of the model heuristic criteria are given for selecting a proper the method is illustrated by some examples from the literature

simple strong glass forming models mean field solution with activation we introduce simple models inspired by previous models for froths and covalent glasses with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems these models are also a generalization of backgammon or urn models to a non constant number of particles where entropic barriers are replaced by energy barriers allowing for the existence of activated processes we formulate a mean field version of the models which keeps most of the features of the finite dimensional ones and solve analytically the out of equilibrium dynamics in the low temperature regime where activation plays an essential role

universality in the off equilibrium critical dynamics of the three dimensional diluted ising model we study the off equilibrium critical dynamics of the three dimensional diluted ising model we compute the dynamical critical exponent z and we show that it is independent of the dilution only when we take into account the scaling corrections to the dynamics finally we will compare our results with the experimental data

response of non equilibrium systems with long range initial correlations the long time dynamics of the d dimensional spherical model with a non conserved order parameter and quenched from an initial state with long range correlations is studied through the exact calculation of the two time autocorrelation and autoresponse functions in the ageing regime these are given in terms of non trivial universal scaling functions of both time variables at criticality five distinct types of ageing are found depending on the form of the initial correlations while at low temperatures only a single type of ageing exists the autocorrelation and autoresponse exponents are shown to be generically different and to depend on the initial conditions the scaling form of the two time response functions agrees with a recent prediction coming from conformal invariance

dynamic siso and miso system approximations based on optimal laguerre models a general procedure based on the knowledge of the input and the output signals is proposed to approximate the prescribed linear time invariant lti systems by means of optimal laguerre models the main contribution of this paper is to apply the newton raphson s iterative technique to compute the so called optimal laguerre pole in a continuous time case or optimal time scale factor in a discrete time case and especially to show that the gradient and the hessian can be expressed analytically moreover the excitations used are not limited to the ones that ensure the orthogonality of the outputs of laguerre filters i e dirac delta or white noise as is usually done in existing methods however persistently exciting input signal s are used the proposed procedure will be directly formulated for siso systems siso systems being a special case with the number of inputs equal to one the proposed algorithm has direct applications in system identification model reduction and noisy modeling

the fluctuation dissipation relation in phase ordering kinetics abstract the properties of the response function and the fluctuation dissipation relation in phase ordering systems are discussed these issues are shown to be highly nontrivial even in the relatively simple case of coarsening dynamics considered here it is discussed how the connection between statics and dynamics fails in particular cases and the origin of this phenomenon is considered

a hybrid genetic algorithm for estimating the optimal time scale of linear systems approximations using laguerre models we deal with the problem of finding the optimal time scale of the truncated laguerre series using numerical search techniques we develop a hybrid genetic algorithm ga to search the nonlinear multimodal squared error function that results from least squares approximations of the impulse response of causal linear time invariant stable systems the hybrid ga incorporates a newton raphson nr local optimizer for fast convergence to the global minimum point the proposed method competes favorably with the pure ga in solution accuracy the number of function evaluations being the same and with an established gradient directed optimization algorithm in number of function evaluations the solution accuracy being the same

lattice valued fuzzy measure and lattice valued fuzzy integral abstract in this paper 1 the concepts of lattice valued fuzzy measure with no valuation property and lower resp upper lattice valued fuzzy integral are proposed which give the unified discription to the fuzzy measures and fuzzy integrals studied by delgado and moral qiao ralescu adams sugeno wang and zhang 2 some asymptotic structural characteristics of lattice valued fuzzy measures are introduced and some relations between them are given 3 some concepts of convergences for lattice valued functions are defined and riesz theorem egoroff s theorems and lebesgue s theorem for lattice valued measurable function are proved 4 the monotone increasing resp decreasing convergence theorem and almost resp pseudo almost everywhere convergence theorrem for lower resp upper lattice valued fuzzy integral are shown under some weak conditions

a far from equilibrium fluctuation dissipation relation for an ising glauber like model we derive an exact expression of the response function to an infinitesimal magnetic field for an ising glauber like model with arbitrary exchange couplings the result is expressed in terms of thermodynamic averages and does not depend on the initial conditions or on the dimension of the space the response function is related to time derivatives of a complicated correlation function and so the expression is a generalization of the equilibrium fluctuation dissipation theorem in the special case of this model correspondence with the ising glauber model is discussed a discrete time version of the relation is implemented in monte carlo simulations and then used to study the ageing regime of the ferromagnetic two dimensional ising glauber model quenched from the paramagnetic phase to the ferromagnetic one our approach has the originality to give direct access to the response function and the fluctuation dissipation ratio

general solutions for multispin two time correlation and response functions in the glauber ising chain the kinetic glauber ising spin chain is one of the very few exactly solvable models of non equilibrium statistical mechanics nevertheless existing solutions do not yield tractable expressions for two time correlation and response functions of observables involving products of more than one or two spins we use a new approach to solve explicitly the full hierarchy of differential equations for the correlation and response functions from this general solution follow closed expressions for arbitrary multispin two time correlation and response functions for the case where the system is quenched from equilibrium at ti 0 to some arbitrary t 0 by way of application we give the results for two and four spin two time correlation and response functions from the standard mapping these also imply new exact results for two time particle correlation and response functions in one dimensional diffusion limited annihilation

2d partial unwinding a novel non linear phase decomposition of images this paper aims at proposing a novel 2d non linear phase decomposition of images which performs the image processing tasks better than the traditional fourier transformation linear phase decomposition but further it has additional mathematical properties allowing more effective image analysis including adaptive decomposition components and positive instantaneous phase derivatives 1d unwinding blaschke decomposition has recently been proposed and studied through factorization it expresses arbitrary 1d signal into an infinite linear combination of blaschke products it offers fast converging positive frequency decomposition in the form of rational approximation however in the multi dimensional cases the usual factorization mechanism does not work as a consequence there is no genuine unwinding decomposition for multi dimensions in this paper a 2d partial unwinding decomposition based on algebraic transforms reducing multi dimensions to the 1d case is proposed and analyzed the result shows that the fast convergence offers efficient image reconstruction the tensor type decomposing terms are mutually orthogonal giving rise to 2d positive frequency decomposition the comparison results show that the proposed method outperforms the standard greedy algorithm and the most commonly used methods in the fourier category an application in watermarking is presented to demonstrate its potential in applications

correlation and response in the backgammon model the ehrenfest legacy we pursue our investigation of the non equilibrium dynamics of the backgammon model a dynamical urn model which exhibits aging and glassy behaviour at low temperature we present an analytical study of the scaling behaviour of the local correlation and response functions of the density fluctuations of the model and of the associated fluctuation dissipation ratios throughout the regime of low temperature and long times this analysis includes the aging regime the convergence to equilibrium and the crossover behaviour between them

a unified approach to define fuzzy integrals recently the two most general and well known fuzzy integrals sugeno s integral and choquet s integral were characterized it was also shown how both integrals fitted the same formal model and they only differed in the operators used in this paper we try to analyze whether it is possible to improve those characterization theorems and we also study the possibility of defining other fuzzy integrals following the same model but using other operators in a recent paper campos and bolafios 6 characterized two general and well known fuzzy integrals sugeno s integral 11 and choquet s integral 7 the last one also called monotone expectation 2 4 5 6 the two characterization theorems are based on the same formal model of four properties which only differ in the operators used sum and product for choquet s integral maximum and minimum for sugeno s integral two important questions remained open one involved the characterization theorems of these integrals in an attempt to further refine them the second question was to investigate the possibility of defining other fuzzy integrals using different operators but following the same model in this paper we give answers to those problems section 2 is devoted to describing fuzzy integrals defined on sugeno s fuzzy measures particularly sugeno s and choquet s integrals and their characterizations in section 3 we show how the characterization of choquet s integral can be refined whereas the same cannot be made for sugeno s integral finally other fuzzy integrals fitting our formal model are obtained in section 4

a consequence of local equilibration and heterogeneity in glassy materials the existence of a generalized fluctuation dissipation theorem observed in simulations and experiments performed in various glassy materials is related to the concepts of local equilibration and heterogeneity in space assuming the existence of a dynamic coherence length scale up to which the system is locally equilibrated we extend previous generalizations of the fdt relating static to dynamic quantities to the physically relevant domain where asymptotic limits of large times and sizes are not reached the formulation relies on a simple scaling argument and thus does not have the character of a theorem extensive numerical simulations support this proposition our results quite generally apply to systems with slow dynamics independently of the space dimensionality the chosen dynamics or the presence of disorder

testing mode coupling theory for a supercooled binary lennard jones mixture i the van hove correlation function we report the results of a large scale computer simulation of a binary supercooled lennard jones liquid we find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time td t where d t is the diffusion constant the time range for which these curves follow the master curve is identified with the ensuremath alpha relaxation regime of mode coupling theory mct this master curve is fitted well by a functional form suggested by mct in accordance with idealized mct d t shows a power law behavior at low temperatures the critical temperature of this power law is the same for both types of particles and also the critical exponents are very similar however contrary to a prediction of mct these exponents are not equal to the ones determined previously for the divergence of the relaxation times of the intermediate scattering function phys rev lett 73 1376 1994 at low temperatures the van hove correlation function self as well as distinct part shows almost no sign of relaxation in a time interval that extends over about three decades in time this time interval can be interpreted as the ensuremath beta relaxation regime of mct from the investigation of these correlation functions we conclude the hopping processes are not important on the time scale of the ensuremath beta relaxation for this system and for the temperature range investigated we test whether the factorization property predicted by mct holds and find that this is indeed the case for all correlation functions investigated the distance dependences of the critical amplitudes are in qualitative agreement with the ones predicted by mct for some other mixtures the non gaussian parameter for the self part of the van hove correlation function for different temperatures follows a master curve when plotted against time t

on backward shift algorithm for estimating poles of systems abstract in this paper we present an algorithm for estimating poles of linear time invariant systems by using the backward shift operator we prove that poles of rational functions including zeros and multiplicities are solutions to an algebraic equation which can be obtained by taking backward shift operator to the shifted cauchy kernels in the unit disc case the algorithm is accordingly developed for frequency domain identification we also prove the robustness of this algorithm some illustrative examples are presented to show the efficiency in systems with distinguished and multiple poles

monte carlo simulations of the violation of the fluctuation dissipation theorem in domain growth processes numerical simulations of various domain growth systems are reported in order to compute the parameter describing the violation of fluctuation dissipation theorem fdt in aging phenomena we compute two time correlation and response functions and find that as expected from the exact solution of a certain mean field model equivalent to the o n model in three dimensions in the limit of n going to infinity this parameter is equal to one no violation of fdt in the quasiequilibrium regime short separation of times and zero in the aging regime

an iterative svd krylov based method for model reduction of large scale dynamical systems abstract in this paper we propose a model reduction algorithm for approximation of large scale linear time invariant dynamical systems the method is a two sided projection combining features of the singular value decomposition svd based and the krylov based model reduction techniques while the svd side of the projection depends on the observability gramian the krylov side is obtained via iterative rational krylov steps the reduced model is asymptotically stable matches certain moments and solves a restricted h 2 minimization problem we present modifications to the proposed approach for employing low rank gramians in the reduction step and also for reducing discrete time systems several numerical examples from various disciplines verify the effectiveness of the proposed approach it performs significantly better than the q cover a yousouff r e skelton covariance equivalent realizations with applications to model reduction of large scale systems in c t leondes ed control and dynamic systems vol 22 academic press 1985 pp 273 348 a yousouff d a wagie r e skelton linear system approximation via covariance equivalent realizations journal of math anal and appl 196 1985 91 115 and the least squares s gugercin a c antoulas model reduction of large scale systems by least squares linear algebra appl 415 2 3 2006 290 321 methods that have a similar projection structure to the proposed method also in terms of both the h 2 and h error measures its performance is comparable to or sometimes better than that of balanced truncation moreover the method proves to be robust with respect to the perturbations due to usage of approximate gramians

optimality conditions for truncated kautz networks with two periodically repeating complex conjugate poles presents optimality conditions for the approximation of a siso system by a truncated kautz network with two repeating complex conjugate poles both the continuous and the discrete time cases are discussed the author approaches the problem in a system approximation framework and he does not assume that the input signal is white or an impulse the results obtained generalize the results already known for truncated laguerre networks

scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics in this paper we investigate the relation between the scaling properties of the linear response function r t s of the thermoremanent magnetization trm and of the zero field cooled zfc magnetization in the context of phase ordering kinetics we explain why the retrieval of the scaling properties of r t s from those of trm and zfc magnetization is not trivial preasymptotic contributions generate a long crossover in trm while zfc magnetization is affected by a dangerous irrelevant variable lack of understanding of both these points has generated some confusion in the literature the full picture relating the exponents of all the quantities involved is explicitly illustrated in the framework of the large n model following this scheme an assessment of the present status of numerical simulations for the ising model can be made we reach the conclusion that on the basis of the data available up to now statements on the scaling properties of r t s can be made from zfc magnetization but not from trm from zfc data for the ising model with d 2 3 4 we confirm the previously found linear dependence on dimensionality of the exponent a entering r t s ensuremath sim s ensuremath 1 a f t s we also find evidence that a recently derived form of the scaling function f x using local scale invariance arguments m henkel m pleimling c godr eche and j m luck phys rev lett 87 265701 2001 does not hold for the ising model

system identification by discrete rational atoms a novel adaptive frequency domain system identification method for linear time invariant systems is proposed in this paper it finds poles for discrete rational atoms with discrete frequency responses the theoretical foundation including adaptive decomposition principle and decomposition convergence rate is established the algorithm of the adaptive pursuit is also provided in this paper

improved routh pade spl acute approximants a computer aided approach a geometric programming based computer aided method to derive a reduced order rth order approximant for a given stable siso linear continuous time system is presented in this method stability and the first r time moments markov parameters are preserved as well as the errors between a set of subsequent time moments markov parameters of the system and those of the model are minimized

on the metastable autocorrelation and susceptibility of markovian systems abstract we show numerically that the metastable autocorrelation of the magnetization in a bidimensional ising model with glauber dynamics follows a power law in particular we show that it has the form of a q exponential for a wide set of parameters this shows that the result is very robust from this result we obtain the form of the metastable susceptibility in terms of transcendental functions

off equilibrium generalization of the fluctuation dissipation theorem for ising spins and measurement of the linear response function we derive for ising spins an off equilibrium generalization of the fluctuation dissipation theorem which is formally identical to the one previously obtained for soft spins with langevin dynamics l f cugliandolo j kurchan and g parisi j phys i 4 1641 1994 the result is quite general and holds both for dynamics with conserved and nonconserved order parameters on the basis of this fluctuation dissipation relation we construct an efficient numerical algorithm for the computation of the linear response function without imposing the perturbing field which is alternative to those of chatelain j phys a 36 10 739 2003 and ricci tersenghi phys rev e 68 065104 r 2003 as applications of the new algorithm we present very accurate data for the linear response function of the ising chain with conserved and nonconserved order parameter dynamics finding that in both cases the structure is the same with a very simple physical interpretation we also compute the integrated response function of the two dimensional ising model confirming that it obeys scaling ensuremath chi t t w ensuremath simeq t w ensuremath a f t t w with a 0 26 ifmmode pm else textpm fi 0 01 as previously found with a different method

on worst case approximation of feasible system sets via orthonormal basis functions this note deals with the approximation of sets of linear time invariant systems via orthonormal basis functions this problem is relevant to conditional set membership identification where a set of feasible systems is available from observed data and a reduced complexity model must be estimated the basis of the model class is made of impulse responses of linear filters the objective of the note is to select the basis function poles according to a worst case optimality criterion suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors

sugeno integral in a finite boolean algebra the aim of this paper is to provide a representation theorem of the sugeno integral when the evaluation scale is a finite boolean algebra this result is a generalisation of a result proved when the evaluation scale is totally ordered a major difficulty is the renunciation of the comonotonic functions which have to be replaced by the co included functions so we need to care about the properties satisfied by the sugeno integral when the evaluation scale is a finite totally ordered set to begin we show that when the scale is totally ordered the co included functions are solely needed to characterise the sugeno integral and that they are less constraining than the comonotonic functions classically used next we focus on finite boolean algebra and in this new context we define the sugeno integral and we present the properties still satisfied to end this article we present a representation theorem of the sugeno integral on a finite boolean algebra

a fast adaptive model reduction method based on takenaka malmquist systems abstract an adaptive model reduction method is proposed for linear time invariant systems based on the continuous time rational orthogonal basis takenaka malmquist basis the method is to find an adaptive approximation in the energy sense by selecting optimal points for the rational orthogonal basis the stability of the reduced models holds and the steady state values of step responses are kept to be equal furthermore the method automatically ensures the reduced system to be in the hardy space h 2 the existence of the best approximation in the hardy space h 2 by n blaschke forms is proved in the proposed approach the effectivity of this method is illustrated through three well known examples

large time nonequilibrium dynamics of a particle in a random potential we study the off equilibrium dynamics of a particle in a general n dimensional random potential when n to infty we demonstrate the existence of two asymptotic time regimes it i stationary dynamics it ii slow aging dynamics with violation of equilibrium theorems we derive the equations obeyed by the slowly varying part of the two times correlation and response functions and obtain an analytical solution of these equations for short range correlated potentials we find that it i the scaling function is non analytic at similar times and this behaviour crosses over to ultrametricity when the correlations become long range it ii aging dynamics persists in the limit of zero confining mass with universal features for widely separated times we compare with the numerical solution to the dynamical equations and generalize the dynamical equations to finite n by extending the variational method to the dynamics

nonlinear response and fluctuation dissipation relations a unified derivation of the off equilibrium fluctuation dissipation relations fdrs is given for ising and continuous spins to arbitrary order within the framework of markovian stochastic dynamics knowledge of the fdrs allows one to develop zero field algorithms for the efficient numerical computation of the response functions two applications are presented in the first one the problem of probing for the existence of a growing cooperative length scale is considered in those cases like in glassy systems where the linear fdr is of no use the effectiveness of an appropriate second order fdr is illustrated in the test case of the edwards anderson spin glass in one and two dimensions in the second application the important problem of the definition of an off equilibrium effective temperature through the nonlinear fdr is considered it is shown that in the case of coarsening systems the effective temperature derived from the second order fdr is consistent with the one obtained from the linear fdr

chaotic behavior of an extended system abstract some general aspects of spatiotemporal chaos are considered with emphasis on long range correlations and response an attempt is made to characterize the statistical steady state of a chaotic system by analogy with the description of a system near thermal equilibrium the one dimensional kuramoto sivashinsky equation is considered as an example and our present understanding of its statistical behavior is reviewed

comment on scaling of the linear response in simple aging systems without disorder we have repeated the simulations of henkel paessens and pleimling hpp phys rev e 69 056109 2004 for the field cooled susceptibility ensuremath chi mathit fc t ensuremath ensuremath chi 0 ensuremath sim t ensuremath a in the quench of ferromagnetic systems to and below t c we show that contrary to the statement made by hpp the exponent a coincides with the exponent a of the linear response function r t s ensuremath sim s ensuremath 1 a f r t s we point out what are the assumptions in the argument of hpp that lead them to the conclusion ala

kinetics of the long range spherical model the kinetic spherical model with long range interactions is studied after a quench to t tc or to t tc for the two time response and correlation functions of the order parameter as well as for composite fields such as the energy density the ageing exponents and the corresponding scaling functions are derived the results are compared to the predictions which follow from local scale invariance

off equilibrium response function in coarsening systems abstract in the late stage dynamics of systems evolving via domain coarsening the linear response function splits into the sum of a stationary term due to thermal fluctuations within domains and of an aging term due to off equilibrium interface dynamics the latter contribution is analyzed in the pure ising model under variation of space dimensionality and in the random field ising model in one dimension the variety of behaviors observed can be accounted for in terms of the effective response associated to a single interface implications for the connection between static and dynamic properties are discussed

ageing phenomena without detailed balance the contact process the long time dynamics of the 1d contact process suddenly brought out of an uncorrelated initial state is studied through a light cone transfer matrix renormalization group approach at criticality the system undergoes ageing which is characterized through the dynamical scaling of the two times autocorrelation and autoresponse functions the observed non equality of the ageing exponents a and b excludes the possibility of a finite fluctuation dissipation ratio in the ageing regime the scaling form of the critical autoresponse function is in agreement with the prediction of local scale invariance

identification and rational l 2 approximation a gradient algorithm this paper deals with the identification of linear constant dynamical systems when formalized as a rational approximation problem the criterion is the l2 norm of the transfer function which is of interest in a stochastic context the problem can be expressed as nonlinear optimization in a hilbert space but standard algorithms are usually not well adapted we present a generic recursive procedure to find a local optimum of the criterion in the case of scalar systems our methods are borrowed from differential theory mixed with a bit of classical complex analysis to our knowledge the algorithm described in this paper is the first that ensures convergence to a local minimum

fluctuation dissipation ratio in the one dimensional kinetic ising model the exact relation between the response function r t t and the two time correlation function c t t is derived analytically in the one dimensional kinetic ising model subjected to a temperature quench the fluctuation dissipation ratio x t t is found to depend on time through c t t in the time region where scaling c t t f t t holds the crossover from the nontrivial form x c t t to x t t identical with1 takes place as the waiting time t w is increased from below to above the equilibration time t eq

off equilibrium response function in the one dimensional random field ising model a thorough numerical investigation of the slow dynamics in the d 1 random field ising model in the limit of an infinite ferromagnetic coupling is presented in this paper crossovers from the preasymptotic pure regime tothe asymptotic sinai regime are investigated for the average domain size the autocorrelation function and staggered magnetization by switching on an additional small random field at the time t w the linear off equilibrium response function is obtained which displays as well the crossover from the nontrivial behavior of the d 1 pure ising model to the asymptotic behavior where it vanishes identically

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

tapping thermodynamics of the one dimensional ising model we analyse the steady state regime of a one dimensional ising model under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media the idea that the steady state regime may be described by a flat measure over metastable states of fixed energy is tested by comparing various steady state time averaged quantities in extensive numerical simulations with the corresponding ensemble averages computed analytically with this flat measure the agreement between the two averages is excellent in all the cases examined showing that a static approach is capable of predicting certain measurable properties of the steady state regime

ageing properties of critical systems in the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest ageing phenomena are observed during this everlasting non equilibrium evolution a simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high temperature phase to the critical point the aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case particular emphasis is put on the field theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities fluctuation dissipation relations are discussed and in particular the concept of fluctuation dissipation ratio fdr is reviewed emphasizing its connection with the definition of a possible effective temperature the renormalization group approach to critical dynamics is summarized and the scaling forms of the time dependent non equilibrium correlation and response functions of a generic observable are discussed from them the universality of the associated fdr follows as an amplitude ratio it is then possible to provide predictions for ageing quantities in a variety of different models in particular the results for models a b and c dynamics of the o n ginzburg landau hamiltonian and model a dynamics of the weakly dilute ising magnet and of the 3 theory are reviewed and compared with the available numerical results and exact solutions the effect of a planar surface on the ageing behaviour of model a dynamics is also addressed within the mean field approximation

quasi equilibrium interpretation of ageing dynamics we develop an interpretation of the off equilibrium dynamical solution of mean field glassy models in terms of quasi equilibrium concepts we show that the relaxation of the thermo remanent magnetization follows a generalized version of the onsager regression postulate of induced fluctuations we then find the rationale for the equality between the fluctuation dissipation ratio and the rate of growth of the configurational entropy close to the asymptotic state found empirically in mean field solutions