exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

a new artificial neural network based fuzzy inference system with moving consequents in if then rules and selected applications abstract in this paper a new artificial neural network based fuzzy inference system annbfis has been described the novelty of the system consists in the moving fuzzy consequent in if then rules the location of this fuzzy set is determined by a linear combination of system inputs this system also automatically generates rules from numerical data the proposed system operates with gaussian membership functions in premise part parameter estimation has been made by connection of both gradient and least squares methods for initialization of unknown parameter values of premises a preliminary fuzzy c means clustering method has been employed for evaluation of the number of if then rules the indexes of xie beni and fukujama sugeno have been applied the applications to prediction of chaotic time series pattern recognition and system identification are considered in this paper as well

phase separation and coarsening in one dimensional driven diffusive systems local dynamics leading to long range hamiltonians a driven system of three species of particles diffusing on a ring is studied in detail the dynamics is local and conserves the three densities a simple argument suggesting that the model should phase separate and break the translational symmetry is given we show that for the special case where the three densities are equal the model obeys detailed balance and the steady state distribution is governed by a hamiltonian with asymmetric long range interactions this provides an explicit demonstration of a simple mechanism for breaking of ergodicity in one dimension the steady state of finite size systems is studied using a generalized matrix product ansatz the coarsening process leading to phase separation is studied numerically and in a mean field model the system exhibits slow dynamics due to trapping in metastable states whose number is exponentially large in the system size the typical domain size is shown to grow logarithmically in time generalizations to a larger number of species are discussed

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

universality classes in two component driven diffusive systems we study time dependent density fluctuations in the stationary state of driven diffusive systems with two conserved densities rho lambda using monte carlo simulations of two coupled single lane asymmetric simple exclusion processes we present numerical evidence for universality classes with dynamical exponents z 1 sqrt 5 2 and z 3 2 but different from the kardar parisi zhang kpz universality class which have not been reported yet for driven diffusive systems the numerical asymmetry of the dynamical structure functions converges slowly for some of the non kpz superdiffusive modes for which mode coupling theory predicts maximally asymmetric z stable levy scaling functions we show that all universality classes predicted by mode coupling theory for two conservation laws are generic they occur in two component systems with nonlinearities in the associated currents already of the minimal order rho lambda 2 rho mu the macroscopic stationary current density relation and the compressibility matrix determine completely all permissible universality classes through the mode coupling coefficients which we compute explicitly for general two component systems

spatial particle condensation for an exclusion process on a ring abstract we study the stationary state of a simple exclusion process on a ring which was recently introduced by arndt et al j phys a 31 1998 l45 j stat phys 97 1999 1 this model exhibits spatial condensation of particles it has been argued j phys a 31 1998 l45 cond mat 9809123 that the model has a phase transition from a mixed phase to a disordered phase however in this paper exact calculations are presented which we believe show that in the framework of a grand canonical ensemble there is no such phase transition an analysis of the fluctuations in the particle density strongly suggests that the same result also holds for the canonical ensemble and suggests the existence of extremely long but finite correlation lengths for example 1070 sites in the infinite system at moderate parameter values in the mixed regime

multifractal decompositions of moran fractals we present a rigorous construction and generalization of the multifractal decomposition for moran fractals with infinite product measure the generalization is specified by a system of nonnegative weights in the partition sum all the usual smooth properties of the f theory are recovered for the case that the weights are equal to unity the generalized spectrum f w is invariant to a group of gauge transformations of the weights and in addition need no longer be concave in case the fractal is a cantor set generated by an iterated function system of similarities is the pointwise dimension of the measure we discuss properties of some examples

the multifractal spectrum of quasi self similar measures abstract we define the notion of quasi self similar measures and show that for such measures their generalised hausdorff and packing measures are positive and finite at the critical exponent in practice this allows easy calculation of their dimension functions we then show that a coarse form of the multifractal formalism automatically holds for quasi self similar measures examples of quasi self similar measures include many of the standard constructions of multifractal measures satisfying a strong separation condition in particular self similar measures

phase diagram of a generalized abc model on the interval we study the equilibrium phase diagram of a generalized abc model on an interval of the one dimensional lattice each site i 1 n is occupied by a particle of type a b c with the average density of each particle species n n r fixed these particles interact via a mean field nonreflection symmetric pair interaction the interaction need not be invariant under cyclic permutation of the particle species as in the standard abc model studied earlier we prove in some cases and conjecture in others that the scaled infinite system n i n x 0 1 has a unique density profile x except for some special values of the r for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature t c 3 sqrt r a r b r c 2 pi

relation between spectral classes of a self similar cantor set a self similar cantor set is completely decomposed as a class of the lower upper distribution sets we give a relationship between the distribution sets in the distribution class and the subsets in a spectral class generated by the lower upper local dimensions of a self similar measure in particular we show that each subset of a spectral class is exactly a distribution set having full measure of a self similar measure related to the distribution set using the strong law of large numbers this gives essential information of its hausdorff and packing dimensions in fact the spectral class by the lower upper local dimensions of every self similar measure except for a singular one is characterized by the lower or upper distribution class finally we compare our results with those of other authors

twenty five years after kls a celebration of non equilibrium statistical mechanics when lenz proposed a simple model for phase transitions in magnetism he couldn t have imagined that the ising model was to become a jewel in field of equilibrium statistical mechanics its role spans the spectrum from a good pedagogical example to a universality class in critical phenomena a quarter century ago katz lebowitz and spohn found a similar treasure by introducing a seemingly trivial modification to the ising lattice gas they took it into the vast realms of non equilibrium statistical mechanics an abundant variety of unexpected behavior emerged and caught many of us by surprise we present a brief review of some of the new insights garnered and some of the outstanding puzzles as well as speculate on the model s role in the future of non equilibrium statistical physics

sharp crossover and anomalously large correlation length in driven systems models of one dimensional driven diffusive systems sometimes exhibit an abrupt increase in the correlation length to an anomalously large but finite value as the parameters of the model are varied this behaviour may be misinterpreted as a genuine phase transition a simple mechanism for this sharp increase is presented the mechanism is introduced within the framework of a recently suggested correspondence between driven diffusive systems and zero range processes it is shown that when the dynamics of the model is such that small domains are suppressed in the steady state distribution anomalously large correlation lengths may build up the mechanism is examined in detail in two models

dynamical windings of random walks and exclusion models part i thermodynamic limit in bbb z2 we consider a system consisting of a planar random walk on a square lattice subjected to stochastic elementary local deformations both numerical and theoretical results are reported depending on the deformation transition rates and specifically on a parameter which breaks the symmetry between the left and right orientation the winding distribution of the walk is modified and the system can be in three different phases folded stretched and glassy an explicit mapping is found leading to consider the system as a coupling of two exclusion processes particles of the first one move in a landscape defined by particles of the second one and vice versa this can be viewed as an inhomogeneous exclusion process for all closed or periodic initial sample paths a convenient scaling permits to show a convergence in law or almost surely on a modified probability space to a continuous curve the equation of which is given by a system of two non linear stochastic differential equations the deterministic part of this system is explicitly analyzed via elliptic functions in a similar way by using a formal fluid limit approach the dynamics of the system is shown to be equivalent to a system of two coupled burgers equations

a new hybrid artificial neural networks and fuzzy regression model for time series forecasting quantitative methods have nowadays become very important tools for forecasting purposes in financial markets as for improved decisions and investments forecasting accuracy is one of the most important factors involved in selecting a forecasting method hence never has research directed at improving upon the effectiveness of time series models stopped artificial neural networks anns are flexible computing frameworks and universal approximators that can be applied to a wide range of forecasting problems with a high degree of accuracy however anns need a large amount of historical data in order to yield accurate results in a real world situation and in financial markets specifically the environment is full of uncertainties and changes occur rapidly thus future situations must be usually forecasted using the scant data made available over a short span of time therefore forecasting in these situations requires methods that work efficiently with incomplete data although fuzzy forecasting methods are suitable for incomplete data situations their performance is not always satisfactory in this paper based on the basic concepts of anns and fuzzy regression models a new hybrid method is proposed that yields more accurate results with incomplete data sets in our proposed model the advantages of anns and fuzzy regression are combined to overcome the limitations in both anns and fuzzy regression models the empirical results of financial market forecasting indicate that the proposed model can be an effective way of improving forecasting accuracy

a multifractal formalism let x be a metric space and a borel probability measure on x for q t r and e x write formula then hq t and pq t are borel measures hq t is a multifractal generalization of the centered hausdorff measure and pq t is a multifractal generalization of the packing measure the measures hq t and pq t define for a fixed q in the usual way a generalized hausdorff dimension dimq e and a generalized packing dimension dimq e of subsets e of x we study the functions b q dimq supp b q dimq supp and their relation to the so called multifractal spectra functions of formula we prove among other things that f f is bounded from above by the legendre transform of b b and that equality holds for graph directed self similar measures and cookie cutter measures finally we discuss the connection with generalized renyi dimensions

phase diagram of the abc model on an interval the three species asymmetric abc model was initially defined on a ring by evans kafri koduvely and mukamel and the weakly asymmetric version was later studied by clincy derrida and evans here the latter model is studied on a one dimensional lattice of n sites with closed zero flux boundaries in this geometry the local particle conserving dynamics satisfies detailed balance with respect to a canonical gibbs measure with long range asymmetric pair interactions this generalizes results for the ring case where detailed balance holds and in fact the steady state measure is known only for the case of equal densities of the different species in the latter case the stationary states of the system on a ring and on an interval are the same we prove that in the limit n the scaled density profiles are given by pieces of the periodic trajectory of a particle moving in a quartic confining potential we further prove uniqueness of the profiles i e the existence of a single phase in all regions of the parameter space of average densities and temperature except at low temperature with all densities equal in this case a continuum of phases differing by translation coexist the results for the equal density case apply also to the system on the ring and there extend results of clincy et al

a modified pnn algorithm with optimal pd modeling using the orthogonal least squares method in this paper a modified algorithm is suggested for developing polynomial neural network pnn models optimal partial description pd modeling is introduced at each layer of the pnn expansion a task accomplished using the orthogonal least squares ols method based on the initial pd models determined by the polynomial order and the number of pd inputs ols selects the most significant regressor terms reducing the output error variance the method produces pnn models exhibiting a high level of accuracy and superior generalization capabilities additionally parsimonious models are obtained comprising a considerably smaller number of parameters compared to the ones generated by means of the conventional pnn algorithm three benchmark examples are elaborated including modeling of the gas furnace process as well as the iris and wine classification problems extensive simulation results and comparison with other methods in the literature demonstrate the effectiveness of the suggested modeling approach

exact solution of the totally asymmetric simple exclusion process shock profiles the microscopic structure of macroscopic shocks in the one dimensional totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model system containing two types of particles first and second class this nonequilibrium steady state factorizes about any second class particle which implies factorization in the one component system about the random shock position it also exhibits several other interesting features including long range correlations in the limit of zero density of the second class particles the solution also shows that a finite number of second class particles in a uniform background of first class particles form a weakly bound state

generalized weighted conditional fuzzy clustering fuzzy clustering helps to find natural vague boundaries in data the fuzzy c means method is one of the most popular clustering methods based on minimization of a criterion function among many existing modifications of this method conditional or context dependent c means is the most interesting one in this method data vectors are clustered under conditions based on linguistic terms represented by fuzzy sets this paper introduces a family of generalized weighted conditional fuzzy c means clustering algorithms this family include both the well known fuzzy c means method and the conditional fuzzy c means method performance of the new clustering algorithm is experimentally compared with fuzzy c means using synthetic data with outliers and the box jenkins database

replica field theory for deterministic models i binary sequences with low autocorrelation we study systems without quenched disorder with a complex landscape and we use replica symmetry theory to describe them we discuss the golay bernasconi derrida approximation of the low autocorrelation model and we reconstruct it by using replica calculations we then consider the full model its low t properties with the help of number theory and a hartree fock resummation of the high temperature series we show that replica theory allows us to solve the model in the high t phase our solution is based on one link integral techniques and is based on substituting a fourier transform with a generic unitary transformation we discuss this approach as a powerful tool to describe systems with a complex landscape in the absence of quenched disorder

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

stochastic dynamics of discrete curves and multi type exclusion processes this study deals with continuous limits of interacting one dimensional diffusive systems arising from stochastic distortions of discrete curves with various kinds of coding representations these systems are essentially of a reaction diffusion nature in the non reversible case the invariant measure has in general a non gibbs form the corresponding steady state regime is analyzed in detail by using a tagged particle together with a state graph cycle expansion of the probability currents as a consequence the constants appearing in lotka volterra equations which describe the fluid limits of stationary states can be traced back directly at the discrete level to tagged particle cycles coefficients current fluctuations are also studied and the lagrangian is obtained via an iterative scheme the related hamilton jacobi equation which leads to the large deviation functional is investigated and solved in the reversible case just for the sake of checking

on support vector regression machines with linguistic interpretation of the kernel matrix initially the idea of approximate reasoning using generalized modus ponens and a fuzzy implication is recalled next a fuzzy system based on logical interpretation of if then rules and with parametric conclusions is presented then it is shown that global and local e insensitive learning of the above fuzzy system may be presented as the learning of a support vector regression machine with a special type of a kernel matrix obtained from clustering the kernel matrix may be interpreted in terms of linguistic values based on the premises of if then rules a new method of obtaining a fuzzy system by means of a support vector machine svm with a data dependent kernel matrix is introduced this paper contains examples of a svm used to design fuzzy models of real life data simulation results show an improvement in the generalization ability of a fuzzy system learned by the new method compared with traditional learning methods

cumulants of the three state potts model and of nonequilibrium models with c3v symmetry the critical behaviour of two dimensional stochastic lattice gas models with c3v symmetry is analysed we study the cumulants of the order parameter for the three state equilibrium potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group c3v by means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behaviour of the systems in particular we find that the binder reduced fourth order cumulant takes a universal value u which is the same for the three state potts model and for the irreversible models the same universal behaviour is observed for the reduced third order cumulant

smooth transition autoregressive models and fuzzy rule based systems functional equivalence and consequences in this work we will explore the theoretical connections existing between fuzzy rule based systems frbs applied on univariate time series and two statistical reference tools the autoregressive ar models and the smooth transition autoregressive star model we will show that a tsk fuzzy rule happens to be a localised ar model and that a star model can hence be interpreted as a restricted frbs several consequences derive from this fact and we will explore some of them including a statistical inference based procedure to incrementally build frbs or the linguistic interpretation of star models finally an econometric example is given to illustrate the core idea

phase transition in the abc model recent studies have shown that one dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules the mathrm abc model which comprises three particle species that diffuse asymmetrically around a ring shows anomalous coarsening into a phase separated steady state in the limiting case in which the dynamics is symmetric and the parameter q describing the asymmetry tends to one no phase separation occurs and the steady state of the system is disordered in the present work we consider the weak asymmetry regime q mathrm exp ensuremath ensuremath beta n where n is the system size and study how the disordered state is approached in the case of equal densities we find that the system exhibits a second order phase transition at some nonzero ensuremath beta c the value of ensuremath beta c 2 ensuremath pi sqrt 3 and the optimal profiles can be obtained by writing the exact large deviation functional for nonequal densities we write down mean field equations and analyze some of their predictions

the grand canonical abc model a reflection asymmetric mean field potts model we investigate the phase diagram of a three component system of particles on a one dimensional filled lattice or equivalently of a one dimensional three state potts model with reflection asymmetric mean field interactions the three types of particles are designated as a b and c the system is described by a grand canonical ensemble with temperature t and chemical potentials t a t b and t c we find that for a b c the system undergoes a phase transition from a uniform density to a continuum of phases at a critical temperature for other values of the chemical potentials the system has a unique equilibrium state as is the case for the canonical ensemble for this abc model the grand canonical ensemble is the stationary measure satisfying detailed balance for a natural dynamics we note that where tc is the critical temperature for a similar transition in the canonical ensemble at fixed equal densities ra rb rc 1 3

an improved multifractal formalism and self similar measures abstract to characterize the geometry of a measure its generalized dimensions dq have been introduced recently the mathematically precise definition given by falconer fractal geometry 1990 turns out to be unsatisfactory for reasons of convergence as well as of undesired sensitivity to the particular choice of coordinates in the negative q range a new definition is introduced which is also based on box counting but which carries relevant information about for negative q also in particular the legendre connection between generalized dimensions and the multifractal spectrum is established using large deviations and rigorous proofs are provided for the implicit formula giving the generalized dimensions of selfsimilar measures which was until now known only for positive q