some convergence estimates for semidiscrete type schemes for time dependent nonselfadjoint parabolic equations l2 norm error estimates are shown for semidiscrete continuous in time galerkin finite element type approximations to solutions of general time dependent nonselfadjoint second order parabolic equations under dirichlet boundary conditions the semidiscrete solutions are defined in terms of given methods for the corresponding elliptic problem such as the standard galerkin method in which the boundary conditions are satisfied exactly but also methods for which this is not necessary the results are proved by energy arguments and include estimates for the homogeneous equation with both smooth and nonsmooth initial data

stationary distributions for systems with competing creation annihilation dynamics we have developed a simple systematic method to investigate the existence of stationary probability distributions spds for interacting particle or spin lattice systems exhibiting steady non equilibrium states the latter originate in a competition between several creation annihilation spin flip kinetic mechanisms say each acting presuming a different bath temperature particle spin interactions strength or chemical potential magnetic field it follows the existence of spds for a large class of these systems which may thus be studied by simply applying the techniques of equilibrium theory the method is illustrated with several examples bearing a practical interest

critical phenomena at surfaces in a model of nonequilibrium phase transitions critical phenomena at surfaces are studied in a simple two dimensional model of non equilibrium phase transitions belonging to the class of interacting particle systems the mean field renormalization group approach and numerical simulations are used to determine the phase diagram for this system and some of the critical exponents associated with ordinary special extraordinary and surface phase transitions

preliminary study on wilcoxon learning machines as is well known in statistics the resulting linear regressors by using the rank based wilcoxon approach to linear regression problems are usually robust against or insensitive to outliers this motivates us to introduce in this paper the wilcoxon approach to the area of machine learning specifically we investigate four new learning machines namely wilcoxon neural network wnn wilcoxon generalized radial basis function network wgrbfn wilcoxon fuzzy neural network wfnn and kernel based wilcoxon regressor kwr these provide alternative learning machines when faced with general nonlinear learning problems simple weights updating rules based on gradient descent will be derived some numerical examples will be provided to compare the robustness against outliers for various learning machines simulation results show that the wilcoxon learning machines proposed in this paper have good robustness against outliers we firmly believe that the wilcoxon approach will provide a promising methodology for many machine learning problems

convergence estimates for semidiscrete parabolic equation approximations semidiscrete methods for approximating the solutions of initial boundary value problems for parabolic equations are studied the construction of these semidiscrete methods is based upon the availability of several different galerkin type approximation methods for the associated elliptic steadystate problem the properties required of the spacial discretization methods are listed and estimates of the error made by the resulting semidiscrete approximations and of their time derivatives are given in particular estimates are given that require only weak smoothness assumptions on the initial data verifications of the required properties for various galerkin type methods are provided

on maximum likelihood fuzzy neural networks in this paper m estimators where m stands for maximum likelihood used in robust regression theory for linear parametric regression problems will be generalized to nonparametric maximum likelihood fuzzy neural networks mfnns for nonlinear regression problems emphasis is put particularly on the robustness against outliers this provides alternative learning machines when faced with general nonlinear learning problems simple weight updating rules based on gradient descent and iteratively reweighted least squares irls will be derived some numerical examples will be provided to compare the robustness against outliers for usual fuzzy neural networks fnns and the proposed mfnns simulation results show that the mfnns proposed in this paper have good robustness against outliers

higher order single step fully discrete approximations for second order hyperbolic equations with time dependent coefficients error estimates are proved for finite element approximations to the solution of an initial boundary value problem for a second order hyperbolic partial differential equation with time dependent coefficients optimal order rates of convergence in l 2 are shown for single step fully discrete schemes the order nu of the single step schemes is greater than or equal to one and less than or equal to four a class of iterative methods for approximately solving the fully discrete equations is analyzed and optimal order rates of convergence are also obtained these methods avoid the repeated work of new matrix factorizations at each time level

nonequilibrium lattice models series analysis of steady states a perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state the expansion is expressed directly in terms of the kinetic parameter creation rate rather than in powers of the interaction an algorithm for generating series expansions for local properties is described order parameter series 16 terms and precise estimates of critical properties are presented for the one dimensional contact process and several related models

dynamical critical exponent for the majority vote model we investigate the dynamical behavior of the isotropic majority vote model on a square lattice using a combination of damage spreading and finite size scaling methods for initial damage d 0 1 2 the dynamical phase diagram exhibits a chaotic frozen phase transition at a critical noise parameter qc 0 0818 0 0002 while for d 0 1 2 the damage does not propagate for any value of the model s parameter 0 q 1 2 from simulations at qc we find that the dynamical critical exponent is z 0 65 0 05

critical behaviour of the non equilibrium ising model with locally competing temperatures the author uses a method which combines the ideas of the renormalisation group and mean field theory to obtain the phase diagram of two and three dimensional non equilibrium ising models with two locally competing temperatures comparison is made with available results of other authors an estimate of critical exponent nu is derived

single index fuzzy neural networks using locally weighted polynomial regression abstract the novel single index fuzzy neural network models are proposed in this paper for general machine learning problems the proposed models are different from the usual fuzzy neural network models in that the output nodes of the networks are replaced by nonparametric single index models specifically instead of pre specifying the output activation functions as in the usual models they are re estimated adaptively during the training process via loess local regression a powerful nonparametric scatterplot smoother these estimated activation functions are not necessarily the usual sigmoidal or identity functions it is interesting to find that in many cases the estimated output activation functions are well approximated by simple polynomial or generalized hyperbolic tangent functions these problem tailored simple functions can if necessary then be used as the actual output activation functions for neural network training and prediction particle swarm optimization a commonly used evolutionary computation technique is adopted in this study to search the optimal connection weights of the neural networks the main advantages of the single index fuzzy neural network models are that they are well suited in situations when one lacks the information about the probability distribution of the response and it is not necessary to specify the output activation functions of the neural networks simulation results show that the proposed models usually provide better fits than the usual models for the data at hand

isotropic majority vote model on a square lattice the stationary critical properties of the isotropic majority vote model on a square lattice are calculated by monte carlo simulations and finite size analysis the critical exponents and are found to be the same as those of the ising model and the critical noise parameter is found to beqc 0 075 0 001

fuzzy identification using fuzzy neural networks with stable learning algorithms in general fuzzy neural networks cannot match nonlinear systems exactly unmodeled dynamic leads parameters drift and even instability problem according to system identification theory robust modification terms must be included in order to guarantee lyapunov stability this paper suggests new learning laws for mamdani and takagi sugeno kang type fuzzy neural networks based on input to state stability approach the new learning schemes employ a time varying learning rate that is determined from input output data and model structure stable learning algorithms for the premise and the consequence parts of fuzzy rules are proposed the calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds this offer an advantage compared to other techniques using robust modification

nonlinear q voter model we introduce a nonlinear variant of the voter model the q voter model in which q neighbors with possible repetition are consulted for a voter to change opinion if the q neighbors agree the voter takes their opinion if they do not have a unanimous opinion still a voter can flip its state with probability epsilon we solve the model on a fully connected network i e in mean field and compute the exit probability as well as the average time to reach consensus by employing the backward fokker planck formalism and scaling arguments we analyze the results in the perspective of a recently proposed langevin equation aimed at describing generic phase transitions in systems with two z2 symmetric absorbing states in particular by deriving explicitly the coefficients of such a langevin equation as a function of the microscopic flipping probabilities we find that in mean field the q voter model exhibits a disordered phase for high epsilon and an ordered one for low epsilon with three possible ways to go from one to the other i a unique generalized voter like transition ii a series of two consecutive transitions one ising like in which the z2 symmetry is broken and a separate one in the directed percolation class in which the system falls into an absorbing state and iii a series of two transitions including an intermediate regime in which the final state depends on initial conditions this third so far unexplored scenario in which a type of ordering dynamics emerges is rationalized and found to be specific of mean field i e fluctuations are explicitly shown to wash it out in spatially extended systems

semidiscrete and single step fully discrete approximations for second order hyperbolic equations with time dependent coefficients l2 norm error estimates are proved for finite element approximations to the solutions of initial boundary value problems for second order hyperbolic partial differential equations with time dependent coefficients optimal order rates of convergence are shown for semidiscrete and single step fully discrete schemes using specially constructed initial data the initial data are designed so that the data used for the fully discrete equation is reasonable to compute and so that the optimal order estimates can be proved

robust tsk fuzzy modeling for function approximation with outliers the takagi sugeno kang tsk type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications most approaches for modeling tsk fuzzy rules define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions besides training data sets algorithms often contain outliers which seriously affect least square error minimization clustering and learning algorithms a robust tsk fuzzy modeling approach is presented in the approach a clustering algorithm termed as robust fuzzy regression agglomeration rfra is proposed to define fuzzy subspaces in a fuzzy regression manner with robust capability against outliers to obtain a more precision model a robust fine tuning algorithm is then employed various examples are used to verify the effectiveness of the proposed approach from the simulation results the proposed robust tsk fuzzy modeling indeed showed superior performance over other approaches

mean field analysis of the q voter model on networks we present a detailed investigation of the behavior of the nonlinear q voter model for opinion dynamics at the mean field level we derive analytically for any value of the number q of agents involved in the elementary update the phase diagram the exit probability and the consensus time at the transition point the mean field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks we finally discuss the case of random regular networks and compare analytical results with simulations

cosine methods for nonlinear second order hyperbolic equations construction et analyse des methodes efficaces avec une precision d ordre eleve pour l approximation des solutions regulieres d une classe d equations hyperboliques non lineaires du second ordre application des discretisations de type galerkin et des schemas a deux pas estimations d erreurs d ordre optimal

nonequilibrium spin models with ising universal behaviour the properties of a family of nonequilibrium spin models with up down symmetry on a square lattice are determined by a mean field pair approximation and by monte carlo simulation the phase diagram in the parameter space displays a critical line that terminates at a first order critical point it is found that the critical exponents are the same as those of the equilibrium ising model

majority vote model with different agents abstract we consider the majority vote model with noise in a network of social interactions for a system with two classes of individuals class and class for the two agent model each class has its own dynamics with individuals of class being influenced by neighbors of both classes while the individuals of type are influenced only by neighbors of that class we use monte carlo simulations and finite size scaling techniques to estimate the critical properties of the system in the stationary state the calculated values of the critical noise parameters q and q allow us to identify five distinct regions in the phase diagram on the q q plane the critical exponents for each class are the same and we conclude that the present model belongs to the same universality class as the two dimensional ising model

fuzzy systems as universal approximators an additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy an additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input output state space and averaging patches that overlap the fuzzy system computes a conditional expectation e y x if we view the fuzzy sets as random sets each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state space geometry neural or statistical clustering systems can approximate the unknown fuzzy patches from training data these adaptive fuzzy systems approximate a function at two levels at the local level the neural system approximates and tunes the fuzzy rules at the global level the rules or patches approximate the function

higher order single step fully discrete approximations for nonlinear second order hyperbolic equations abstract error estimates are proved for finite element approximations to the solution of an initial boundary value problem for nonlinear second order hyperbolic partial differential equations optimal order rates of convergence in l 2 are shown for single step fully discrete schemes which are linearized by extrapolations the order of accuracy in time is 2 3 or 4 a class of iterative methods for approximately solving the fully discrete equations is analyzed and optimal order rates of convergence are also obtained

entropy production in the majority vote model we analyzed the entropy production in the majority vote model by using a mean field approximation and monte carlo simulations the dynamical rules of the model do not obey detailed balance so that entropy is continuously being produced this nonequilibrium stochastic model is known to have a critical behavior belonging to the universality class of the equilibrium ising model we show that the entropy production exhibits a singularity at the critical point whose exponent is estimated numerically

majority vote model with a bimodal distribution of noises in small world networks abstract we consider a generalized version of the majority vote model in small world networks in our model each site of the network has noise q 0 and q 0 with probability f and 1 f respectively the connections of the two dimensional square lattice are rewired with probability p we performed monte carlo simulations to characterize the order disorder phase transition of the system through finite size scaling analysis we calculated the critical noise value q c and the standard critical exponents 1 our results suggest that these exponents are different from those of the isotropic majority vote model we concluded that the zero noise fraction f when combined with the rewiring probability p drive the system to a different universality class from that of the isotropic majority vote model

universal and nonuniversal features of the generalized voter class for ordering dynamics in two dimensions by considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions dornic et al phys rev lett 87 045701 2001 we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture of up and down spins in particular we show that for nonlinear voter models the exit probability probability to end with all spins up when starting with an initial fraction x of them assumes a nontrivial shape this is the first time a nontrivial exit probability is observed in two dimensional systems the change is traced back to the strong nonconservation of the average magnetization during the early stages of dynamics also the time needed to reach the final consensus state tn x has an anomalous nonuniversal dependence on x

anisotropic voter model a majority vote model subject to anisotropic voting rules is studied in two dimensions using a first order mean field approximation and monte carlo simulations the critical behavior is consistent with the 2d ising universality class

majority vote model on hyperbolic lattices we study the critical properties of a nonequilibrium statistical model the majority vote model on heptagonal and dual heptagonal lattices such lattices have the special feature that they only ca

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations abstract optimal order rates of convergence are proved for fully discrete approximations for nonlinear second order hyperbolic equations which are based on a finite element approximation in the space variables and a single step method in the time variable the r h s of the differential equation can depend on u u 1 or u and the coefficients can depend on u this paper generalizes the work of bales where the r h s and coefficients were allowed to depend on u

robust interval regression analysis using neural networks abstract as a very important tool for dealing with both crisp data and fuzzy data fuzzy regression analysis based on interval regression analysis has become an active area of research some neural network related methods for nonlinear interval regression analysis have been proposed on the assumption that given training data are totally good data the performance of these methods will significantly worsen when the training data are spoiled by outliers in this paper we introduce the concepts of polarity and quality of the training data on the basis of which we propose two robust learning algorithms for determining a robust nonlinear interval regression model which makes a feature of a new cost function for reflecting not only the polarity of the training data but also the estimated knowledge about the quality of the training data the two robust algorithms are derived in a manner similar to the back propagation bp algorithm simulation results show that our robust algorithms outperform the existing methods remarkably in two aspects when outliers are present 1 they are robust against outliers 2 their rates of convergence are improved to some extent

spanning forests and the q state potts model in the limit q 0 we study the q state potts model with nearest neighbor coupling v e j 1 in the limit q v 0 with the ratio w v q held fixed combinatorially this limit gives rise to the generating polynomial of spanning forests physically it provides information about the potts model phase diagram in the neighborhood of q v 0 0 we have studied this model on the square and triangular lattices using a transfer matrix approach at both real and complex values of w for both lattices we have computed the symbolic transfer matrices for cylindrical strips of widths 2 l 10 as well as the limiting curves b of partition function zeros in the complex w plane for real w we find two distinct phases separated by a transition point w w0 where w0 1 4 resp w0 0 1753 0 0002 for the square resp triangular lattice for w w0 we find a non critical disordered phase that is compatible with the predicted asymptotic freedom as w for w w0 our results are compatible with a massless berker kadanoff phase with central charge c 2 and leading thermal scaling dimension xt 1 2 marginally irrelevant operator at w w0 we find a first order critical point the first derivative of the free energy is discontinuous at w0 while the correlation length diverges as w w0 and is infinite at w w0 the critical ehavior at w w0 seems to be the same for both lattices and it differs from that of the berker kadanoff phase our results suggest that the central charge is c 1 the leading thermal scaling dimension is xt 1 0 and the critical exponents are 1 d 1 2 and 1

non equilibrium ising model with competing glauber dynamics the authors consider a kinetic ising model with ferromagnetic interactions that evolves in time according to two competing glauber dynamics at different temperatures the steady states of this non equilibrium model are studied by using a dynamic pair approximation when the temperatures are low enough the system orders in a ferromagnetic state but if one of the temperatures is allowed to be negative the system may have an antiferromagnetic order they obtain the phase diagram for the case of a square lattice in this case they calculate the critical exponent v by using a mean field renormalization group method the numerical results indicate that the model falls into the same universality class of the equilibrium ising model they also show that one particular case of the non equilibrium model studied here is equivalent to the majority vote model

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

length scaling in mfrg the mean field renormalisation group mfrg has so far given poor estimates for critical indices it is argued that this can be traced to an unsatisfactory definition of the length scaling factor a new definition that improves the estimates in most cases is proposed

critical behaviour of nonequilibrium three state systems the phase diagram of two different nonequilibrium three state systems is here studied by means of mfrg and computer simulations critical exponents are obtained by a finite size scaling analysis of the mc data a symmetry argument used by grinstein et al to predict the critical behaviour of two state nonequilibrium systems with up down symmetry is shown to apply to these three state systems with symmetry of interchange between two of those states

finite element approximations of nonlinear elastic waves in this paper we study finite element methods for a class of problems of nonlinear elastodynamics we discretize the equations in space using galerkin methods for the temporal discretization the construction of our schemes is based on rational approximations of cos x and ex we analyze semidiscrete as well as secondand fourth order accurate in time fully discrete methods for the approximation of the solution of the problem and prove optimal order l2 error estimates for some schemes a taylor type technique is used so that only linear systems of equations need be solved at each time step in the proofs we need various estimates for a nonlinear elliptic projection the proofs of which are also established in the paper

tsk fuzzy modeling based on spl epsiv insensitive learning in this paper new learning methods tolerant to imprecision are introduced and applied to fuzzy modeling based on the takagi sugeno kang fuzzy system the fuzzy modeling has an intrinsic inconsistency it may perform thinking tolerant to imprecision but learning methods are zero tolerant to imprecision the proposed methods make it possible to exclude this intrinsic inconsistency of a fuzzy modeling where zero tolerance learning is used to obtain fuzzy model tolerant to imprecision these new methods can be called spl epsiv insensitive learning or spl epsiv learning where in order to fit the fuzzy model to real data the spl epsiv insensitive loss function is used this leads to a weighted or fuzzified version of vapnik s support vector regression machine this paper introduces two approaches to solving the spl epsiv insensitive learning problem the first approach leads to the quadratic programming problem with bound constraints and one linear equality constraint the second approach leads to a problem of solving a system of linear inequalities two computationally efficient numerical methods for the spl epsiv insensitive learning are proposed the spl epsiv insensitive learning leads to a model with the minimal vapnik chervonenkis dimension which results in an improved generalization ability of this model and its outliers robustness finally numerical examples are given to demonstrate the validity of the introduced methods

majority vote model with a bimodal distribution of noises abstract we consider the majority vote dynamics where the noise parameter associated with each spin on a two dimensional square lattice is a bimodally distributed random variable defined as q with probability 1 f or zero with probability f where 0 f 1 is the proportion of noiseless sites we use monte carlo simulations and finite size scaling theory to characterize the ordered and disordered phases and study the phase transition of the model we conclude that in the thermodynamic limit the value of the critical noise below which there exists an ordered phase increases with f the fraction of sites with zero noise the calculation of the critical exponents shows that the introduction of disorder in the noise parameter does not alter the ising critical behavior of the model system