persistence exponents and scaling in two dimensional xy model and a nematic model the persistence exponents associated with the t 0 quenching dynamics of the two dimensional xy model and a two dimensional uniaxial spin nematic model have been evaluated using a numerical simulation the site persistence or the probability that the sign of a local spin component does not change starting from initial time t 0 up to a certain time t is found to decay as l t l t is the linear domain length scale with 0 305 0 020 for the two dimensional xy model and 0 199 0 009 for the two dimensional uniaxial spin nematic model we have also investigated the scaling at the late time of phase ordering associated with the correlated persistent sites in both models the persistence correlation length was found to grow in the same way as l t

control design of uncertain quantum systems with fuzzy estimators an approach of control design using fuzzy estimators fes is proposed for quantum systems with uncertainties two types of quantum control problems are considered 1 control of a pure state quantum system in the presence of uncertainties and 2 control design of quantum systems with initial mixed states and uncertainties for the first type of tasks a partial feedback control scheme with an fe is presented to design controllers in this scheme an fe is trained to estimate the quantum state for feedback control of a quantum system and controlled projective measurement is used to assist in controlling the system for the second type of quantum control tasks a probabilistic fuzzy estimator pfe is trained to estimate the quantum state for control design of a quantum system with an initial mixed state and a corresponding control algorithm is proposed to design a control law that drives the system from the mixed state to a target pure state two examples of two spin 1 2 systems are also presented and analyzed to demonstrate the process of control design and potential applications of the proposed approach

a probabilistic fuzzy logic system for modeling and control in this paper a probabilistic fuzzy logic system pfls is proposed for the modeling and control problems similar to the ordinary fuzzy logic system fls the pfls consists of the fuzzification inference engine and defuzzification operation to process the fuzzy information different to the fls it uses the probabilistic modeling method to improve the stochastic modeling capability by using a three dimensional membership function mf the pfls is able to handle the effect of random noise and stochastic uncertainties existing in the process a unique defuzzification method is proposed to simplify the complex operation finally the proposed pfls is applied to a function approximation problem and a robotic system it shows a better performance than an ordinary fls in stochastic circumstance

conditional density estimation using probabilistic fuzzy systems we consider conditional density approximation by fuzzy systems fuzzy systems are typically used to approximate deterministic functions in which the stochastic uncertainty is ignored we propose probabilistic fuzzy systems pfss in which the probabilistic nature of uncertainty is taken into account these systems take also fuzzy uncertainty into account by their fuzzy partitioning of input and output spaces we discuss an additive reasoning scheme for pfss that leads to the estimation of conditional probability densities and prove how such fuzzy systems compute the expected value of this conditional density function we show that some of the most commonly used fuzzy systems can compute the same expected output value and we derive how their parameters should be selected in order to achieve this goal the additional information and process understanding provided by the different interpretations of the pfs models are illustrated using a real world example

combinatorial lower bound arguments for deterministic and nondeterministic turing machines on introduit de nouvelles techniques combinatoires pour etablir des bornes inferieures quadratiques des machines de turing deterministes et non deterministes a une bande

simulation of random fuzzy variables an empirical approach to statistical probabilistic studies with fuzzy experimental data in this paper we simulate different types of random fuzzy variables to get some conclusions concerning fuzzy valued random variables this simulation was carried out to illustrate certain limit results formalizing the convergence of the arithmetic mean of sampled fuzzy data to the population mean or an expected value of the random fuzzy variable like the well known strong law of large numbers and the law of iterated logarithm since the theoretical results have recently been proved this simulation analysis represents a complementary study in which we can determine sample sizes providing us with suitable approximations finally future directions regarding statistical inference with fuzzy data and other applications are commented

unusual dynamical scaling in the spatial distribution of persistent sites in one dimensional potts models the distribution n k t of the interval sizes k between clusters of persistent sites in the dynamical evolution of the one dimensional q state potts model is studied using a combination of numerical simulations scaling arguments and exact analysis it is shown to have the scaling form n k t t 2z f k t z with z max 1 2 straight theta where straight theta q is the persistence exponent which describes the fraction p t approximately t straight theta of sites which have not changed their state up to time t when straight theta 1 2 the scaling length t straight theta for the interval size distribution is larger than the coarsening length scale t 1 2 that characterizes spatial correlations of the potts variables

an efficient configuration for probabilistic fuzzy logic system a novel inference configuration is proposed to improve the computational efficiency and information loss in the probabilistic fuzzy inference process the probabilistic inference and the fuzzy inference are unified in one operation based on the continuous form of the probabilistic fuzzy set besides the faster inference operation it is able to produce fuzzy outputs in a complete probabilistic distribution that in turn will provide information about the approximation bound the computational analyses of six different fuzzy systems demonstrate the inference efficiency of the proposed method its effectiveness can be further demonstrated on the application to modeling of an industrial curing process the robust modeling performance discloses its potential in process modeling under complex environment

persistence in one dimensional ising models with parallel dynamics we study persistence in one dimensional ferromagnetic and antiferromagnetic nearest neighbor ising models with parallel dynamics the probability p t that a given spin has not flipped up to time t when the system evolves from an initial random configuration decays as p t ensuremath sim 1 t ensuremath theta p with ensuremath theta p ensuremath simeq 0 75 numerically a mapping to the dynamics of two decoupled a stackrel ensuremath rightarrow a 0 models yields ensuremath theta p 3 4 exactly a finite size scaling analysis clarifies the nature of dynamical scaling in the distribution of persistent sites obtained under this dynamics

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

persistence in nonequilibrium surface growth persistence probabilities of the interface height in 1 1 and 2 1 dimensional atomistic solid on solid stochastic models of surface growth are studied using kinetic monte carlo simulations with emphasis on models that belong to the molecular beam epitaxy mbe universality class both the initial transient and the long time steady state regimes are investigated we show that for growth models in the mbe universality class the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady state regimes for the mbe universality class the positive and negative persistence exponents in the steady state are found to be 0 66 0 02 and 0 78 0 02 respectively in 1 1 dimensions and 0 76 0 02 and 0 85 0 02 respectively in 2 1 dimensions the noise reduction technique is applied on some of the 1 1 dimensional models in order to obtain accurate values of the persistence exponents we show analytically that a relation between the steady state persistence exponent and the dynamic growth exponent found earlier to be valid for linear models should be satisfied by the smaller of the two steady state persistence exponents in the nonlinear models our numerical results for the persistence exponents are consistent with this prediction we also find that the steady state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state the dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form

probability distribution of persistent spins in an ising chain we study the probability distribution q n t of n t the fraction of spins unflipped up to time t in an ising chain with ferromagnetic interactions the distribution shows a peak at n nmax and in general is non gaussian and asymmetric in nature however for n nmax it shows a gaussian decay data collapse can be obtained when q n t l versus n nmax l is plotted with 0 45 and 0 6 interestingly nmax t shows different behaviour compared to n t p t the persistence probability which follows the well known behaviour p t t a quantitative estimate of the asymmetry and non gaussian nature of q n t is made by calculating its skewness and kurtosis

random sequential adsorption of lines and ellipses infinitely many lines of zero thickness may be adsorbed onto a plane without overlap and it is shown that the number of lines adsorbed should scale as 13 where is the number of adsorption trials per unit area of surface this is confirmed by numerical simulation the adsorption of ellipses with major and minor axes 2a 2b respectively is also studied the area coverage theta approaches its maximum value theta max as alpha as to infinity where alpha is typically 1 3 as b a decreases from unity theta max first increases to a maximum value 0 58 or 0 01 when b approximately 0 5 and then decreases a feature not noted in previous work

two nonlinear lower bounds for on line computations the following lower bounds for on line computation are proved 1 simulating two tape nondeterministic machines by one tape machines requires n log n time 2 simulating k tape deterministic machines by machines with k pushdown stores requires n log1 k 1 n time

experimental measurement of the persistence exponent of the planar ising model using a twisted nematic liquid crystal system exhibiting planar ising model dynamics we have measured the scaling exponent ensuremath theta which characterizes the time evolution p t ensuremath sim t ensuremath ensuremath theta of the probability p t that the local order parameter has not switched its state by the time t for 0 4 sec 200 sec following the phase quench the system exhibits scaling behavior and measured over this interval ensuremath theta 0 19 ifmmode pm else textpm fi 0 03 in good agreement with theoretical analysis and numerical simulations

spin block persistence at finite temperature we explore a new definition of the persistence exponent measuring the probability that a spin never flips after a quench of an ising like model at a temperature while the usual definition only makes sense at t 0 this probability is now defined for spin blocks and a general scaling for it involving time and block linear size is introduced and illustrated by extensive simulations

asymptotic results for the random sequential addition of unoriented objects asymptotic kinetics for random sequential addition of unoriented nonspherical objects is characterized by an algebraic time dependence by studying 1 d systems we show that the exponents describing the random sequential addition of objects with and without proper area are not simply related whereas the asymptotic behavior for rectangles follows the expected t 1 2 law the long time kinetics for infinitely thin line segments is governed by a nontrivial irrational exponent t 2 1 which results from a competition between creation and destruction of targets in the asymptotic regime

systems control with generalized probabilistic fuzzy reinforcement learning reinforcement learning rl is a valuable learning method when the systems require a selection of control actions whose consequences emerge over long periods for which input output data are not available in most combinations of fuzzy systems and rl the environment is considered to be deterministic in many problems however the consequence of an action may be uncertain or stochastic in nature in this paper we propose a novel rl approach to combine the universal function approximation capability of fuzzy systems with consideration of probability distributions over possible consequences of an action the proposed generalized probabilistic fuzzy rl gpfrl method is a modified version of the actor critic ac learning architecture the learning is enhanced by the introduction of a probability measure into the learning structure where an incremental gradient descent weight updating algorithm provides convergence our results show that the proposed approach is robust under probabilistic uncertainty while also having an enhanced learning speed and good overall performance

scaling and fractal formation in persistence the spatial distribution of unvisited persistent sites in 1d a a o model is studied numerically over length scales smaller than a cut off t tz the set of unvisited sites is found to be a fractal the fractal dimension df dynamical exponent z and persistence exponent are related through z 1 df the observed values of df and z are found to be sensitive to the initial density of particles we argue that this may be due to the existence of two competing length scales and discuss the possibility of a crossover at late times

exact exponent for the number of persistent spins in the zero temperature dynamics of the one dimensional potts model for the zero temperature glauber dynamics of theq state potts model the fractionr q t of spins which never flip up to timet decays like a power lawr q t t q when the initial condition is random by mapping the problem onto an exactly soluble one species coagulation model a a a or alternatively by transforming the problem into a free fermion model we obtain the exact expression of q for all values ofq the exponent q is in general irrational 3 0 53795082 4 0 63151575 with the exception ofq 2 andq for which 2 3 8 and 1

upper bound on the coarsening rate for an epitaxial growth model we study a specific example of energy driven coarsening in two space dimensions the energy is u 2 1 u 2 2 the evolution is the fourth order pde representing steepest descent this equation has been proposed as a model of epitaxial growth for systems with slope selection numerical simulations and heuristic arguments indicate that the standard deviation of u grows like t1 3 and the energy per unit area decays like t 1 3 we prove a weak one sided version of the latter statement the time averaged energy per unit area decays no faster than t 1 3 our argument follows a strategy introduced by kohn and otto in the context of phase separation combining i a dissipation relation ii an isoperimetric inequality and iii an ode lemma the interpolation inequality is new and rather subtle our proof is by contradiction relying on recent compactness results for the aviles giga energy 2003 wiley periodicals inc

energy scaling approach to phase ordering growth laws we present a simple unified approach to determining the growth law for the characteristic length scale l t in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase this approach based on a scaling assumption for pair correlations determines l t self consistently for purely dissipative dynamics by computig the time dependence of the energy in two ways we derive growth laws for conserved and nonconserved o n models including two dimensional xy models and systems with textures we demonstrate that the growth laws for other systems such as liquid crystals and potts models are determined by the type of topological defect in the order parameter field that dominates the energy we also obtain generalized porod laws for systems with topological textures

discussion probability theory and fuzzy logic are complementary rather than competitive the relationship between probability theory and fuzzy logic has long been an object of discussion and some controversy the position articulated in this article is that probability theory by itself is not sufficient for dealing with uncertainty and imprecision in real world settings to enhance its effectiveness probability theory needs an infusion of concepts and techniques drawn from fuzzy logic especially the concept of a linguistic variable and the calculus of fuzzy if then rules in the final analysis probability theory and fuzzy logic are complementary rather than competitive

iterative fuzzy clustering algorithm with supervision to construct probabilistic fuzzy rule base from numerical data to deal with data patterns with linguistic ambiguity and with probabilistic uncertainty in a single framework we construct an interpretable probabilistic fuzzy rule based system that requires less human intervention and less prior knowledge than other state of the art methods specifically we present a new iterative fuzzy clustering algorithm that incorporates a supervisory scheme into an unsupervised fuzzy clustering process the learning process starts in a fully unsupervised manner using fuzzy c means fcm clustering algorithm and a cluster validity criterion and then gradually constructs meaningful fuzzy partitions over the input space the corresponding fuzzy rules with probabilities are obtained through an iterative learning process of selecting clusters with supervisory guidance based on the notions of cluster pureness and class separability the proposed algorithm is tested first with synthetic data sets and benchmark data sets from the uci repository of machine learning database and then with real facial expression data and tv viewing data

coarsening dynamics of the one dimensional cahn hilliard model the dynamics of one dimensional cahn hilliard model is studied the stationary and particle type solutions the bubbles are perused as a function of initial conditions boundary conditions and system size we characterize the bubble solutions which are involved in the coarsening dynamics and establish the bifurcation scenarios of the system a set of ordinary differential equation permits us to describe the coarsening dynamics in very good agreement with numerical simulations we also compare these dynamics with the bubble dynamics deduced from the classical kink interaction computation where our model seems to be more appropriated in the case of two bubbles we deduce analytical expressions for the bubble s position and the bubble s width besides a simple description of the ulterior dynamics is presented

what does a probabilistic interpretation of fuzzy sets mean in this paper we propose a statistics model to better understand the probabilistic interpretation for fuzzy sets the model shows the relationship between the two kinds of statistics the set valued statistics for fuzzy sets and the conventional probability statistics for membership functions our model overcomes the shortcomings in previous approaches the results of this paper provide a theoretical interpretation to zadeh s insight that possibility relates to soft constraints restricting the values of language variables

kinetics of phase ordering in the o n model with a conserved order parameter we study the phase ordering dynamics of the o n model with a conserved order parameter for systems with topological defects we present results from both cell dynamical simulations and predictions of a gaussian auxiliary field gaf approximation for the xy n 2 model in two and three dimensions and the heisenberg n 3 model in three dimensions we describe the results for the structure factor s q and growth law l t from simulations the growth laws obtained are consistent with theoretical predictions based on energy scaling arguments the structure factor shows good dynamical scaling using a length extracted from its first moment the simulations are compared with the theoretical predictions of the gaf for the scaling functions our results show that the gaf gives a good qualitative description of most features of the structure factor however it overestimates the amplitude of the porod tail in the large q limit moreover for small q the structure factor exhibits a q2 behaviour instead of the expected generalized yeung result of q4

unity and diversity of fuzziness spl minus from a probability viewpoint like the fields of probability and statistics fuzzy set theory is characterized by a variety of viewpoints adherents of fuzzy methods however consistently maintain that probability is not necessarily the optimal representation of uncertainty we rebut this view

universal fuzzy models and universal fuzzy controllers for stochastic nonaffine nonlinear systems this paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems the underlying mechanism of stochastic fuzzy logic is first discussed and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given based on their function approximation capability these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions an approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized takagi sugeno t s fuzzy approximation models then the results of universal fuzzy controllers for two classes of stochastic nonlinear systems along with constructive procedures to obtain the universal fuzzy controllers are also provided respectively finally a numerical example is presented to illustrate the effectiveness of the proposed approach

exponents appearing in the zero temperature dynamics of the 1d potts model for the glauber dynamics of the one dimensional q state potts model at zero temperature the fraction of spins which have never flipped up to time t decreases as t theta q where the exponent theta q varies continuously with q the calculation of the q dependence of this exponent can be reduced to the study of a simple reaction diffusion model using finite size scaling this allows one to obtain accurate estimates of b q for all values of q one can also show that for 1 1 epsilon the expansion of theta y is given by theta 1 2 pi epsilon o epsilon 2

exact persistence exponent for one dimensional potts models with parallel dynamics we obtain p q 2 s q for one dimensional q state ferromagnetic potts models evolving under parallel fully synchronous dynamics at zero temperature from an initially disordered state where p q is the persistence exponent for parallel dynamics and s q 1 8 2 2 cos 1 2 q q 2 1 2 2 is the persistence exponent under serial asynchronous dynamics this result is a consequence of an exact albeit non trivial mapping of the evolution of configurations of potts spins under parallel dynamics to the dynamics of two decoupled reaction diffusion systems

asymptotic behavior of densities for two particle annihilating random walks consider the system of particles on d where particles are of two types a andb and execute simple random walks in continuous time particles do not interact with their own type but when ana particle meets ab particle both disappear i e are annihilated this system serves as a model for the chemical reactiona b inert we analyze the limiting behavior of the densities a t and b t when the initial state is given by homogeneous poisson random fields we prove that for equal initial densities a 0 b 0 there is a change in behavior fromd 4 where a t b t c t d 4 tod 4 where a t b t c tast for unequal initial densities a 0 b 0 a t e c l ind 1 a t e ct logt ind 2 and a t e ct ind 3 the termc depends on the initial densities and changes withd techniques are from interacting particle systems the behavior for this two particle annihilation process has similarities to those for coalescing random walks a a a and annihilating random walks a a inert the analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system

persistence exponents and the statistics of crossings and occupation times for gaussian stationary processes we consider the persistence probability the occupation time distribution and the distribution of the number of zero crossings for discrete or equivalently discretely sampled gaussian stationary processes gsps of zero mean we first consider the ornstein uhlenbeck process finding expressions for the mean and variance of the number of crossings and the partial survival probability we then elaborate on the correlator expansion developed in an earlier paper g c m a ehrhardt and a j bray phys rev lett 88 070602 2002 to calculate discretely sampled persistence exponents of gsps of known correlator by means of a series expansion in the correlator we apply this method to the processes d n x dt n ensuremath eta t with ng 3 incorporating an extrapolation of the series to the limit of continuous sampling we then extend the correlator method to calculate the occupation time and crossing number distributions as well as their partial survival distributions and the means and variances of the occupation time and number of crossings we apply these general methods to the d n x dt n ensuremath eta t processes for n 1 random walk n 2 random acceleration and larger n and to simple diffusion from random initial conditions in one to three dimensions the results for discrete sampling are extrapolated to the continuum limit where possible

non trivial exponents in the zero temperature dynamics of the 1d ising and potts models we consider the glauber dynamics of the q state potts model in one dimension at zero temperature starting with a random initial configuration we measure the density r t of spins which have never flipped from the beginning of the simulation until time t we find that for large t the density r t has a power law decay left r t sim t theta right where the exponent theta varies with q our simulations lead to theta simeq 37 for q 2 theta simeq 53 for q 3 and theta longrightarrow 1 as q longrightarrow infty

nearest neighbor distances in diffusion controlled reactions modelled by a single mobile trap we consider a system consisting of an infinite number of identical particles on a latttce initially uniformly distributed which diffuse in the presence of a single mobile trap and ask for the time dependent behavior of the distance of the trap from the nearest particle this quantity is a measure of the tendency of the system to self segregate we show by a simulation incorporating the exact enumeration method that in one dtmension the expected distance l t scales as l t t as t 0 where the exponent a depends only on the ratio of the diffusion constants a heuristic expression for a ts suggested analogous to a rigorous exponent found by ben avraham for a similar but not identical problem the flux into the trap is found to vary as t t independent of the dtffusion constants

universal scaling function for domain growth in the glauber ising chain the equal time correlation function is calculated at t 0 for the one dimensional ising model with glauber dynamics random initial conditions appropriate to a sudden quench from non zero temperature are imposed averaging over initial conditions yields the scaling form c r t f r2 t the scaling function is given by f x integral 01 dy pi y 1 y 1 2 exp x 4y and is universal i e independent of the probability distribution for the initial conditions

dob fuzzy controller design for non gaussian stochastic distribution systems using two step fuzzy identification this paper presents a novel non gaussian stochastic control framework for the problem of disturbance estimation and rejection by combining fuzzy identification technology with disturbance observer design first fuzzy logic models are used to approximate the output probability density functions pdfs of non gaussian processes such that the task of pdf shape control can be reduced to a fuzzy weight dynamics modeling and control problem next takagi sugeno fuzzy models with multiple disturbances are employed to describe the nonlinear relations between fuzzy weight dynamics and the control input in which a novel disturbance observer based pi type fuzzy feedback controller is designed to ensure the system stability and convergence of the tracking error to zero meanwhile the disturbance estimation and attenuation performance as well as the state constrained requirement can also be guaranteed moreover the novel composite observer is constructed by augmenting the disturbance estimation into the full state estimation the satisfactory tracking performance and full state observation effect can be achieved by the designed optimization algorithm finally simulations for paper making process are given to show the efficiency of the proposed approach

kinetics of random sequential parking on a line we study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line for the simplest fixed length parking distribution the model reduces to the known car parking problem and we present an alternate solution to this problem we also consider the general homogeneous case when the parking distribution varies asx 1 atx 1 with the lengthx of the filling interval we develop a scaling theory describing such mixture deposition processes and show that the scaled hole size distribution with xtz a scaling variable decays with the scaled mass as exp const 1 as we determine scaling exponentsz and and find that at large times the coverage t has a power law form 1 t t v with nonuniversal exponent 2 1 depending on the homogeneity index

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

a hierarchical structure of observer based adaptive fuzzy neural controller for mimo systems an observer based adaptive controller developed from a hierarchical fuzzy neural network hfnn is employed to solve the controller time delay problem for a class of multi input multi output mimo non affine nonlinear systems under the constraint that only system outputs are available for measurement by using the implicit function theorem and taylor series expansion the observer based control law and the weight update law of the hfnn adaptive controller are derived according to the design of the hfnn hierarchical fuzzy neural network the observer based adaptive controller can alleviate the online computation burden moreover the common adaptive controller is utilized to control all the mimo subsystems hence the number of adjusted parameters of the hfnn can be further reduced in this paper we prove that the proposed observer based adaptive controller can guarantee that all signals involved are bounded and that the outputs of the closed loop system track asymptotically the desired output trajectories

non markovian persistence and nonequilibrium critical dynamics the persistence exponent ensuremath theta for the global order parameter m t of a system quenched from the disordered phase to its critical point describes the probability p t ensuremath sim t ensuremath ensuremath theta that m t does not change sign in the time interval t following the quench we calculate ensuremath theta to o ensuremath epsilon 2 for model a of hohenberg and halperin rev mod phys 49 435 1977 and to order ensuremath epsilon for model c and show that at this order m t is a non markov process consequently to our knowledge ensuremath theta is a new exponent the calculation is performed by expanding around a markov process using a simplified version of the perturbation theory recently introduced by majumdar and sire phys rev lett 77 1420 1996