alternative proof for the localization of sinai s walk we give an alternative proof of the localization of sinai s random walk in random environment under weaker hypothesis than the ones used by sinai moreover we give estimates that are stronger than the one of sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood

transport in random correlated fields a review is given of recent developments in the diffusion properties of particles in the presence of local random fields as well as the conductivity of the analog random resistor network the effect of long range ferro and antiferro type correlations between the local fields on the diffusion and conductivity properties is considered a physical realization for such spatial correlations is diffusion on linear polymers in the presence of external uniform bias field for this case a universal diffusion law was found independent of the fractal dimension of the polymer chain or the euclidean dimension in which the polymer is embedded recent results for diffusion in two dimensions in the presence of a special case of correlated local fields are also reviewed

statistical properties of functionals of the paths of a particle diffusing in a one dimensional random potential we present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one dimensional quenched random potential we demonstrate the implementation of the formalism in two specific examples 1 where the functional corresponds to the local time spent by the particle around the origin and 2 where the functional corresponds to the occupation time spent by the particle on the positive side of the origin within an observation time window of size t we compute the disorder average distributions of the local time the inverse local time the occupation time and the inverse occupation time and show that in many cases disorder modifies the behavior drastically

using an efficient immune symbiotic evolution learning for compensatory neuro fuzzy controller this paper presents an efficient immune symbiotic evolution learning isel algorithm for the compensatory neuro fuzzy controller cnfc the proposed isel method includes three major components initial population subgroup symbiotic evolution and immune system algorithm first the self clustering algorithm that determines proper input space partitioning and finds the mean and variance of the gaussian membership functions and number of rules is applied to the initial population second the subgroup symbiotic evolution method that uses each subantibody represents a single fuzzy rule and the evolution of the rule itself third the immune system algorithm uses the clonal selection principle such that antibodies between others of high similar degree are canceled and these antibodies after processing will have higher quality accelerating the search and increasing the global search capacity finally the proposed cnfc with isel cnfc isel method is adopted to solve several nonlinear control problems the simulation results have shown that the proposed cnfc isel can outperform other methods

the orbifold chow ring of toric deligne mumford stacks the orbifold chow ring of a deligne mumford stack defined by abramovich graber and vistoli 2 is the algebraic version of the orbifold cohomology ring in troduced by w chen and ruan 7 8 by design this ring incorporates numerical invariants such as the orbifold euler characteristic and the orbifold hodge num bers of the underlying variety the product structure is induced by the degree zero part of the quantum product in particular it involves gromov witten invariants inspired by string theory and results in batyrev 3 and yasuda 28 one expects that in nice situations the orbifold chow ring coincides with the chow ring of a resolution of singularities fantechi and g ttsche 14 and uribe 25 verify this conjecture when the orbifold is symn 5 where 5 is a smooth projective surface with ks 0 and the resolution is hilbn the initial motivation for this project was to compare the orbifold chow ring of a simplicial toric variety with the chow ring of a cr pant resolution to achieve this goal we first develop the theory of toric deligne mumford stacks modeled on simplicial toric varieties a toric deligne mumford stack corresponds to a combinatorial object called a stacky fan as a first approximation this object is a simplicial fan with a distinguished lattice point on each ray in the fan more precisely a stacky fan s is a triple consisting of a finitely generated abelian group n a simplicial fan e in q z n with n rays and a map zn n where the image of the standard basis in zn generates the rays in e a rational simplicial fan e produces a canonical stacky fan s n e where n is the distinguished lattice and is the map defined by the minimal lattice points on the rays hence there is a natural toric deligne mumford stack associated to every simplicial toric variety a stacky fan encodes a group action on a quasi affine variety and the toric deligne mumford stack is the quotient if e corresponds to a smooth toric variety x e and s is the canonical stacky fan associated to e then we simply have x z we show that many of the basic concepts such as open and closed toric substacks line bundles and maps between toric deligne mumford stacks correspond to combinatorial notions we expect that many more results about toric varieties lift to the realm of stacks and hope that toric deligne mumford stacks will serve as a useful testing ground for general theories

selecting fuzzy if then rules for classification problems using genetic algorithms this paper proposes a genetic algorithm based method for selecting a small number of significant fuzzy if then rules to construct a compact fuzzy classification system with high classification power the rule selection problem is formulated as a combinatorial optimization problem with two objectives to maximize the number of correctly classified patterns and to minimize the number of fuzzy if then rules genetic algorithms are applied to this problem a set of fuzzy if then rules is coded into a string and treated as an individual in genetic algorithms the fitness of each individual is specified by the two objectives in the combinatorial optimization problem the performance of the proposed method for training data and test data is examined by computer simulations on the iris data of fisher

dct yager fnn a novel yager based fuzzy neural network with the discrete clustering technique earlier clustering techniques such as the modified learning vector quantization mlvq and the fuzzy kohonen partitioning fkp techniques have focused on the derivation of a certain set of parameters so as to define the fuzzy sets in terms of an algebraic function the fuzzy membership functions thus generated are uniform normal and convex since any irregular training data is clustered into uniform fuzzy sets gaussian triangular or trapezoidal the clustering may not be exact and some amount of information may be lost in this paper two clustering techniques using a kohonen like self organizing neural network architecture namely the unsupervised discrete clustering technique udct and the supervised discrete clustering technique sdct are proposed the udct and sdct algorithms reduce this data loss by introducing nonuniform normal fuzzy sets that are not necessarily convex the training data range is divided into discrete points at equal intervals and the membership value corresponding to each discrete point is generated hence the fuzzy sets obtained contain pairs of values each pair corresponding to a discrete point and its membership grade thus it can be argued that fuzzy membership functions generated using this kind of a discrete methodology provide a more accurate representation of the actual input data this fact has been demonstrated by comparing the membership functions generated by the udct and sdct algorithms against those generated by the mlvq fkp and pseudofuzzy kohonen partitioning pfkp algorithms in addition to these clustering techniques a novel pattern classifying network called the yager fuzzy neural network fnn is proposed in this paper this network corresponds completely to the yager inference rule and exhibits remarkable generalization abilities a modified version of the pseudo outer product pop yager fnn called the modified yager fnn is introduced that eliminates the drawbacks of the earlier network and yields superior performance extensive experiments have been conducted to test the effectiveness of these two networks using various clustering algorithms it follows that the sdct and udct clustering algorithms are particularly suited to networks based on the yager inference rule

mellin barnes integrals as fourier mukai transforms we study the generalized hypergeometric system introduced by gelfand kapranov and zelevinsky and its relationship with the toric deligne mumford dm stacks recently studied by borisov chen and smith we construct series solutions with values in a combinatorial version of the chen ruan orbifold cohomology and in the k theory of the associated dm stacks in the spirit of the homological mirror symmetry conjecture of kontsevich we show that the k theory action of the fourier mukai functors associated to basic toric birational maps of dm stacks are mirrored by analytic continuation transformations of mellin barnes type

dynamics of excitation in systems with a randomly modulated decay channel abstract we have investigated the kinetics of excitation in the frame of the conventional pauli master equation for a molecular aggregate with a decay channel attached to one distinguished molecule or site as a principally new feature we assume the rate of probability flow through the decay channel to be a randomly modulated function of time the modulation is described by a markoff stochastic process and we do not invoke the white noise assumption an exact calculation is given for a broad family of stochastic processes which bridges and includes the asymmetric random telegraph signal and the gaussian process the general method is then applied in three physically relevant situations one molecule aggregate cyclic antenna system and infinite linear chain in these models we discuss the site occupation probabilities the aggregate excitation function and the mean de excitation time

lingering random walks in random environment on a strip we consider a recurrent random walk rw in random environment re on a strip we prove that if the re is i i d and its distribution is not supported by an algebraic subsurface in the space of parameters defining the re then the rw exhibits the log t 2 asymptotic behaviour the exceptional algebraic subsurface is described by an explicit system of algebraic equations

random walk in a random medium in one dimension applying scaling and universality arguments the long time behavior of the probability distribution for a random walk in a one dimensional random medium satisfying sinai s constraint is obtained analytically the convergence to this asymptotic limit and the fluctuations of this distribution are evaluated by solving numerically the stochastic equations for this walk

limit theorems for one dimensional diffusions and random walks in random environments the limiting behavior of one dimensional diffusion process in an asymptotically self similar random environment is investigated through the extension of brox s method similar problems are then discussed for a random walk in a random environment with the aid of optional sampling from a diffusion model an extension of the result of sinai is given in the case of asymptotically self similar random environments

einstein s relation between diffusion constant and mobility for a diffusion model an ornstein uhlenbeck process in a periodic potential inr d is considered it has been shown previously that this process satisfies a central limit theorem in the sense that by rescaling space and time in a suitable way the distribution of the process converges to that of a wiener process with nonsingular diffusion matrix here a rigorous proof is given of a version of einstein s formula for this model relating the diffusion constant to the mobility of the system

rspop rough set based pseudo outer product fuzzy rule identification algorithm system modeling with neuro fuzzy systems involves two contradictory requirements interpretability verses accuracy the pseudo outer product pop rule identification algorithm used in the family of pseudo outer product based fuzzy neural networks popfnn suffered from an exponential increase in the number of identified fuzzy rules and computational complexity arising from high dimensional data this decreases the interpretability of the popfnn in linguistic fuzzy modeling this article proposes a novel rough set based pseudo outer product rspop algorithm that integrates the sound concept of knowledge reduction from rough set theory with the pop algorithm the proposed algorithm not only performs feature selection through the reduction of attributes but also extends the reduction to rules without redundant attributes as many possible reducts exist in a given rule set an objective measure is developed for popfnn to correctly identify the reducts that improve the inferred consequence experimental results are presented using published data sets and real world application involving highway traffic flow prediction to evaluate the effectiveness of using the proposed algorithm to identify fuzzy rules in the popfnn using compositional rule of inference and singleton fuzzifier popfnn cri s architecture results showed that the proposed rough set based pseudo outer product algorithm reduces computational complexity improves the interpretability of neuro fuzzy systems by identifying significantly fewer fuzzy rules and improves the accuracy of the popfnn

an efficient immune based symbiotic particle swarm optimization learning algorithm for tsk type neuro fuzzy networks design in this paper we propose a new learning algorithm that can be used to design tsk type neuro fuzzy networks though there has been a great deal of interest in the use of immune algorithms ias for computer science and engineering in terms of fundamental methodologies they are not dramatically different from other algorithms in order to enhance the ia performance we propose the immune based symbiotic particle swarm optimization ispso for use in tsk type neuro fuzzy networks for solving the prediction and skin color detection problems the proposed ispso embeds the symbiotic evolution scheme in an ia and utilizes particle swarm optimization pso to improve the mutation mechanism in order to avoid trapping in a local optimal solution and to ensure the search capability of a near global optimal solution mutation plays an important role therefore we employed the advantages of pso to improve the mutation mechanism and used a method that introduces chaotic mapping with certainty ergodicity and the stochastic property into pso to improve global convergence unlike the ia that uses each individual in a population as a full solution to a problem symbiotic evolution assumes that each individual in a population represents only a partial solution to a problem complex solutions combine several individuals in the population

singular behaviour of certain infinite products of random 2 2 matrices the authors consider an infinite product of random matrices which appears in several physical problems in particular the ising chain in a random field the random matrices depend analytically on a parameter epsilon in such a way that for 0 they all commute under certain conditions they find that the lyapunov index of this product behaves approximately as c 2 for to 0 their approach is based on the decomposition of an exact integral equation for this problem into two reduced equations they give an expression for the exponent alpha in terms of the probability distribution of the matrices and for the proportionality constant c in terms of the solutions of the reduced integral equations in cases where exact results are available agreement is obtained the physical consequences for disordered one dimensional systems are pointed out

exact solutions for the statistics of extrema of some random 1d landscapes application to the equilibrium and the dynamics of the toy model abstract the real space renormalization group rsrg method introduced previously for the brownian landscape is generalized to obtain the joint probability distribution of the subset of the important extrema at large scales of other one dimensional landscapes for a large class of models we give exact solutions obtained either by the use of constrained path integrals in the continuum limit or by solving the rsrg equations via an ansatz which leads to the liouville equation we apply in particular our results to the toy model energy landscape which consists in a quadratic potential plus a brownian potential which describes among others the energy of a single domain wall in a 1d random field ising model rfim in the presence of a field gradient the measure of the renormalized landscape is obtained explicitly in terms of airy functions and allows to study in detail the boltzmann equilibrium of a particle at low temperature as well as its non equilibrium dynamics for the equilibrium we give results for the statistics of the absolute minimum which dominates at zero temperature and for the configurations with nearly degenerate minima which govern the thermal fluctuations at very low temperature for the dynamics we compute the distribution over samples of the equilibration time or equivalently the distribution of the largest barrier in the system we also study the properties of the rare configurations presenting an anomalously large equilibration time which govern the long time dynamics we compute the disorder averaged diffusion front which interpolates between the kesten distribution of the sinai model at short rescaled time and the reaching of equilibrium at long rescaled time finally the method allows to describe the full coarsening i e many domain walls of the 1d rfim in a field gradient as well as its equilibrium

a self adaptive neural fuzzy network with group based symbiotic evolution and its prediction applications in this paper we propose a self adaptive neural fuzzy network with group based symbiotic evolution sanfn gse method a self adaptive learning algorithm consists of two major components first a self clustering algorithm sca identifies a parsimonious internal structure an internal structure is said to be parsimonious in the sense that the number of clusters fuzzy rules is equal to the true number of clusters in a given training data set the proposed sca is an online method and is a distance based connectionist clustering method unlike the traditional cluster techniques that only consider the total variation to updates the only one mean and deviation the proposed sca method considers the variation of each dimension for the input data second a group based symbiotic evolution learning gse method is used to adjust the parameters for the desired outputs the gse method is different from traditional gas genetic algorithms with each chromosome in the gse method representing a fuzzy system moreover in the gse method there are several groups in the population each group represents a set of the chromosomes that belong to a cluster computing by the sca in this paper we used numerical time series examples one step ahead prediction mackey glass chaotic time series and sunspot number forecasting to evaluate the proposed sanfn gse model the performance of the sanfn gse model compares excellently with other existing models in our time series simulations

intermittency in random maps abstract the escape probability for a random walk on a one dimensional lattice is discussed in terms of random maps the global dynamics is found to be intermittent the laminar regions with long sojourn near the upper fixed point are broken by irregular bursts intermittency emerges even if the sinai condition is not satisfied it is shown that if p is the probability of choosing the upper map the average laminar length diverges as 1 p

gensofnn a generic self organizing fuzzy neural network existing neural fuzzy neuro fuzzy networks proposed in the literature can be broadly classified into two groups the first group is essentially fuzzy systems with self tuning capabilities and requires an initial rule base to be specified prior to training the second group of neural fuzzy networks on the other hand is able to automatically formulate the fuzzy rules from the numerical training data no initial rule base needs to be specified prior to training a cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters however most existing neural fuzzy systems whether they belong to the first or second group encountered one or more of the following major problems they are 1 inconsistent rule base 2 heuristically defined node operations 3 susceptibility to noisy training data and the stability plasticity dilemma and 4 needs for prior knowledge such as the number of clusters to be computed hence a novel neural fuzzy system that is immune to the above mentioned deficiencies is proposed in this paper this new neural fuzzy system is named the generic self organizing fuzzy neural network gensofnn the gensofnn network has strong noise tolerance capability by employing a new clustering technique known as discrete incremental clustering dic the fuzzy rule base of the gensofnn network is consistent and compact as gensofnn has built in mechanisms to identify and prune redundant and or obsolete rules extensive simulations were conducted using the proposed gensofnn network and its performance is encouraging when benchmarked against other neural and neural fuzzy systems

a new class of long tailed pausing time densities for the ctrw we present some asymptotic results for the family of pausing time densities having the asymptotic t property t t ln1 t t 1 in particular we show that for this class of pausing time densities the mean squared displacement r2 t is asymptotically proportional to ln t t and the asymptotic distribution of the displacement has a negative exponential form

tilting sheaves on toric varieties in 19 a king states the following conjecture any smooth complete toric variety has a tilting bundle whose summands are line bundles the goal of this paper is to prove king s conjecture for the following types of smooth complete toric varieties i any d dimensional smooth complete toric variety with splitting fan ii any d dimensional smooth complete toric variety with picard number 2 iii the blow up of any smooth complete minimal toric surface at t invariants points

frobenius morphisms and derived categories on two dimensional toric deligne mumford stacks abstract for a toric deligne mumford dm stack x we can consider a certain generalization of the frobenius endomorphism for such an endomorphism f x x on a 2 dimensional toric dm stack x we show that the push forward f o x of the structure sheaf generates the bounded derived category of coherent sheaves on x we also choose a full strong exceptional collection from the set of direct summands of f o x in several examples of two dimensional toric dm orbifolds x

zero white noise limit through dirichlet forms with application to diffusions in a random medium we study the zero white noise limit for diffusions in a continuous multidimensional medium given a continuous function on n w we consider diffusions whose drift term is the gradient ofw and whose diffusion coefficient is constant equal to e we describe the asymptotics of the exit time from a domain and of the law of the process when e tends to zero by applying these results to a random self similar mediumw we prove limit theorems for a diffusion in a random medium our theorems agree with results usually proved through the large deviation principle although in our setup this last tool is not available we extend to the multidimensional case properties of diffusions in a random medium already known in one dimension

localisation and universal fluctuations in ultraslow diffusion processes we study ultraslow diffusion processes with logarithmic mean squared displacement msd comparison of annealed renewal continuous time random walks ctrws with logarithmic waiting time distribution and sinai diffusion in quenched random landscapes reveals striking similarities despite the great differences in their physical nature in particular they exhibit a weakly non ergodic disparity of the time averaged and ensemble averaged msds remarkably for the ctrw we observe that the fluctuations of time averages become universal with an exponential suppression of mobile trajectories we discuss the fundamental connection between the golosov localization effect and non ergodicity in the sense of the disparity between ensemble averaged msd and time averaged msd

diffusion in a one dimensional lattice with random asymmetric transition rates the authors study one dimensional continuous time random walks for which the pairs wn wn 1 of nearest neighbour transition rates are assumed to be independent equally distributed random variables the long time asymptotic behaviour of the mean displacement x t is determined exactly for a specific model system in which diodes u 0 and two way bonds lambda v v occur with probabilities p and 1 p respectively for lambda 1 p we find that x t approximately tnu f beta 1ln t where nu ln 1 p ln lambda and beta ln lambda and where f is a periodic function with period 1 the mean displacement thus not only increases slower than linearly in time but exhibits superimposed non decaying oscillations

dynamical properties of a random walk in a one dimensional random medium abstract the random motion of a particle in a one dimensional continuous random medium with random forces is investigated by making use of the large scale equivalence of the properties of the walk with those of a directed random walk on a discrete lattice when the disorder is weak enough a normal drift diffusion regime takes place whereas for strong disorder anomalous behaviours occur it is shown that these results may be obtained by introducing a renormalized lattice with a finite spacing in the normal phase this spacing appears explicitly in the result while it turns out to be irrelevant in the anomalous ones the dynamical exponents as well as the prefactors of the power laws of the particle position and of its average dispresion are explicitly calculated in the anomalous phases

localization of random walks in one dimensional random environments we consider a random walk on the one dimensional semi lattice 0 1 2 we prove that the moving particle walks mainly in a finite neighbourhood of a point depending only on time and a realization of the random environment the size of this neighbourhood is estimated the limit parameters of the walks are also determined

slow movement of a random walk on the range of a random walk in the presence of an external field in this article a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions d ge 5 this demonstrates that unlike in the supercritical percolation setting a slowdown effect occurs as soon as a non trivial bias is introduced the proof applies a decomposition of the underlying simple random walk path at its cut times to relate the associated biased random walk to a one dimensional random walk in a random environment in sinai s regime via this approach a corresponding aging result is also proved

ito versus stratonovich a survey is given of the facts and fancies concerning the nonlinear langevin or ito equation actually it is merely a pre equation which becomes an equation when an interpretation rule is added the rules of ito and stratonovich differ but both are mathematically consistent and therefore equally admissible conventions the reason why they seem to lead to physical differences is that the langevin approach used to arrive at the equation involves a tacit assumption for systems with external noise this assumption can be justified and it is then clear that the stratonovich rule applies systems with internal noise however can only be properly described by a master equation and the ito stratonovich controversy never enters afterward one is free to model the resulting fluctuations either with an ito or a stratonovich scheme but that does not lead to any new information

persistence of randomly coupled fluctuating interfaces we study the persistence properties in a simple model of two coupled interfaces characterized by heights h 1 and h 2 respectively each growing over a d dimensional substrate the first interface evolves independently of the second and can correspond to any generic growing interface e g of the edwards wilkinson or of the kardar parisi zhang variety the evolution of h 2 however is coupled to h 1 via a quenched random velocity field in the limit d ensuremath rightarrow 0 our model reduces to the matheron de marsily model in two dimensions for d 1 our model describes a rouse polymer chain in two dimensions advected by a transverse velocity field we show analytically that after a long waiting time t 0 ensuremath rightarrow ensuremath infty the stochastic process h 2 at a fixed point in space but as a function of time becomes a fractional brownian motion with a hurst exponent h 2 1 ensuremath ensuremath beta 1 2 where ensuremath beta 1 is the growth exponent characterizing the first interface the associated persistence exponent is shown to be ensuremath theta s 2 1 ensuremath h 2 ensuremath beta 1 2 these analytical results are verified by numerical simulations

an extension to fuzzy cognitive maps for classification and prediction fuzzy cognitive maps fcms as an illustrative causative representation of modeling and manipulation of complex systems can be used to model the dynamic behavior of the investigated systems however due to defects in expression and architecture the traditional fcms and most of their relevant extensions are not applicable to classification problems to solve this problem this paper presents an approach that directly extends the model by translating the reasoning mechanism of traditional fcms to a set of fuzzy if then rules moreover the proposed approach fully considers the contribution of the inputs to the activation of the fuzzy rules and quantifies the causalities using mutual subsethood which works in conjunction with volume defuzziflcation in a gradient descent learning framework in this manner our approach enhances the capability of the conventional fcms to automatically identify membership functions and quantify causalities despite the increase in the number of tunable parameters experimental results show that the proposed approach efficiently extends the application of the traditional fcms into classification problems while keeping the ability for prediction and approximation

fuzzy artmap a neural network architecture for incremental supervised learning of analog multidimensional maps a neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors which may represent fuzzy or crisp sets of features the architecture called fuzzy artmap achieves a synthesis of fuzzy logic and adaptive resonance theory art neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and art category choice resonance and learning four classes of simulation illustrated fuzzy artmap performance in relation to benchmark backpropagation and generic algorithm systems these simulations include finding points inside versus outside a circle learning to tell two spirals apart incremental approximation of a piecewise continuous function and a letter recognition database the fuzzy artmap system is also compared with salzberg s nge systems and with simpson s fmmc system

tail estimates for one dimensional random walk in random environment suppose that the integers are assigned i i d random variables x taking values in the unit interval which serve as an environment this environment defines a random walk x k called a rwre which when atx moves one step to the right with probability x and one step to the left with probability 1 x solomon 1975 determined the almost sure asymptotic speed rate of escape of a rwre for certain environment distributions where the drifts 2 x 1 can take both positive and negative values we show that the chance of the rwre deviating below this speed has a polynomial rate of decay and determine the exponent in this power law for environments which allow only positive and zero drifts we show that these large deviation probabilities decay like exp cn1 3 this differs sharply from the rates derived by greven and den hollander 1994 for large deviation probabilities conditioned on the environment as a by product we also provide precise tail and moment estimates for the total population size in a branching process with random environment

diffusion in periodic correlated random forcing landscapes we study the dynamics of a brownian particle in a strongly correlated quenched random potential defined as a periodically extended with period l finite trajectory of a fractional brownian motion with arbitrary hurst exponent h in 0 1 while the periodicity ensures that the ultimate long time behavior is diffusive the generalised sinai potential considered here leads to a strong logarithmic confinement of particle trajectories at intermediate times these two competing trends lead to dynamical frustration and result in a rich statistical behavior of the diffusion coefficient d l although one has the typical value d rm typ l sim exp beta l h we show via an exact analytical approach that the positive moments k 0 scale like langle d k l rangle sim exp c k beta l h 1 1 h and the negative ones as langle d k l rangle sim exp a k beta l h 2 c and a being numerical constants and beta the inverse temperature these results demonstrate that d l is strongly non self averaging we further show that the probability distribution of d l has a log normal left tail and a highly singular one sided log stable right tail reminiscent of a lifshitz singularity

beyond aztec castles toric cascades in the dp 3 quiver given one of an infinite class of supersymmetric quiver gauge theories string theorists can associate a corresponding toric variety which is a calabi yau 3 fold as well as an associated combinatorial model known as a brane tiling in combinatorial language a brane tiling is a bipartite graph on a torus and its perfect matchings are of interest to both combinatorialists and physicists alike a cluster algebra may also be associated to such quivers and in this paper we study the generators of this algebra known as cluster variables for the quiver associated to the cone over the del pezzo surface d p 3 in particular mutation sequences involving mutations exclusively at vertices with two in coming arrows and two out going arrows are referred to as toric cascades in the string theory literature such toric cascades give rise to interesting discrete integrable systems on the level of cluster variable dynamics we provide an explicit algebraic formula for all cluster variables that are reachable by toric cascades as well as a combinatorial interpretation involving perfect matchings of subgraphs of the d p 3 brane tiling for these formulas in most cases

random walk in a two dimensional self affine random potential properties of the anomalous diffusion phase at small external force we study the dynamical response to an external force f for a particle performing a random walk in a two dimensional quenched random potential of hurst exponent h 1 2 we present numerical results on the statistics of first passage times that satisfy closed backward master equations we find that there exists a zero velocity phase in a finite region of the external force 0lfl f c where the dynamics follows the anomalous diffusion law x t ensuremath sim ensuremath xi f t ensuremath mu f the anomalous exponent 0l ensuremath mu f l1 and the correlation length ensuremath xi f vary continuously with f in the limit of vanishing force f ensuremath rightarrow 0 we measure the following power laws the anomalous exponent vanishes as ensuremath mu f ensuremath propto f a with a ensuremath simeq 0 6 instead of a 1 in dimension d 1 and the correlation length diverges as ensuremath xi f ensuremath propto f ensuremath ensuremath nu with ensuremath nu ensuremath simeq 1 29 instead of ensuremath nu 2 in dimension d 1 our main conclusion is thus that the dynamics renormalizes onto an effective directed trap model where the traps are characterized by a typical length ensuremath xi f along the direction of the force and by a typical barrier 1 ensuremath mu f the fact that these traps are smaller in linear size and in depth than in dimension d 1 means that the particle uses the transverse direction to find lower barriers

statistical and dynamical properties of the discrete sinai model at finite times we study the sinai model for the diffusion of a particle in a one dimensional quenched random energy landscape we consider the particular case of discrete energy landscapes made of random jumps on the semi infinite line with a reflecting wall at the origin we compare the statistical distribution of the successive local minima of the energy landscapes which we derive explicitly with the dynamical distribution of the position of the diffusing particle which we obtain numerically at high temperature the two distributions match only in the large time asymptotic regime at low temperature however we find even at finite times a clear correspondence between the statistical and dynamical distributions with additional interesting oscillatory behaviours

infinite moments of the partition function for random walks in a random potential we consider a system of random walks directed polymers in a potential which is random in space and time investigations into untypical behavior and the inverse of the partition function leads to the result that regardless of the strength of the potential and in all dimensions all higher moments of the partition function are unbounded as time goes to infinity one can interpret this result in a many body quantum mechanical setting as saying that no matter how small the strength of an attractive potential in any dimension one can find n the number of particles large enough so that there is a bound state

monodromy of monomially admissible fukaya seidel categories mirror to toric varieties abstract mirror symmetry for a toric variety involves laurent polynomials whose symplectic topology is related to the algebraic geometry of the toric variety we show that there is a monodromy action on the monomially admissible fukaya seidel categories of these laurent polynomials as the arguments of their coefficients vary that corresponds under homological mirror symmetry to tensoring by a line bundle naturally associated to the monomials whose coefficients are rotated in the process we introduce the monomially admissible fukaya seidel category as a new interpretation of the fukaya seidel category of a laurent polynomial on c n which has other potential applications and give evidence of homological mirror symmetry for non compact toric varieties

continuity and anomalous fluctuations in random walks in dynamic random environments numerics phase diagrams and conjectures we perform simulations for one dimensional continuous time random walks in two dynamic random environments with fast independent spin flips and slow simple symmetric exclusion decay of space time correlations respectively we focus on the asymptotic speeds and the scaling limits of such random walks we observe different behaviors depending on the dynamics of the underlying random environment and the ratio between the jump rate of the random walk and the one of the environment we compare our data with well known results for static random environment we observe that the non diffusive regime known so far only for the static case can occur in the dynamical setup too such anomalous fluctuations give rise to a new phase diagram further we discuss possible consequences for more general static and dynamic random environments

the effect of boundaries on the spectrum of a one dimensional random mass dirac hamiltonian the average density of states dos of the one dimensional dirac hamiltonian with a random mass on a finite interval 0 l is derived our method relies on the eigenvalue distributions extreme value statistics problem which are obtained explicitly the well known dyson singularity is recovered above the crossover energy below c we find a log normal suppression of the average dos

a novel generic hebbian ordering based fuzzy rule base reduction approach to mamdani neuro fuzzy system there are two important issues in neuro fuzzy modeling 1 interpretability the ability to describe the behavior of the system in an interpretable way and 2 accuracy the ability to approximate the outcome of the system accurately as these two objectives usually exert contradictory requirements on the neuro fuzzy model certain compromise has to be undertaken this letter proposes a novel rule reduction algorithm namely hebb rule reduction and an iterative tuning process to balance interpretability and accuracy the hebb rule reduction algorithm uses hebbian ordering which represents the degree of coverage of the samples by the rule as an importance measure of each rule to merge the membership functions and hence reduces the number of the rules similar membership functions mfs are merged by a specified similarity measure in an order of hebbian importance and the resultant equivalent rules are deleted from the rule base the rule with a higher hebbian importance will be retained among a set of rules the mfs are tuned through the least mean square lms algorithm to reduce the modeling error the tuning of the mfs and the reduction of the rules proceed iteratively to achieve a balance between interpretability and accuracy three published data sets by nakanishi nakanishi turksen sugeno 1993 the pat synthetic data set pal mitra mitra 2003 and the traffic flow density prediction data set are used as benchmarks to demonstrate the effectiveness of the proposed method good interpretability as well as high modeling accuracy are derivable simultaneously and are suitably benchmarked against other well established neuro fuzzy models

distribution of dynamical quantities in the contact process random walks and quantum spin chains in random environments we study the distribution of dynamical quantities in various one dimensional disordered models the critical behavior of which is described by an infinite randomness fixed point in the disordered contact process the survival probability mathcal p t is found to show multiscaling in the critical point meaning that mathcal p t t ensuremath ensuremath delta where the environment and time dependent exponent ensuremath delta has a universal limit distribution when t ensuremath rightarrow ensuremath infty the limit distribution is determined by the strong disorder renormalization group method analytically in the end point of a semi infinite lattice where it is found to be exponential while in the infinite system conjectures on its limiting behaviors for small and large ensuremath delta which are based on numerical results are formulated by the same method the survival probability in the problem of random walks in random environments is also shown to exhibit multiscaling with an exponential limit distribution in addition to this the imaginary time spin spin autocorrelation function of the random transverse field ising chain is found to have a form similar to that of survival probability of the contact process at the level of the renormalization approach consequently a relationship between the corresponding limit distributions in the two problems can be established finally the distribution of the spontaneous magnetization in this model is also discussed

on the conjecture of king for smooth toric deligne mumford stacks abstract we construct full strong exceptional collections of line bundles on smooth toric fano deligne mumford stacks of picard number at most two and of any picard number in dimension two it is hoped that the approach of this paper will eventually lead to the proof of the existence of such collections on all smooth toric nef fano deligne mumford stacks

exact results on sinai s diffusion we study the continuum version of sinai s problem of a random walker in a random force field in one dimension a method of stochastic representation is used to represent various probability distributions in this problem mean probability density function and first passage time distributions this method reproduces already known rigorous results and also confirms directly some recent results derived using approximation schemes we demonstrate clearly in the sinai scaling regime that the disorder dominates the problem and that the thermal distributions tend to zero one laws

large deviations for a brownian motion in a drifted brownian potential we derive a large deviation principle both quenched and annealed for a one dimensional diffusion process in a drifted brownian environment providing the continuous time analogue of what comets gantert and zeitouni recently establish for the random walk in random environment a key ingredient kotani s lemma allows us to compute the corresponding rate functions the results are more explicit than in the discrete time setting

discrete schemes for processes in random media we present discrete schemes for processes in random media we prove two results the first one is the convergence of sinai s random walks in random environments to the brox model the second one is the convergence of random walks in media with random gates to a continuous process in a poisson potential the proofs are based on the following idea we consider the discrete media as random potentials for continuous models

the limit distribution of sinai s random walk in random environment abstract recently sinai proved that if x n is a one dimensional random walk in random environment which is recurrent then log n 2 x n converges in distribution here we calculate the limit distribution explicitly

simplified interval type 2 fuzzy neural networks this paper describes a self evolving interval type 2 fuzzy neural network fnn for various applications as type 1 fuzzy systems cannot effectively handle uncertainties in information within the knowledge base we propose a simple interval type 2 fnn which uses interval type 2 fuzzy sets in the premise and the takagi sugeno kang tsk type in the consequent of the fuzzy rule the tsk type consequent of fuzzy rule is a linear combination of exogenous input variables given an initially empty the rule base all rules are generated with on line type 2 fuzzy clustering instead of the time consuming k m iterative procedure the design factors ql and qr are learned to adaptively adjust the upper and lower positions on the left and right limit outputs using the parameter update rule based on a gradient descent algorithm simulation results demonstrate that our approach yields fewer test errors and less computational complexity than other type 2 fnns

a robust competitive clustering algorithm with applications in computer vision this paper addresses three major issues associated with conventional partitional clustering namely sensitivity to initialization difficulty in determining the number of clusters and sensitivity to noise and outliers the proposed robust competitive agglomeration rca algorithm starts with a large number of clusters to reduce the sensitivity to initialization and determines the actual number of clusters by a process of competitive agglomeration noise immunity is achieved by incorporating concepts from robust statistics into the algorithm rca assigns two different sets of weights for each data point the first set of constrained weights represents degrees of sharing and is used to create a competitive environment and to generate a fuzzy partition of the data set the second set corresponds to robust weights and is used to obtain robust estimates of the cluster prototypes by choosing an appropriate distance measure in the objective function rca can be used to find an unknown number of clusters of various shapes in noisy data sets as well as to fit an unknown number of parametric models simultaneously several examples such as clustering mixture decomposition line plane fitting segmentation of range images and estimation of motion parameters of multiple objects are shown

projective toric varieties as fine moduli spaces of quiver representations this paper proves that every projective toric variety is the fine moduli space for stable representations of an appropriate bound quiver to accomplish this we study the quiver q with relations r corresponding to the finite dimensional algebra mathop rm end nolimits textstyle bigoplus nolimits i 0 r l i where cal l scr o x l 1 ldots l r is a list of line bundles on a projective toric variety x the quiver q defines a smooth projective toric variety called the multilinear series cal l and a map x longrightarrow cal l we provide necessary and sufficient conditions for the induced map to be a closed embedding as a consequence we obtain a new geometric quotient construction of projective toric varieties under slightly stronger hypotheses on cal l the closed embedding identifies x with the fine moduli space of stable representations for the bound quiver q r

one dimensional diffusion in a semiinfinite poisson random force we consider the one dimensional diffusion of a particle on a semiinfinite line and in a piecewise linear random potential we first present a new formalism which yields an analytical expression for the green function of the fokker planck equation valid for any deterministic construction of the potential profile the force is then taken to be an asymmetric dichotomic process solving the corresponding energy dependent stochastic riccati equation in the space asymptotic regime we give an exact probabilistic description of returns to the origin this method allows for a time asymptotic characterization of the underlying dynamical phases when the two values taken by the dichotomic force are of different signs there occur trapping potential wells with a broad distribution of trapping times and dynamical phases may appear depending on the man force if both values are negative the time asymptotic mean value of the probability density at the origin is proportional to the absolute value of the mean force if they are both positive traps no longer exist and the dynamics is always normal problems with a shot noise force and with a gaussian white noise force are solved as appropriate limiting cases

random walk in a one dimensional random medium abstract the random walk of a particle in a one dimensional random medium is examined by means of the equivalent transfer rates technique in the discrete as well as in the continuous version of the model the probability distributions of the energy dependent equivalent transfer rates are found analytically either by a matching procedure in the discrete case or exactly in the continuous model both discrete and continuous models are shown to belong to the same universality class the average probability of presence of the particle at its initial point is then computed for a non zero global bias it decreases at large times according to a negative power law with an exponent depending on disorder and bias when there is no global bias sinai s model the decay at large times follows a logarithmic law

exact results and self averaging properties for random random walks on a one dimensional infinite lattice we present new exact results for a one dimensional asymmetric disordered hopping model the lattice is taken infinite from the start and we do not resort to the periodization scheme used by derrida an explicit resummation allows for the calculation of the velocityv and the diffusion constantd which are found to coincide with those given by derrida and for demonstrating thatv is indeed a self averaging quantity the same property is established ford in the limiting case of a directed walk