pseudolikelihood decimation algorithm improving the inference of the interaction network in a general class of ising models in this letter we propose a new method to infer the topology of the interaction network in pairwise models with ising variables by using the pseudolikelihood method plm at high temperature it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups however at lower temperatures the plm is much less effective and the result depends on subjective choices such as the value of the l1 regularizer and that of the threshold to separate nonzero couplings from null ones we introduce a decimation procedure based on the plm that recursively sets to zero the less significant couplings until the variation of the pseudolikelihood signals that relevant couplings are being removed the new method is fully automated and does not require any subjective choice by the user numerical tests have been performed on a wide class of ising models having different topologies from random graphs to finite dimensional lattices and different couplings both diluted ferromagnets in a field and spin glasses these numerical results show that the new algorithm performs better than standard plm

direct model reference takagi sugeno fuzzy control of siso nonlinear systems this study presents a novel direct model reference fuzzy controller it relaxes the special conditions on the reference model that is required by some of the approaches described in the literature as well as covering a more general class of takagi sugeno t s systems the stability of the proposed method is proved using a proper lyapunov function in addition the effects of modeling errors on the proposed controller are considered and a robust modification algorithm to alleviate this problem is introduced and analyzed the proposed method is then simulated on a flexible joint robot in a feedback linearization form and on chua s chaotic electrical circuit finally it is implemented and tested on a nonlinear dc motor with nonlinear state dependent disturbance

vertexwise criteria for admissibility of alcoves we give a new description of the set rm adm mu of admissible alcoves as an intersection of certain obtuse cones of alcoves and we show this description may be given by imposing conditions vertexwise we use this to prove the vertexwise admissibility conjecture of pappas rapoport smithling the same idea gives simple proofs of two ingredients used in the proof of the kottwitz rapoport conjecture on existence of crystals with additional structure

a ga based fuzzy modeling approach for generating tsk models this paper proposes a new genetic based modeling method for building simple and well defined tsk models with scatter type input partitions our approach manages all attributes characterizing the structure of a tsk model simultaneously particularly it determines the number of rules the input partition the participating inputs in each rule and the consequent parameters the model building process is divided into two phases in phase one the structure learning task is formulated as a multi objective optimization problem which is resolved using a novel genetic based structure learning gbsl scheme apart from the mean square error mse and the number of rules three additional criteria are introduced in the fitness function for measuring the quality of the partitions optimization of these measures leads to models with representative rules small overlapping and efficient data cover in order to obtain models with accurate data fitting and good local performance the consequent parameters are determined using a local mse function while the overall model is evaluated on the basis of a global mse function the search capabilities of the suggested structure learning scheme are significantly enhanced by including a highly effective local search operator implemented by a micro genetic algorithm and four problem specific operators finally a genetic based parameter learning gbpl scheme is suggested in phase two which performs fine tuning of the initial models obtained after structure learning the performance of the proposed modeling approach is evaluated using a static example and a well known dynamic benchmark problem simulation results demonstrate that our models outperform those suggested by other methods with regard to simplicity model structure and accuracy

dimension formula for the affine deligne lusztig variety x mu b x μ b the study of certain union x mu b of affine deligne lusztig varieties in the affine flag varieties arose from the study of shimura varieties with iwahori level structure in this paper we give an explicit dimension formula for x mu b associated to sufficiently large dominant coweight mu

consistency of pseudolikelihood estimation of fully visible boltzmann machines a boltzmann machine is a classic model of neural computation and a number of methods have been proposed for its estimation most methods are plagued by either very slow convergence or asymptotic bias in the resulting estimates here we consider estimation in the basic case of fully visible boltzmann machines we show that the old principle of pseudolikelihood estimation provides an estimator that is computationally very simple yet statistically consistent

construction of central elements in the affine hecke algebra via nearby cycles 0 1 overview let g be a connected reductive group over a finite field fq and let g k be the corresponding group over the local field k fq t let g o g k be a maximal compact subgroup of g k here o fq t and let hsph denote the hecke algebra of g k with respect to g o in other words hsph as a vector space consists of compactly supported bi g o invariant functions g k q and the product is defined by

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

on the flatness of models of certain shimura varieties of pel type consider a pel shimura variety associated to a unitary group that splits over an unramified extension of q p rapoport and zink have defined a model of the shimura variety over the ring of integers of the completion of the reflex field at a place lying over p with parahoric level structures at p we show that this model is flat as conjectured by rapoport and zink and that its special fibre is reduced

topological flatness of local models in the ramified case local models are schemes defined in terms of linear algebra which can be used to study the local structure of integral models of certain shimura varieties with parahoric level structure we investigate the local models for groups of the form open image in new window is a totally ramified extension as defined by pappas and rapoport and show that they are topologically flat in the linear case flatness can be deduced from this

the supersingular locus in siegel modular varieties with iwahori level structure we study moduli spaces of abelian varieties in positive characteristic more specifically the moduli space of principally polarized abelian varieties on the one hand and the analogous space with iwahori type level structure on the other hand we investigate the ekedahl oort stratification on the former the kottwitz rapoport stratification on the latter and their relationship in this way we obtain structural results about the supersingular locus in the case of iwahori level structure for instance a formula for its dimension in case g is even

inverse ising inference using all the data we show that a method based on logistic regression using all the data solves the inverse ising problem far better than mean field calculations relying only on sample pairwise correlation functions while still computationally feasible for hundreds of nodes the largest improvement in reconstruction occurs for strong interactions using two examples a diluted sherrington kirkpatrick model and a two dimensional lattice we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of l 1 regularization is beneficial in this process pushing inference abilities further into low temperature regimes

ideal triangles in euclidean buildings and branching to levi subgroups abstract let g denote a connected reductive group defined and split over z and let m g denote a levi subgroup in this paper we study varieties of geodesic triangles with fixed vector valued side lengths in the bruhat tits buildings associated to g along with varieties of ideal triangles associated to the pair m g the ideal triangles have a fixed side containing a fixed base vertex and a fixed infinite vertex such that other infinite side containing has fixed ideal length and the remaining finite side has fixed length we establish an isomorphism between varieties in the second family and certain varieties in the first family the pair and the triple satisfy a certain relation we apply these results to the study of the hecke ring of g and the restriction homomorphism r g r m between representation rings we deduce some new saturation theorems for constant term coefficients and for the structure constants of the restriction homomorphism

dynamic output feedback predictive control for nonlinear systems represented by a takagi sugeno model this paper addresses the output feedback predictive control for a takagi sugeno t s fuzzy system with bounded noise the controller optimizes an infinite horizon objective function respecting the input and state constraints the control law is parameterized as a dynamic output feedback that is dependent on the membership functions and the closed loop stability is specified by the notion of quadratic boundedness online algorithms that guarantee the recursive feasibility of the convex optimization problem and the convergence of the augmented state to a neighborhood of the equilibrium point are proposed in this paper a numerical example is given to illustrate the effectiveness of the proposed output feedback controllers

approximate learning algorithm in boltzmann machines boltzmann machines can be regarded as markov random fields for binary cases they are equivalent to the ising spin model in statistical mechanics learning systems in boltzmann machines are one of the np hard problems thus in general we have to use approximate methods to construct practical learning algorithms in this context in this letter we propose new and practical learning algorithms for boltzmann machines by using the belief propagation algorithm and the linear response approximation which are often referred as advanced mean field methods finally we show the validity of our algorithm using numerical experiments

uber die lokale zetafunktion von shimuravarietaten monodromiefiltration und verschwindende zyklen in ungleicher charakteristik

topological flatness of orthogonal local models in the split even case i local models are schemes defined in terms of linear algebra that were introduced by rapoport and zink to study the etale local structure of integral models of certain pel shimura varieties over p adic fields a basic requirement for the integral models or equivalently for the local models is that they be flat in the case of local models for even orthogonal groups genestier observed that the original definition of the local model does not yield a flat scheme in a recent article pappas and rapoport introduced a new condition to the moduli problem defining the local model the so called spin condition and conjectured that the resulting spin local model is flat we prove a preliminary form of their conjecture in the split iwahori case namely that the spin local model is topologically flat an essential combinatorial ingredient is the equivalence of admissibility and permissibility for two minuscule cocharacters in root systems of type d

optifel a convergent heterogeneous particle swarm optimization algorithm for takagi sugeno fuzzy modeling data driven design of accurate and reliable takagi sugeno t s fuzzy systems has attracted a lot of attention where the model structures and parameters are important and often solved in an optimization framework the particle swarm optimization pso algorithm is widely applied in the field however the classical pso suffers from premature convergence and it is trapped easily into local optima which will significantly affect the model accuracy to overcome these drawbacks we have developed a new t s fuzzy system parameters searching strategy called optifel with a heterogeneous multiswarm pso mspso to enhance the searching performance mspso groups the whole population into multiple cooperative subswarms which perform different search behaviors for the potential solutions we have found that the multiple subswarms strategy proposed in this paper is greatly helpful for finding the optimal parameters suitable for the subspaces of the t s fuzzy model our theoretical proof has also demonstrated that the cooperation among the subswarms can maintain a balance between exploration and exploitation to ensure the particles converge to stable points experimental results show that mspso performs significantly better than traditional pso algorithms on six benchmark functions with the improved mspso optifel can generate a good fuzzy system model with high accuracy and strong generalization ability

simple method for inference in inverse ising problem using full data abstract we consider inference in the inverse ising problem using full data which means incorporating sets of spin configurations we approximate the boltzmann distribution of the system to generate a frequency distribution derived from the given data then the ratio between two boltzmann distributions with different spin configurations eliminates the partition function and we obtain linear equations which can be solved to yield statistical parameters our method is applicable to cases where the absolute values of the coupling parameters and external fields are large compared to pseudolikelihood maximization the accuracy of the inference obtained from our method is similar although our approach is less labor intensive

connected components of closed affine deligne lusztig varieties for rese fgln abstract let f be a p adic field and let e f be a finite unramified extension for the weil restriction res e f g l n of the general linear group g l n we determine the connected components of closed affine deligne lusztig varieties of arbitrary parahoric level

a genetic based neuro fuzzy approach for modeling and control of dynamical systems linguistic modeling of complex irregular systems constitutes the heart of many control and decision making systems and fuzzy logic represents one of the most effective algorithms to build such linguistic models in this paper a linguistic qualitative modeling approach is proposed the approach combines the merits of the fuzzy logic theory neural networks and genetic algorithms gas the proposed model is presented in a fuzzy neural network fnn form which can handle both quantitative numerical and qualitative linguistic knowledge the learning algorithm of a fnn is composed of three phases the first phase is used to find the initial membership functions of the fuzzy model in the second phase a new algorithm is developed and used to extract the linguistic fuzzy rules in the third phase a multiresolutional dynamic genetic algorithm mrd ga is proposed and used for optimized tuning of membership functions of the proposed model two well known benchmarks are used to evaluate the performance of the proposed modeling approach and compare it with other modeling approaches

a fast learning algorithm for deep belief nets we show how to use complementary priors to eliminate the explaining away effects that make inference difficult in densely connected belief nets that have many hidden layers using complementary priors we derive a fast greedy algorithm that can learn deep directed belief networks one layer at a time provided the top two layers form an undirected associative memory the fast greedy algorithm is used to initialize a slower learning procedure that fine tunes the weights using a contrastive version of the wake sleep algorithm after fine tuning a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels this generative model gives better digit classification than the best discriminative learning algorithms the low dimensional manifolds on which the digits lie are modeled by long ravines in the free energy landscape of the top level associative memory and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind

new method for parameter estimation in probabilistic models minimum probability flow fitting probabilistic models to data is often difficult due to the general intractability of the partition function we propose a new parameter fitting method minimum probability flow mpf which is applicable to any parametric model we demonstrate parameter estimation using mpf in two cases a continuous state space model and an ising spin glass in the latter case mpf outperforms current techniques by at least an order of magnitude in convergence time with lower error in the recovered coupling parameters

t s fuzzy model identification with a gravitational search based hyperplane clustering algorithm in order to improve the performance of the fuzzy clustering algorithm in fuzzy space partition in the identification of the takagi sugeno t s fuzzy model a hyperplane prototype fuzzy clustering model is proposed to solve the clustering objective function which could not be handled by the gradient method as the traditional clustering method fuzzy c means does a newly developed excellent global search method which is the gravitational search algorithm gsa is employed then the gsa based hyperplane clustering algorithm gshpc is proposed and illuminated gshpc is used to partition the fuzzy space and identify premise parameters of the t s fuzzy model and orthogonal least squares is exploited to identify the consequent parameters comparative experiments are designed to verify the validity of the proposed clustering algorithm and the t s fuzzy model identification method and the results show that the new method is effective in describing a complicated nonlinear system with significantly high accuracies compared with approaches in the literature

vers le socle localement analytique pour mathrm gl _n ii on conjecture que certaines representations localement mathbb q p analytiques irreductibles de mathrm gl n l pour l mathbb q p infty apparaissent en sous objet dans des espaces hecke isotypiques de formes automorphes p adiques lorsque l mathbb q p on demontre quelques resultats partiels dans la direction de cette conjecture en utilisant des resultats recents sur les varietes de hecke et une nouvelle formule d adjonction pour le foncteur localement analytique de jacquet emerton

how to expand around mean field theory using high temperature expansions high temperature expansions performed at a fixed order parameter provide a simple and systematic way to derive and correct mean field theories for statistical mechanical models for models like spin glasses which have general couplings between spins the authors show that these expansions generate the thouless anderson palmer equations at low order they explicitly calculate the corrections to tap theory for these models for ferromagnetic models they show that their expansions can easily be converted into 1 d expansions around mean field theory where d is the number of spatial dimensions only a small finite number of graphs need to be calculated to generate each order in 1 d for thermodynamic quantities like free energy or magnetization unlike previous 1 d expansions the expansions are valid in the low temperature phases of the models considered they consider alternative ways to expand around mean field theory besides 1 d expansions in contrast to the 1 d expansion for the critical temperature which is presumably asymptotic these schemes can be used to devise convergent expansions for the critical temperature they also appear to give convergent series for thermodynamic quantities and critical exponents they test the schemes using the spherical model where their properties can be studied using exact expressions

formulae relating the bernstein and iwahori matsumoto presentations of an affine hecke algebra abstract we consider the anti dominant variants of the elements occurring in the bernstein presentation of an affine hecke algebra h we find explicit formulae for in terms of the iwahori matsumoto generators tw w ranging over the extended affine weyl group of the root system r in the case i r is arbitrary and is a minuscule coweight or ii r is attached to gln and mek where ek is a standard basis vector and m 1 in the above cases certain minimal expressions for play a crucial role such minimal expressions exist in fact for any coweight for gln we give a sheaf theoretic interpretation of the existence of a minimal expression for the corresponding perverse sheaf on the affine schubert variety x t is the push forward of an explicit perverse sheaf on the demazure resolution m x t x t this approach yields for a minuscule coweight of any r or for an arbitrary coweight of gln a conceptual albeit less explicit expression for the coefficient w of the basis element tw in terms of the cohomology of a fiber of the demazure resolution

a transformed input domain approach to fuzzy modeling this paper presents an explanation of a fuzzy model considering the correlation among components of input data generally fuzzy models have a capability of dividing an input space into several subspaces compared to a linear model but hitherto suggested fuzzy modeling algorithms have not taken into consideration the correlation among components of sample data and have addressed them independently which results in an ineffective partition of the input space in order to solve this problem this paper proposes a new fuzzy modeling algorithm which partitions the input space more effectively than conventional fuzzy modeling algorithms by taking into consideration the correlation among components of sample data as a way to use the correlation and divide the input space the method of principal component is used finally the results of the computer simulation are given to demonstrate the validity of this algorithm

approximate inference in boltzmann machines inference in boltzmann machines is np hard in general as a result approximations are often necessary we discuss first order mean field and second order onsager truncations of the plefka expansion of the gibbs free energy the bethe free energy is introduced and rewritten as a gibbs free energy from there a convergent belief optimization algorithm is derived to minimize the bethe free energy an analytic expression for the linear response estimate of the covariances is found which is exact on boltzmann trees finally a number of theorems is proven concerning the plefka expansion relating the first order mean field and the second order onsager approximation to the bethe approximation experiments compare mean field approximation onsager approximation belief propagation and belief optimization

modeling nonlinear dynamic biological systems with human readable fuzzy rules optimized by convergent heterogeneous particle swarm abstract it is an important issue to model the dynamic biological networks from their time course response datasets which is critical to understand the system behaviors this task includes two sub tasks network structure identification and associated parameters estimation in most existing methods the two sub tasks are dealt with step by step which may result in inconsistence between them and hence inaccuracy of the final model another challenge is how to transparently understand the derived model which cannot be achieved by the traditional black box methods a human readable fuzzy rule based model denoted as mopath is developed for the identification of both structure topology and associated parameters simultaneously of a biological network within an optimization framework mopath encodes the fuzzy rules into particles of heterogeneous particle swarm optimization chpso algorithm to generate the optimal model theoretically we demonstrate that the cooperation in chpso can maintain a balance between exploration and exploitation to guarantee the particles converge to stable points which is greatly helpful for finding the optimal model consisting of both the network topology and parameters we demonstrate mopath on two dynamic biological networks and successfully generate a few human readable rules that can well represent the network with high accuracy and good robustness

a neuro fuzzy system modeling with self constructing rule generationand hybrid svd based learning we propose an approach for neuro fuzzy system modeling a neuro fuzzy system for a given set of input output data is obtained in two steps first the data set is partitioned automatically into a set of clusters based on input similarity and output similarity tests membership functions associated with each cluster are defined according to statistical means and variances of the data points included in the cluster then a fuzzy if then rule is extracted from each cluster to form a fuzzy rule base second a fuzzy neural network is constructed accordingly and parameters are refined to increase the precision of the fuzzy rule base to decrease the size of the search space and to speed up the convergence we develop a hybrid learning algorithm which combines a recursive singular value decomposition based least squares estimator and the gradient descent method the proposed approach has advantages of determining the number of rules automatically and matching membership functions closely with the real distribution of the training data points besides it learns faster consumes less memory and produces lower approximation errors than other methods

the jordan holder series for nearby cycles on some shimura varieties and affine flag varieties we study the jordan holder series for nearby cycles on certain shimura varieties and rapoport zink local models and on finite dimensional pieces of beilinson s deformation of the affine grassmannian to the affine flag variety and their p adic analogues we give a formula for the multiplicities of irreducible constituents in terms of certain cohomology groups and we also provide an algorithm to compute multiplicities in terms of the affine hecke algebra msc classification 14m15 14g35 20c08

improved contact prediction in proteins using pseudolikelihoods to infer potts models spatially proximate amino acids in a protein tend to coevolve a protein s three dimensional 3d structure hence leaves an echo of correlations in the evolutionary record reverse engineering 3d structures from such correlations is an open problem in structural biology pursued with increasing vigor as more and more protein sequences continue to fill the data banks within this task lies a statistical inference problem rooted in the following correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network propagated via intermediate sites observed correlation is not enough to guarantee proximity to separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics where the task is to learn model parameters fields couplings from observables magnetizations correlations samples in large systems in the context of protein sequences the approach has been referred to as direct coupling analysis here we show that the pseudolikelihood method applied to 21 state potts models describing the statistical properties of families of evolutionarily related proteins significantly outperforms existing approaches to the direct coupling analysis the latter being based on standard mean field techniques this improved performance also relies on a modified score for the coupling strength the results are verified using known crystal structures of specific sequence instances of various protein families code implementing the new method can be found at http plmdca csc kth se

zadeh s extension principle for continuous functions of non interactive variables a parallel optimization approach there is a growing interest in the use of fuzzy intervals in many engineering applications however a direct implementation of zadeh s extension principle which forms the basis for computing with fuzzy intervals is still computationally too demanding for practical use in the case of a continuous function and fuzzy intervals that describe non interactive variables as inputs the output is a fuzzy interval as well and can be determined for each cut separately the problem thus reduces to finding the endpoints of these cuts which amounts to a number of interwoven optimization problems in the case of a non monotone continuous function however these optimization problems are non trivial in this paper different optimization algorithms are applied for that purpose gradient descent based on sequential quadratic programming simplex simulated annealing particle swarm optimization and particle swarm optimization combined with gradient descent in addition two approaches are followed to determine a suitable number of cuts either a fixed predetermined number is used or an initially very small number is chosen that is subsequently increased according to a linearity criterion both a non parallel and a parallel implementation are designed the parallel version is restricted to work with particle swarm optimization and employs communication to optimize its internal performance by exploiting the dependence between the various optimization problems different configurations are evaluated on a set of benchmark functions in terms of the mean area under the output fuzzy interval and the number of function evaluations particle swarm optimization combined with gradient descent starting from a small number of cuts leads to the most accurate fuzzy intervals at the cost of a relatively large number of function evaluations

exact output regulation for nonlinear systems described by takagi sugeno fuzzy models the exact output regulation for takagi sugeno t s fuzzy models depends on two conditions 1 the local steady state zero error manifolds have to be the same for every local subsystem and 2 the local input matrices have to be the same for every local subsystem included in the t s fuzzy model these conditions are difficult to satisfy in general in this paper those conditions are relaxed by solving the fuzzy regulation problem directly on the overall t s fuzzy model instead of constructing the fuzzy regulator on the basis of linear local controllers by considering the fuzzy model as a special class of linear time varying systems existence conditions are rigorously derived these new conditions which can be solved by means of any mathematical software depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and or the exosystem two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach

high dimensional ising model selection using l1 regularized logistic regression we consider the problem of estimating the graph associated with a binary ising markov random field we describe a method based on l1 regularized logistic regression in which the neighborhood of any given node is estimated by performing logistic regression subject to an l1 constraint the method is analyzed under high dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n our main results provide sufficient conditions on the triple n p d and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously with coherence conditions imposed on the population fisher information matrix we prove that consistent neighborhood selection can be obtained for sample sizes n d3log p with exponentially decaying error when these same conditions are imposed directly on the sample matrices we show that a reduced sample size of n d2log p suffices for the method to estimate neighborhoods consistently although this paper focuses on the binary graphical models we indicate how a generalization of the method of the paper would apply to general discrete markov random fields

on the μ admissible set in the extended affine weyl groups of e6 and e7 giving explicit examples we show that the admissible set and the permissible set do not agree for non trivial minuscule coweights in the cases of e6 and e7

connected components of closed affine deligne lusztig varieties for split reductive algebraic groups we determine the sets of connected components of closed affine deligne lusztig varieties with parahoric level structure

exponential stabilization for a class of nonlinear parabolic pde systems via fuzzy control approach this paper deals with the exponential stabilization problem for a class of nonlinear spatially distributed processes that are modeled by semilinear parabolic partial differential equations pdes for which a finite number of actuators are used a fuzzy control design methodology is developed for these systems by combining the pde theory and the takagi sugeno t s fuzzy model based control technique initially a t s fuzzy parabolic pde model is proposed to accurately represent a semilinear parabolic pde system then based on the t s fuzzy model a lyapunov technique is used to design a continuous fuzzy state feedback controller such that the closed loop pde system is exponentially stable with a given decay rate the stabilization condition is presented in terms of a set of spatial differential linear matrix inequalities sdlmis furthermore a recursive algorithm is presented to solve the sdlmis via the existing linear matrix inequality optimization techniques finally numerical simulations on the temperature profile control of a catalytic rod are given to verify the effectiveness of the proposed design method

a study of particle swarm optimization particle trajectories particle swarm optimization pso has shown to be an efficient robust and simple optimization algorithm most of the pso studies are empirical with only a few theoretical analyses that concentrate on understanding particle trajectories these theoretical studies concentrate mainly on simplified pso systems this paper overviews current theoretical studies and extend these studies to investigate particle trajectories for general swarms to include the influence of the inertia term the paper also provides a formal proof that each particle converges to a stable point an empirical analysis of multi dimensional stochastic particles is also presented experimental results are provided to support the conclusions drawn from the theoretical findings

small correlation expansions for the inverse ising problem we present a systematic small correlation expansion to solve the inverse ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations couplings are calculated up to the third order in the correlations for generic magnetizations and to the seventh order in the case of zero magnetizations in addition we show how to sum some useful classes of diagrams exactly the resulting expansion outperforms existing algorithms on the sherrington kirkpatrick spin glass model

structure identification and parameter optimization for non linear fuzzy modeling this work presents a method for non linear fuzzy model identification the main characteristic of the method is the automatic determination of the number and position of the fuzzy sets in the domain of each variable the resultant fuzzy rule base allows model interpretation by domain experts the main contribution of this work is a formulation that allows the optimization of output parameters by a least squares error lse minimization a numerical solution of the lse problem is developed based on the singular value decomposition of the regressor matrix the whole methodology is applied to some numerical examples found in the literature

implementation of evolutionary fuzzy systems evolutionary fuzzy systems are discussed in which the membership function shapes and types and the fuzzy rule set including the number of rules inside it are evolved using a genetic evolutionary algorithm in addition the genetic parameters operators of the evolutionary algorithm are adapted via a fuzzy system benefits of the methodology are illustrated in the process of classifying the iris data set possible extensions of the methods are summarized

training products of experts by minimizing contrastive divergence it is possible to combine multiple latent variable models of the same data by multiplying their probability distributions together and then renormalizing this way of combining individual expert models makes it hard to generate samples from the combined model but easy to infer the values of the latent variables of each expert because the combination rule ensures that the latent variables of different experts are conditionally independent when given the data a product of experts poe is therefore an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary training a poe by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule fortunately a poe can be trained using a different objective function called contrastive divergence whose derivatives with regard to the parameters can be approximated accurately and efficiently examples are presented of contrastive divergence learning using several types of expert on several types of data

weight elimination in serre type conjectures we prove the weight elimination direction of the serre weight conjectures as formulated by herzig for forms of u n which are compact at infinity and split at places dividing p in generic situations that is we show that all modular weights for a mod p galois representation are contained in the set predicted by herzig under some additional hypotheses we also show modularity of all the obvious weights

alcoves associated to special fibers of local models the special fiber of the local model of a pel shimura variety with iwahori type level structure admits a cellular decomposition the set of strata is in a natural way a finite subset of the affine weyl group determined by the shimura data in this paper we generalize and give a new proof of a theorem of kottwitz and rapoport concerning the description of this set for the case of linear and symplectic groups for higher rank groups not of type an we produce counterexamples showing the situation is not as nice in general we also recover a theorem of deodhar characterizing the bruhat order on sn the local geometry can be approached using the rapoport zink local model m j 13 this protective op scheme is a local model for the singularities in the special fiber of sh g x9 k 9 but it is defined in terms of the pair g p using linear algebra and is somewhat easier to deal with than the shimura variety itself in this paper we address certain combinatorial questions which arise in the study of the special fiber m f of m to fix ideas consider the case where g is split it turns out that m f can be regarded as a finite dimensional union of iwahori orbits in the affine flag variety for g fp t see 5 and 8 it follows that m f has a stratification indexed by a finite set perm p of the extended affine weyl group w g for g equivalently perm p can be regarded as a finite set of alcoves in the affine coxeter complex determined by a splitting for g let wo denote the finite weyl group of g for each translation in the wo orbit

topological flatness of local models for ramified unitary groups i the odd dimensional case abstract local models are certain schemes defined in terms of linear algebraic moduli problems which give etale local neighborhoods of integral models of certain p adic pel shimura varieties defined by rapoport and zink when the group defining the shimura variety ramifies at p the local models and hence the shimura models as originally defined can fail to be flat and it becomes desirable to modify their definition so as to obtain a flat scheme in the case of unitary similitude groups whose localizations at q p are ramified quasi split gu n pappas and rapoport have added new conditions the so called wedge and spin conditions to the moduli problem defining the original local models and conjectured that their new local models are flat we prove a preliminary form of their conjecture namely that their new models are topologically flat in the case n is odd

convergence condition of the tap equation for the infinite ranged ising spin glass model it is shown that the power expansion of the gibbs potential of the sk model up to second order in the exchange couplings leads to the tap equation this result remains valid for the general including a ferromagnetic exchange sk model theorems of power expansions and resolvent techniques are employed to solve the convergence problem the convergence condition is presented for the whole temperature range and for general distributions of the local magnetisations

parameter inference in a probabilistic model from data regulation of transition rate in the monte carlo method abstract we consider the inference of parameters in a probabilistic model from a data set which is generated by an unknown probabilistic model the monte carlo method is a tool for obtaining a data set obeying a given probability distribution a set of transition rates is required to satisfy three conditions irreducible aperiodic and stationary for a sampled data set to represent a probability distribution we utilize the stationary condition of a probability distribution with respect to transition rates to infer parameters a frequency distribution by a data set substitutes for an unknown probability distribution in the condition our method includes minimum probability flow as a special case and becomes superior to it as the number of samples increases

local models of shimura varieties and a conjecture of kottwitz we give a group theoretic definition of local models as sought after in the theory of shimura varieties these are projective schemes over the integers of a p adic local field that are expected to model the singularities of integral models of shimura varieties with parahoric level structure our local models are certain mixed characteristic degenerations of grassmannian varieties they are obtained by extending constructions of beilinson drinfeld gaitsgory and the second named author to mixed characteristics and to the case of general tamely ramified reductive groups we study the singularities of local models and hence also of the corresponding integral models of shimura varieties in particular we study the monodromy inertia action and show a commutativity property for the sheaves of nearby cycles as a result we prove a conjecture of kottwitz which asserts that the semi simple trace of frobenius on the nearby cycles gives a function which is central in the parahoric hecke algebra

reduction of fuzzy rule base via singular value decomposition introduces a singular value based method for reducing a given fuzzy rule set the method conducts singular value decomposition of the rule consequents and generates certain linear combinations of the original membership functions to form new ones for the reduced set the present work characterizes membership functions by the conditions of sum normalization sn nonnegativeness nn and normality no algorithms to preserve the sn and nn conditions in the new membership functions are presented preservation of the no condition relates to a high dimensional convex hull problem and is not always feasible in which case a closed to no solution may be sought the proposed method is applicable regardless of the adopted inference paradigms with product sum gravity inference and singleton support fuzzy rule base output errors between the full and reduced fuzzy set are bounded by the sum of the discarded singular values the work discusses three specific applications of fuzzy reduction fuzzy rule base with singleton support fuzzy rule base with nonsingleton support which includes the case of missing rules and the takagi sugeno kang tsk model numerical examples are presented to illustrate the reduction process

efficient learning in boltzmann machines using linear response theory the learning process in boltzmann machines is computationally very expensive the computational complexity of the exact algorithm is exponential in the number of neurons we present a new approximate learning algorithm for boltzmann machines based on mean field theory and the linear response theorem the computational complexity of the algorithm is cubic in the number of neurons in the absence of hidden units we show how the weights can be directly computed from the fixed point equation of the learning rules thus in this case we do not need to use a gradient descent procedure for the learning process we show that the solutions of this method are close to the optimal solutions and give a significant improvement when correlations play a significant role finally we apply the method to a pattern completion task and show good performance for networks up to 100 neurons

a new approach to fuzzy modeling this paper proposes a new approach to fuzzy modeling the suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as takagi and sugeno s model 1985 because it has the same structure as that of takagi and sugeno s model it is also as easy to implement as sugeno and yasukawa s model 1993 because its identification mimics the simple identification procedure of sugeno and yasukawa s model the suggested algorithm is composed of two steps coarse tuning and fine tuning in coarse tuning fuzzy c regression model fcrm clustering is used which is a modified version of fuzzy c means fcm in fine tuning gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models finally some examples are given to demonstrate the validity of this algorithm

t s fuzzy model identification based on a novel hyperplane shaped membership function the fuzzy membership function is a crucial factor that may affect the model structure and modeling accuracy although hyperplane shaped clustering hpsc has been widely used in takagi sugeno t s fuzzy model identification there is no well designed membership function in these approaches the commonly used bell shaped gaussian function is actually inappropriate to employ together with hpsc in fuzzy modeling in this paper a hyperplane shaped fuzzy membership function is designed to match hpsc for t s fuzzy model identification for the first time experimental results on several benchmark problems indicate that modeling accuracies have been greatly improved from the original modeling approach by replacing the proposed membership function

mean field theory of boltzmann machine learning i present a mean field theory for boltzmann machine learning derived by employing thouless anderson palmer free energy formalism to a full extent using the plefka expansion an extended theory that takes higher order correction to mean field free energy formalism into consideration is presented from which the mean field approximation of general orders along with the linear response correction are derived by truncating the plefka expansion up to desired orders a theoretical foundation for an effective trick of using diagonal weights introduced by kappen and rodr i guez is also given because of the finite system size and a lack of scaling assumptions on interaction coefficients the truncated free energy formalism cannot provide an exact description in the case of boltzmann machines accuracies of mean field approximations of several orders are compared by computer simulations

automatic design of hierarchical takagi sugeno type fuzzy systems using evolutionary algorithms this paper presents an automatic way of evolving hierarchical takagi sugeno fuzzy systems ts fs the hierarchical structure is evolved using probabilistic incremental program evolution pipe with specific instructions the fine tuning of the if then rule s parameters encoded in the structure is accomplished using evolutionary programming ep the proposed method interleaves both pipe and ep optimizations starting with random structures and rules parameters it first tries to improve the hierarchical structure and then as soon as an improved structure is found it further fine tunes the rules parameters it then goes back to improve the structure and the rules parameters this loop continues until a satisfactory solution hierarchical ts fs model is found or a time limit is reached the proposed hierarchical ts fs is evaluated using some well known benchmark applications namely identification of nonlinear systems prediction of the mackey glass chaotic time series and some classification problems when compared to other neural networks and fuzzy systems the developed hierarchical ts fs exhibits competing results with high accuracy and smaller size of hierarchical architecture

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

consistent inference of a general model using the pseudolikelihood method recently a maximum pseudolikelihood mpl inference method has been successfully applied to statistical physics models with intractable likelihoods we use information theory to derive a relation between the pseudolikelihood and likelihood functions furthermore we show the consistency of the pseudolikelihood method for a general model

a simple but powerful heuristic method for generating fuzzy rules from numerical data abstract in this paper we propose a simple but powerful heuristic method for automatically generating fuzzy if then rules from numerical data fuzzy if then rules with nonfuzzy singletons i e real numbers in the consequent parts are generated by the proposed heuristic method the main advantage of the proposed heuristic method is its simplicity i e it involves neither time consuming iterative learning procedures nor complicated rule generation mechanisms we also suggest a linguistic representation method for deriving linguistic rules from fuzzy if then rules with consequent real numbers the proposed linguistic approximation method consists of two linguistic rule tables which can realize exactly the same nonlinear mapping as an original system based on fuzzy if then rules with consequent real numbers using computer simulations on rice taste data we demonstrate the high performance of the proposed heuristic method and illustrate the proposed linguistic representation method

pro p iwahori hecke ring and supersingular representations the motivation of this paper is the search for a langlands correspondence modulo p we show that the pro p iwahori hecke ring open image in new window of a split reductive p adic group g over a local field f of finite residue field fq with q elements admits an iwahori matsumoto presentation and a bernstein z basis and we determine its centre we prove that the ring open image in new window is finitely generated as a module over its centre these results are proved in 11 only for the iwahori hecke ring let p be the prime number dividing q and let k be an algebraically closed field of characteristic p a character from the centre of open image in new window to k which is as null as possible will be called null the simple open image in new window modules with a null central character are called supersingular when g gl n we show that each simple open image in new window module of dimension n containing a character of the affine subring open image in new window is supersingular using the minimal expressions of haines generalized to open image in new window and that the number of such modules is equal to the number of irreducible k representations of the weil group wf of dimension n when the action of an uniformizer pf in the hecke algebra side and of the determinant of a frobenius frf in the galois side are fixed i e the number nn q of unitary irreducible polynomials in fq x of degree n one knows that the converse is true by explicit computations when n 2 10 and when n 3 rachel ollivier

computing the alternating trace of frobenius on the sheaves of nearby cycles on local models for gl4 and gl5 abstract consider a shimura variety defined over some number field and assume we have a model over the ring of integers at some prime of bad reduction it is then interesting to know the alternating trace of frobenius on the invariants under the inertia group of the sheaf of nearby cycles since these traces are related to the local factor of the hasse weil zeta function in this article we compute the semi simple alternating trace of frobenius for shimura varieties associated to the groups gu 2 2 and gu 3 2 with level structure of iwahori type by investigating the equations of the local model defined by rapoport and zink and by performing explicit blowing ups