conditional gauge and potential theory for the schrodinger operator on etend le theoreme de jauge conditionnelle a des operateurs plus generaux et a des domaines moins reguliers on obtient des resultats de theorie du potentiel pour l equation de schrodinger

general gauge and conditional gauge theorems general gauge and conditional gauge theorems are established for a large class of not necessarily symmetric strong markov processes including brownian motions with singular drifts and symmetric stable processes furthermore new classes of functions are introduced under which the general gauge and conditional gauge theorems hold these classes are larger than the classical kato class when the process is brownian motion in a bounded c 1 1 domain

constructing a fuzzy controller from data abstract fuzzy control at the executive level can be interpreted as an approximation technique for a control function based on typical imprecisely specified input output tuples that are represented by fuzzy sets the imprecision is characterized by similarity relations that are induced by transformations of the canonical distance function between real numbers taking this interpretation of fuzzy controllers into account in order to derive a fuzzy controller from observed data typical input output tuples have to be identified in addition a concept of similarity based on a transformations of the canonical distance is needed in order to characterize the typical input output tuples by suitable fuzzy sets a variety of fuzzy clustering algorithms that are exactly working in this spirit exists they identify prototypes and assign fuzzy sets to the prototypes on the basis of a suitable transformed distance in this paper we discuss how such fuzzy clustering techniques can be applied to construct a fuzzy controller from data and introduce special clustering algorithms that are tailored for this problem

intrinsic ultracontractivity and eigenfunction estimates for schrodinger operators let d be a domain in rn n 2 and let h h0 v where h0 is a divergence form uniformly elliptic operator with dirichlet boundary conditions and v is in the kato class intrinsic ultracontractivity is proved for the semigroup of h when d is holder domain of order 0 or a uniformly holder domain of order for 0 2 for every 2 there exists a uniformly holder domain of order for which the dirichlet laplacian is not intrinsically ultracontractive for a large class of domains it is shown that the heat kernels for h0 and h decay at the same rate at the boundary applications are given to the lifetime of conditioned brownian motion some of our results seem to be new even for smooth domains

sharp bounds on the density green function and jumping function of subordinate killed bm subordination of a killed brownian motion in a domain d r d via an 2 sta ble subordinator gives rise to a process zt whose infinitesimal generator is d 2 the fractional power of the negative dirichlet laplacian in this paper we establish upper and lower estimates for the density green function and jumping function of zt when d is either a bounded c 1 1 domain or an exterior c 1 1 domain our estimates are sharp in the sense that the upper and lower estimates differ only by a multiplicative constant

gaugeability and conditional gaugeability new kato classes are introduced for general transient borel right processes for which gauge and conditional gauge theorems hold these new classes are the genuine extensions of the green tight measures in the classical brownian motion case however the main focus of this paper is on establishing various equivalent conditions and consequences of gaugeability and conditional gaugeability we show that gaugeability conditional gaugeability and the subcriticality for the associated schrodinger operators are equivalent for transient borel right processes with strong duals analytic characterizations of gaugeability and conditional gaugeability are given for general symmetric markov processes these analytic characterizations are very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases connections with the positivity of the spectral radii of the associated schrodinger operators are also established

large deviations for occupation time profiles of random interlacements we derive a large deviation principle for the density profile of occupation times of random interlacements at a fixed level in a large box of mathbb z d d ge 3 as an application we analyze the asymptotic behavior of the probability that atypically high values of the density profile insulate a macroscopic body in a large box as a step in this program we obtain a similar large deviation principle for the occupation time measure of brownian interlacements at a fixed level in a large box of mathbb r d and we derive a new identity for the laplace transform of the occupation time measure which is based on the analysis of certain schrodinger semi groups

potential theory of truncated stable processes for any alpha in 0 2 a truncated symmetric stable process is a symmetric levy process in mathbb r d with a levy density given by c x d alpha 1 x 1 for some constant c in this paper we study the potential theory of truncated symmetric stable processes in detail we prove a harnack inequality for nonnegative harmonic functions of these processes we also establish a boundary harnack principle for nonnegative functions which are harmonic with respect to these processes in bounded convex domains we give an example of a non convex domain for which the boundary harnack principle fails

riesz decompositions in markov process theory riesz decompositions of excessive measures and excessive functions are obtained by probabilistic methods without regularity assumptions the decomposition of excessive measures is given for borel right processes the results for excessive functions are formulated within the framework of weak duality these results extend and generalize the pioneering work of hunt in this area

relative fatou s theorem for δ α 2 harmonic functions in bounded κ fat open sets recently it was shown in p kim fatou s theorem for censored stable processes stochastic process appl 108 1 2003 63 92 that fatou s theorem for transient censored stable processes in a bounded c1 1 open set is true here we give a probabilistic proof of relative fatou s theorem for 2 harmonic functions equivalently for symmetric stable processes in bounded fat open set where 0 2 that is if u is positive 2 harmonic function in a bounded fat open set d and h is singular positive 2 harmonic function in d then nontangential limits of u h exist almost everywhere with respect to the martin representing measure of h this extends the result of bogdan and dyda k bogdan b dyda relative fatou theorem for harmonic functions of rotation invariant stable processes in smooth domain studia math 157 1 2003 83 96 it is also shown that under the gaugeability assumption relative fatou s theorem is true for operators obtained from the generator of the killed stable process in bounded fat open set d through nonlocal feynman kac transforms as an application relative fatou s theorem for relativistic stable processes is also true if d is bounded c1 1 open set

subcriticality and gaugeability of the schrodinger operator we investigate a schrodinger operator 2 v in r d d 3 with a potential v in the class k d satisfying a similar kato condition at infinity and prove an equivalence theorem connecting various conditions on subcriticality strong positivity and gaugeability of the operator

on the estimation of a covariance matrix in designing parzen classifiers the design of the parzen classifiers requires careful attention to the window width as well as kernel covariance matrices although a considerable amount of effort has been devoted to the selection of the window width the problem of estimating kernel covariance matrices has received little attention in the past in this paper we discuss the kernel covariance estimators for the design of the parzen classifiers we compare the performance of the parzen classifiers based on several kernel covariance estimators such as the toeplitz ness s and orthogonal expansion estimators on three artificial data sets from experimental results we recommend the use of the toeplitz estimator particularly in high dimensional spaces

absorption semigroups their generators and schrodinger semigroups on presente des resultats de perturbations pour des c 0 semi groupes on considere le probleme aux valeurs initiales pour l equation de la chaleur avec absorption avec une solution dans l p r v avec une mauvaise fonction v r r on considere le meme probleme dans l 2 r pour l equation de schrodinger

modified quadratic discriminant functions and the application to chinese character recognition issues in the quadratic discriminant functions qdf are discussed and two types of modified quadratic disriminant functions mqdf1 mqdf2 which are less sensitive to the estimation error of the covariance matrices are proposed the mqdf1 is a function which employs a kind of a pseudo bayesian estimate of the covariance matrix instead of the maximum likelihood estimate ordinarily used in the qdf the mqdf2 is a variation of the mqdf1 to save the required computation time and storage two discriminant functions were applied to chinese character recognition to evaluate their effectiveness and remarkable improvement was observed in their performance

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

a survey of full length nonlinear shift register cycle algorithms shift registers have been used to generate sequences of 0 s and 1 s for over thirty years a wide variety of applications has been made of these sequences principally communications have made use of the sequences generated one particular class of shift register sequences for which applications exist is the full length nonlinear shift register sequences these sequences are periodic and of length 2 n and all 2 n different binary n tuples appear exactly one time in a periodic portion of the sequence in this paper we discuss various algorithms which have been suggested for generating these sequences

gauge theorems for resolvents with application to markov processes letv v 0 be a not necessarily sub markovian resolvent such that the kernelv for some 0 is compact and irreducible we prove the following general gauge theorem if there exists at least onev excessive function which is notv inviriant thenv0 is bounded

on a new kato class and positive solutions of dirichlet problems for the fractional laplacian in bounded domains abstract the purpose of this paper is to extend some results of the potential theory of an elliptic operator to the fractional laplacian 2 0 2 in a bounded c 1 1 domain d in r n in particular we introduce a new kato class k d and we exploit the properties of this class to study the existence of positive solutions of some dirichlet problems for the fractional laplacian

blow up boundary solutions of some semilinear fractional equations in the unit ball for 0 we are interested in blow up solutions u c b of the fractional problem in the unit ball b we distinguish particularly two orders of singularity at the boundary solutions exploding at the same rate than 2 1 denotes the euclidean distance and those higher singular than 2 1 as a consequence it will be shown that the classical keller osserman condition cannot be readopted in the fractional setting

the number of cross join pairs in maximum length linear sequences it has been conjectured by t chang et al 1990 that the number of cross join pairs in a maximum length linear sequence equals 2 sup n 1 1 2 sup n 1 2 6 a maximum length linear sequence an m sequence of length 2 sup n 1 is a binary sequence which satisfies a linear recurrence whose characteristic polynomial is primitive of degree n the number of primitive polynomials is given by phi 2 sup n 1 n where phi is euler s phi function a proof of the conjecture is given

conditional gauge theorem for non local feynman kac transforms feynman kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of markov processes general gauge and conditional gauge theorems are established for such transforms furthermore the l 2 infinitesimal generator of the schrodinger semigroup given by a non local feynman kac transform is determined in terms of its associated bilinear form

pointwise eigenfunction estimates and intrinsic ultracontractivity type properties of feynman kac semigroups for a class of levy processes we introduce a class of l evy processes subject to specific regularity conditions and consider their feynman kac semigroups given under a kato class potential using new techniques first we analyze the rate of decay of eigenfunctions at infinity we prove bounds on subaveraging functions from which we derive two sided sharp pointwise estimates on the ground state and obtain upper bounds on all other eigenfunctions next by using these results we analyze intrinsic ultracontractivity and related properties of the semigroup refining them by the concept of ground state domination and asymptotic versions we establish the relationships of these properties derive sharp necessary and sufficient conditions for their validity in terms of the behavior of the l evy density and the potential at infinity define the concept of borderline potential for the asymptotic properties and give probabilistic and variational characterizations these results are amply illustrated by key examples

algorithms for the generation of full length shift register sequences two algorithms are presented for the generation of full length shift register cycles also referred to as de bruijn sequences the first algorithm generates 2 k cdot g n k full cycles of length 2 n using 3n k cdot g n k bits of storage where k is a free parameter in the range 1 leq k leq 2 n 4 2 and g n k is of the order of n 2 log k the second algorithm generates about 2 n 2 4 full cycles of length 2 n using about n 2 2 bits of storage in both algorithms the time required to produce the next bit from the last n bits is close to n a possible application to the construction of stream ciphers is indicated

an efficient implementation of the d homomorphism for generation of de bruijn sequences an efficient implementation of the d homomorphism for generating de bruijn 1946 sequences is presented the number of exclusive or operations required to generate the next bit for de bruijn sequences of order n from a de bruijn function of order k is shown to be approximately k 2 sup w n k 1 where w r is the number of one s in the binary representation of r therefore the number of required operations can be reduced to k if the de bruijn function is selected appropriately as an application the stream cipher is indicated

time reversal and elliptic boundary value problems in this paper we prove that there exists a unique bounded continuous weak solution to the dirichlet boundary value problem for a general class of second order elliptic operators with singular coefficients which does not necessarily have the maximum principle our method is probabilistic the time reversal of symmetric markov processes and the theory of dirichlet forms play a crucial role in our approach

convergence properties of the generalized fuzzy c means clustering algorithms fuzzy c means fcm clustering algorithms have been widely used to solve clustering problems yang and yu 1 extended these to optimization procedures with respect to any probability distribution they showed that the optimal cluster centers are the fixed points of these generalized fcm clustering algorithms the convergence properties of algorithms are the important theoretical issue in this paper we present convergence properties of the generalized fcm clustering algorithms these are global convergence local convergence and its rate of convergence

optimal design of radial basis function neural networks for fuzzy rule extraction in high dimensional data abstract the design of an optimal radial basis function neural network rbfnf is not a straightforward procedure in this paper we take advantage of the functional equivalence between rbfn and fuzzy inference systems to propose a novel efficient approach to rbfn design for fuzzy rule extraction the method is based on advanced fuzzy clustering techniques solutions to practical problems are proposed by combining these different solutions a general methodology is derived the efficiency of our method is demonstrated on challenging synthetic and real world data sets

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

green function for schrodinger operator and conditioned feynman kac gauge consider the schrodinger operator h 2 q in a bounded c1 1 domain d with q klocd d q satisfies the condition sup spec 2 q d v x y g x y e y x exp 0 t q x t d t x y d where xt is the conditioned brownian motion starting at x and ending at y with the life time t and v g can be extended to a continuous and positive function on d d specifically we give the comparison theorem there exists a constant c c d q 0 such that 1 c g x y v x y c g x y x y d another result is that v nz x z x d z d exists and represents the poisson kernel for the dirichlet problem corresponding to schrodinger operator h

norm estimate of green operator perturbation of green function and integrability of superharmonic functions an operator norm estimate of the green operator for the laplace equation on an open set in the euclidean space is given in terms of capacity this applies to the perturbation of the green function for the schrodinger equation a sufficient condition for the green function for the schrodinger equation to have decay near the boundary comparable to that for the laplace equation is given in terms of an integrable condition for the potential of the schrodinger equation this has an application to the martin boundary of a smooth domain with respect to the schrodinger equation also it is related to the cranston mcconnell inequality about the life time estimate and the integrability of nonnegative superharmonic functions 1991 mathematics subject classification 31a35 31b35 31c35

a scalable method for constructing galois nlfsrs with period 2 n 1 using cross join pairs a method for constructing n stage galois nlfsrs with period 2n 1 from n stage maximum length lfsrs is presented nonlinearity is introduced into state cycles by adding a nonlinear boolean function to the feedback polynomial of the lfsr each assignment of variables for which this function evaluates to 1 acts as a crossing point for the lfsr state cycle the effect of nonlinearity is cancelled and state cycles are joined back by adding a copy of the same function to a later stage of the register the presented method requires no extra time steps and it has a smaller area overhead compared to the previous approaches based on cross join pairs it is feasible for large n

a probabilistic principle and generalized schrodinger perturbation abstract we present a probabilistic principle for an additive functional of certain markov processes its smallness with time is equivalent to its smalness with space and apply it to a perturbation problem for relativistic schrodinger operators

estimates on green functions and schrodinger type equations for non symmetric diffusions with measure valued drifts abstract in this paper we establish sharp two sided estimates for the green functions of non symmetric diffusions with measure valued drifts in bounded lipschitz domains as consequences of these estimates we get a 3g type theorem and a conditional gauge theorem for these diffusions in bounded lipschitz domains informally the schrodinger type operators we consider are of the form l where l is a uniformly elliptic second order differential operator is a vector valued signed measure belonging to k d 1 and is a signed measure belonging to k d 2 in this paper we establish two sided estimates for the heat kernels of schrodinger type operators in bounded c 1 1 domains and a scale invariant boundary harnack principle for the positive harmonic functions with respect to schrodinger type operators in bounded lipschitz domains

global comparison of perturbed green functions given a green function g e g with respect to 2 0 2 on a region x where g has a generalized triangle property and given a g bounded signed measure on x necessary and sufficient conditions are given for the existence of a perturbed green function which is comparable with g this is done in the general setting of measurable spaces applications to c1 1 regions in rd and for the classical case 2 to finitely connected regions in 2 are given

conditioned brownian motion in planar domains we give an upper bound for the green functions of conditioned brownian motion in planar domains a corollary is the conditional gauge theorem in bounded planar domains

generalized 3g theorem and application to relativistic stable process on non smooth open sets let g x y and gd x y be the green functions of rotationally invariant symmetric stable process in rd and in an open set d respectively where 0 2 the inequality gd x y gd y z gd x z c g x y g y z is a very useful tool in studying local schrodinger operators when the above inequality is true with c c d 0 then we say that the 3g theorem holds in d in this paper we establish a generalized version of 3g theorem when d is a bounded fat open set which includes a bounded john domain the 3g we consider is of the form gd x y gd z w gd x w where y may be different from z when y z we recover the usual 3g the 3g form gd x y gd z w gd x w appears in non local schrodinger operator theory using our generalized 3g theorem we give a concrete class of functions belonging to the non local kato class introduced by chen and song on fat open sets as an application we discuss relativistic stable processes relativistic hamiltonian when 1 in fat open sets we identify the martin boundary and the minimal martin boundary with the euclidean boundary for relativistic stable processes in fat open sets furthermore we show that relative fatou type theorem is true for relativistic stable processes in fat open sets the main results of this paper hold for a large class of symmetric markov processes as are illustrated in the last section of this paper we also discuss the generalized 3g theorem for a large class of symmetric stable levy processes

functional equivalence between radial basis function networks and fuzzy inference systems it is shown that under some minor restrictions the functional behavior of radial basis function networks rbfns and that of fuzzy inference systems are actually equivalent this functional equivalence makes it possible to apply what has been discovered learning rule representational power etc for one of the models to the other and vice versa it is of interest to observe that two models stemming from different origins turn out to be functionally equivalent

criticality and ground states for second order elliptic equations abstract let p be a second order elliptic operator in a domain r n suppose that p admits a positive minimal green function g p in it is the main purpose of this paper to prove that if w c is a small perturbation of p in then max w x 0 min w x 0 t u u g p outside a compact set in

a transformation from the fibonacci to the galois nlfsrs conventional nonlinear feedback shift registers nlfsrs use the fibonacci configuration in which the feedback is applied to the last bit only in this paper we show how to transform a fibonacci nlfsr into an equivalent nlfsr in the galois configuration in which the feedback can be applied to every bit such a transformation can potentially reduce the depth of the circuits implementing feedback functions thus decreasing the propagation time and increasing the throughput

on minimum period of nonlinear feedback shift registers in grain like structure grain is one of three hardware oriented finalists of the estream project a nonlinear feedback shift register nfsr in grain like structure is a cascade connection of a linear feedback shift register lfsr into an nfsr in which the characteristic polynomial of the lfsr is primitive and the feedback function of the nfsr is nonsingular in 2011 hu and gong pointed out that the period of the sequence generated by an nfsr in grain like structure is a multiple of the period of the sequence generated by its lfsr if the initial state of the lfsr is nonzero meanwhile they proposed an open problem for fixed feedback functions of an nfsr and an lfsr determine whether the sequences generated by the nfsr in grain like structure can achieve the minimum period i e the period of the lfsr when the initial state of the lfsr is nonzero and if they can achieve provide at least one pair of the initial states of the nfsr and lfsr clearly from a security point of view it is not preferable if the sequences generated by an nfsr in grain like structure achieve the minimum period this paper converts the open problem into a problem of solving an integer equation with respect to two unknown integers that uniquely correspond to the initial states of the nfsr and lfsr by viewing the nfsr as a boolean control network based on the integer equation this paper shows that for any given initial state of an n stage nfsr and any given nonzero initial state of an m stage lfsr the probability that the sequence generated by the nfsr in grain like structure achieves the minimum period 2 m 1 is at most 2 n this implies that the probability of the cascade connection used in grain achieving the minimum period is very small

fuzzy clustering with high contrast in a fuzzy clustering an object typically receives strictly positive memberships to all clusters even when the object clearly belongs to one particular cluster consequently each cluster s estimated center and scatter matrix are influenced by many objects that have small positive memberships to it this effect may keep the fuzzy method from finding the true clusters we analyze the cause and propose a remedy which is a modification of the objective function and the corresponding algorithm the resulting clustering has a high contrast in the sense that outlying and bridging objects remain fuzzy whereas the other objects become crisp the enhanced version of fuzzy k means is illustrated with an example as well as the enhanced version of the fuzzy minimum volume method

construction of de bruijn sequences from lfsrs with reducible characteristic polynomials in this paper a family of new de bruijn sequences is proposed through the construction of maximum length nonlinear feedback shift registers nfsrs let k be a positive integer and p 0 x p 1 x ldots p k x be the primitive polynomials in mathbb f 2 x with their degrees strictly increasing and pairwise coprime we determine the cycle structure and adjacency graphs of linear feedback shift registers lfsrs with characteristic polynomial q x prod nolimits i 0 k p i x in the case that p 0 x 1 x an algorithm is proposed to produce maximum length nfsrs from these lfsrs and it is shown that the algorithm can generate o 2 2 k 1 n n stage maximum length nfsrs with memory complexity o 2 k kn and time complexity o 2 n d k kn where n and d k are the degrees of q x and p k x respectively finally we illustrate the proposed algorithm in the case of k 2 in this case we prove that for any integer n geq 8 the algorithm can produce n stage maximum length nfsrs with time complexity as low as o n rm log log n

an almost sure scaling limit theorem for dawson watanabe superprocesses abstract we establish a scaling limit theorem for a large class of dawson watanabe superprocesses whose underlying spatial motions are symmetric hunt processes where the convergence is in the sense of convergence in probability when the underling process is a symmetric diffusion with c b 1 coefficients or a symmetric levy process on r d whose levy exponent is bounded from below by c for some c 0 and 0 2 when is large a stronger almost sure limit theorem is established for the superprocess our approach uses the principal eigenvalue and the ground state for some associated schrodinger operator the limit theorems are established under the assumption that an associated schrodinger operator has a spectral gap

differentiability of spectral functions for symmetric alpha stable processes let be a signed radon measure in the kato class and define a schrodinger type operator h 1 2 2 on r d we show that its spectral bound c inf h is differentiable if d 2 and is green tight

analytic characterization of conditional gaugeability for non local feynman kac transforms abstract an analytic characterization of gaugeability and conditional gaugeability is given for non local or discontinuous feynman kac transforms of general symmetric markov processes this analytic characterization is very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases

decision trees can initialize radial basis function networks successful implementations of radial basis function rbf networks for classification tasks must deal with architectural issues the burden of irrelevant attributes scaling and some other problems this paper addresses these issues by initializing rbf networks with decision trees that define relatively pure regions in the instance space each of these regions then determines one basis function the resulting network is compact easy to induce and has favorable classification accuracy

drift transforms and green function estimates for discontinuous processes in this paper we consider girsanov transforms of pure jump type for discontinuous markov processes we show that under some quite natural conditions the green functions of the girsanov transformed process are comparable to those of the original process as an application of the general results the drift transform of symmetric stable processes is studied in detail in particular we show that the relativistic a stable process in a bounded c 1 1 smooth open set d can be obtained from symmetric a stable process in d through a combination of a pure jump girsanov transform and a feynman kac transform from this we deduce that the green functions for these two processes in d are comparable

intrinsic ultracontractivity and conditional gauge for symmetric stable processes abstract it is shown in this paper that the conditional gauge theorem holds for symmetric stable processes on bounded c 1 1 domains in r n where 0 n 2 two of the major tools used to prove this conditional gauge theorem are logarithmic sobolev inequality and intrinsic ultracontractivity

tuning of fuzzy models by fuzzy neural networks it is relatively easy to construct a rough fuzzy model with expert knowledge it is difficult however to fine tune the parameters of the fuzzy model in order to get improved behavior for the purpose of tackling this problem we propose a fuzzy neural network model the proposed model utilizes a prior expert knowledge for target systems and embodies fuzzy models which consist of fuzzy rules whose antecedent and consequent are fuzzy sets the model is equipped with a fuzzy inferencing and tuning mechanism for model parameters by learning it allows us to tune such parameters of fuzzy models as linguistic terms and relative rule importance in addition to show its applicability we perform some experiments and present the results

correction to on cluster validity for the fuzzy c means model correspondence validation of partitions produced by the fuzzy c means fcm clustering algorithm was discussed by pal and bezdek 1 two tables in 1 contain erroneous values this errata reports the correct values and notes that the conclusions drawn in 1 based on these simulations remain unchanged

stability of martin boundary under non local feynman kac perturbations recently the authors showed that the martin boundary and the minimal martin boundary for a censored or resurrected stable process y in a bounded c 1 1 open set d with 1 2 can all be identified with the euclidean boundary d of d under the gaugeability assumption we show that the martin boundary and the minimal martin boundary for the schrodinger operator obtained from y through a non local feynman kac transform can all be identified with d in other words the martin boundary and the minimal martin boundary are stable under non local feynman kac perturbations moreover an integral representation of nonnegative excessive functions for the schrodinger operator is explicitly given these results in fact hold for a large class of strong markov processes as are illustrated in the last section of this paper as an application the martin boundary for censored relativistic stable processes in bounded c 1 1 smooth open sets is studied in detail

on the excursions of markov processes in classical duality on obtient des resultats comparables a ceux de getoor et sharpe 1982 sous des hypotheses de dualite classique