image and texture segmentation using local spectral histograms we present a method for segmenting images consisting of texture and nontexture regions based on local spectral histograms defined as a vector consisting of marginal distributions of chosen filter responses local spectral histograms provide a feature statistic for both types of regions using local spectral histograms of homogeneous regions we decompose the segmentation process into three stages the first is the initial classification stage where probability models for homogeneous texture and nontexture regions are derived and an initial segmentation result is obtained by classifying local windows in the second stage we give an algorithm that iteratively updates the segmentation using the derived probability models the third is the boundary localization stage where region boundaries are localized by building refined probability models that are sensitive to spatial patterns in segmented regions we present segmentation results on texture as well as nontexture images our comparison with other methods shows that the proposed method produces more accurate segmentation results

time dependent differential inclusions cocycle attractors and fuzzy differential equations traditional formulations of fuzzy differential equations do not reproduce the rich and varied behavior of crisp differential equations des a recent interpretation in terms of differential inclusions expressed level setwise overcomes this deficiency and opens up for profitable investigation such properties as stability attraction periodicity and the like this is especially important for investigating continuous systems which are uncertain or incompletely specified this paper studies attractors of fuzzy des in terms of cocycles and encompasses both the time dependent and autonomous cases

invariant and attractor sets for fuzzy dynamical systems abstract in this work we establish conditions for the existence and stability of invariant sets for dynamical systems defined on metric space of fuzzy subsets of r n we show that the results presented in this work generalize some conditions of existence and stability of equilibrium points and periodicity of fuzzy differential equations solutions

brief note on the variation of constants formula for fuzzy differential equations this note gives a theory of state transition matrices for linear systems of fuzzy differential equations this is used to give a fuzzy version of the classical variation of constants formula a simple example of a time independent control system is used to illustrate the methods while similar problems to the crisp case arise for time dependent systems in time independent cases the calculations are elementary solutions of eigenvalue eigenvector problems in particular for nonnegative or nonpositive matrices the problems at each level set can easily be solved in matlab to give the level sets of the fuzzy solution

fuzzy differential equations and the extension principle we study the cauchy problem for differential equations considering its parameters and or initial conditions given by fuzzy sets these fuzzy differential equations are approached in two different ways a by using a family of differential inclusions and b the zadeh extension principle for the solution of the model we conclude that the solutions of the cauchy problem obtained by both are the same we also provide some illustrative examples

attractors and asymptotic stability for fuzzy dynamical systems abstract in this work we study the asymptotic properties of maps on fuzzy spaces which are extensions of maps on the main results are in section 4 see theorem 21 and we give an illustrative example in the last section

differential equations with fuzzy parameters via differential inclusions abstract we give a definition of solutions of ordinary differential equations in r n containing parameters which are described by changing in time fuzzy sets they are defined as fuzzy subsets of the space of absolutely continuous functions we introduce a hypograph metric in the space of fuzzy sets and prove a theorem on continuous dependence of fuzzy solutions on parameters and initial conditions with respect to that metric

tripled fuzzy metric spaces and fixed point theorem abstract one of the most important topics of research in fuzzy sets is to get an appropriate notion of fuzzy metric space fms in the paper we propose a new fms tripled fuzzy metric space tfms which is a new generalization of george and veeramani s fms then we present some related examples topological properties convergence of sequences cauchy sequence cs and completeness of the tfms moreover we introduce two kinds of notions of generalized fuzzy contractive f c mappings and derive a fixed point theorem fpt on the mappings in the space

on connectedness a solution based on oscillatory correlation a long standing problem in neural computation has been the problem of connectedness first identified by minsky and papert 1969 this problem served as the cornerstone for them to establish analytically that perceptrons are fundamentally limited in computing geometrical topological properties a solution to this problem is offered by a different class of neural networks oscillator networks to solve the problem the representation of oscillatory correlation is employed whereby one pattern is represented as a synchronized block of oscillators and different patterns are represented by distinct blocks that desynchronize from each other oscillatory correlation emerges from legion locally excitatory globally inhibitory oscillator network whose architecture consists of local excitation and global inhibition among neural oscillators it is further shown that these oscillator networks exhibit sensitivity to topological structure which may lay a neurocomputational foundation for explaining the psychophysical phenomenon of topological perception

superparamagnetic segmentation by excitable neural systems magnetic modeling for clustering or segmentation purposes can either associate the image data to external quenched fields or to the interactions among a set of auxiliary variables the latter gives rise to superparamagnetic segmentation and is usually done with potts systems we have used the superparamagnetic clustering technique to segment images with the aid of different associated systems results using potts model are comparable to those obtained using excitable fitzhugh nagumo and morris lecar model neurons interactions between the associated system components are a function of the difference of luminosity on a gray scale of neighbor pixels and the difference of membrane potential

cubic unipotent arthur parameters and multiplicities of square integrable automorphic forms l g f g a ld g f g a lcont g f g a into the direct sum of its discrete spectrum and its continuous spectrum the theory of eisenstein series reduces the description of lcont g f g a to that of the discrete spectrum of certain reductive subgroups of g and thus the basic question is the understanding of the discrete spectrum ld g f g a the discrete spectrum has a further orthogonal decomposition

existence theorem to the cauchy problem of fuzzy differential equations under compactness type conditions kaleva fuzzy sets and systems 35 1990 389 396 has concluded that the peano theorem does not hold for fuzzy differential equations on en d this paper deals with the cauchy problem of fuzzy differential equations the existence theorems under compactness type conditions are obtained

on the fuzzy initial value problem abstract the initial value problem x t f t x t x 0 x 0 with fuzzy initial value and with deterministic or fuzzy function f is considered two different approaches viz the extension principle and the use of extremal solutions of deterministic initial value problems are applied generalizations to fuzzy integral equations and fuzzy functional differential equations are indicated

on differential equations with interactive fuzzy parameter via t norms abstract in this paper we study fuzzy differential equations with uncertain parameters modeled by interactive fuzzy numbers the interactivity is formalized with the help of upper semicontinuous t norms to obtain solutions to fuzzy differential equations we use two different approaches the first uses a family of differential inclusions while the second is the fuzzification of the deterministic problem using the zadeh extension principle we show that the solutions obtained by the two methods are equal interactivity among the parameters and variable of the problem are studies with respect two methods we show that a hierarchy in uncertainties of the solutions arises when we chose one of the basic t norm the minimum the t norm of the product the t norm of lukasiewicz and t norm of the drastic product to model the interaction between parameters finally to illustrate the concepts introduced in the paper we study the malthusian model with interactive parameters

range image segmentation using a relaxation oscillator network a locally excitatory globally inhibitory oscillator network legion is constructed and applied to range image segmentation where each oscillator has excitatory lateral connections to the oscillators in its local neighborhood as well as a connection with a global inhibitor a feature vector consisting of depth surface normal and mean and gaussian curvatures is associated with each oscillator and is estimated from local windows at its corresponding pixel location a context sensitive method is applied in order to obtain more reliable and accurate estimations the lateral connection between two oscillators is established based on a similarity measure of their feature vectors the emergent behavior of the legion network gives rise to segmentation due to the flexible representation through phases our method needs no assumption about the underlying structures in image data and no prior knowledge regarding the number of regions more importantly the network is guaranteed to converge rapidly under general conditions these unique properties may lead to a real time approach for range image segmentation in machine perception

pixel clustering by adaptive pixel moving and chaotic synchronization in this paper a network of coupled chaotic maps for pixel clustering is proposed time evolutions of chaotic maps in the network corresponding to a pixel cluster are synchronized with each other those synchronized trajectories are desynchronized with respect to the time evolutions of chaotic maps corresponding to other pixel clusters in the same image a pixel motion mechanism is also introduced which makes each group of pixels more compact and consequently makes the model robust enough to classify ambiguous pixels another feature of the proposed model is that the number of pixel clusters does not need to be previously known

parametric representation of fuzzy numbers and application to fuzzy calculus we present several models to obtain simple parametric representations of the fuzzy numbers or intervals based on the use of piecewise monotonic functions of different forms the representations have the advantage of allowing flexible and easy to control shapes of the fuzzy numbers we use the standard cuts setting but also the membership functions are obtained immediately and can be used directly to obtain error controlled approximations of the fuzzy calculus in terms of a finite set of parameters the general setting is the hermite type interpolation where the values and the slopes of the monotonic interpolators are given by appropriate parameters and the overall errors of the fuzzy computations can be controlled within a prefixed tolerance by eventually augmenting the total number of pieces and of the parameters by which the results are obtained the representations are designed to model the lower and the upper extremal values of each cut compact intervals of the fuzzy numbers and are able to produce almost any possible configuration differentiable continuous or with a finite number of discontinuity points by using parametric monotonic functions of different types we show applications in the standard fuzzy calculus and we stress the generality and the applicability of the proposed representation to a large class of problems including the numerical solution of fuzzy differential equations the fuzzy linear regression and the stochastic extensions of the fuzzy mathematics the proposed model is called the lower upper representation and we denote the associated fuzzy numbers or intervals as lu fuzzy

on the stability of fuzzy dynamical systems abstract in this work we study the asymptotic behavior of fuzzy solutions obtained by using zadeh s extension at the deterministic solutions of initial value problems we obtain some result regarding the existence of fuzzy equilibrium points that generalize the already known results as show earlier the membership function of the fuzzy equilibrium points may be obtained in a relatively simple way also we study the projection of the fuzzy solution on the appropriate subspaces of the phase space several examples are given to illustrate the obtained results

generalized differentiability of fuzzy valued functions in the present paper using novel generalizations of the hukuhara difference for fuzzy sets we introduce and study new generalized differentiability concepts for fuzzy valued functions several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them characterization and relatively simple expressions are provided for the new derivatives

on possibilistic correlation in 2004 fuller and majlender introduced the notion of covariance between fuzzy numbers by their joint possibility distribution to measure the degree to which they interact based on this approach in this paper we will present the concept of possibilistic correlation representing an average degree of interaction between marginal distributions of a joint possibility distribution as compared to their respective dispersions moreover we will formulate the classical cauchy schwarz inequality in this possibilistic environment and show that the measure of possibilistic correlation satisfies the same property as its probabilistic counterpart in particular applying the idea of transforming level sets of possibility distributions into uniform probability distributions we will point out a fundamental relationship between our proposed possibilistic approach and the classical probabilistic approach to measuring correlation

on fuzzy uncertainties on the logistic equation abstract it is recognized that handling uncertainty is essential to obtain more reliable results in modeling and computer simulation this paper aims to discuss the logistic equation subject to fuzzy uncertainties in the initial conditions and parameters here we consider the population density at a specific time as a fuzzy variable in which the possibility distribution function depends on the possibility distribution functions of the environmental carrying capacity the initial population density and the intrinsic growth rate we provide closed form expressions for the expected value of the fuzzy variables population density and for the time of maximum growth we also perform some numerical simulations to illustrate our main results

automorphic forms with degenerate fourier coefficients the main theme of this paper is that singular automorphic forms on classical groups are given by theta series liftings we establish several inequalities relating the automorphic multiplicities of a given representation and that of its abstract theta lift our methods allow one to lift noncuspidal square integrable automorphic forms when the dual pair involved is in the stable range in this way we construct new families of singular automorphic forms many of which are clearly unipotent in fact starting from one dimensional representations and repeating the procedure of lifting in the stable range one may obtain all automorphic forms which are quadratic unipotent in the sense of moeglin

motion segmentation based on motion brightness integration and oscillatory correlation a segmentation method based on the integration of motion and brightness is proposed for image sequences the method is composed of two parallel pathways that process motion and brightness respectively inspired by the visual system the motion pathway has two stages the first stage estimates local motion at locations with reliable information the second stage performs segmentation based on local motion estimates in the brightness pathway the input scene is segmented into regions based on brightness distribution subsequently segmentation results from the two pathways are integrated to refine motion estimates the final segmentation is performed in the motion network based on refined estimates for segmentation locally excitatory globally inhibitory oscillator network legion architecture is employed whereby the oscillators corresponding to a region of similar motion brightness oscillate in synchrony and different regions attain different phases results on synthetic and real image sequences are provided and comparisons with other methods are made

image segmentation based on oscillatory correlation we study image segmentation on the basis of locally excitatory globally inhibitory oscillator networks legion whereby the phases of oscillators encode the binding of pixels we introduce a lateral potential for each oscillator so that only oscillators with strong connections from their neighborhood can develop high potentials based on the concept of the lateral potential a solution to remove noisy regions in an image is proposed for legion so that it suppresses the oscillators corresponding to noisy regions but without affecting those corresponding to major regions we show that the resulting oscillator network separates an image into several major regions plus a background consisting of all noisy regions and we illustrate network properties by computer simulation the network exhibits a natural capacity in segmenting images the oscillatory dynamics leads to a computer algorithm which is applied successfully to segmenting real gray level images a number of issues regarding biological plausibility and perceptual organization are discussed we argue that legion provides a novel and effective framework for image segmentation and figure ground segregation

boundary detection by constrained optimization a statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions the model is a joint probability distribution for the array of pixel gray levels and an array of labels in boundary finding the labels are binary zero or one representing the absence or presence of boundary elements in partitioning the label values are generic two labels are the same when the corresponding scene locations are considered to belong to the same region the distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels using the kolmogorov smirnov nonparametric measures of difference between the distributions of these features the number of model parameters is minimized by forbidding label configurations which are assigned probability zero the maximum a posteriori estimator of boundary placements and partitionings is examined the forbidden states introduce constraints into the calculation of these configurations stochastic relaxation methods are extended to accommodate constrained optimization

fuzzy and set valued stochastic differential equations with local lipschitz condition we are concerned with the fuzzy stochastic differential equations driven by multidimensional brownian motion viewed as a tool used to describe the behavior of dynamic systems operating in fuzzy environments with stochastic noises under the uniform lipschitz condition we prove the local uniqueness theorem for the solutions of fuzzy stochastic differential equations next we show assuming the lipschitz condition is satisfied only locally that these equations have a unique solution the fact that the solution is bounded is also proved we conclude the paper with a number of corresponding results holding for the deterministic fuzzy differential equations and set valued stochastic differential equations with local lipschitz condition

metric spaces of fuzzy sets two classes of metrics are introduced for spaces of fuzzy sets their equivalence is discussed and basic properties established a characterisation of compact and locally compact subsets is given in terms of boundedness and p mean equileft continuity and the spaces shown to be locally compact complete and separable metric spaces

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

a note on fuzzy differential equations and the extension principle in this note we show by an example that the main result in a paper by bassanezi et al m t mizukoshi l c barros y chalco cano h roman flores r c bassanezi fuzzy differential equations and the extension principle information sciences 177 2007 3627 3635 is incorrect

locally excitatory globally inhibitory oscillator networks a novel class of locally excitatory globally inhibitory oscillator networks legion is proposed and investigated the model of each oscillator corresponds to a standard relaxation oscillator with two time scales in the network an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern while preventing other oscillators from jumping up computer simulations demonstrate that the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks this model lays a physical foundation for the oscillatory correlation theory of feature binding and may provide an effective computational framework for scene segmentation and figure ground segregation in real time

parallel activation of memories in an oscillatory neural network we describe a feedback neural network whose elements possess dynamic thresholds this network has an oscillatory mode that we investigate by measuring the activities of memory patterns as functions of time we observe spontaneous and induced transitions between the different oscillating memories moreover the network exhibits pattern segmentation by oscillating between different memories that are included as a mixture in a constant input the efficiency of pattern segmentation decreases strongly as the number of the input memories is increased using oscillatory inputs we observe resonance behavior

an approximation to the extension principle using decomposition of fuzzy intervals this article presents a proposal for the decomposition of large ranges of uncertainty associated with the cartesian product of two fuzzy intervals we compute an approximation of the fuzzy set obtained by applying extension principle to a real function by means of this decomposition and piecewise linearization of the function it is proved the efficiency of the method via convergence in d metric we also extend the method to the case when the function has more than two arguments some examples are included to illustrate the proposed method and to compare it with others

fuzzy differential equations for universal oscillators abstract this study considers universal oscillator fuzzy differential equations the differential inclusion method is applied to this problem by considering the universal oscillator fuzzy differential equations as universal oscillator uncertain dynamical systems three types of damped oscillators are considered comprising underdamped critically damped and overdamped oscillators the existence and uniqueness of the solutions to each case are discussed and proofs are given under some certain conditions for universal oscillator uncertain dynamical systems with an undamped forcing function the existence and uniqueness of the solutions and big solutions are also verified while the scopes of the trajectories to the solutions are obtained based on the inclusion relationship between solutions and big solutions we also prove the existence and uniqueness of solutions to universal oscillator uncertain dynamical systems with a damped forcing function by using other more direct conditions

synchrony and desynchrony in integrate and fire oscillators due to many experimental reports of synchronous neural activity in the brain there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization contrary to hopfield and herz 1995 we find that networks of locally coupled integrate and fire oscillators can quickly synchronize furthermore we examine the time needed to synchronize such networks we observe that these networks synchronize at times proportional to the logarithm of their size and we give the parameters used to control the rate of synchronization inspired by locally excitatory globally inhibitory oscillator network legion dynamics with relaxation oscillators terman wang 1995 we find that global inhibition can play a similar role of desynchronization in a network of integrate and fire oscillators we illustrate that a legion architecture with integrate and fire oscillators can be similarly used to address image analysis

fast numerical integration of relaxation oscillator networks based on singular limit solutions relaxation oscillations exhibiting more than one time scale arise naturally from many physical systems when relaxation oscillators are coupled in a way that resembles chemical synapses we propose a fast method to numerically integrate such networks the numerical technique called the singular limit method is derived from analysis of relaxation oscillations in the singular limit in such a limit system evolution gives rise to time instants at which fast dynamics take place and intervals between them during which slow dynamics take place a full description of the method is given for a locally excitatory globally inhibitory oscillator network legion where fast dynamics characterized by jumping which leads to dramatic phase shifts is captured in this method by iterative operation and slow dynamics is entirely solved the singular limit method is evaluated by computer experiments and it produces remarkable speedup compared to other methods of integrating these systems the speedup makes it possible to simulate large scale oscillator networks

simulating continuous fuzzy systems abstract in previous studies we concentrated on utilizing crisp numeric simulation to produce discrete event fuzzy systems simulations then we extended this research to the simulation of continuous fuzzy systems models in this study we continue our study of continuous fuzzy systems using crisp continuous simulation consider a crisp continuous system whose process of evolution depends on differential equations such a system contains a number of parameters that must be estimated usually point estimates are computed and used in the model however these point estimates typically have uncertainty associated with them we propose to incorporate uncertainty by using fuzzy numbers as estimates of these unknown parameters fuzzy parameters convert the crisp system into a fuzzy system trajectories describing the behavior of the system become fuzzy curves we will employ crisp continuous simulation to estimate these fuzzy trajectories three examples are discussed

towards the theory of fuzzy differential equations comparative analysis of two ideologically distinct approaches in the theory of fuzzy differential equations is given domains of applications advantages and shortcomings of those approaches are described new definitions of solutions to fuzzy differential equations are proposed

stability and periodicity in fuzzy differential equations formulations of fuzzy differential equations des in terms of the hukuhara derivative do not reproduce the rich and varied behavior of crisp des another interpretation in terms of differential inclusions expressed level setwise overcomes much of this deficiency and opens up for profitable investigation such properties as stability attraction periodicity and the like this is especially important for investigating continuous systems which are uncertain or incompletely specified this paper studies studies lyapunov stability of fuzzy des and the periodicity of the fuzzy solution set for both the time dependent and autonomous cases

a note on zadeh s extensions let f rn rn and f f rn f r n be zadeh s extension of f to the space of fuzzy compact sets f rn the aim of this paper is to show that if f is continuous then f f rn d f rn d is also continuous d being the supremum over hausdorff distances between their corresponding level sets

revisiting fuzzy differential equations abstract we revisit the original formulation of fuzzy differential equations fdes and provide examples to show that the theory of fdes is richer than the corresponding theory of ordinary differential equations odes and therefore need not be rejected the alternative formulation in terms of differential inclusions does not always have advantage over odes as claimed we also discuss a stability result via lyapunov functions in this setup

recurrent network with large representational capacity a recurrent network is proposed with the ability to bind image features into a unified surface representation within a single layer and without capacity limitations or border effects a group of cells belonging to the same object or surface is labeled with the same activity amplitude while cells in different groups are kept segregated due to lateral inhibition labeling is achieved by activity spreading through local excitatory connections in order to prevent uncontrolled spreading a separate network computes the intensity difference between neighboring locations and signals the presence of the surface boundary which constrains local excitation the quality of surface representation is not compromised due to the self excitation the model is also applied on gray level images in order to remove small noisy regions a feedforward network is proposed that computes the size of surfaces size estimation is based on the difference of dendritic inhibition in lateral excitatory and inhibitory pathways which allows the network to selectively integrate signals only from cells with the same activity amplitude when the output of the size estimation network is combined with the recurrent network good segmentation results are obtained both networks are based on biophysically realistic mechanisms such as dendritic inhibition and multiplicative integration among different dendritic branches

some properties of solutions for a class of semi linear uncertain dynamical systems in this paper some properties of solutions are obtained for semi linear fuzzy differential equations understood as differential inclusions i e semi linear uncertain dynamical systems the definitions of the solution to the semi linear uncertain dynamical system and its corresponding big solution are given the existence of the two kinds of solutions is established and the inclusion relation between them is also obtained

periodic boundary value problems for impulsive fuzzy differential equations the peculiarity of the hukuhara derivative makes it impossible to find periodic solutions for fuzzy differential equations with the exception of very restrictive situations in this work we consider a boundary value problem associated with an impulsive fuzzy differential equation and approximate the extremal solutions in a fuzzy functional interval using the monotone method fuzzy comparison results are useful in our procedure and the expression of the solution for some impulsive periodic linear differential problems is also provided

pattern segmentation in associative memory the goal of this paper is to show how to modify associative memory such that it can discriminate several stored patterns in a composite input and represent them simultaneously segmention of patterns takes place in the temporal domain components of one pattern becoming temporally correlated with each other and anticorrelated with the components of all other patterns correlations are created naturally by the usual associative connections in our simulations temporal patterns take the form of oscillatory bursts of activity model oscillators consist of pairs of local cell populations connected appropriately transition of activity from one pattern to another is induced by delayed self inhibition or simply by noise

color image segmentation using competitive learning presents a color image segmentation method which divides the color space into clusters competitive learning is used as a tool for clustering the color space based on the least sum of squares criterion we show that competitive learning converges to approximate the optimum solution based on this criterion theoretically and experimentally we apply this method to various color scenes and show its efficiency as a color image segmentation method we also show the effects of using different color coordinates to be clustered with some experimental results

construction of discrete series for classical p adic groups in this paper the authors complete the classification of irreducible square integrable representations of classical p adic groups assuming a natural assumption which is expected to hold in general this classification implies a parameterization of irreducible tempered representations of these groups and it implies a classification of the non unitary duals of these groups modulo cuspidal data

texture segmentation using gaussian markov random fields and neural oscillator networks we propose an image segmentation method based on texture analysis our method is composed of two parts the first part determines a novel set of texture features derived from a gaussian markov random fields gmrf model unlike a gmrf based approach our method does not employ model parameters as features or require the extraction of features for a fixed set of texture types a priori the second part is a 2d array of locally excitatory globally inhibitory oscillator networks legion after being filtered for noise suppression features are used to determine the local couplings in the network when legion runs the oscillators corresponding to the same texture tend to synchronize whereas different texture regions tend to correspond to distinct phases in simulations a large system of differential equations is solved for the first time using a recently proposed method for integrating relaxation oscillator networks we provide results on real texture images to demonstrate the performance of our method

a unified approach to boundary perception edges textures and illusory contours a model consisting of a multistage system which extracts and groups salient features in the image at different spatial scales or frequencies is used in the first stage a gabor wavelet decomposition provides a representation of the image which is orientation selective and has optimal localization properties in space and frequency this decomposition is useful in detecting significant features such as step and line edges at different scales and orientations in the image following the wavelet transformation local competitive interactions are introduced to reduce the effects of noise and changes in illumination interscale interactions help in localizing the line ends and corners and play a crucial role in boundary perception the final stage groups similar features aiding in boundary completion the different stages can be identified with processing by simple complex and hypercomplex cells in the visual cortex of mammals experimental results demonstrate the performance of this model in detecting boundaries both real and illusory in real and synthetic images

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

fuzzy dynamical systems a fuzzy dynamical system on an underlying complete locally compact metric state space x is defined axiomatically in terms of a fuzzy attainability set mapping on x this definition includes as special cases crisp single and multivalued dynamical systems on x it is shown that the support of such a fuzzy dynamical system on x is a crisp multivalued dynamical system on x and that such a fuzzy dynamical system can be considered as a crisp dynamical system on a state space of nonempty compact fuzzy subsets of x in addition fuzzy trajectories are defined their existence established and various properties investigated

generalized hukuhara differentiability of interval valued functions and interval differential equations abstract in the present paper we use a recently proposed generalization of the hukuhara difference for compact convex sets to introduce and study a generalization of the hukuhara differentiability to the case of interval valued functions we also consider several possible definitions for the derivative of an interval valued function recently proposed in the literature and we study connections between them and their properties using these concepts we study interval differential equations local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ode systems several examples are also shown

low dimensional dynamics and bifurcations in oscillator networks via bi orthogonal spectral decomposition many natural neural systems are functionally or hierarchically organized into interacting ensembles of neural populations to investigate the dynamics in a hierarchical system of coupled bistable van der pol oscillators we apply the bi orthogonal decomposition into empirical orthogonal spatial and temporal modes within this method the dynamics and synchronized patterns are characterized by global temporal and spatial entropy and energy different states of the network activity are identified as synchronous or asynchronous dynamics induced by external periodic input of particular interest is the ability of the bi orthogonal decomposition to detect bifurcations following variations of the system parameter bifurcations correspond to crossings of the eigenvalues where an exchange of dominant modes takes place in our simulations we observe a bifurcation induced by variations of input frequency and strength identified as a saddle node bifurcation of the unstable stable pair of limit cycles

the role of weight normalization in competitive learning the effect of different kinds of weight normalization on the outcome of a simple competitive learning rule is analyzed it is shown that there are important differences in the representation formed depending on whether the constraint is enforced by dividing each weight by the same amount divisive enforcement or subtracting a fixed amount from each weight subtractive enforcement for the divisive cases weight vectors spread out over the space so as to evenly represent typical inputs whereas for the subtractive cases the weight vectors tend to the axes of the space so as to represent extreme inputs the consequences of these differences are examined

dynamics and bifurcations of fuzzy nonlinear dynamical systems this article presents a study on how changes in fuzzy parameters can affect the behavior of fuzzy solutions such fuzzy solutions are obtained by applying the zadeh extension principle on deterministic solutions of autonomous differential equations we define the concepts of topological equivalence and fuzzy bifurcation value for fuzzy flows using these notions we prove some results for the existence of such bifurcation values we also provide some examples and computational simulations to illustrate the results

fuzzy differential equations we will concentrate on the second order linear constant coefficient ordinary differential equation for x in interval i i can be 0 t for t 0 or i can be 0 the initial conditions are y 0 0 y 0 1 we assume g is continuous on i

comparation between some approaches to solve fuzzy differential equations in this paper we study the class of fuzzy differential equations where the dynamics is given by a continuous fuzzy mapping which is obtained via zadeh s extension principle we get a fuzzy solution for this class of fuzzy differential equations and several illustrative examples are presented we also give some properties and we show the relationships with others interpretation finally we propose a numerical procedure for obtaining the fuzzy solution

embedding of level continuous fuzzy sets on banach spaces abstract in this paper we present an extension of the minkowski embedding theorem showing the existence of an isometric embedding between the class f c x of compact convex and level continuous fuzzy sets on a real separable banach space x and c 0 1 b x the banach space of real continuous functions defined on the cartesian product between 0 1 and the unit ball b x in the dual space x also by using this embedding we give some applications to the characterization of relatively compact subsets of f c x in particular an ascoli arzela type theorem is proved and applied to solving the cauchy problem x t f t x t x t0 x0 on f c x

global competition and local cooperation in a network of neural oscillators abstract an architecture of locally excitatory globally inhibitory oscillator networks is proposed and investigated both analytically and by computer simulation the model for each oscillator corresponds to a standard relaxation oscillator with two time scales oscillators are locally coupled by a scheme that resembles excitatory synaptic coupling and each oscillator also inhibits other oscillators through a common inhibitor oscillators are driven to be oscillatory by external stimulation the network exhibits a mechanism of selective gating whereby an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern while preventing the other oscillators from jumping up we show analytically that with the selective gating mechanism the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks computer simulations demonstrate the model s promising ability for segmenting multiple input patterns in real time this model lays a physical foundation for the oscillatory correlation theory of feature binding and may provide an effective computational framework for scene segmentation and figure ground segregation

self organization of pulse coupled oscillators with application to clustering we introduce an efficient synchronization model that organizes a population of integrate and fire oscillators into stable and structured groups each oscillator fires synchronously with all the others within its group but the groups themselves fire with a constant phase difference the structure of the synchronized groups depends on the choice of the coupling function we show that by defining the interaction between oscillators according to the relative distance between them our model can be used as a general clustering algorithm unlike existing models our model incorporates techniques from relational and prototype based clustering methods and results in a clustering algorithm that is simple efficient robust unbiased by the size of the clusters and that can find an arbitrary number of clusters in addition to helping the model self organize into stable groups the synergy between clustering and synchronization reduces the computational complexity significantly the resulting clustering algorithm has several advantages over conventional clustering techniques in particular it can generate a nested sequence of partitions and it can determine the optimum number of clusters in an efficient manner moreover since our approach does not involve optimizing an objective function it is not sensitive to initialization and it can incorporate nonmetric similarity measures we illustrate the performance of our algorithms with several synthetic and real data sets

computing with arrays of coupled oscillators an application to preattentive texture discrimination recent experimental findings gray et al 1989 eckhorn et al 1988 seem to indicate that rapid oscillations and phase lockings of different populations of cortical neurons play an important role in neural computations in particular global stimulus properties could be reflected in the correlated firing of spatially distant cells here we describe how simple coupled oscillator networks can be used to model the data and to investigate whether useful tasks can be performed by oscillator architectures a specific demonstration is given for the problem of preattentive texture discrimination texture images are convolved with different sets of gabor filters feeding into several corresponding arrays of coupled oscillators after a brief transient the dynamic evolution in the arrays leads to a separation of the textures by a phase labeling mechanism the importance of noise and of long range connections is briefly discussed

periodic orbits for fuzzy flows abstract periodic solutions are present in many of the various mathematical models that describe physical chemical or biological phenomena in this work we investigate the existence of periodic solutions for fuzzy initial value problem we will show that fuzzy solutions can present periodic points and we will develop tools of qualitative analysis for such solutions some models are presented to illustrate the results obtained in this paper