reduction of attributes in averaged similarities abstract similarity relations may be constructed from a set of fuzzy attributes each fuzzy attribute generates a simple similarity and these simple similarities are combined into a complex similarity afterwards the representation theorem establishes one such way of combining similarities while averaging them is a different and more realistic approach in applied domains in this paper given an averaged similarity by a family of attributes we propose a method to find families of new attributes having fewer elements that generate the same similarity more generally the paper studies the structure of this important class of fuzzy relations

dynamics of one and two dimensional fronts in a bistable equation with time delayed global feedback propagation failure and control mechanisms we study the evolution of fronts in a bistable equation with time delayed global feedback in the fast reaction and slow diffusion regime this equation generalizes the hodgkin grafstein and allen cahn equations we derive a nonlinear equation governing the motion of fronts which includes a term with delay in the one dimensional case this equation is linear we study the motion of one and two dimensional fronts finding a much richer dynamics than for the previously studied cases without time delayed global feedback we explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a hopf bifurcation as the delay time increases we show that for certain delay times the prevailing phase is different from that corresponding to the system in the absence of global coupling numerical simulations of the partial differential equation are in agreement with the analytical predictions

spatiotemporal coding in an electrochemical oscillatory network a network consisting of n relaxation electrochemical oscillators mutually coupled by all to all inhibitory connections can have n ensuremath 1 coexisting out of phase states each state being a permutation of a periodic spiking sequence the modification of the out of phase states by shots of laser pulse perturbations is shown in such networks the phase relation of the oscillators is stored as a coded pattern the ability of the network to function as a rewritable memory of n ensuremath 1 different spatiotemporal patterns is demonstrated experimentally for n 4

maps preserving the local spectrum of jordan product of matrices abstract let m n c be the algebra of all n n complex matrices and fix a nonzero vector x 0 c n we show that a map from m n c into itself satisfies t s s t x 0 t s s t x 0 t s m n c if and only if there exists an invertible matrix a m n c such that a x 0 x 0 and t a t a 1 for all t m n c

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

nonlinear maps preserving the minimum and surjectivity moduli abstract let x and y be infinite dimensional complex banach spaces and let b x resp b y denote the algebra of all bounded linear operators on x resp on y we describe maps from b x onto b y satisfying c s t c s t for all s t b x where c stands either for the minimum modulus or the surjectivity modulus or the maximum modulus we also obtain analog results for the finite dimensional case

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

synchronization and desynchronization in a network of locally coupled wilson cowan oscillators a network of wilson cowan wc oscillators is constructed and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis the network is a 2d matrix where each oscillator is coupled only to its neighbors we show analytically that a chain of locally coupled oscillators the piecewise linear approximation to the wc oscillator synchronizes and we present a technique to rapidly entrain finite numbers of oscillators the coupling strengths change on a fast time scale based on a hebbian rule a global separator is introduced which receives input from and sends feedback to each oscillator in the matrix the global separator is used to desynchronize different oscillator groups unlike many other models the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding gestalt principles of feature grouping the ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure ground segregation based on oscillatory correlation

linear maps preserving the spectral radius abstract let x be a complex banach space if b x b x is a surjective linear map such that a and a have the same spectral radius for every a b x then c where is either an algebra automorphism or an antiautomorphism of b x and c is a complex constant such that c 1

local spectrum linear preservers at non fixed vectors abstract for a complex n n matrix t and a vector x c n we denote by t x respectively by r t x the local spectrum respectively the local spectral radius of t at x we prove that m n m n linear has the property that for each t m n there exists a nonzero x t c n such that t x t t x t if and only if there exists a m n invertible such that either t a t a 1 for each t m n or t a t t a 1 for each t m n modulo a multiplication by a unimodular complex number we arrive at the same conclusion by supposing that for each t m n there exists a nonzero x t c n such that r t x t r t x t

multistability of clustered states in a globally inhibitory network abstract we study a network of m identical excitatory cells projecting excitatory synaptic connections onto a single inhibitory interneuron which is reciprocally coupled to all excitatory cells through inhibitory synapses possessing short term synaptic depression we find that such a network with global inhibition possesses multiple stable activity patterns with distinct periods characterized by the clustering of the excitatory cells into synchronized sub populations we prove the existence and stability of n cluster solutions in a m cell network using methods of geometric singular perturbation theory we show that any n cluster solution must satisfy a set of consistency conditions that can be geometrically derived we then characterize the basin of attraction of each solution although frequency dependent depression is not necessary for multistability we discuss how it plays a key role in determining network behavior we find a functional relationship between the level of synaptic depression the number of clusters and the interspike interval between neurons this relationship is much less pronounced in the absence of depression implications for temporal coding and memory storage are discussed

structural analysis of indistinguishability operators and related concepts given an indistinguishability operator e it is possible to obtain the set of extensional fuzzy subsets h e and the respective operators of upper and lower approximations by extensional sets f e and j e reciprocally given any of these objects the initial indistinguishability operator e can be retrieved it is well known that these concepts are in bijection in this paper we will prove that the relation underlying them is a lattice isomorphism we will also consider further operators such as natural means and finally show the robustness of the results with respect to isomorphisms of t norms

on spectrally bounded linear maps on b x abstract let x be a complex banach space and denote by b x the algebra of all linear bounded operators on x for t b x denote by r t its spectral radius we prove that if b x b x is a linear and surjective map such that i given any a b b x there exists a positive real number m a b such that r a b m a b r a b for all complex numbers satisfying 1 ii r t 0 implies r t 0 then there exist a linear functional f b x c a nonzero complex number c and either a bounded invertible linear map u x x such that t c u t u 1 f t i t b x or a bounded invertible linear map u x x such that t c u t u 1 f t i t b x also the linear functional f satisfies the property that given any a b b x there exists n a b 0 such that f a f b n a b r a b for all complex numbers satisfying 1

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

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

on the structure of f indistinguishability operators abstract some properties concerning the structure of f indistinguishability operators are analyzed it is shown that any of such operators is generated by a family of fuzzy subsets this result since it gives the way to construct f indistinguishabilities facilitates new applications of fuzzy relations the links between f indistinguishability operators and a kind of generalized metrics in the unit interval which are also explored are used to define the canonical generators of an f indistinguishability operator that is the fuzzy partition associated with the operator

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

partial synchronization in a network of neural oscillators a network with three types of model neurons is considered these are designated as excitatory fast inhibitory and slow inhibitory cells each excitatory cell is modeled as a relaxation oscillator while for simplicity the inhibitory cells are modeled by a single equation the coupling between cells is modeled in a way that mimics chemical synapses this network is introduced as a simplification of the model in traub and miles neuronal networks of the hippocampus cambridge university press new york 1991 for oscillations in the ca3 region of the hippocampus a geometric approach for analyzing the solution structure of the network is developed the analysis clarifies the role that each type of cell and each parameter plays in obtaining partially synchronized rhythms determines how the parameters should be chosen for this collective behavior and indicates possible instabilities which arise as parameters are varied a symbolic scheme is derived which accurately determines the firing patterns for a l

relaxation oscillators with time delay coupling abstract we study networks of relaxation oscillators coupled with time delays synapses a pair of oscillators is analyzed and shown to attain loosely synchronous solutions for a wide range of initial conditions and time delays simulations of one and two dimensional oscillator networks indicate that locally coupled oscillators are also loosely synchronous desynchronous solutions are possible when system parameters are varied to characterize lossely synchronous networks we introduce a measure of synchrony the maximum time difference between any two oscillators in locally excitatory globally inhibitory oscillator networks with time delays we find that desynchronous solutions for different groups of oscillators are maintained and the number of groups that can be segregated is related to the maximum time difference within each group to examine the maximum time difference we display its histograms for oscillator networks in one and two dimensions also a range of initial conditions is given so that the maximum time difference is contained as the system evolves

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

spectrum preserving linear maps abstract let x and y be banach spaces we show that a spectrum preserving surjective linear map from b x to b y is either of the form t ata 1 for an isomorphism a of x onto y or the form t bt b 1 for an isomorphism b of x onto y

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

linear maps on mn c preserving the local spectrum let x0 cn be a nonzero vector we prove that if a linear map mn c mn c preserves the local spectrum at x0 i e t x0 t x0 for all t mn c then there exists an invertible matrix a such that a x0 x0 and t ata 1 for every t

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

more elementary operators that are spectrally bounded we study spectrally bounded elementary operators of length two on a complex unital banach algebra a some related conditions are investigated as well in particular we show that if s is an elementary operator of length two such that s x is quasi nilpotent for every x a then s x 3 rada for every x a