a classification of types of extensions from top to qftop abstract by making use of the concept of the introduced quasi fuzzy topological space c y zheng fuzzy sets and systems 14 1984 273 280 we introduce the concept of s extensions mainly we generalize and characterize the concepts of good extensions r lowen j math anal appl 56 1976 621 633 weak inducement h w martin j math anal appl 78 1980 634 639 and s extensions by introducing some relations between the category of topological spaces and the category of quasi topological spaces

image recovery and segmentation using competitive learning in a layered network in this study we have used the principle of competitive learning to develop an iterative algorithm for image recovery and segmentation within the framework of markov random fields mrfs the image recovery problem is transformed to the problem of minimization of an energy function a local update rule for each pixel point is then developed in a stepwise fashion and is shown to be a gradient descent rule for an associated global energy function the relationship of the update rule to kohonen s update rule is shown quantitative measures of edge preservation and edge enhancement for synthetic images are introduced as compared to recently published results using mean field approximation our algorithm shows consistently better performance in edge preservation and comparable performance in enhancing within the boundaries these results are based on simulation experiments on a set of synthetic images corrupted by gaussian noise and on a set of real images

minimal nonsquare spectral factors we consider the problem of parametrizing the set of all nonsquare minimal spectral factors of a rational matrix function taking positive semidefinite values on the imaginary axis

existence of minimal nonsquare j symmetric factorizations for self adjoint rational matrix functions in this paper we show that any rational matrix function having hermitian values on the imaginary axis and with constant signature and constant pole signature admits a minimal symmetric factorization with possibly nonsquare factors our proof is based on a construction which shows that any such function can be extended preserving its mcmillan degree to a function that admits j symmetric factorization with square factors also we consider other properties of the factors in j symmetric factorizations particular attention is given to the study of the common invariant zero structure of these factors

fuzzy closure spaces abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems but many results can be extended to what are called fuzzy closure spaces or fcs s for short the notions of a subspace a sum and a product are extended to fcs s the hereditary additivity and productivity behaviour of compactness in fcs s is investigated and some weak forms of compactness and fuzzy continuous functions in fcs s are introduced the interaction between fuzzy proximity spaces and fcs s is investigated a necessary background is included for completeness

numerical algorithms and existence results on lq control of descriptor systems with conditions on x 0 and stability we present a numerical algorithm based on using orthogonal matrices and sufficient existence conditions for an lq control problem of descriptor systems which generalise the existing results the associated hamiltonian pencil may be singular and may have infinite generalised eigenvalues iges of multiplicity 1 besides on x 0 we present optimality conditions on x 0 we present sufficient conditions for stability of the optimal closed loop descriptor system as well as a stabilisation algorithm

numerical j spectral factorization of general para hermitian matrices a numerical algorithm for j spectral factorization of para hermitian rational matrices is presented based on a generalization of the notion of separated realization of a para hermitian matrix the transformations used preserve the para hermitian matrix pencil structure

soft input soft output equalizers for turbo receivers a statistical physics perspective many algorithms in signal processing and digital communications must deal with the problem of computing the probabilities of the hidden state variables given the observations i e the inference problem as well as with the problem of estimating the model parameters such an inference and estimation problem is encountered for example in adaptive turbo equalization demodulation where soft information about the transmitted data symbols has to be inferred in the presence of the channel uncertainty given the received signal samples and a priori information provided by the decoder an exact inference algorithm computes the a posteriori probability app values for all transmitted symbols but the computation of app s is known to be an np hard problem thus rendering this approach computationally prohibitive in most cases we show in this paper how may of the well known low complexity soft input soft output siso equalizers including the channel matched filter based linear siso equalizers and minimum mean square error mmse siso equalizers as well as the expectation maximization em algorithm based siso demodulators in the presence of the rayleigh fading channel can be formulated as solutons to a variational optimization problem the variational optimization is a well established methodology for low complexity inference and estimation originating from statistical physics importantly the imposed variational optimization framework provides an interesting link between the app demodulators and the linear siso equalizers moreover it provides a new set of insights into the structure and performance of these widely celebrated linear siso equalizers while suggesting some fine tuning of them as well

a new approach to fuzzy bitopological spaces abstract given a fuzzy bitopological space x 1 2 we have used the operator c12 ix ix defined by c 12 1 cl 2 cl i x which is a supra fuzzy closure operator fuzzy sets and systems 74 1995 353 to generate a family s which is a supra fuzzy topology loc cit 1995 so the space x s is a supra fuzzy topological space associated to the fuzzy bitopological space x 1 2 we extend the notions of fti strong fti and ultra fti due to fuzzy sets and system 43 1991 95 to the space x s the properties of fuzzy bitopological spaces have been studied by using their associated supra fuzzy topological spaces we introduce the notions of fp ti s fp ti and u fp ti by using the level supratopology s of s we investigate the relationship between these notions the notions fp ti loc cit 1995 i 1 2 3 4 and the notions fpti resp s fpti u fpti fuzzy sets and systems 105 1999 459 we give a number of examples which illustrate that these concepts are not equivalent also we extend the notions of f continuous open strong f continuous open and ultra f continuous open due to fuzzy sets and systems 38 1990 115 to the class of supra fuzzy topological spaces associated to the class of fuzzy bitopological spaces we study some properties of fp ti resp s fp ti u fp ti under these mappings

unsupervised texture segmentation in a deterministic annealing framework we present a novel optimization framework for unsupervised texture segmentation that relies on statistical tests as a measure of homogeneity texture segmentation is formulated as a data clustering problem based on sparse proximity data dissimilarities of pairs of textured regions are computed from a multiscale gabor filter image representation we discuss and compare a class of clustering objective functions which is systematically derived from invariance principles as a general optimization framework we propose deterministic annealing based on a mean field approximation the canonical way to derive clustering algorithms within this framework as well as an efficient implementation of mean field annealing and the closely related gibbs sampler are presented we apply both annealing variants to brodatz like microtexture mixtures and real word images

nonsquare spectral factors via factorizations of a unitary function abstract we consider the problem of parametrizing the set of nonsquare minimal spectral factors of a rational matrix function taking positive semidefinite values on the imaginary axis the tool here is the use of factorizations of a certain type of the function w 1w where w resp w is the minimal square spectral factor that has all its poles and zeros in the right resp left halfplane

weak continuity with structural constraints nonlinear regression and nonlinear regularization are two powerful approaches to segmentation and nonlinear filtering in this correspondence we propose a hybrid approach that effectively combines the best of both worlds and can be efficiently implemented via the viterbi algorithm

on polynomial matrix spectral factorization by symmetric extraction we revise the 1963 davis algorithm 2 for the spectral factorization of a para hermitian nonnegative polynomial matrix phi by symmetric factor extraction this algorithm is careless about zeros at infinity by introducing the notion of diagonal reducedness of phi we obtain an easy sufficient test for the absence of zeros at infinity we show then how to get phi diagonally reduced by diagonal excess reduction steps similar to the oono and yasuura steps removing all zeros at infinity and then how to remove synunetrically finite zeros while keeping el diagonally reduced hence free of zeros at infinity this results in a revised symmetric extraction spectral factorization algorithm with monotone degree control an example shows the didactical conceptual simplicity of the method appropriate symmetric extraction is discovered by revising and discovering important particular one sided factor extraction properties of polynomial matrices

mean field annealing a formalism for constructing gnc like algorithms optimization problems are approached using mean field annealing mfa which is a deterministic approximation using mean field theory and based on peierls s inequality to simulated annealing the mfa mathematics are applied to three different objective function examples in each case mfa produces a minimization algorithm that is a type of graduated nonconvexity when applied to the weak membrane objective mfa results in an algorithm qualitatively identical to the published gnc algorithm one of the examples mfa applied to a piecewise constant objective function is then compared experimentally with the corresponding gnc weak membrane algorithm the mathematics of mfa are shown to provide a powerful and general tool for deriving optimization algorithms

spectral factorization via hermitian pencils abstract the spectral factorization problem is solved for state space systems via results on the canonical forms and inertia of hermitian matrix pencils these algebraic results then give a deflation method for spectral factorization

on fuzzy syntopogenous structures and preorder abstract in this paper we combine fuzzy topological structure on x with algebraic structure on x and investigate their corresponding structures and their properties first we study the preorder relation generated by an l fuzzy syntopogenous structure conversely we research the l fuzzy syntopogenous structure defined by a preorder relation second we define increasing decreasing l fuzzy syntopogenous spaces with preorder and study some properties of them finally we give an important example of increasing l fuzzy syntopogenous space i e r s r

physical consideration of an image in image restoration using bayes formula abstract we consider image restoration by bayes formula and investigate the relationship between an image and a prior probability from the following two viewpoints hyperparameter estimation and the accuracy of a restored image the q ising model is adopted as a prior probability in bayes formula not the q ising energy but the potts energy plays an important role in the hyperparameter estimation from the viewpoint of the hyperparameter estimation the relationship between a natural image and a prior probability is characterized through the potts energy and magnetization of an image the potts energy and magnetization of an image are defined by a set of pixels state of an image the closer to the average potts energy and magnetization over a prior probability the potts energy and magnetization of a natural image is the closer to the true value of a hyperparameter the estimated value of a hyperparameter from a degraded image is for the accuracy of a restored image the image which has a smaller q ising energy is better restored by bayes formula composed of the q ising prior the consideration for the relationship between an image and a prior probability is expected to be valid for a more complicated prior probability

fuzzy uniform spaces in this paper we introduce the notion of fuzzy uniform spaces in section 2 we give some basic results and show how a fuzzy topology is derived from a fuzzy uniformity in sections 3 and 4 we prove that the notions which are introduced are good extensions and we prove that the category of uniform spaces is nicely injected in the category of fuzzy uniform spaces finally in section 5 we prove some basic results

fuzzy proximities and totally bounded fuzzy uniformities after the classical papers of zadeh 181 and chang 3 many concepts of general topology have been extended to fuzzy set theory in this paper we are interested to develop the study of fuzzy uniformities fuzzy proximities and of the connexions between such structures fuzzy uniformities have been introduced by lowen in 9 and with slight modifications in lo and by hutton in 5 the two approaches are quite different however the one proposed by hutton seems to suit much better to fuzzy set theory also because it allows to generalize a lot of results in the most proper way therefore in this paper we shall deal with hutton fuzzy uniformities the concept of fuzzy proximity used up to now see e g 7 8 15 1 is quite unsatisfactory indeed its fuzzyness is rather poor since these fuzzy proximities are in a canonical l 1 correspondence with the usual proximities see remark 2 6 moreover the open sets of the induced topologies are crisp and though every lowen fuzzy uniformity induces a fuzzy proximity this correspondence cannot work well since the two structures do not give the same fuzzy topology for these reasons we propose a new definition of fuzzy proximity it differs from the old one only in axiom p5 in short we could say that we privilege complementation with respect to intersection an agreement between the two operations being problematic in fuzzy set theory we point out that as a consequence a fuzzy set may be far from itself however this fact ought not to amaze anyone since it may happen just for pale sets which in a certain sense resemble the empty set nevertheless this modification enables us to associate a topology in a completely different way moreover every fuzzy uniformity induces a fuzzy proximity and vice versa we succeed to construct a fuzzy uniformity starting with a given fuzzy proximity and the induced topologies do not change at any step this implies that the topologies which admit a fuzzy proximity are exactly the completely regular ones moreover we prove that there exists a l l correspondence between fuzzy proximity spaces and a

thresholding implied by truncated quadratic regularization we address the problem of the estimation of an unknown signal that is known to involve sharp edges from noisy data given at the output of a linear system the sought solution is defined to be the global minimizer of an objective function combining a quadratic data fidelity term and a regularization term the latter term is a sum whose entries are obtained by applying a truncated quadratic potential function to every difference between adjacent samples such objective functions are naturally formulated either in a statistical framework or in a variational framework and they are customarily used in signal and image reconstruction however these objective functions are nonsmooth and highly nonconvex and many questions related to their minimization as well as to the features of the resulting solutions remain open we present some new facts characterizing the features exhibited by the minimizers of such objective functions our main result states that the magnitude of the differences between adjacent samples of a global minimizer are either smaller than a first threshold or larger than a second strictly larger threshold conversely no difference corresponding to a global minimizer of the objective function can be placed among these thresholds for any data this explains how edges are recovered in a signal and estimated using truncated quadratic regularization these thresholds are independent of the data but are related to the observation system and to the regularization parameters they can be used to derive necessary conditions for the choice of the regularization parameters we also show that the chance to get data for which the objective function has two or more global minimizers is null numerical experiments corroborate the obtained theoretical results

algorithm for solving algebraic riccati equation which has singular hamiltonian matrix the algorithm of construction of the solution of are with hamiltonian matrix having zero eigenvalues is developed the algorithm generalizes the schur method on are with singular hamiltonian matrix and could be used for j factorization of matrix polynomial which has zero roots

the semi stabilizing solution of generalized algebraic riccati equation for descriptor systems this paper considers the generalized algebraic riccati equation gare associated with a non standard j spectral factorization problem ns j sfp for descriptor systems of which system matrices have full column rank we derive necessary and sufficient conditions for the existence of a semi stabilizing solution of the gare based on the hamiltonian matrix pencil approach and gives a parametrization of all the semi stabilizing solutions then we provide a nonstandard j spectral factor ns j sf in terms of a particular semi stabilizing solution of the gare a simple numerical result is also included

spectral factorization of non symmetric polynomial matrices the topic of the paper is spectral factorization of rectangular and possibly non full rank polynomial matrices to each polynomial matrix we associate a matrix pencil by direct assignment of the coefficients the associated matrix pencil has its finite generalized eigenvalues equal to the zeros of the polynomial matrix the matrix dimensions of the pencil we obtain by solving an integer linear programming ilp minimization problem then by extracting a deflating subspace of the pencil we come to the required spectral factorization we apply the algorithm to most general case of inner outer factorization regardless continuous or discrete time case and to finding the greatest common divisor of polynomial matrices

the extended j spectral factorization for descriptor systems in this paper we study an extended j spectral factorization problem i e j spectral factorization problem for descriptor systems which may not have full column normal rank and may exhibit poles and zeros on the extended imaginary axis we present necessary and sufficient solvability conditions and develop a numerically reliable method for the underlying problem our method is implemented by using only orthogonal transformations and has an acceptable computational complexity

image relaxation restoration and feature extraction the techniques of a posteriori image restoration and iterative image feature extraction are described and compared image feature extraction methods known as graduated nonconvexity gnc variable conductance diffusion vcd anisotropic diffusion and biased anisotropic diffusion bad which extract edges from noisy images are compared with a restoration feature extraction method known as mean field annealing mfa all are shown to be performing the same basic operation image relaxation this equivalence shows the relationship between energy minimization methods and spatial analysis methods and between their respective parameters of temperature and scale as a result of the equivalence vcd is demonstrated to minimize a cost function and that cost is specified explicitly furthermore operations over scale space are shown to be a method of avoiding local minima

the category of pointwise s proximity spaces first it is proved that the category of pointwise quasi uniform spaces and pointwise quasi uniformly continuous morphisms is topological then the concept of pointwise s quasi proximity on lattice valued fuzzy set theory is introduced in such a way as to be compatible with pointwise quasi uniformity and pointwise p q metric each co topology can be induced by a pointwise s quasi proximity when a valued lattice is a completely distributive lattices equipped with an order reversing involution the concept of pointwise s proximity can be defined by means of pointwise s quasi proximity the relation between pointwise s quasi proximities and pointwise quasi uniformities is discussed it is proved that the category of pointwise s quasi proximity spaces is isomorphic to the category of totally bounded pointwise quasi uniform spaces the category of pointwise s proximity spaces is isomorphic to a subcategory of totally bounded pointwise uniform spaces hence they are topological

fuzzy t perfect irreducible mappings and fuzzy t proximity spaces abstract in this paper we introduce and study the concepts of fuzzy perfect fuzzy continuous fuzzy irreducible and fuzzy perfect mappings it is shown that the small image of a canonical open fuzzy set remains canonical open under fuzzy closed irreducible mapping also we introduce and study the concept of fuzzy proximity spaces and point out their interrelation with separated fuzzy proximity spaces by means of fuzzy perfect irreducible mappings

l fuzzy smirnov compactifications in this paper we get the pointwise characterization of the l fuzzy topology induced by an l fuzzy proximity space and study some important properties of l fuzzy proximity induced spaces also we discuss the n compactness separated relations and separation axioms of l fuzzy proximity spaces on the base of the method of induced spaces and above conclusions we establish the l fuzzy smirnov compactification and construct an example for l fuzzy smirnov compactifications

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

graduated nonconvexity by functional focusing reconstruction of noise corrupted surfaces may be stated as a in general nonconvex functional minimization problem for functionals with quadratic data term this paper addresses the criteria for such functionals to be convex and the variational approach for minimization i present two automatic and general methods of approximation with convex functionals based on gaussian convolution they are compared to the blake zisserman graduated nonconvexity gnc method 1987 and bilbro et al 1992 and geiger and girosi s 1991 mean field annealing mfa of a weak membrane

a fuzzy r 1 separation axiom abstract we introduce a new r 1 separation axiom for fuzzy topological spaces we identify from the literature which lower fuzzy separation axioms are compatible with our r 1 axiom we provide alternative descriptions for this r 1 axiom in the special setting of fuzzy neighborhood spaces this special case has standard higher fuzzy separation axioms in it we establish aspects of compatibility of our r 1 axiom with those higher separation axioms as well as with fuzzy compactness

minimal square spectral factors abstract recently there has been renewed interest in the problem of spectral factorization and in particular the problem of parametrizing all square minimal spectral factors of a given spectrum for instance let us mention two recent papers in this journal one of which dealing with more computational aspects of this problem clements 1993 the other giving a parametrization under additional constraints ferrante et al 1993 this paper is motivated in a large part by ferrante et al 1993 in fact we shall show that a parametrization similar to the one given there can be achieved without one of the additional constraints imposed in ferrante et al 1993 a secondary aim of this paper is to give an overview of several parametrizations available in the literature

extended neuro fuzzy models of multilayer perceptrons in this paper the famous neural model the multilayer perceptron is extended to a new neural model that is called the additive takagi sugeno type multilayer perceptron the present study proves that this new model can also act as a universal approximator and thus it can be used in many fields such as system modeling and identification the concept of f duality and the fuzzy operator interactive or are used to prove that the proposed neural model is functionally equal to a kind of fuzzy inference system further this paper presents another new neuro fuzzy model that is called the sigmoid adaptive network based fuzzy inference system simulation studies show that our proposed models both have stronger approximation capability than multilayer perceptrons

on smooth topological spaces ii separation axioms in the present paper we introduce the notions of smooth separation axioms in several ways and investigate some of their properties and the relations between them in the general framework of smooth topological spaces

lq control of descriptor systems a spectral factorisation approach a spectral factorisation algorithm of improper matrices and existence results under controllability conditions are presented based on these results an algorithm for linear quadratic lq control of rectangular descriptor systems without the detectability and infinite observability conditions is presented the matrix pencil associated with the euler lagrange differential equations can be singular can have finite generalised eigenvalues on the imaginary axis and infinite generalised eigenvalues of any multiplicity in the class of optimal state feedback controls we find a control that renders the closed loop system marginally stable and impulse free also we find conditions on x 0 that guarantee the optimality it is shown how the disturbance attenuation problem of descriptor systems can be re formulated as an optimal state feedback feedforward control problem for which the results of this article can be applied when applied to state space systems the algorithm of this article which is based on

on spatial quantization of color images image quantization and digital halftoning two fundamental image processing problems are generally performed sequentially and in most cases independent of each other color reduction with a pixel wise defined distortion measure and the halftoning process with its local averaging neighborhood typically optimize different quality criteria or frequently follow a heuristic approach without reference to any quantitative quality measure in this paper we propose a new model to simultaneously quantize and halftone color images the method is based on a rigorous cost function approach which optimizes a quality criterion derived from a simplified model of human perception it incorporates spatial and contextual information into the quantization and thus overcomes the artificial separation of quantization and halftoning optimization is performed by an efficient multiscale procedure which substantially alleviates the computational burden the quality criterion and the optimization algorithms are evaluated on a representative set of artificial and real world images showing a significant image quality improvement compared to standard color reduction approaches applying the developed cost function we also suggest a new distortion measure for evaluating the overall quality of color reduction schemes

on fuzzy metrizability abstract in this paper we answer two questions raised by m a erceg j math anal appl 69 1979 205 230 precisely we show that the fuzzy unit interval is never t0 except in the standard case and that a fuzzy pseudo metrizable t0 space is metrizable in the sense of erceg ibid hence the two definitions of metrizable space given in b hutton and i reilly fuzzy sets and systems3 1980 93 104 and erceg ibid are equivalent

fuzzy hausdorff topological spaces abstract we introduce the notion of a fuzzy hausdorff topological space and make a few observations to establish the appropriateness of this notion

l contiguities and their order structure the present paper introduces l contiguity and l merotopy and presents a unified study of l proximity l contiguity and l merotopy on a set x corresponding to each l contiguity there is an l merotopy which is contigual if this l contiguity is obtained by restricting the cardinality of a given l merotopy then the two l merotopies in hand are the same it is shown that the family of all l contiguities and the family of all l contiguities which induce a given l proximity form complete distributive lattices

rational spectral factorization using state space methods abstract we describe a state space based algorithm to find the minimum phase spectral factor of any rational spectral density whether it be proper improper or polynomial

cluster expansions for the deterministic computation of bayesian estimators based on markov random fields we describe a family of approximations denoted by cluster approximations for the computation of the mean of a markov random field mrf this is a key computation in image processing when applied to the a posteriori mrf the approximation is to account exactly for only spatially local interactions application of the approximation requires the solution of a nonlinear multivariable fixed point equation for which we prove several existence uniqueness and convergence of algorithm results four numerical examples are presented including comparison with monte carlo calculations

statistical mechanical approach to image processing the basic frameworks and techniques of the bayesian approach to image restoration are reviewed from the statistical mechanical point of view first a few basic notions in digital image processing are explained to convince the reader that statistical mechanics has a close formal similarity to this problem second the basic formulation of the statistical estimation from the observed degraded image by using the bayes formula is demonstrated the relationship between bayesian statistics and statistical mechanics is also listed particularly it is explained that some correlation inequalities on the nishimori line of the random spin model also play an important role in bayesian image restoration third the framework of bayesian image restoration for binary images by means of the ising model is reviewed some practical algorithms for binary image restoration are given by employing the mean field and the bethe approximations finally bayesian image restoration for a grey level image using the gaussian model is reviewed and the gaussian model is extended to a more practical probabilistic model by introducing the line state to treat the effects of edges the line state is also extended to quantized values

l proximities and totally bounded pointwise l uniformities in this paper we shall develop the study of connections between l quasi proximities in the sense of katsaras liu artico moresco and pointwise l quasi uniformities in the sense of shi we shall prove that there exists a one to one correspondence between l quasi proximity spaces and totally bounded pointwise l quasi uniform spaces

hopfield neural networks and mean field annealing for seismic deconvolution and multiple attenuation we describe a global optimization method called mean field annealing mfa and its application to two basic problems in seismic data processing seismic deconvolution and surface related multiple attenuation mfa replaces the stochastic nature of the simulated annealing method with a set of deterministic update rules that act on the average value of the variables rather than on the variables themselves based on the mean field approximation as the temperature is lowered the mfa rules update the variables in terms of their values at a previous temperature by minimizing averages it is possible to converge to an equilibrium state considerably faster than a standard simulated annealing method the update rules are dependent on the form of the cost function and are obtained easily when the cost function resembles the energy function of a hopfield network the mapping of a problem onto a hopfield network is not a precondition for using mfa but it makes analytic calculations simpler the seismic deconvoluti

generalized deterministic annealing we develop a general formalism for computing high quality low cost solutions to nonconvex combinatorial optimization problems expressible as distributed interacting local constraints for problems of this type generalized deterministic annealing gda avoids the performance related sacrifices of current techniques gda exploits the localized structure of such problems by assigning k state neurons to each optimization variable the neuron values correspond to the probability densities of k state local markov chains and may be updated serially or in parallel the markov model is derived from the markov model of simulated annealing sa although it is greatly simplified theorems are presented that firmly establish the convergence properties of gda as well as supplying practical guidelines for selecting the initial and final temperatures in the annealing process a benchmark image enhancement application is provided where the performance of gda is compared to other optimization methods the empirical data taken in conjunction with the formal analytical results suggest that gda enjoys significant performance advantages relative to current methods for combinatorial optimization

realization and canonicity for implicit systems this paper studies realization theory and canonicity conditions for implicit systems here an implicit system is any system defined by an input output finite dimensional linear time invariant relation in discrete or continuous time they are also called generalized or descriptor systems in the literature the familiar definitions of canonicity and minimality are extended to such systems and a so called reduced form proves that as for classical systems minimality and canonicity are two equivalent concepts we replace the notion of transfer function by a notion of external form and prove that minimal realization can always be achieved

a relationship between classical and fuzzy proximities abstract for a known classical basic proximity separated ef lo ri or p proximity a mechanism is developed to construct a corresponding fuzzy proximity the order structure of the families of fuzzy basic proximities due to kotze comm ifsa math chapter 1 1987 12 and that based on artico and moresco fuzzy sets and systems 21 1987 85 are also considered

on separation axioms in fuzzy bitopological spaces abstract in this paper new separation axioms in fuzzy bitopological spaces are defined and studied in terms of quasi coincidence q neighbourhoods and ij ij closure operators several characterizations and properties of such spaces have been obtained it will be seen that the definitions of these axioms ar good extensions in the sense of lowen 1976 due to lowen

on fuzzy topological spaces abstract in this paper a few separation properties and some aspects of subspace fuzzy topology have been studied where both the crisp and the fuzzy elements have been taken into consideration since the conventional definition of compactness is not quite meaningful in hausdorff fuzzy spaces as introduced by us a new more natural definition of proper compactness is given and a few properties resulting from this are established

markovian reconstruction using a gnc approach this paper is concerned with the reconstruction of images or signals from incomplete noisy data obtained at the output of an observation system the solution is defined in maximum a posteriori map sense and it appears as the global minimum of an energy function joining a convex data fidelity term and a markovian prior energy the sought images are composed of nearly homogeneous zones separated by edges and the prior term accounts for this knowledge this term combines general nonconvex potential functions pfs which are applied to the differences between neighboring pixels the resultant map energy generally exhibits numerous local minima calculating its local minimum placed in the vicinity of the maximum likelihood estimate is inexpensive but the resultant estimate is usually disappointing optimization using simulated annealing is practical only in restricted situations several deterministic suboptimal techniques approach the global minimum of special map energies employed in the field of image denoising at a reasonable numerical cost the latter techniques are not directly applicable to general observation systems nor to general markovian prior energies this work is devoted to the generalization of one of them the graduated nonconvexity gnc algorithm in order to calculate nearly optimal map solutions in a wide range of situations in fact gnc provides a solution by tracking a set of minima along a sequence of approximate energies starting from a convex energy and progressing toward the original energy in this paper we develop a common method to derive efficient gnc algorithms for the minimization of map energies which arise in the context of any observation system giving rise to a convex data fidelity term and of markov random field mrf energies involving any nonconvex and or nonsmooth pfs as a side result we propose how to construct pertinent initializations which allow us to obtain meaningful solutions using local minimization of these map energies two numerical experiments an image deblurring and an emission tomography reconstruction illustrate the performance of the proposed technique

decorrelated hebbian learning for clustering and function approximation this paper presents a new learning paradigm that consists of a hebbian and anti hebbian learning a layer of radial basis functions is adapted in an unsupervised fashion by minimizing a two element

mean field annealing using compound gauss markov random fields for edge detection and image estimation the authors consider the problem of edge detection and image estimation in nonstationary images corrupted by additive gaussian noise the noise free image is represented using the compound gauss markov random field developed by f c jeng and j w woods 1990 and the problem of image estimation and edge detection is posed as a maximum a posteriori estimation problem since the a posteriori probability function is nonconvex computationally intensive stochastic relaxation algorithms are normally required a deterministic relaxation method based on mean field annealing with a compound gauss markov random cgmrf field model is proposed the authors present a set of iterative equations for the mean values of the intensity and both horizontal and vertical line processes with or without taking into account some interaction between them the relationship between this technique and two other methods is considered edge detection and image estimation results on several noisy images are included

inversion of large support ill posed linear operators using a piecewise gaussian mrf we propose a method for the reconstruction of signals and images observed partially through a linear operator with a large support e g a fourier transform on a sparse set this inverse problem is ill posed and we resolve it by incorporating the prior information that the reconstructed objects are composed of smooth regions separated by sharp transitions this feature is modeled by a piecewise gaussian pg markov random field mrf known also as the weak string in one dimension and the weak membrane in two dimensions the reconstruction is defined as the maximum a posteriori estimate the prerequisite for the use of such a prior is the success of the optimization stage the posterior energy corresponding to a pg mrf is generally multimodal and its minimization is particularly problematic in this context general forms of simulated annealing rapidly become intractable when the observation operator extends over a large support global optimization is dealt with by extending the graduated nonconvexity gnc algorithm to ill posed linear inverse problems gnc has been pioneered by blake and zisserman 1987 in the field of image segmentation the resulting algorithm is mathematically suboptimal but it is seen to be very efficient in practice we show that the original gnc does not correctly apply to ill posed problems our extension is based on a proper theoretical analysis which provides further insight into the gnc the performance of the proposed algorithm is corroborated by a synthetic example in the area of diffraction tomography

functions and as closedness in fuzzy topological spaces abstract in this paper we discuss s closedness in fuzzy topological spaces and we give some characterizations of s closedness also we investigate the image and the inverse image of s closed spaces under some types of functions and we improve and generalize some results on s closed spaces in fuzzy setting

fast gradient based methods for bayesian reconstruction of transmission and emission pet images the authors describe conjugate gradient algorithms for reconstruction of transmission and emission pet images the reconstructions are based on a bayesian formulation where the data are modeled as a collection of independent poisson random variables and the image is modeled using a markov random field a conjugate gradient algorithm is used to compute a maximum a posteriori map estimate of the image by maximizing over the posterior density to ensure nonnegativity of the solution a penalty function is used to convert the problem to one of unconstrained optimization preconditioners are used to enhance convergence rates these methods generally achieve effective convergence in 15 25 iterations reconstructions are presented of an sup 18 fdg whole body scan from data collected using a siemens cti ecat931 whole body system these results indicate significant improvements in emission image quality using the bayesian approach in comparison to filtered backprojection particularly when reprojections of the map transmission image are used in place of the standard attenuation correction factors

l fuzzy basic proximity spaces abstract we use the concept of l quasi coincident in fuzzy set theory to define l fuzzy basic proximity which is a generalization of l fuzzy proximity as defined in 10 we study the following problems characterization of an l fuzzy basic proximity l fuzzy basic proximity neighbourhoods the l fuzzy closure induced by an l fuzzy basic proximity and the l fuzzy basic proximity compatible with an l fuzzy closure operator

regularity axioms in fuzzy topological spaces and fr i proximities abstract the purpose of this paper is to study the regularity axioms for the proximity notion in fuzzy topology we redefine the notion of cech proximity on i x which has been extended to fuzzy sets in 11 and we study the families m x c and m 1 x also we show that every fr i space can be derived from an r i proximity on i x and vice versa

on fuzzy bitopological spaces abstract in this paper we have used the fuzzy topologies 1 and 2 to generate a family s which is a supra fuzzy topology on x using the family s we introduce and study the concepts of separation axioms continuity resp openness closedness of a mapping and compactness for a fuzzy bitopological space x 1 2 our definitions preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spaces we then investigate the relationship between these concepts and their correspondence with the fuzzy bitopological spaces kandil and el shafee 1991

parametrization of minimal spectral factors of discrete time rational spectral densities in this paper the problem of providing a complete parametrization of the minimal spectral factors of a discrete time rational spectral density is considered the desired parametrization given in terms of the all pass divisors of a certain all pass function is established in the most general setting after several partial results mostly in the continuous time case this is indeed the first complete parametrization obtained without resorting to any facilitating assumption this result provides a positive answer to a conjecture raised in 2016

computation of general inner outer and spectral factorizations in this paper we solve two problems in linear systems theory the computation of the inner outer and spectral factorizations of a continuous time system considered in the most general setting we show that these factorization problems rely essentially on solving for the stabilizing solution a standard algebraic riccati equation of order usually much smaller than the mcmillan degree of the transfer function matrix of the system the proposed procedures are completely general being applicable for a polynomial proper improper system whose transfer function matrix could be rank deficient and could have poles zeros on the imaginary axis or at infinity as an application we discuss the extension to the case of rational matrices of the complete orthogonal decomposition of a constant matrix numerical refinements and examples illustrating the proposed approach are discussed in detail

fuzzy proximity spaces redefined abstract we use the concept l quasi coincident in fuzzy set theory to redefine l fuzzy proximity space and we study the following problems proximity of l fuzzy normal spaces l fuzzy filters proximity neighborhoods and the l fuzzy topology induced by the l fuzzy proximity

generalized quasi proximities this paper studies several kinds of fuzzy quasi proximities firstly we introduce generalized pointwise s quasi proximities and prove that s fpqps the category of generalized pointwise s quasi proximity spaces is isomorphic to tfrns the category of topological fuzzy remote neighborhood spaces secondly we introduce generalized s quasi proximities and prove that s fqps the category of generalized s quasi proximity spaces is isomorphic to s fpqps finally we study generalized quasi proximities and discuss the relationships between this kind of quasi proximities and generalized pointwise quasi uniformities

non linear minimal square spectral factorization recent work has identified a correspondence between minimal square spectral factors of a given spectral density invariant subspaces of an associated hamiltonian matrix solutions of an appropriate algebraic riccati equation and minimal unitary left divisors of a certain unitary function on the imaginary line the purpose of this report is to obtain a natural extension of these ideas to a non linear setting at least for the special case where only minimal square stable spectral factors are considered

uniformity and proximity of l fuzzy topological spaces abstract in 3 4 a k katsaras defined fuzzy proximity spaces and studied some of their properties in 5 we used the concept l quasi coincident in fuzzy set theory and fuzzy topology to redefine l fuzzy proximity space in such a way that it takes fuzzy proximity space as a special case also some pathologic properties were avoided for example proposition 2 1 in 4 in 5 we proved also some results analogous to those that hold for ordinary proximity spaces in this paper we continue the study of l fuzzy proximity spaces we shall prove that the partially ordered set x of all l fuzzy proximities on x is a complete lattice theorem 2 5 and we shall discuss the relationship between l fuzzy uniform spaces and l fuzzy proximity spaces theorem 3 4 4 1