clustering spatiotemporal data an augmented fuzzy c means in spatiotemporal data commonly encountered in geographical systems biomedical signals and the like each datum is composed of features comprising a spatial component and a temporal part clustering of data of this nature poses challenges especially in terms of a suitable treatment of the spatial and temporal components of the data in this study proceeding with the objective function based clustering such as e g fuzzy c means we revisit and augment the algorithm to make it applicable to spatiotemporal data an augmented distance function is discussed and the resulting clustering algorithm is provided two optimization criteria i e a reconstruction error and a prediction error are introduced and used as a vehicle to optimize the performance of the clustering method experimental results obtained for synthetic and real world data are reported

a modified fuzzy c means algorithm for bias field estimation and segmentation of mri data we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging mri data and estimation of intensity inhomogeneities using fuzzy logic mri intensity inhomogeneities can be attributed to imperfections in the radio frequency coils or to problems associated with the acquisition sequences the result is a slowly varying shading artifact over the image that can produce errors with conventional intensity based classification our algorithm is formulated by modifying the objective function of the standard fuzzy c means fcm algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel voxel to be influenced by the labels in its immediate neighborhood the neighborhood effect acts as a regularizer and biases the solution toward piecewise homogeneous labelings such a regularization is useful in segmenting scans corrupted by salt and pepper noise experimental results on both synthetic images and mr data are given to demonstrate the effectiveness and efficiency of the proposed algorithm

second order optimality conditions in nonlinear programming obtained by way of epi derivatives dedicated to the memory of robin w chaney second order optimality conditions for finite dimensional smooth and nonsmooth nonlinear programming are obtained by a new method that emphasizes a close connection with geometrical approximation of the essential objective function the approximation is secured by the use of certain epi derivatives defined by epiconvergence the optimality conditions are expressed in a form that covers general interval constraints and their possible representation through penalties or an augmented lagrangian an abstract constraint involving restriction to a convex polyhedron is incorporated

segmentation of m fish images for improved classification of chromosomes with an adaptive fuzzy c means clustering algorithm an adaptive fuzzy c means algorithm was developed and applied to the segmentation and classification of multicolor fluorescence in situ hybridization m fish images which can be used to detect chromosomal abnormalities for cancer and genetic disease diagnosis the algorithm improves the classical fuzzy c means algorithm fcm by the use of a gain field which models and corrects intensity inhomogeneities caused by a microscope imaging system flairs of targets chromosomes and uneven hybridization of dna other than directly simulating the inhomogeneousely distributed intensities over the image the gain field regulates centers of each intensity cluster the algorithm has been tested on an m fish database that we have established which demonstrates improved performance in both segmentation and classification when compared with other fcm clustering based algorithms and a recently reported region based segmentation and classification algorithm our method gave the lowest segmentation and classification error which will contribute to improved diagnosis of genetic diseases and cancers

normal and anomalous scaling of turbulence a non gaussian model of the probability density function pdf of ensuremath delta u r is proposed to study how the scaling exponents s p of the structure function ensuremath delta u r p of finite reynolds number turbulence depends upon the taylor microscale reynolds number r ensuremath lambda here ensuremath delta u r is the longitudinal velocity difference across a distance r and is the statistical average the model not only predicts anomalous scaling s p lp 3 for pg3 observed in experiments at a finite reynolds number but also predicts that s p approaches normal scaling p 3 while r ensuremath lambda is very high hence in contrast to the prevailing multiscaling models the non gaussian pdf model suggests a completely different picture of scaling of isotropic turbulence the anomalous scaling observed in experiments is a finite reynolds number effect and the normal scaling is valid in the real kolmogorov inertial range corresponding to an infinite reynolds number

first and second order necessary conditions for control problems with constraints second order necessary conditions are developed for an abstract nonsmooth control problem with mixed state control equality and inequality constraints as well as a constraint of the form g x u e if where f is a closed convex set of a banach space with nonempty interior the inequality constraints g s x u 0 depend on a parameter s belonging to a compact metric space s the equality constraints are split into two sets of equations k x u 0 and h x u 0 where the first equation is an abstract control equation and h is assumed to have a full rank property in u the objective function is maxtet f t x u where t is a compact metric space f is upper semicontinuous in t and lipschitz in x u the results are in terms of a function a that disappears when the parameter spaces t and s are discrete we apply these results to control problems governed by ordinary differential equations and having pure state inequality constraints and control state equality and inequality constraints thus we obtain a generalization and extension of the existing results on this problem

conjugate points for variational problems with equality and inequality state constraints in this paper variational problems with equality and inequality state constraints are considered the theory of conjugate points for these problems is developed and necessary conditions for weak local optimality are derived in terms of this concept and the legendre condition for the case of inequality constraints the envelope like effect is taken into consideration in the accessory problem

optimal control problems with partially polyhedric constraints this paper discusses a class of state constrained optimal control problems for which it is possible to formulate second order necessary or sufficient conditions for local optimality or quadratic growth that do not involve all curvature terms for the constraints this kind of result is classical in the case of polyhedric control constraints our theory of optimization problems with partially polyhedric constraints allows to extend these results to the case when the control constraints are polyhedric in the presence of state constraints satisfying some specific hypotheses the analysis is based on the assumption that some strict semilinearized qualification condition is satisfied we apply the theory to some optimal control problems of elliptic equations with state and control constraints

optimality conditions for non finite valued convex composite functions burke 1987 has recently developed second order necessary and sufficient conditions for convex composite optimization in the case where the convex function is finite valued in this note we present a technique for reducing the infinite valued case to the finite valued one we then use this technique to extend the results in burke 1987 to the case in which the convex function may take infinite values we conclude by comparing these results with those established by rockafellar 1989 for the piecewise linear quadratic case

closure approach to high order structure functions of turbulence let t p be the structure function of order p of turbulence first t2 is determined then t3 is derived from t2 and finally t p p 3 are derived from t2 and t3 this closure scheme is realized by a non gaussian statistical model we use it to study the scaling law of t p and we find that the available data on scaling exponents favor kolmogorov s 1941 theory rather than his 1962 theory we also predict the high order universal constants of inertial range scaling

first order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysis mathematical programs in which the constraint set is partially defined by the solutions of an elliptic variational inequality so called elliptic mpecs are formulated in reflexive banach spaces with the goal of deriving explicit first order optimality conditions amenable to the development of numerical procedures variational analytic concepts are both applied and further developed the paper is split into two main parts the first part concerns the derivation of conditions in which the lower level state constraints are assumed to be polyhedric sets this part is then completed by two examples the latter of which involves pointwise bilateral bounds on the gradient of the state the second part focuses on an important nonpolyhedric example namely when the lower level state constraints are presented by pointwise bounds on the euclidean norm of the gradient of the state a formula for the second order mosco epiderivative of the indicator function for this convex set is derived this result is then used to demonstrate the hadamard directional differentiability of the solution mapping of the variational inequality which then leads to the derivation of explicit strong stationarity conditions for this problem

supervised parametric and non parametric classification of chromosome images this paper describes a fully automatic chromosome classification algorithm for multiplex fluorescence in situ hybridization m fish images using supervised parametric and non parametric techniques m fish is a recently developed chromosome imaging method in which each chromosome is labelled with 5 fluors dyes and a dna stain the classification problem is modelled as a 25 class 6 feature pixel by pixel classification task the 25 classes are the 24 types of human chromosomes and the background while the six features correspond to the brightness of the dyes at each pixel maximum likelihood estimation nearest neighbor and k nearest neighbor methods are implemented for the classification the highest classification accuracy is achieved with the k nearest neighbor method and k 7 is an optimal value for this classification task

the upper and lower second order directional derivatives of a sup type function the purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup type functions x sup f x t t t in terms of the first and second derivatives off x t wheret is a compact set in a metric space and we assume thatf f x and 2f x2 are continuous on n t we will give a geometrical meaning of the formula we will moreover give a sufficient condition fors x to be directionally twice differentiable

geometrical fuzzy clustering algorithms fuzzy clustering algorithms are a basic tool for cluster analysis among these the geometrical fuzzy clustering algorithms are used when the clustering problem can be viewed as trying to find linear or ellipsoidal concentrations in data this paper provides a theoretical framework in which currently used geometrical fuzzy clustering algorithms become special cases also a family of functions called feasible are defined which can be used to construct such algorithms and convergence results are obtained

on the scaling of three dimensional homogeneous and isotropic turbulence abstract in this paper we investigate the scaling properties of three dimensional isotropic and homogeneous turbulence we analyze a new form of scaling extended self similarity recently introduced in the literature we found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low reynolds number and it extends over a much wider range of scales with respect to the inertial range

velocity probability density functions of high reynolds number turbulence abstract this paper deals with the probability density function pdf of velocity differences between two points separated by distance r measurements of pdfs were made for r lying in the inertial range for two different flows in a jet with r 852 and in a wind tunnel with r 2720 these pdfs have a characteristic non gaussian shape with exponential tails following kolmogorov s general ideas of log normality a new model for the pdf is developed which contains two parameters determined by experiments this empirical model agrees with the experimental results that the tails of the pdf deviate from a truly exponential behaviour in particular for small r in addition the model leads to the general scaling law ln e 2 r r 0 differenr from kolmogorov s third hypothesis ln e 2 ln r r 0 restricted to the inertial range only x is x x we develop also a formalism based on an extremum principle which is consistent with both the log normality of e and the above mentioned power law in this formalism can be interpreted as the codimension of dissipative structures and asymptotically varies as 1 ln r

variational analysis of a composite function a formula for the lower second order epi derivative an exact formula is established for the lower second order epi derivative of a function of the form g f x where f is a smooth map from one banach space into another and g is a convex function generally not everywhere finite unconstrained minimization of such functions typically arise as an equivalent in one or another sense reduction form for many important classes of constrained optimization problems the formula is further applied to study epi differentiability of the max function x max q x q q

inertial range and the finite reynolds number effect of turbulence the kolmogorov law which is the unique exact relationship of inertial range statistics is applied to investigate the finite reynolds number effect in particular to study how the width of the inertial range of finite reynolds number turbulence changes with the taylor microscale reynolds number mathrm r ensuremath lambda it is found that there is no inertial range when mathrm r ensuremath lambda ensuremath leqslant 2000 and within tolerance of 1 error mathrm r ensuremath lambda should be higher than 10 4 in order to have an inertial range wider than one decade the so called inertial range found in experiments and simulations is just a scaling range and is not the same as kolmogorov s inertial range the finite reynolds number effect cannot be neglected within such a scaling range and should be considered in comparing experiments or simulations with theories of the inertial range statistics

legendre type optimality conditions for a variational problem with inequality state constraints they differ from the legendre clebsch condition they give information about the hesse matrix of the integrand at not only inactive points but also active points on the other hand since the inequality state constraints can be regarded as an infinite number of inequality constraints they sometimes form an envelope according to a general theory 9 one has to take the envelope into consideration when one consider second order necessary optimality conditions for an abstract optimization problem with a generalized inequality constraint however we show that we do not need to take it into account when we consider legendre type conditions finally we show that any inequality state constraint forms envelopes except two trivial cases we prove it by presenting an envelope in a visible form

second order optimality conditions based on parabolic second order tangent sets in this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints our analysis is based on various concepts of second order tangent sets and parametric duality we introduce a condition called second order regularity under which there is no gap between the corresponding second order necessary and second order sufficient conditions we show that the second order regularity condition always holds in the case of semidefinite programming

second order necessary and sufficient conditions for convex composite ndo in convex composite ndo one studies the problem of minimizing functions of the formf h f whereh m is a finite valued convex function andf n m is continuously differentiable this problem model has a wide range of application in mathematical programming since many important problem classes can be cast within its framework e g convex inclusions minimax problems and penalty methods for constrained optimization in the present work we extend the second order theory developed by a d ioffe in 11 12 13 for the case in whichh is sublinear to arbitrary finite valued convex functionsh moreover a discussion of the second order regularity conditions is given that illuminates their essentially geometric nature

turbulent cascade and intermittency growth most embodiments of kolmogorov s idea of turbulent cascade rest on heuristic modelling rather than mathematical treatment of the navier stokes equations however low order systematic approximation via renormalized perturbation theory also exists it supports the 5 3 inertial range spectrum law and yields quantitatively good predictions of both the kolmogorov constant and the dissipation spectrum pressure plays an essential role in the inertial range this is highlighted by the qualitatively different predictions of the same theory applied to burgers turbulence a recent non perturbative analytical approach via nonlinear mapping of gaussian fields may contribute to the resolution of questions of intermittency corrections to the inertial and dissipation ranges again comparison with burgers turbulence is illuminating whatever the tools it is crucial that a theory be able to describe what happens at finite reynolds numbers both to understand the limit of infinite reynolds number and to interpret correctly the data from existing experiments and simulations

second order global optimality conditions for convex composite optimization in recent years second order sufficient conditions of an isolated local minimizer for convex composite optimization problems have been established in this paper second order optimality conditions are obtained of aglobal minimizer for convex composite problems with a non finite valued convex function and a twice strictly differentiable function by introducing a generalized representation condition this result is applied to a minimization problem with a closed convex set constraint which is shown to satisfy the basic constraint qualification in particular second order necessary and sufficient conditions of a solution for a variational inequality problem with convex composite inequality constraints are obtained 1998 the mathematical programming society inc published by elsevier science b v

feature normalization via expectation maximization and unsupervised nonparametric classification for m fish chromosome images multicolor fluorescence in situ hybridization m fish techniques provide color karyotyping that allows simultaneous analysis of numerical and structural abnormalities of whole human chromosomes chromosomes are stained combinatorially in m fish by analyzing the intensity combinations of each pixel all chromosome pixels in an image are classified often the intensity distributions between different images are found to be considerably different and the difference becomes the source of misclassifications of the pixels improved pixel classification accuracy is the most important task to ensure the success of the m fish technique in this paper we introduce a new feature normalization method for m fish images that reduces the difference in the feature distributions among different images using the expectation maximization em algorithm we also introduce a new unsupervised nonparametric classification method for m fish images the performance of the classifier is as accurate as the maximum likelihood classifier whose accuracy also significantly improved after the em normalization we would expect that any classifier will likely produce an improved classification accuracy following the em normalization since the developed classification method does not require training data it is highly convenient when ground truth does not exist a significant improvement was achieved on the pixel classification accuracy after the new feature normalization indeed the overall pixel classification accuracy improved by 20 after em normalization

perturbed optimization in banach spaces ii a theory based on a strong directional constraint qualification we study the sensitivity of the optimal value and optimal solutions of perturbed optimization problems in two cases the first one is when multipliers exist but only the weak and not the strong second order sufficient optimality condition is satisfied the second case is when no lagrange multipliers exist to deal with these pathological cases we are led to introduce a directional constraint qualification stronger than in part i of this paper which reduces to the latter in the important case of equality inequality constrained problems we give sharp upper estimates of the cost based on paths varying as the square root of the perturbation parameter and under a no gap condition obtain the first term of the expansion for the cost when multipliers exist we study the expansion of approximate solutions as well we show in the appendix that the strong directional constraint qualification is satisfied for a large class of problems including regular problems in the sense of robinson

a new fuzzy c means method with total variation regularization for segmentation of images with noisy and incomplete data the objective function of the original fuzzy c mean method is modified by a regularizing functional in the form of total variation tv with regard to gradient sparsity and a regularization parameter is used to balance clustering and smoothing an alternating direction method of multipliers in conjunction with the fast discrete cosine transform is used to solve the tv regularized optimization problem the new algorithm is tested on both synthetic and real data and is demonstrated to be effective and robust in treating images with noise and missing data incomplete data

generalized hessian properties of regularized nonsmooth functions we take up the question of second order expansions for a class of functions of importance in optimization namely moreau envelope regularizations of nonsmooth functions f it is shown that when f is prox regular which includes convex functions and the extended real valued functions representing problems of nonlinear programming the many second order properties that can be formulated around the existence and stability of expansions of the envelopes of f or of their gradient mappings are linked by surprisingly extensive lists of equivalences with each other and with generalized differentiation properties of f itself this clarifies the circumstances conducive to developing computational methods based on envelope functions such as second order approximations in nonsmooth optimization and variants of the proximal point algorithm the results establish that generalized second order expansions of moreau envelopes at least can be counted on in most situations of interest in finite dimensional optimization

second order sufficiency and quadratic growth for nonisolated minima for standard nonlinear programming problems the weak second order sufficient condition is equivalent to the quadratic growth condition as far as the set of minima consists of isolated points and some qualification hypothesis holds this kind of condition is instrumental in the study of numerical algorithms and sensitivity analysis the arm of the paper is to study the relations between various types of sufficient conditions and quadratic growth in cases when the set of minima may have nonisolated points

second order conditions for optimization problems with constraints using a projective approach new necessary conditions and new sufficient conditions for optimization problems with explicit or implicit constraints are examined they are compared to previous ones a particular emphasis is given to mathematical programming problems with non polyhedral constraints this case occurs in particular when the constraints are defined in functional spaces

probability density functions skewness and flatness in large reynolds number turbulence probability density functions pdf of longitudinal velocity increments are measured in an experiment using low temperature helium gas in which a large domain of microscale reynolds numbers mathit r ensuremath lambda from 150 to 5040 is explored the technique of measurement which is essentially hot wire anemometry but operating in nonstandard conditions is described in the inertial range of scales and for a given scale of separation the pdf are found to be independent of the reynolds number at large mathit r ensuremath lambda measurements of the skewness and the flatness of the velocity derivatives are performed in a range of mathit r ensuremath lambda lying between 150 and 3200 the surprising result that we find is that these quantities first increase with the reynolds number up to mathit r ensuremath lambda ensuremath approxeq 700 and then cease to increase further indicating a transitional behavior textcopyright 1996 the american physical society

adaptive fuzzy segmentation of magnetic resonance images an algorithm is presented for the fuzzy segmentation of two dimensional 2 d and three dimensional 3 d multispectral magnetic resonance mr images that have been corrupted by intensity inhomogeneities also known as shading artifacts the algorithm is an extension of the 2 d adaptive fuzzy c means algorithm 2 d afcm presented in previous work by the authors this algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space it iteratively adapts to the intensity inhomogeneities and is completely automated in this paper the authors fully generalize 2 d afcm to three dimensional 3 d multispectral images because of the potential size of 3 d image data they also describe a new faster multigrid based algorithm for its implementation they show using simulated mr data that 3 d afcm yields lower error rates than both the standard fuzzy c means fcm algorithm and two other competing methods when segmenting corrupted images its efficacy is further demonstrated using real 3 d scalar and multispectral mr brain images

on lower bounds of the second order directional derivatives of ben tal zowe and chaney let f be a regular locally lipschitz real valued function defined on an open convex subset of a normed space we show that at any unit direction u the upper second order derivative d 2f u 0 in the sense of dem yanov and pevnyi dem yanov v f a b pevnyi 1974 expansion with respect to a parameter of the extremal values of game problems ussr computational math and math phys 14 33 45 ben tal and zowe ben tal a j zowe 1982 necessary and sufficient optimality conditions for a class of nonsmooth minimization problems math programming24 70 91 has the same lower bounds as the lower second order derivatives d 2f u 0 consequently one can characterize the convexity of f in terms of these derivatives we also obtain the corresponding results in terms of chaney s second order directional derivatives

scaling exponents of the second order structure function of turbulence the kolmogorov equation which is an exact relationship between the second order structure function and the third order structure function is applied to study the relative scaling of against according to the extended self similarity ess method it is found that the relative ess scaling exponent is greater than the real or theoretical inertial range scaling exponent of in the case of normal scaling as well as anomalous scaling when and when therefore the experimental and numerical results favours the kolmogorov 2 3 law rather than anomalous scaling previously the results were interpreted as clear evidence of anomalous scaling based upon the assumption that

generalized hessian for c 1 1 functions in infinite dimensional normed spaces the subject of this paper is the systematic study of second order notions concerning differentiable functions with lipschitz derivative the results and notions are motivated by recent papers of cominetti correa and hiriart urruty the first goal of this paper is the comparison of several known second order directional derivatives the second goal is the introduction of a generalized hessian which is a set of certain symmetric bilinear forms the relation of this generalized hessian to other existing second order derivatives is also described

belief rule based classification system among the computational intelligence techniques employed to solve classification problems the fuzzy rule based classification system frbcs is a popular tool capable of building a linguistic model interpretable to users however it may face lack of accuracy in some complex applications by the fact that the inflexibility of the concept of the linguistic variable imposes hard restrictions on the fuzzy rule structure in this paper we extend the fuzzy rule in frbcs with a belief rule structure and develop a belief rule based classification system brbcs to address imprecise or incomplete information in complex classification problems the two components of the proposed brbcs i e the belief rule base brb and the belief reasoning method brm are designed specifically by taking into account the pattern noise that existes in many real world data sets four experiments based on benchmark data sets are carried out to evaluate the classification accuracy robustness interpretability and time complexity of the proposed method

optimization problems with perturbations a guided tour this paper presents an overview of some recent and significant progress in the theory of optimization problems with perturbations we put the emphasis on methods based on upper and lower estimates of the objective function of the perturbed problems these methods allow one to compute expansions of the optimal value function and approximate optimal solutions in situations where the set of lagrange multipliers is not a singleton may be unbounded or is even empty we give rather complete results for nonlinear programming problems and describe some extensions of the method to more general problems we illustrate the results by computing the equilibrium position of a chain that is almost vertical or horizontal