a convergence analysis of dykstra s algorithm for polyhedral sets let h be a nonempty closed convex set in a hilbert space x determined by the intersection of a finite number of closed half spaces it is well known that given an x 0 in x dykstra s algorithm applied to this collection of closed half spaces generates a sequence of iterates that converge to ph x0 the orthogonal projection of x0 onto h the iterates however do not necessarily lie in h we propose a combined dykstra conjugate gradient method such that given an varepsilon 0 the algorithm computes an x in h with x p h x 0 varepsilon moreover for each iterate xm of dykstra s algorithm we calculate a bound for x m p h x 0 that approaches zero as m tends to infinity applications are made to computing bounds for x m p h x 0 where h is a polyhedral cone numerical results are presented from a sample isotone regression problem

efficient rank reduction of correlation matrices geometric optimisation algorithms are developed that efficiently find the nearest low rank correlation matrix we show in numerical tests that our methods compare favourably with the existing methods in the literature the connection with the lagrange multiplier method is established along with an identification of whether a local minimum is a global minimum an additional benefit of the geometric approach is that any weighted norm can be applied the problem of finding the nearest low rank correlation matrix occurs as part of the calibration of multi factor interest rate market models to correlation

global risk bounds and adaptation in univariate convex regression we consider the problem of nonparametric estimation of a convex regression function phi 0 we study the risk of the least squares estimator lse under the natural squared error loss we show that the risk is always bounded from above by n 4 5 modulo logarithmic factors while being much smaller when phi 0 is well approximable by a piecewise affine convex function with not too many affine pieces in which case the risk is at most 1 n up to logarithmic factors on the other hand when phi 0 has curvature we show that no estimator can have risk smaller than a constant multiple of n 4 5 in a very strong sense by proving a local minimax lower bound we also study the case of model misspecification where we show that the lse exhibits the same global behavior provided the loss is measured from the closest convex projection of the true regression function in the process of deriving our risk bounds we prove new results for the metric entropy of local neighborhoods of the space of univariate convex functions these results which may be of independent interest demonstrate the non uniform nature of the space of univariate convex functions in sharp contrast to classical function spaces based on smoothness constraints

additive conjoint isotonic probabilistic models adisop the isop model or model of twodimensional or bi isotonicity scheiblechner 1995 postulates that the probabilities of ordered response categories increase isotonically in the order of subject ability and item easiness adding a conventional cancellation axiom for the factors of subjects and items gives the adisop model where the c d f s of response categories are functions of an additive item and subject parameter and an ordinal category parameter extending cancellation to the interactions of subjects and categories as well as of items and categories independence axiom of the category factor from the subject and item factor gives the cadisop model completely additive model in which the parallel c d f s are functions of the sum of subject item and category parameters the cadisop model is very close to the unidimensional version of the polytomous rasch model with the logistic item category characteristic s replaced by nonparametric axioms and statistics the axioms representation theorems and algorithms for model fitting of the additive models are presented

computing maximum likelihood estimators of convex density functions we consider the problem of estimating a density function that is known in advance to be convex the maximum likelihood estimator is then the solution of a linearly constrained convex minimization problem this problem turns out to be numerically difficult we show that interior point algorithms perform well on this class of optimization problem though for large samples numerical difficulties are still encountered to eliminate those difficulties we propose a clustering scheme that is reasonable from a statistical point of view we display results for problems with up to 40000 observations we also give a typical picture of the estimated density a piecewise linear function with only very few pieces

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

multiview stereo and silhouette consistency via convex functionals over convex domains we propose a convex formulation for silhouette and stereo fusion in 3d reconstruction from multiple images the key idea is to show that the reconstruction problem can be cast as one of minimizing a convex functional where the exact silhouette consistency is imposed as convex constraints that restrict the domain of feasible functions as a consequence we can retain the original stereo weighted surface area as a cost functional without heuristic modifications of this energy by balloon terms or other strategies yet still obtain meaningful nonempty reconstructions which are guaranteed to be silhouette consistent we prove that the proposed convex relaxation approach provides solutions that lie within a bound of the optimal solution compared to existing alternatives the proposed method does not depend on initialization and leads to a simpler and more robust numerical scheme for imposing silhouette consistency obtained by projection onto convex sets we show that this projection can be solved exactly using an efficient algorithm we propose a parallel implementation of the resulting convex optimization problem on a graphics card given a photoconsistency map and a set of image silhouettes we are able to compute highly accurate and silhouette consistent reconstructions for challenging real world data sets in particular experimental results demonstrate that the proposed silhouette constraints help to preserve fine scale details of the reconstructed shape computation times depend on the resolution of the input imagery and vary between a few seconds and a couple of minutes for all experiments in this paper

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

regular subspaces of a quaternionic hilbert space from quaternionic hermite polynomials and associated coherent states we define quaternionic hermite polynomials by analogy with two families of complex hermite polynomials as in the complex case these polynomials constitute orthogonal families of vectors in ambient quaternionic l2 spaces using these polynomials we then define regular and anti regular subspaces of these l2 spaces the associated reproducing kernels and the ensuing quaternionic coherent states

selective alternating projections to find the nearest sdd matrix we extend and improve recently proposed algorithms to solve the problem of minimizing the distance from a given matrix to the cone of symmetric and diagonally dominant matrices with positive diagonal sdd we present a variety of criteria to select a subset of the supporting hyperplanes of the faces of sdd and also of the polar cone sdd 0 to then apply dykstra s alternating projection method these selections reduce the number of projections and therefore reduce the required computational work in all our new algorithms the symmetry and the diagonal dominance of the obtained matrix are guaranteed preliminary numerical experiments indicate that some of the selection criteria produce a significant reduction in cpu time

how to select good neighboring images in depth map merging based 3d modeling depth map merging based 3d modeling is an effective approach for reconstructing large scale scenes from multiple images in addition to generate high quality depth maps at each image how to select suitable neighboring images for each image is also an important step in the reconstruction pipeline unfortunately to which little attention has been paid in the literature untill now this paper is intended to tackle this issue for large scale scene reconstruction where many unordered images are captured and used with substantial varying scale and view angle changes we formulate the neighboring image selection as a combinatorial optimization problem and use the quantum inspired evolutionary algorithm to seek its optimal solution experimental results on the ground truth data set show that our approach can significantly improve the quality of the depth maps as well as final 3d reconstruction results with high computational efficiency

new complex function space related to both entangled state representation and spin coherent state a new complex function space whose basis is the single variable hermite polynomial h2j 2 is constructed which is related to both entangled state representation and spin coherent state in schwinger bosonic realization new binomial theorem involving two variable hermite polynomial is derived which helps to constitute the new complex function space we also present a new integration transformation of the basis h2j 2 with its reciprocal transformation which is useful to deriving some operator identities

squeezed states and hermite polynomials in a complex variable following the lines of the recent paper of j p gazeau and f h szafraniec j phys a math theor 44 495201 2011 we construct here three types of coherent states related to the hermite polynomials in a complex variable which are orthogonal with respect to a non rotationally invariant measure we investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics we also obtain a second realization of the canonical coherent states in the bargmann space of analytic functions in terms of a squeezed basis all this is done in the flavor of the classical approach of v bargmann commun pure appl math 14 187 1961

riccati equation and the problem of decoherence ii symmetry and the solution of the riccati equation in this paper we revisit the problem of decoherence by applying the block operator matrices analysis the riccati algebraic equation associated with the hamiltonian describing the process of decoherence is studied we prove that if the environment responsible for decoherence is invariant with respect to the antilinear transformation then the antilinear operator solves the riccati equation in question we also argue that this solution leads to neither a linear nor an antilinear operator similarity matrix therefore we cannot use the standard procedure for solving a linear differential equation e g schrodinger equation furthermore the explicit solution of the riccati equation is found for the case where the environmental operators commute with each other we discuss the connection between our results and the standard description of decoherence one that uses the kraus representation we show that the reduced dynamics we obtain does not have the kraus representation if the initial correlations betwee

norm product belief propagation primal dual message passing for approximate inference inference problems in graphical models can be represented as a constrained optimization of a free energy function in this paper we treat both forms of probabilistic inference estimating marginal probabilities of the joint distribution and finding the most probable assignment through a unified message passing algorithm architecture in particular we generalize the belief propagation bp algorithms of sum product and max product and tree reweighted trw sum and max product algorithms trbp and introduce a new set of convergent algorithms based on convex free energy and linear programming lp relaxation as a zero temperature of a convex free energy the main idea of this work arises from taking a general perspective on the existing bp and trbp algorithms while observing that they all are reductions from the basic optimization formula of f ihi where the function f is an extended valued strictly convex but nonsmooth and the functions hi are extended valued functions not necessarily convex we use tools from convex duality to present the primal dual ascent algorithm which is an extension of the bregman successive projection scheme and is designed to handle optimization of the general type f ihi we then map the fractional free energy variational principle for approximate inference onto the optimization formula above and introduce the norm product message passing algorithm special cases of the norm product include sum product and max product bp algorithms trbp and nmplp algorithms when the fractional free energy is set to be convex convex free energy the norm product is globally convergent for the estimation of marginal probabilities and for approximating the lp relaxation we also introduce another branch of the norm product which arises as the zero temperature of the convex free energy which we refer to as the convex max product the convex max product is convergent unlike max product and aims at solving the lp relaxation

dykstra s algorithm for constrained least squares rectangular matrix problems abstract in a recent paper the authors applied dykstra s alternating projection algorithm to solve constrained least squares n n matrix problems we extend these results in two different directions first we make use of the singular value decomposition to solve now constrained least squares rectangular m n matrix problems that arise in several applications second we propose a new and improved implementation of the projection algorithm onto the e positive definite set of matrices this implementation does not require the computation of all eigenvalues and eigenvectors of a matrix per iteration and still guarantees convergence finally encouraging preliminary numerical results are discussed

orthogonal polynomials laguerre fock space and quasi classical asymptotics continuing our earlier investigation of the hermite case s t ali and m englis j math phys 55 042102 2014 we study an unorthodox variant of the berezin toeplitz quantization scheme associated with laguerre polynomials in particular we describe a laguerre analogue of the classical fock segal bargmann space and the relevant semi classical asymptotics of its toeplitz operators the former actually turns out to coincide with the hilbert space appearing in the construction of the well known barut girardello coherent states further extension to the case of legendre polynomials is likewise discussed

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

projection on the intersection of convex sets abstract in this paper we give a solution of the problem of projecting a point onto the intersection of several closed convex sets when a projection on each individual convex set is known the existing solution methods for this problem are sequential in nature here we propose a highly parallelizable method the key idea in our approach is the reformulation of the original problem as a system of semi smooth equations the benefits of the proposed reformulation are twofold a a fast semi smooth newton iterative technique based on clarke s generalized gradients becomes applicable and b the mechanics of the iterative technique is such that an almost decentralized solution method emerges we proved that the corresponding semi smooth newton algorithm converges near the optimal point quadratically these features make the overall method attractive for distributed computing platforms e g sensor networks

estimation of multivariate distributions under stochastic ordering abstract let f and g be the cdf s of two p dimensional multivariate distributions such that f is stochastically larger than g a straightforward derivation is given of the generalized maximum likelihood estimators of f and g based on random samples from each population an algorithmic approach to computing these estimators is described and motivating numerical examples are discussed the special case when f and g correspond to multivariate ordinal contingency tables is also presented the relationship of these results to those of robertson and wright 1974 is considered

shape from silhouette consensus this paper proposes a shape from silhouette algorithm that is robust to inconsistent silhouettes often common in real applications due to occlusions errors in the background subtraction noise or even calibration errors the recovery of the shape that best fits the available data silhouettes is formulated as a continuous energy minimization problem the energy is based on the error between the silhouettes and the shape plus a regularization term thanks to the characterization of the visible surface in each view as a function of the shape we consider the error in the volume space as a result we obtain an iterative volume based algorithm that evolves the initial shape to the shape that is in general agreement with the silhouettes thus being robust to errors in the silhouettes we have implemented the proposed algorithm in a graphics card processor with parallel computing allowing reduced computational times the obtained results compare favorably to those of the state of the art

a measure free approach to coherent states in the process of generalizing coherent states the situation when the measure which is customarily incorporated in their definition is indeterminate becomes unavoidable a more dramatic situation may occur if there is no measure which makes the reproducing kernel hilbert space involved in the construction of coherent states isometrically included in an space therefore it appears that there is a need to redefine coherent states making the definition measure free starting out with the reproducing kernel property we ensure the basic feature of coherent states resolution of the identity to be maintained cf 15 and remark 2 the only investment in the whole undertaking is a sequence n dn 0 satisfying 4 the rest including the aforesaid resolution of the identity is a consequence of our choice the approach is supported by examples which make the circumstances clear under which the sequence n dn 0 appears moment problems or rather orthogonal polynomials are one of them this article is part of a special issue of journal of physics a mathematical and theoretical devoted to coherent states mathematical and physical aspects

riccati equation and the problem of decoherence the block operator matrix theory is used to investigate the problem of a single qubit we establish a connection between the riccati operator equation and the possibility of obtaining an exact reduced dynamics for the qubit in question the model of the half spin particle in the rotating magnetic field coupling with the external environment is discussed we show that the model defined in such a way can be reduced to a time independent problem

a simple approach to testing homogeneity of order constrained means abstract the likelihood ratio test for equality of partially ordered means first proposed by bartholomew is known to possess power characteristics that are generally superior to those of competing procedures a limitation of this test however is that the null distribution of the test statistic is heavily dependent on both the specific form of the order restriction and the group sample sizes it is not readily available for most orderings especially when the group sample sizes are unequal furthermore computation of the test statistics often involves intricate algorithms we propose a class of procedures based upon classical methods for combining independent tests these procedures are generally applicable and easily implemented a study of the power functions of the competing tests indicates that the power of the test based on fisher s combination method compares reasonably with that of the likelihood ratio test it is concluded that the procedure based on fisher s combination method is an effective

graph theoretic representations for proximity matrices through strongly anti robinson or circular strongly anti robinson matrices there are various optimization strategies for approximating through the minimization of a least squares loss function a given symmetric proximity matrix by a sum of matrices each subject to some collection of order constraints on its entries we extend these approaches to include components in the approximating sum that satisfy what are called the strongly anti robinson sar or circular strongly anti robinson csar restrictions a matrix that is sar or csar is representable by a particular graph theoretic structure where each matrix entry is reproducible from certain minimum path lengths in the graph one published proximity matrix is used extensively to illustrate the types of approximation that ensue when the sar or csar constraints are imposed

set intersection problems supporting hyperplanes and quadratic programming we study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem for the problem of finding the closest point in the intersection of closed convex sets we propose an algorithm that like dykstra s algorithm converges strongly in a hilbert space moreover this algorithm converges in finitely many iterations when the closed convex sets are cones in mathbb r n r n satisfying an alignment condition next we propose modifications of the alternating projection algorithm and prove its convergence the algorithm converges superlinearly in mathbb r n r n under some nice conditions under a conical condition the convergence can be finite lastly we discuss the case where the intersection of the sets is empty

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

new orthogonality relations for the hermite polynomials and related hilbert spaces the hermite polynomials give rise to orthonormal bases in bagmann like hilbert spaces xa 0 a 1 consisting of entire functions these hilbert spaces are related to the gelfand shilov space s1212 viz s1212 0 a 1 xa

computational acceleration of projection algorithms for the linear best approximation problem abstract this is an experimental computational account of projection algorithms for the linear best approximation problem we focus on the sequential and simultaneous versions of dykstra s algorithm and the halpern lions wittmann bauschke algorithm for the best approximation problem from a point to the intersection of closed convex sets in the euclidean space these algorithms employ different iterative approaches to reach the same goal but no mathematical connection has yet been found between their algorithmic schemes we compare these algorithms on linear best approximation test problems that we generate so that the solution will be known a priori and enable us to assess the relative computational merits of these algorithms for the simultaneous versions we present a new component averaging variant that substantially accelerates their initial behavior for sparse systems

dykstra s algorithm for constrained least squares doubly symmetric matrix problems in this work we apply dykstra s alternating projection algorithm for minimizing email protected where email protected email protected is the frobenius norm and email protected r m x n email protected r m x n and email protected r n x n are doubly symmetric positive definite matrices with entries within prescribed intervals we first solve the constrained least squares matrix problem by using the special structure properties of doubly symmetric matrices and then use the singular value decomposition to transform the original problem into a simpler one that fits nicely with the algorithm originally developed by r escalante m raydan dykstra s algorithm for a constrained least squares matrix problem numer linear algebra appl 3 1996 459 471

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

solving hankel matrix approximation problem using semidefinite programming positive semidefinite hankel matrices arise in many important applications some of their properties may be lost due to rounding or truncation errors incurred during evaluation the problem is to find the nearest matrix to a given matrix to retrieve these properties the problem is converted into a semidefinite programming problem as well as a problem comprising a semidefined program and second order cone problem the duality and optimality conditions are obtained and the primal dual algorithm is outlined explicit expressions for a diagonal preconditioned and crossover criteria have been presented computational results are presented a possibility for further improvement is indicated

reduced dynamics need not be completely positive the reduced dynamics of a quantum system in contact with a reservoir is generally thought to be completely positive this is certainly true if product initial conditions are used to define the dynamics we show that with correlated initial conditions it need not be so in this case the dynamics can properly be defined only on a subset of initial system states extension by linearity to all possible initial states is trivially possible but the extension may not be physically realizable and may not even be positive let alone completely positive

orthogonality of analytic polynomials a little step further from the constellation mentioned in jones and njastad j comput appl math 105 1999 51 91 we have chosen orthogonality of polynomials and moment problems enriching them with operator theory apparatus thus this essay resumes the theme of szafraniec j comput appl math 49 1993 255 and culminates in updating it with the results of stochel and szafraniec j funct anal 159 1998 432

notes on the riccati operator equation in open quantum systems a recent problem b gardas j math phys 52 042104 2011 concerning an antilinear solution of the riccati equation is solved we also exemplify that a simplification of the riccati equation even under reasonable assumptions can lead to a not equivalent equation

variational principles surface evolution pdes level set methods and the stereo problem we present a novel geometric approach for solving the stereo problem for an arbitrary number of images spl ges 2 it is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images the euler lagrange equations that are deduced from the variational principle provide a set of partial differential equations pdes that are used to deform an initial set of surfaces which then move toward the objects to be detected the level set implementation of these pdes potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformations i e to deal with multiple objects results of an implementation of our theory also dealing with occlusion and visibility are presented on synthetic and real images

a unified approach to likelihood inference on stochastic orderings in a nonparametric context abstract for data in a two way contingency table with ordered margins we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities this leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log likelihood ratio tests the usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases in particular for each of these three orderings we determine the transformation required to apply the estimation algorithm we then consider testing the hypothesis that the rows are identically distributed against the alternative that they are stochastically ordered as well as testing each stochastic order against an u

hybrid methods for solving the educational testing problem abstract methods for solving the educational testing problem are considered one approach glunt 1995 is to formulate the problem as a linear convex programming problem in which the constraint is the intersection of three convex sets this method is globally convergent but the rate of convergence is slow however the method does have the capability of determining the correct rank of the solution matrix and this can be done in relatively few iterations if the correct rank of the solution matrix is known it is shown how to formulate the problem as a smooth nonlinear minimization problem for which a rapid convergence can be obtained by l1sqp method 6 this paper studies hybrid methods that attempt to combine the best features of both types of method an important feature concerns the interfacing of the component methods thus it has to be decided which method to use first and when to switch between methods difficulties such as these are addressed in the paper comparative numerical results are also reported

duality in the quantum harmonic oscillator resuming the theme of a previous paper szafraniec f h 2001 math nachtr at press we show that any abstract creation or annihilation operator is in duality with the finite difference one acting in l2 this duality relation is generic and its spatial character allows both agents to be identified within the class of weighted shifts

an algorithm for restricted least squares regression abstract a commonly occurring problem in statistics is that of minimizing a least squares expression subject to side constraints here a simple iterative algorithm is presented and shown to converge to the desired solution several examples are presented including finding the closest concave convex function to a set of points and other general quadratic programming problems the dual problem to the basic problem is also discussed and a solution for it is given in terms of the algorithm finally extensions to expressions other than least squares are given

a semi smooth newton method for a special piecewise linear system with application to positively constrained convex quadratic programming in this paper a special piecewise linear system is studied it is shown that under a mild assumption the semi smooth newton method applied to this system is well defined and the method generates a sequence that converges linearly to a solution besides we also show that the generated sequence is bounded for any starting point and a formula for any accumulation point of this sequence is presented as an application we study the convex quadratic programming problem under positive constraints the numerical results suggest that the semi smooth newton method achieves accurate solutions to large scale problems in few iterations

holomorphic hermite polynomials and a non commutative plane one more coherent state quantization of a complex plane is presented although the complex plane is equipped with a non rotationally invariant measure we still obtain a canonical commutation rule up to a simple rescaling we explain how the involved coherent states built from holomorphic continuations of hermite polynomials are related to the non commutative plane

a geometrical approach to iterative isotone regression in the present paper we propose and analyze a novel method for estimating a univariate regression function of bounded variation the underpinning idea is to combine two classical tools in nonparametric statistics namely isotonic regression and the estimation of additive models a geometrical interpretation enables us to link this iterative method with von neumann s algorithm moreover making a connection with the general property of isotonicity of projection onto convex cones we derive another equivalent algorithm and go further in the analysis

a penalized method for multivariate concave least squares with application to productivity analysis abstract we propose a penalized method for the least squares estimator of a multivariate concave regression function this estimator is formulated as a quadratic programing qp problem with o n2 constraints where n is the number of observations computing such an estimator is a very time consuming task and the computational burden rises dramatically as the number of observations increases by introducing a quadratic penalty function we reformulate the concave least squares estimator as a qp with only non negativity constraints this reformulation can be adapted for estimating variants of shape restricted least squares i e the monotonic concave convex least squares the experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem the matlab and r codes for implementing the penalized problems are provided in the paper

holomorphic hermite polynomials in two variables abstract generalizations of the hermite polynomials to many variables and or to the complex domain have been located in mathematical and physical literature for some decades polynomials traditionally called complex hermite ones are mostly understood as polynomials in z and z which in fact makes them polynomials in two real variables with complex coefficients the present paper proposes to investigate for the first time holomorphic hermite polynomials in two variables their algebraic and analytic properties are developed here while the algebraic properties do not differ too much for those considered so far their analytic features are based on a kind of non rotational orthogonality invented by van eijndhoven and meyers inspired by their invention we merely follow the idea of bargmann s seminal paper 1961 giving explicit construction of reproducing kernel hilbert spaces based on those polynomials homotopic behaviour of our new formation culminates in comparing it to the very classical bargmann space of two variables on one edge and the aforementioned hermite polynomials in z and z on the other unlike in the case of bargmann s basis our hermite polynomials are not product ones but factorize to it when bonded together with the first case of limit properties leading both to the bargmann basis and suitable form of the reproducing kernel also in the second limit we recover standard results obeyed by hermite polynomials in z and z

a little step towards orthogonality of analytic polynomials abstract orthogonality of polynomials in a complex variable has been investigated rather occasionally faber polynomials and their generalizations are the most customary though different classes of such polynomials appear in any book on complex approximation it turns out that they are of quite different nature than those on the real line here we wish to point out some aspects of their behavior in general as well as to discuss some examples

the visual hull concept for silhouette based image understanding many algorithms for both identifying and reconstructing a 3 d object are based on the 2 d silhouettes of the object in general identifying a nonconvex object using a silhouette based approach implies neglecting some features of its surface as identification clues the same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object this paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette based image understanding for this purpose the geometric concept of visual hull of a 3 d object is introduced this is the closest approximation of object s that can be obtained with the volume intersection approach it is the maximal object silhouette equivalent to s i e which can be substituted for s without affecting any silhouette only the parts of the surface of s that also lie on the surface of the visual hull can be reconstructed or identified using silhouette based algorithms the visual hull depends not only on the object but also on the region allowed to the viewpoint two main viewing regions result in the external and internal visual hull in the former case the viewing region is related to the convex hull of s in the latter it is bounded by s the internal visual hull also admits an interpretation not related to silhouettes algorithms for computing visual hulls are presented and their complexity analyzed in general the visual hull of a 3 d planar face object turns out to be bounded by planar and curved patches

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

order restricted statistical tests on multinomial and poisson parameters the starshaped restriction abstract likelihood ratio statistics for i testing the homogeneity of a collection of multinomial parameters against the alternative which accounts for the restriction that those parameters are starshaped cf shaked ann statist 1979 and for ii testing the null hypothesis that this parameter vector is starshaped are considered for both tests the asymptotic distribution of the test statistic under the null hypothesis is a version of the chi bar square distribution analogous tests on a collection of poisson means are also found to have asymptotic chi bar square distributions author

accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes abstract the von neumann halperin method of alternating projections converges strongly to the projection of a given point onto the intersection of finitely many closed affine subspaces we propose acceleration schemes making use of two ideas firstly each projection onto an affine subspace identifies a hyperplane of codimension 1 containing the intersection and secondly it is easy to project onto a finite intersection of such hyperplanes we give conditions for which our accelerations converge strongly finally we perform numerical experiments to show that these accelerations perform well for a matrix model updating problem

computing the nearest euclidean distance matrix with low embedding dimensions euclidean distance embedding appears in many high profile applications including wireless sensor network localization where not all pairwise distances among sensors are known or accurate the classical multi dimensional scaling cmds generally works well when the partial or contaminated euclidean distance matrix edm is close to the true edm but otherwise performs poorly a natural step preceding cmds would be to calculate the nearest edm to the known matrix a crucial condition on the desired nearest edm is for it to have a low embedding dimension and this makes the problem nonconvex there exists a large body of publications that deal with this problem some try to solve the problem directly and some are the type of convex relaxations of it in this paper we propose a numerical method that aims to solve this problem directly our method is strongly motivated by the majorized penalty method of gao and sun for low rank positive semi definite matrix optimization problems the basic geometric object in our study is the set of edms having a low embedding dimension we establish a zero duality gap result between the problem and its lagrangian dual problem which also motivates the majorization approach adopted numerical results show that the method works well for the euclidean embedding of network coordinate systems and for a class of problems in large scale sensor network localization and molecular conformation

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