a note on the investigation of local and global identifiability in general nonlinear models such as those commonly employed for the analysis of covariance structures are not globally identifiable any investigation of local identifiability must either yield a mapping of identifiability onto the entire parameter space which will rarely be feasible in any applications of interest or confine itself to the neighbourhood of such points of special interest as the maximum likelihood point

polygonal and polyhedral contour reconstruction in computed tomography this paper is about three dimensional 3 d reconstruction of a binary image from its x ray tomographic data we study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation we formulate this problem as a nonlinear inverse problem using the bayesian framework vertice estimation is done without using a voxel approximation of the 3 d image it is based on the construction and optimization of a regularized criterion that accounts for surface smoothness we investigate original deterministic local algorithms based on the exact computation of the line projections their update and their derivatives with respect to the vertice coordinates results are first derived in the two dimensional 2 d case which consists of reconstructing a 2 d object of deformable polygonal contour from its tomographic data then we investigate the 3 d extension that requires technical adaptations simulation results illustrate the performance of polygonal and polyhedral reconstruction algorithms in terms of quality and computation time

a note on upper bounds on the cp rank abstract hanna and laffey gave an upper bound on the cp rank of a completely positive matrix in terms of its rank and the number of zeros in a full rank principal submatrix this bound for the case that the matrix is positive was improved by barioli and berman in this paper a new straightforward proof of both results is given and the same approach is used to improve hanna and laffey s bound in the case that the matrix has a zero entry

chains of dog ears for completely positive matrices abstract a necessary and sufficient condition to determine the complete positivity of a matrixwith a particular graph in dependence of complete positivity of smaller matrices is given under some singularity assumptions this condition furnishes a characterization for completely positive matrices with a non crossing cycle as associated graph in particular the characterization holds for singular pentadiagonal matrices

completely positive matrices and positivity of least squares solutions abstract a sufficient condition for a doubly nonnegative matrix to be completely positive is given in terms of the positivity of the least squares solution of a linear system associated to the matrix some known results on completely positive matrices are derived by this condition

a multitrait multimethod model with minimal assumptions a new model of confirmatory factor analysis cfa for multitrait multimethod mtmm data sets is presented it is shown that this model can be defined by only three assumptions in the framework of classical psychometric test theory ctt all other properties of the model particularly the uncorrelated ness of the trait with the method factors are logical consequences of the definition of the model in the model proposed there are as many trait factors as different traits considered but the number of method factors is one fewer than the number of methods included in an mtmm study the covariance structure implied by this model is derived and it is shown that this model is identified even under conditions under which other cfa mtmm models are not the model is illustrated by two empirical applications furthermore its advantages and limitations are discussed with respect to previously developed cfa models for mtmm data

separation and relaxation for cones of quadratic forms let p subseteq mathfrak r n be a pointed polyhedral cone in this paper we study the cone mathcal c rm cone xx t x in p of quadratic forms understanding the structure of mathcal c is important for globally solving np hard quadratic programs over p we establish key characteristics of mathcal c and construct a separation algorithm for mathcal c provided one can optimize with respect to a related cone over the boundary of p this algorithm leads to a nonlinear representation of mathcal c and a class of tractable relaxations for mathcal c each of which improves a standard polyhedral semidefinite relaxation of mathcal c the relaxation technique can further be applied recursively to obtain a hierarchy of relaxations and for constant recursive depth the hierarchy is tractable we apply this theory to two important cases p is the nonnegative orthant in which case mathcal c is the cone of completely positive matrices and p is the homogenized cone of the box 0 1 n through various results and examples we demonstrate the strength of the theory for these cases for example we achieve for the first time a separation algorithm for 5 5 completely positive matrices

large cone nonnegative matrix factorization nonnegative matrix factorization nmf has been greatly popularized by its parts based interpretation and the effective multiplicative updating rule for searching local solutions in this paper we study the problem of how to obtain an attractive local solution for nmf which not only fits the given training data well but also generalizes well on the unseen test data based on the geometric interpretation of nmf we introduce two large cone penalties for nmf and propose large cone nmf lcnmf algorithms compared with nmf lcnmf will obtain bases comprising a larger simplicial cone and therefore has three advantages 1 the empirical reconstruction error of lcnmf could mostly be smaller 2 the generalization ability of the proposed algorithm is much more powerful and 3 the obtained bases of lcnmf have a low overlapping property which enables the bases to be sparse and makes the proposed algorithms very robust experiments on synthetic and real world data sets confirm the efficiency of lcnmf

reconstruction from projections based on detection and estimation of objects parts i and ii performance analysis and robustness analysis the problem of reconstructing a multidimensional field from noisy limited projection measurements is approached using an object based stochastic field model objects within a cross section are characterized by a finite dimensional set of parameters which are estimated directly from limited noisy projection measurements using maximum likelihood estimation in part i the computational structure and performance of the ml estimation procedure are investigated for the problem of locating a single object in a deterministic background simulations are also presented in part ii the issue of robustness to modeling errors is addressed

markov random field modeling for three dimensional reconstruction of the left ventricle in cardiac angiography this paper reports on a method for left ventricle three dimensional 3 d reconstruction from two orthogonal ventriculograms the proposed algorithm is voxel based and takes into account the conical projection geometry associated with the biplane image acquisition equipment the reconstruction process starts with an initial ellipsoidal approximation derived from the input ventriculograms this model is subsequently deformed in such a way as to match the input projections to this end the object is modeled as a 3 d markov gibbs random field and an energy function is defined so that it includes one term that models the projections compatibility and another one that includes the space time regularity constraints the performance of this reconstruction method is evaluated by considering the reconstruction of mathematically synthesized phantoms and two 3 d binary databases from two orthogonal synthesized projections the method is also tested using real biplane ventriculograms in this case the performance of the reconstruction is expressed in terms of the projection error which attains values between 9 50 and 11 78 for two biplane sequences including a total of 55 images

object based 3 d reconstruction of arterial trees from magnetic resonance angiograms by exploiting a priori knowledge of arterial shape and smoothness subpixel accuracy reconstructions are achieved from only four noisy projection images the method incorporates a priori knowledge of the structure of branching arteries into a natural optimality criterion that encompasses the entire arterial tree an efficient optimization algorithm for object estimation is presented and its performance on simulated phantom and in vivo magnetic resonance angiograms is demonstrated it is shown that accurate reconstruction of bifurcations is achievable with parametric models

0 1 completely positive matrices abstract let s be a subset of the set of real numbers r a is called s factorizable if it can be factorized as a bbt with bij s the smallest possible number of columns of b in such factorization is called the s rank of a and is denoted by ranksa if s is a set of nonnegative numbers then a is called s cp the aim of this work is to study 0 1 cp matrices we characterize 0 1 cp matrices of order less than 4 and give a necessary and sufficient condition for a matrix of order 4 with some zero entries to be 0 1 cp we show that a nonnegative integral jacobi matrix is 0 1 cp if and only if it is diagonally dominant and obtain a necessary condition for a 2 banded symmetric nonnegative integral matrix to be 0 1 cp we give formulae for the exact value of the 0 1 rank of integral symmetric nonnegative diagonally dominant matrices and some other 0 1 cp matrices

combinatorial results on completely positive matrices abstract a sufficient condition for complete positivity of a matrix in terms of complete positivity of smaller matrices is given those patterns for which this condition is also necessary are characterized these results are used to characterize complete positivity of matrices under some acyclicity assumptions on their graph the exact value of the factorization index is given for acyche matrices

completely positive factorizations associated with euclidean distance matrices corresponding to an arithmetic progression abstract euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties we exploit those properties to develop completely positive factorizations of translations of those matrices we show that the minimal translation that makes such a matrix positive semidefinite results in a completely positive matrix we also discuss completely positive factorizations of such matrices over the integers methods developed in the paper can be used to find completely positive factorizations of other matrices with similar properties

a note on 5 5 completely positive matrices abstract in their paper 5 5 completely positive matrices berman and xu 2004 3 attempt to characterize which 5 5 doubly nonnegative matrices are also completely positive most of the analysis in 3 concerns a doubly nonnegative matrix a that has at least one off diagonal zero component to handle the case where a is componentwise strictly positive berman and xu utilize an edge deletion transformation of a that results in a matrix a having an off diagonal zero berman and xu claim that a is completely positive if and only if there is such an edge deleted matrix a that is also completely positive we show that this claim is false we also show that two conjectures made in 3 regarding 5 5 completely positive matrices are both false

the difference between 5 5 doubly nonnegative and completely positive matrices abstract the convex cone of n n completely positive cp matrices and its dual cone of copositive matrices arise in several areas of applied mathematics including optimization every cp matrix is doubly nonnegative dnn i e positive semidefinite and component wise nonnegative and it is known that for n 4 only every dnn matrix is cp in this paper we investigate the difference between 5 5 dnn and cp matrices defining a bad matrix to be one which is dnn but not cp we i design a finite procedure to decompose any n n dnn matrix into the sum of a cp matrix and a bad matrix which itself cannot be further decomposed ii show that every bad 5 5 dnn matrix is the sum of a cp matrix and a single bad extreme matrix and iii demonstrate how to separate bad extreme matrices from the cone of 5 5 cp matrices

on nonnegative factorization of matrices abstract it is shown that a sufficient condition for a nonnegative real symmetric matrix to be completely positive is that the matrix is diagonally dominant

combining and updating of local estimates and regional maps along sets of one dimensional tracks in this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates generated at different times of the same process sample path the first of these cases has applications in decentralized estimation while the second has applications in updating maps of spatially distributed random quantities given measurements along several tracks the method of solution for the second problem uses the result of the first and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields

three dimensional reconstruction from projections with incomplete and noisy data by object estimation an estimation approach to three dimensional reconstruction from parallel ray projections with incomplete and very noisy data is described using a stochastic dynamic model for an object of interest in a probed domain of known background density the reconstruction problem is reformulated as a n onlinear state estimation problem an approximate minimum mean square error globally optimal algorithm for the solution of this problem is presented the algorithm which is recursive in a hybrid frequency space domain operates directly on the fourier transformed projection data eliminating altogether the attempt to invert the projection integral equation the simulation example considered in this paper demonstrates that good object estimates may be obtained with as few as five views in a limited sector of 90 and at a signal to noise ratio as low as 0 db

notes on completely positive matrices abstract let a be a n n symmetric matrix and in the closure of inverse m matrices then a can be factored as a bb t for some nonnegative lower triangular n n matrix b and cp rank a n if a is a positive semidefinite 0 1 matrix then a is completely positive and cp rank a rank a if a is a nonnegative symmetric h matrix then a is completely positive and cp rank a n n 1 2 n n where is the number of connected components of the graph g a

cp rank of completely positive matrices of order 5 abstract j h drew et al linear and multilinear algebra 37 1994 304 conjectured that for n 4 the completely positive cp rank of every n n completely positive matrix is at most n 2 4 in this paper we prove that the cp rank of a 5 5 completely positive matrix which has at least one zero entry is at most 6 thus providing new supporting evidence for the conjecture

two filter formulae for discrete time non linear bayesian smoothing two filler formulae for the bayes solution of the fixed interval discrete time nonlinear smoothing problem are obtained the smoothed a posteriori density is computed under the assumptions of a general markov signal observed through a general memoryless noisy channel the case where there is feedback from the observation to the signal is also considered the derived algorithms complement a two pass algorithm obtained under somewhat more restrictive assumptions by askar and derin 1981 known smoothing results for the linear gaussian case are interpreted in the light of the general bayesian results

the maximal cp rank of rank k completely positive matrices abstract let k be the maximal cp rank of all rank k completely positive matrices we prove that k k k 1 2 1 for k 2 in particular we furnish a procedure to produce for k 2 completely positive matrices with rank k and cp rank k k 1 2 1

conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone we investigate the completely positive semidefinite cone mathcal cs n a new matrix cone consisting of all n times n matrices that admit a gram representation by positive semidefinite matrices of any size in particular we study relationships between this cone and the completely positive and the doubly nonnegative cone and between its dual cone and trace positive noncommutative polynomials we use this new cone to model quantum analogues of the classical independence and chromatic graph parameters alpha g and chi g which are roughly obtained by allowing variables to be positive semidefinite matrices instead of 0 1 scalars in the programs defining the classical parameters we can formulate these quantum parameters as conic linear programs over the cone mathcal cs n using this conic approach we can recover the bounds in terms of the theta number and define further approximations by exploiting the link to trace positive polynomials

completely positive matrices with a book graph abstract a new class of graphs called book graphs extending the class of completely positive graphs is defined necessary and sufficient conditions for the complete positivity of a matrix with graph in this class are given the main questions concerning completely positive matrices with cyclic graph are solved

a bayesian random effects model for testlets standard item response theory irt models fit to dichotomous examination responses ignore the fact that sets of items testlets often come from a single common stimuli e g a reading comprehension passage in this setting all items given to an examinee are unlikely to be conditionally independent given examinee proficiency models that assume conditional independence will overestimate the precision with which examinee proficiency is measured overstatement of precision may lead to inaccurate inferences such as prematurely ending an examination in which the stopping rule is based on the estimated standard error of examinee proficiency e g an adaptive test to model examinations that may be a mixture of independent items and testlets we modified one standard irt model to include an additional random effect for items nested within the same testlet we use a bayesian framework to facilitate posterior inference via a data augmented gibbs sampler dags tanner wong 1987 the modified and standard irt models are both applied to a data set from a disclosed form of the sat we also provide simulation results that indicates that the degree of precision bias is a function of the variability of the testlet effects as well as the testlet design

cfa models with a general factor and multiple sets of secondary factors we propose a class of confirmatory factor analysis models that include multiple sets of secondary or specific factors and a general factor the general factor accounts for the common variance among manifest variables whereas multiple sets of secondary factors account for the remaining source specific dependency among subsets of manifest variables a special case of the model is further proposed which constrains the specific factor loadings to be proportional to the general factor loadings this proportional model substantially reduces the number of model parameters while preserving the essential structure of the general model furthermore the proportional model allows for the interpretation of latent variables as the expected values of the observed manifest variables decomposition of the variances and the inclusion of interactions similar to generalizability theory we provide two applications to illustrate the utility of the proposed class of models

on the relationship between the higher order factor model and the hierarchical factor model the relationship between the higher order factor model and the hierarchical factor model is explored formally we show that the schmid leiman transformation produces constrained hierarchical factor solutions using a generalized schmid leiman transformation and its inverse we show that for any unconstrained hierarchical factor model there is an equivalent higher order factor model with direct effects loadings on the manifest variables from the higher order factors therefore the class of higher order factor models without direct effects of higher order factors is nested within the class of unconstrained hierarchical factor models in light of these formal results we discuss some implications for testing the higher order factor model and the issue of general factor an interesting aspect concerning the efficient fitting of the higher order factor model with direct effects is noted

non bayesian detection and detectability of anomalies from a few noisy tomographic projections the detection of an anomaly from a few noisy tomographic projections is addressed from the statistical point of view an unknown scene is composed of a background considered as a deterministic nuisance parameter with a possibly hidden anomaly because the full pixel by pixel reconstruction is impossible a parametric non bayesian approach is proposed to fill up the gap in the missing data an optimal statistical test which eliminates the background and detects the anomaly is designed the potential advantage of such an approach is its capacity to detect an anomaly target hidden in background designed by an adversary to mask the anomaly a key issue in the non bayesian anomaly detection i e the problem of anomaly detectability is stated and solved in this paper in the case of a bivariate polynomial background defined on an unknown rectangular support the size of detectable anomaly reaches its maximum defined by the number of elementary cells of x ray detector and degree of the polynomial function

computing symmetric nonnegative rank factorizations an algorithm is described for the nonnegative rank factorization nrf of some completely positive cp matrices whose rank is equal to their cp rank the algorithm can compute the symmetric nrf of any nonnegative symmetric rank r matrix that contains a diagonal principal submatrix of that rank and size with leading cost o rm2 operations in the dense case the algorithm is based on geometric considerations and is easy to implement the implications for matrix graphs are also discussed

the symmetric m matrix and symmetric inverse m matrix completion problems abstract the symmetric m matrix and symmetric m 0 matrix completion problems are solved and results of johnson and smith linear algebra appl 290 1999 193 are extended to solve the symmetric inverse m matrix completion problem 1 a pattern i e a list of positions in an n n matrix has symmetric m completion i e every partial symmetric m matrix specifying the pattern can be completed to a symmetric m matrix if and only if the principal subpattern r determined by its diagonal is permutation similar to a pattern that is block diagonal with each diagonal block complete or in graph theoretic terms if and only if each component of the graph of r is a clique 2 a pattern has symmetric m 0 completion if and only if the pattern is permutation similar to a pattern that is block diagonal with each diagonal block either complete or omitting all diagonal positions or in graph theoretic terms if and only if every principal subpattern corresponding to a component of the graph of the pattern either omits all diagonal positions or includes all positions 3 a pattern has symmetric inverse m completion if and only if its graph is block clique and no diagonal position is omitted that corresponds to a vertex in a graph block of order 2 the techniques used are also applied to matrix completion problems for other classes of symmetric matrices

completely positive matrices abstract an n n real matrix a is called completely positive cp if it can be factored as a b b stands for transpose where b is an m n entrywise nonnegative matrix for some integer m the smallest such number m is called the cprank of a in this paper we present a necessary and sufficient condition for any entrywise nonnegative and positive semidefinite matrix to be cp we also present an expression for the cprank of any cp matrix

separating doubly nonnegative and completely positive matrices the cone of completely positive cp matrices can be used to exactly formulate a variety of np hard optimization problems a tractable relaxation for cp matrices is provided by the cone of doubly nonnegative dnn matrices that is matrices that are both positive semidefinite and componentwise nonnegative a natural problem in the optimization setting is then to separate a given dnn but non cp matrix from the cone of cp matrices we describe two different constructions for such a separation that apply to 5 5 matrices that are dnn but non cp we also describe a generalization that applies to larger dnn but non cp matrices having block structure computational results illustrate the applicability of these separation procedures to generate improved bounds on difficult problems

estimation of dynamically evolving ellipsoids with applications to medical imaging the estimation of dynamically evolving ellipsoids from noisy lower dimensional projections is examined in particular this work describes a model based approach using geometric reconstruction and recursive estimation techniques to obtain a dynamic estimate of left ventricular ejection fraction from a gated set of planar myocardial perfusion images the proposed approach differs from current ejection fraction estimation techniques both in the imaging modality used and in the subsequent processing which yields a dynamic ejection fraction estimate for this work the left ventricle is modeled as a dynamically evolving three dimensional 3 d ellipsoid the left ventricular outline observed in the myocardial perfusion images is then modeled as a dynamic two dimensional 2 d ellipsoid obtained as the projection of the former 3 d ellipsoid this data is processed in two ways first as a 3 d dynamic ellipsoid reconstruction problem second each view is considered as a 2 d dynamic ellipse estimation problem and then the 3 d ejection fraction is obtained by combining the effective 2 d ejection fractions of each view the approximating ellipsoids are reconstructed using a rauch tung striebel smoothing filter which produces an ejection fraction estimate that is more robust to noise since it is based on the entire data set in contrast traditional ejection fraction estimates are based only on true frames of data further numerical studies of the sensitivity of this approach to unknown dynamics and projection geometry are presented providing a rational basis for specifying system parameters this investigation includes estimation of ejection fraction from both simulated and real data

detection of edges from projections in a number of applications of computerized tomography the ultimate goal is to detect and characterize objects within a cross section detection of edges of different contrast regions yields the required information the problem of detecting edges from projection data is addressed it is shown that the class of linear edge detection operators used on images can be used for detection of edges directly from projection data this not only reduces the computational burden but also avoids the difficulties of postprocessing a reconstructed image this is accomplished by a convolution backprojection operation for example with the marr hildreth edge detection operator the filtering function that is to be used on the projection data is the radon transform of the laplacian of the 2 d gaussian function which is combined with the reconstruction filter simulation results showing the efficacy of the proposed method and a comparison with edges detected from the reconstructed image are presented

copositive optimization recent developments and applications due to its versatility copositive optimization receives increasing interest in the operational research community and is a rapidly expanding and fertile field of research it is a special case of conic optimization which consists of minimizing a linear function over a cone subject to linear constraints the diversity of copositive formulations in different domains of optimization is impressive since problem classes both in the continuous and discrete world as well as both deterministic and stochastic models are covered copositivity appears in local and global optimality conditions for quadratic optimization but can also yield tighter bounds for np hard combinatorial optimization problems here some of the recent success stories are told along with principles algorithms and applications

a note on diagonally dominant matrices abstract the set d n of diagonally dominant symmetric real matrices of order n with nonnegative diagonal elements is a polyhedral convex cone based on its extreme rays we derive a description of the kernel of each matrix in d n in terms of a certain support graph moreover the doubly stochastic matrices in d n are studied

maximum likelihood estimation of object location in diffraction tomography the problem is formulated within the context of diffraction tomography where the complex phase of the diffracted wavefield is modeled using the rytov approximation and the measurements consist of noisy renditions of this complex phase at a single frequency the log likelihood function is computed for the case of additive zero mean gaussian white noise and shown to be expressible in the form of the filtered backpropagation algorithm of diffraction tomography in this form however the filter function is no longer the rho filter appropriate to least square reconstruction but is now the generalized projection propagation of the object centered at the origin onto the line s parallel to the measurement line s but passing through the origin this result allows the estimation problem to be solved via a diffraction tomographic imaging procedure where the noisy data is filtered and backpropagated in a first step and the point of maximum value of the resulting image is then the maximum likelihood ml estimate of the object s location the authors include a calculation of the cramer rao bound for the estimation error and a computer simulation study illustrating the estimation procedure

complete positivity of matrices of special form abstract given that b c 2 c k are positive semidefinite psd n by n real matrices and b is entrywise nonnegative we characterize fully for n 2 and partially for n 3 when b may be written as b i 2 k b i so that b i and b i c i are psd and b i is entrywise nonnegative i 2 k these characterizations are used to give conditions under which an entrywise nonnegative psd matrix a with a special block form can be written as a bb t in which b is entrywise nonnegative

nonparametric fixed interval smoothing of nonlinear vector valued measurements the problem of estimating a smooth vector valued function given noisy nonlinear vector valued measurements of that function is addressed a nonparametric optimality criterion for this estimation problem is presented and a computationally efficient iterative algorithm for its solution is developed the criterion is the natural generalization of previously published work on vector splines with linear measurement models the algorithm provides an alternative to the extended kalman filter as it does not require a parametric state space model an automatic procedure that uses the measurements to determine how much to smooth is presented the algorithm s subpixel estimation accuracy is demonstrated on the estimation of a curved edge in a noisy image and on a biomedical image processing application

nonnegative factorization of completely positive matrices abstract let a be a real symmetric n n matrix of rank k and suppose that a bb for some real n m matrix b with nonnegative entries for some m such an a is called completely positive it is shown that such a b exists with m 1 2 k k 1 n where 2n is the maximal number of off diagonal entries which equal zero in a nonsingular principal submatrix of a an example is given where the least m which works is k 1 2 4 k odd k k 2 4 k even

5 5 completely positive matrices abstract we study the problem of determining whether a given 5 5 matrix is completely positive by investigating the number of negative entries of a schur complement of a we show that if this number is not 4 then a is completely positive and present some sufficient conditions for a to be cp when this number is 4 we also show that the complete positivity of an elementwise positive doubly nonnegative 5 5 matrix is equivalent to the complete positivity of a related 5 5 doubly nonnegative matrix that is not elementwise positive

a bayesian approach to reconstruction from incomplete projections of a multiple object 3d domain an estimation approach is described for three dimensional reconstruction from line integral projections using incomplete and very noisy data generalized cylinders parameterized by stochastic dynamic models are used to represent prior knowledge about the properties of objects of interest in the probed domain the object models a statistical measurement model and the maximum a posteriori probability performance criterion are combined to reformulate the reconstruction problem as a computationally challenging nonlinear estimation problem for computational feasibility a suboptimal hierarchical algorithm is described whose individual steps are locally optimal and are combined to satisfy a global optimality criterion the formulation and algorithm are restricted to objects whose center axis is a single valued function of a fixed spatial coordinate simulation examples demonstrate accurate reconstructions with as few as four views in a 135 degrees sector at an average signal to noise ratio of 3 3