generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

the mean number in system vector range for multiclass queueing networks in a multiclass network of queues natural sufficient conditions are given for the mean number in system vector to cover the nonnegative orthant as the arrival rate vector varies over the stable domain

r norm bounds and metric properties for zero loci of real analytic functions abstract we consider the problem of deciding whether or not a zero locus x of multivariate real analytic functions crosses a given r norm ball in the real n dimensional affine space we perform a local study of the problem and we provide both necessary and sufficient conditions to answer the question our conditions derive from the analysis of differential geometric properties of x at the center of the ball an algorithm to evaluate r norms distances is proposed

an adaptive linear approximation algorithm for copositive programs we study linear optimization problems over the cone of copositive matrices these problems appear in nonconvex quadratic and binary optimization for instance the maximum clique problem and other combinatorial problems can be reformulated as such problems we present new polyhedral inner and outer approximations of the copositive cone which we show to be exact in the limit in contrast to previous approximation schemes our approximation is not necessarily uniform for the whole cone but can be guided adaptively through the objective function yielding a good approximation in those parts of the cone that are relevant for the optimization and only a coarse approximation in those parts that are not using these approximations we derive an adaptive linear approximation algorithm for copositive programs numerical experiments show that our algorithm gives very good results for certain nonconvex quadratic problems

the stability of two station multitype fluid networks this paper studies the fluid models of two station multiclass queueing networks with deterministic routing a fluid model is globally stable if the fluid network eventually empties under each nonidling dispatch policy we explicitly characterize the global stability region in terms of the arrival and service rates we show that the global stability region is defined by the nominal workload conditions and the virtual workload conditions and we introduce two intuitively appealing phenomena virtual stations and push starts that explain the virtual workload conditions when any of the workload conditions is violated we construct a fluid solution that cycles to infinity showing that the fluid network is unstable when all the workload conditions are satisfied we solve a network flow problem to find the coefficients of a piecewise linear lyapunov function the lyapunov function decreases to zero proving that the fluid level eventually reaches zero under any nonidling dispatch policy under certain assumptions on the inter arrival and service time distributions a queueing network is stable or positive harris recurrent if the corresponding fluid network is stable thus the workload conditions are sufficient to ensure the global stability of two station multiclass queueing networks with deterministic routing

representing periodic structures efficiently as substructures abstract periodic structures structures comprising a number of identical bays arranged sequentially and having identical connection properties between all pairs of adjacent bays have certain properties which can be used to advantage in the computation and understanding of their behaviour in various dynamical situations it is proposed in this paper that a free ended periodic structure can be represented very efficiently as a substructure in a larger edifice by making full use of the similarity between it and a rotationally periodic structure it is shown that this concept can provide a very significant acceleration of analysis in virtually all dynamic substructuring analyses regardless of which method of composite structure assembly method is used it also transpires that by using this approach the resonance frequencies and natural modes of the general periodic structure can be computed much more easily than previously

on reduced semidefinite programs for second order moment bounds with applications we show that the complexity of computing the second order moment bound on the expected optimal value of a mixed integer linear program with a random objective coefficient vector is closely related to the complexity of characterizing the convex hull of the points 1 atopwithdelims varvec x 1 atopwithdelims varvec x varvec x in mathcal x 1x1x x x where mathcal x x is the feasible region in fact we can replace the completely positive programming formulation for the moment bound on mathcal x x with an associated semidefinite program provided we have a linear or a semidefinite representation of this convex hull as an application of the result we identify a new polynomial time solvable semidefinite relaxation of the distributionally robust multi item newsvendor problem by exploiting results from the boolean quadric polytope for mathcal x x described explicitly by a finite set of points our formulation leads to a reduction in the size of the semidefinite program we illustrate the usefulness of the reduced semidefinite programming bounds in estimating the expected range of random variables with two applications arising in random walks and best worst choice models

stability of queueing networks and scheduling policies we develop a programmatic procedure for establishing the stability of queueing networks and scheduling policies the method uses linear or nonlinear programming to determine what is an appropriate quadratic functional to use as a lyapunov function if the underlying system is markovian our method establishes not only positive recurrence and the existence of a steady state probability distribution but also the geometric convergence of an exponential moment we illustrate this method on several example problems

perturbation of polynomials and applications to the hough transform abstract let f and g be complex polynomials of the same degree we provide a new lower bound on the euclidean distance of points belonging to their zero loci in terms of bombieri s norm we also present a minimization of the bombieri s norm of the difference g f for c in the real case we apply the results above in the setting of the hough transform a standard technique to detect curves in images suggesting a bombieri s norm based recognition algorithm

irreducible elements of the copositive cone we call an element a of the n n copositive cone cn irreducible with respect to the nonnegative cone nn if it cannot be written as a nontrivial sum a c n of a copositive matrix c and an elementwise nonnegative matrix n note that our concept of irreducibility differs from the standard one normally studied in matrix theory this property was studied by baumert 1965 2 who gave a characterisation of irreducible matrices we demonstrate here that baumert s characterisation is incorrect and give a correct version of his theorem which establishes a necessary and sufficient condition for a copositive matrix to be irreducible for the case of 5 5 copositive matrices we give a complete characterisation of all irreducible matrices we show that those irreducible matrices in c5 which are not positive semidefinite can be parameterized in a semi trigonometric way finally we prove that every 5 5 copositive matrix which is not the sum of a nonnegative and a semidefinite matrix can be expressed as the sum of a nonnegative matrix with zero diagonal and a single irreducible matrix

sequencing and routing in multiclass queueing networks part i feedback regulation this paper establishes new criteria for stability and for instability of multiclass network models under a given stationary policy it also extends previous results on the approximation of the solution to the average cost optimality equations through an associated fluid model it is shown that an optimized network possesses a fluid limit model which is itself optimal with respect to a total cost criterion a general framework for constructing control algorithms for multiclass queueing networks is proposed based on these general results network sequencing and routing problems are considered as special cases the following aspects of the resulting feedback regulation policies are developed in the paper the policies are stabilizing and are in fact geometrically ergodic for a markovian model numerical examples are given in each case it is shown that the feedback regulation policy closely resembles the average cost optimal policy a method is proposed for reducing variance in simulation for a network controlled using a feedback regulation policy

copositive programming motivated bounds on the stability and the chromatic numbers the lovasz theta number of a graph g can be viewed as a semidefinite programming relaxation of the stability number of g it has recently been shown that a copositive strengthening of this semidefinite program in fact equals the stability number of g we introduce a related strengthening of the lovasz theta number toward the chromatic number of g which is shown to be equal to the fractional chromatic number of g solving copositive programs is np hard this motivates the study of tractable approximations of the copositive cone we investigate the parrilo hierarchy to approximate this cone and provide computational simplifications for the approximation of the chromatic number of vertex transitive graphs we provide some computational results indicating that the lovasz theta number can be strengthened significantly toward the fractional chromatic number of g on some hamming graphs

moore penrose approach in the hough transform framework abstract let f x a be a real polynomial in two sets of variables x and a that is linear with respect to one of the variable sets say a in this paper we deal with two of the main steps of the hough transform framework for the pattern recognition technique to detect loci in images more precisely we present an algorithmic process based on the moore penrose pseudo inverse to provide a region of analysis in the parameter space in addition we state an upper bound for the sampling distance of the discretization of the parameter space region

approximation algorithms for indefinite quadratic programming we consider approximation schemes for indefinite quadratic programming we argue that such an approximation can be found in polynomial time for fixed andt wheret denotes the number of negative eigenvalues of the quadratic term our algorithm is polynomial in 1 for fixedt and exponential int for fixed we next look at the special case of knapsack problems showing that a more efficient polynomial int approximation algorithm exists

the complexity of optimal queuing network control we show that several well known optimization problems related to the optimal control of queues are provably intractable independently of any unproven conjecture such as p np in particular we show that several versions of the problem of optimally controlling a simple network of queues with simple arrival and service distributions and multiple customer classes is complete for exponential time this is perhaps the first such intractability result for a well known optimization problem we also show that the restless bandit problem the generalization of the multi armed bandit problem to the case in which the unselected processes are not quiescent is complete for polynomial space

finding a sparse vector in a subspace linear sparsity using alternating directions is it possible to find the sparsest vector direction in a generic subspace mathcal s subseteq mathbb r p with text dim left mathcal s right n this problem can be considered a homogeneous variant of the sparse recovery problem and finds connections to sparse dictionary learning sparse pca and many other problems in signal processing and machine learning in this paper we focus on a planted sparse model for the subspace the target sparse vector is embedded in an otherwise random subspace simple convex heuristics for this planted recovery problem provably break down when the fraction of nonzero entries in the target sparse vector substantially exceeds o 1 sqrt n in contrast we exhibit a relatively simple nonconvex approach based on alternating directions which provably succeeds even when the fraction of nonzero entries is omega 1 to the best of our knowledge this is the first practical algorithm to achieve linear scaling under the planted sparse model empirically our proposed algorithm also succeeds in more challenging data models e g sparse dictionary learning

which are the important modes of a subsystem a linearly behaving vibrational substructure or more generally a linear dynamic subsystem attached to a main structure or a main dynamic system is considered after discretization the substructure is represented by afinite typically large number of degrees of freedom n and hence also by n s eigenmodes in order to reduce the computational effort it is common to apply modal reduction to the subsystem such that only n r modes out of the total number of n modes are retained where n r n s the following question then arises which n r modes should be retained in structural dynamics it is traditional to retain those modes associated with the lowest frequencies in this paper the question is answered by solving an appropriate optimization problem the most important modes of the subsystem are shown to be those whose coupling matrices which are defined in a particular way have the highest norm this leads to a simple and effective algorithm for optimal modal reduction the new criterion for modal importance is explained both mathematically and physically and is demonstrated by numerical examples

closed form line segment extraction using the hough transform this paper proposes a novel closed form solution to complete line segment extraction given a voting angle in image space the voting distribution is analyzed and two functional relationships are deduced regarding the corresponding column in hough space voting along the distance axis is considered as being a random variable and voting values in cells are considered as forming a probability distribution statistical characteristics of this distribution are used to fit a quadratic polynomial curve and a linear curve direction length and width of a line segment are simultaneously computed in a closed form based on coefficients of fitted quadratic polynomial curves the midpoint of a line segment is determined based on the fitted linear curve the method is tested on simulated and real world images results show that the proposed closed form solution is feasible in the presence of quantization errors or image noise highlightswe proposed a method for obtaining the complete set of line segment parameters the direction length and width of a line segment are extracted simul taneously in a closed form we provided a complete theoretical derivation of voting variance with respect to voting angle the midpoint of a line segment is determined by the coefficients of the fitted linear curve parallel crossing and aligned line segments are discussed by analysing events in image space and hough space

a complementary pivoting approach to the maximum weight clique problem given an undirected graph with positive weights on the vertices the maximum weight clique problem mwcp is to find a subset of mutually adjacent vertices i e a clique having largest total weight the problem is known to be np hard even to approximate motivated by a recent quadratic programming formulation which generalizes an earlier remarkable result of motzkin and straus in this paper we propose a new framework for the mwcp based on the corresponding linear complementarity problem lcp we show that generically all stationary points of the mwcp quadratic program exhibit strict complementarity despite this regularity result however the lcp turns out to be inherently degenerate and we find that lemke s well known pivoting method equipped with standard degeneracy resolution strategies yields unsatisfactory experimental results we exploit the degeneracy inherent in the problem to develop a variant of lemke s algorithm which incorporates a new and effective look ahead pivot rule the resulting algorithm is tested extensively on various instances of random as well as dimacs benchmark graphs and the results obtained show the effectiveness of our method

duality and linear programs for stability and performance analysis of queuing networks and scheduling policies we consider the problems of performance analysis and stability instability determination of queuing networks and scheduling policies we exhibit a strong duality relationship between the performance of a system and its stability analysis via mean drift we obtain a variety of linear programs lps to conduct such stability and performance analyses a certain lp called the performance lp bounds the performance of all stationary nonidling scheduling policies if it is bounded then its dual called the drift lp has a feasible solution which is a copositive matrix the quadratic form associated with this copositive matrix has a negative drift showing that all stationary nonidling scheduling policies result in a geometrically converging exponential moment these results carry over to fluid models allowing the study of networks with nonexponential distributions if a modification of the performance lp called the monotone lp is bounded then the system is stable finally there is a another modification of the performance lp called the finite time lp it provides transient bounds on the performance of the system from any initial condition

the copositive completion problem abstract an n n real symmetric matrix a is called strictly copositive if x t ax 0 0 whenever x r n satisfies x 0 x 0 and x 0 the strictly copositive matrix completion problem asks which partial strictly copositive matrices have a completion to a strictly copositive matrix we prove that every partial strictly copositive matrix has a strictly copositive matrix completion and give a lower bound on the values used in the completion we answer affirmatively an open question whether an n n copositive matrix a a ij with all diagonal entries a ii 1 stays copositive if each off diagonal entry of a is replaced by min a ij 1

optimality of mixed policies for average continuous time markov decision processes with constraints this article concerns the average criteria for continuous time markov decision processes with n constraints we show the following a every extreme point of the space of performance vectors corresponding to the set of stable measures is generated by a deterministic stationary policy and b there exists a mixed optimal policy where the mixture is over no more than n 1 deterministic stationary policies

edge detection methods based on rbf interpolation abstract edge detection is a widely used tool in signal image processing with the aim of identifying abrupt changes or discontinuities in a signal digital image for the detection of jump discontinuities in 1d problems we present an iterative method based on interpolation with variably scaled kernels vsks this is shown to outperform an existing iterative edge detection method based on multiquadric mq radial basis function interpolation to extend our purely one dimensional edge detector to any dimension we then introduce an innovative non iterative technique that detects jumps edges by identifying the local maxima of the normalized absolute values of the rbf interpolant coefficients the rbf interpolant is built upon the compactly supported c 2 wendland function and exploits its advantageous properties to provide a robust and low cost method numerical examples in 1d and 2d are included to illustrate its effectiveness and efficiency in the context of edge detection for digital images comparisons with canny method are also presented

a simplex algorithm for rational cp factorization in this paper we provide an algorithm similar to the simplex algorithm which determines a rational cp factorization of a given matrix whenever the matrix allows such a factorization this algorithm can be used to show that every integral completely positive 2 times 2 matrix has an integral cp factorization

randomized circle detection with isophotes curvature analysis circle detection is a critical issue in image analysis and object detection although hough transform based solvers are largely used randomized approaches based on the iterative sampling of the edge pixels are object of research in order to provide solutions less computationally expensive this work presents a randomized iterative work flow which exploits geometrical properties of isophotes in the image to select the most meaningful edge pixels and to classify them in subsets of equal isophote curvature the analysis of candidate circles is then performed with a kernel density estimation based voting strategy followed by a refinement algorithm based on linear error compensation the method has been applied to a set of real images on which it has also been compared with two leading state of the art approaches and hough transform based solutions the achieved results show how discarding up to 57 of unnecessary edge pixels it is able to accurately detect circles within a limited number of iterations maintaining a sub pixel accuracy even in the presence of high level of noise highlightsan iterative randomized circle detection algorithm is proposed curvature of isophotes is used to reduce the number of necessary iterations edges on circumference s are selected by a kernel density estimation strategy sub pixel accuracy was maintained on real images even in presence of high noise levels isophotes analysis reduces the influence of the used edge map on the results

using spin images for efficient object recognition in cluttered 3d scenes we present a 3d shape based object recognition system for simultaneous recognition of multiple objects in scenes containing clutter and occlusion recognition is based on matching surfaces by matching points using the spin image representation the spin image is a data level shape descriptor that is used to match surfaces represented as surface meshes we present a compression scheme for spin images that results in efficient multiple object recognition which we verify with results showing the simultaneous recognition of multiple objects from a library of 20 models furthermore we demonstrate the robust performance of recognition in the presence of clutter and occlusion through analysis of recognition trials on 100 scenes

the policy iteration algorithm for average reward markov decision processes with general state space the average cost optimal control problem is addressed for markov decision processes with unbounded cost it is found that the policy iteration algorithm generates a sequence of policies which are c regular where c is the cost function under consideration this result only requires the existence of an initial c regular policy and an irreducibility condition on the state space furthermore under these conditions the sequence of relative value functions generated by the algorithm is bounded from below and nearly decreasing from which it follows that the algorithm is always convergent under further conditions it is shown that the algorithm does compute a solution to the optimality equations and hence an optimal average cost policy these results provide elementary criteria for the existence of optimal policies for markov decision processes with unbounded cost and recover known results for the standard linear quadratic gaussian problem in particular in the control of multiclass queueing networks it is found that there is a close connection between optimization of the network and optimal control of a far simpler fluid network model

toward unified analysis and controller synthesis for a class of hybrid systems abstract this work defines a new class of hybrid systems called state based switched sbs systems that have numerous important engineering applications the characterizing feature of these systems is that the discrete event dynamics are associated with the continuous time state making a specific function be equal to zero the choice of this function is application specific and for the closed loop sbs systems defined in this paper it is related to the execution of a desired set of tasks from a pre specified mission plan for this broad class of sbs systems the paper presents a unified analysis and controller synthesis methodology based on lyapunov theory depending on the details of the mission plan the closed loop hybrid system will be divided into two subclasses sequential and non sequential the controller design procedure for both subclasses consists of the same two steps finding a control law and finding a stabilizing switching rule for static state and output feedback of sequential hybrid systems the paper proposes a new hybrid sequential sliding mode controller it is proven that the control mission can be accomplished for sequential hybrid systems under static state and output feedback using this new controller a similar framework is investigated for the more complex class of nonsequential hybrid systems and a systematic procedure for designing the switching rule is presented for some specific instances of these systems

factorization and cutting planes for completely positive matrices by copositive projection we consider the problem of projecting a matrix onto the cones of copositive and completely positive matrices as this can not be done directly we use polyhedral approximations of the cones with the help of these projections we obtain a technique to compute factorizations of completely positive matrices we also describe a method to determine a cutting plane which cuts off an arbitrary matrix from the completely positive or copositive cone

approximation of the stability number of a graph via copositive programming lovasz and schrijver siam j optim 1 1991 pp 166 190 showed how to formulate increasingly tight approximations of the stable set polytope of a graph by solving semidefinite programs sdps of increasing size lift and project method in this paper we present a similar idea we show how the stability number can be computed as the solution of a conic linear program lp over the cone of copositive matrices subsequently we show how to approximate the copositive cone ever more closely via a hierarchy of linear or semidefinite programs of increasing size liftings the latter idea is based on recent work by parrilo structured semidefinite programs and semi algebraic geometry methods in robustness and optimization ph d thesis california institute of technology pasadena ca 2000 in this way we can compute the stability number alpha g of any graph g v e after at most alpha g 2 successive liftings for the lp based approximations one can compare this to the n alpha g 1 bound for the lp based lift and project scheme of lovasz and schrijver our approach therefore requires fewer liftings for families of graphs where alpha g o sqrt n we show that the first sdp based approximation for alpha g in our series of increasingly tight approximations coincides with the vartheta function of schrijver ieee trans inform theory 25 1979 pp 425 429 we further show that the second approximation is tight for complements of triangle free graphs and for odd cycles

semi automatic spline fitting of planar curvilinear profiles in digital images using the hough transform abstract we develop a novel method for the recognition of curvilinear profiles in digital images the proposed method semi automatic for both closed and open planar profiles essentially consists of a preprocessing step exploiting an edge detection algorithm and a main step involving the hough transform technique in the preprocessing step a canny edge detection algorithm is applied in order to obtain a reduced point set describing the profile curve to be reconstructed also to identify in the profile possible sharp points like cusps we additionally use an algorithm to find the approximated tangent vector of every edge point in the subsequent main step we then use a piecewisely defined hough transform to locally recognize from the point set a low degree piecewise polynomial curve the final outcome of the algorithm is thus a spline curve approximating the underlined profile image the output curve consists of polynomial pieces connected g 1 continuously except in correspondence of the identified cusps where the order of continuity is only c 0 as expected to illustrate effectiveness and efficiency of the new profile detection technique we present several numerical results dealing with detection of open and closed profiles in images of different type i e medical and photographic images

on the solution of concave knapsack problems we consider a version of the knapsack problem which gives rise to a separable concave minimization problem subject to bounds on the variables and one equality constraint we characterize strict local miniimizers of concave minimization problems subject to linear constraints and use this characterization to show that although the problem of determining a global minimizer of the concave knapsack problem is np hard it is possible to determine a local minimizer of this problem with at most o n logn operations and 1 logn evaluations of the function if the function is quadratic this algorithm requires at most o n logn operations

multivariate nonnegative quadratic mappings in this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain with nonnegativity defined by a prespecified conic order in particular we consider the set cone of nonnegative quadratic mappings defined with respect to the positive semidefinite matrix cone and study when it can be represented by linear matrix inequalities we also discuss the applications of the results in robust optimization especially the robust quadratic matrix inequalities and the robust linear programming models in the latter application the implementational errors of the solution are taken into account and the problem is formulated as a semidefinite program

partitioned component mode synthesis via a flexibility approach a new flexibility based component mode synthesis method is presented which is derived by approximating the partitioned equations of motion that employ a localized method of lagrange multipliers the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes hence the resulting interface flexibility matrices are uniquely determined and well suited for the present method development an attractive feature of the present method is its substructural mode selection criterion that is independent of loading conditions numerical experiments show that the present modal selection criterion is reliable and that the proposed flexibility based component mode synthesis method performs well relative to the classical craig bampton method in terms of accuracy and of its ability to include dominant substructural modes for simple plates and a relatively complex solid ring

a new iterative order reduction ior method for eigensolutions of large structures order reduction is a computationally efficient method to estimate some lowest eigenvalues and the corresponding eigenvectors of large structural systems by reducing the order of the original model to a smaller one but its accuracy is limited to a small range of frequencies that depends on the selection of the retained degrees of freedom this paper proposes a new iterative order reduction ior technique to obtain accurately the eigensolutions of large structural systems the technique retains all the inertia terms associated with the removed degrees of freedom this hence leads to the reduced mass matrix being in an iterated form and the reduced stiffness matrix constant from these mass and stiffness matrices the eigensolutions of the reduced system can be obtained iteratively on convergence the reduced system reproduces the eigensolutions of the original structure a proof of the convergence property is also presented applications of the method to a practical garteur structure as well as a plate have demonstrated that the proposed method is comparable to the commonly used subspace iteration method in terms of numerical accuracy moreover it has been found that the proposed method is computationally more efficient than the subspace iteration method copyright 2003 john wiley sons ltd

the delay of open markovian queueing networks uniform functional bounds heavy traffic pole multiplicities and stability for open markovian queueing networks we study the functional dependence of the mean number in the system and thus also the mean delay since it is proportional to it by little s theorem on the arrival rate or load factor we obtain linear programs lps which provide bounds on the pole multiplicity m of the mean number in the system and automatically obtain lower and upper bounds on the coefficients ci of the expansion cm 1 m cm 1 1 m 1 c1 1 c0 where is the load factor which are valid for all 0 1 our lps can thus establish the stability of open networks for all arrival rates within capacity while providing uniformly bounding functional expansions for the mean delay valid for all arrival rates in the capacity region the coefficients ci can be optimized to provide the best bound at any desired value of the load factor while still maintaining its validity for all 0 1 while the above lps feature ll 1m 1 2 variables where l is the number of buffers in the network for balanced systems we further provide a lower dimensional lp featuring just ss 1 2 variables where s is the number of stations in the network this bound asymptotically dominates in heavy traffic a bound obtainable from the pollaczek khintchine formula and can capture interactions between multiple bottleneck stations in heavy traffic we also provide an explicit upper bound for all scheduling policies in acyclic networks and for the fbfs policy in open re entrant lines

a cone programming approach to the bilinear matrix inequality problem and its geometry we discuss an approach for solving the bilinear matrix inequality bmi based on its connections with certain problems defined over matrix cones these problems are among others the cone generalization of the linear programming lp and the linear complementarity problem lcp referred to as the cone lp and the cone lcp respectively specifically we show that solving a given bmi is equivalent to examining the solution set of a suitably constructed cone lp or cone lcp this approach facilitates our understanding of the geometry of the bmi and opens up new avenues for the development of the computational procedures for its solution

some np complete problems in quadratic and nonlinear programming in continuous variable smooth nonconvex nonlinear programming we analyze the complexity of checking whether a a given feasible solution is not a local minimum and b the objective function is not bounded below on the set of feasible solutions we construct a special class of indefinite quadratic programs with simple constraints and integer data and show that checking a or b on this class is np complete as a corollary we show that checking whether a given integer square matrix is not copositive is np complete

recognition of feature curves on 3d shapes using an algebraic approach to hough transforms abstract feature curves are largely adopted to highlight shape features such as sharp lines or to divide surfaces into meaningful segments like convex or concave regions extracting these curves is not sufficient to convey prominent and meaningful information about a shape we have first to separate the curves belonging to features from those caused by noise and then to select the lines which describe non trivial portions of a surface the automatic detection of such features is crucial for the identification and or annotation of relevant parts of a given shape to do this the hough transform ht is a feature extraction technique widely used in image analysis computer vision and digital image processing while for 3d shapes the extraction of salient feature curves is still an open problem thanks to algebraic geometry concepts the ht technique has been recently extended to include a vast class of algebraic curves thus proving to be a competitive tool for yielding an explicit representation of the diverse feature lines equations in the paper for the first time we apply this novel extension of the ht technique to the realm of 3d shapes in order to identify and localize semantic features like patterns decorations or anatomical details on 3d objects both complete and fragments even in the case of features partially damaged or incomplete the method recognizes various features possibly compound and it selects the most suitable feature profiles among families of algebraic curves

lyapounov functions for jackson networks we construct explicitly lyapounov functions for markovian jackson networks two direct corollaries are obtained first a proof of the necessary and sufficient conditions for ergodicity without using the famous jackson s product form secondly an exponential convergence rate to the stationary distribution we also consider small perturbations of the transition probabilities yielding thus non jackson networks and prove that the corresponding stationary distribution is an analytic function of these perturbations

semidefinite approximations for global unconstrained polynomial optimization we consider the problem of minimizing a polynomial function on mathbb r n known to be hard even for degree 4 polynomials therefore approximation algorithms are of interest lasserre siam j optim 11 2001 pp 796 817 and parrilo math program 96 2003 pp 293 320 have proposed approximating the minimum of the original problem using a hierarchy of lower bounds obtained via semidefinite programming relaxations we propose here a method for computing tight upper bounds based on perturbing the original polynomial and using semidefinite programming the method is applied to several examples

on computational complexity of invalidating structured uncertainty models abstract in this paper we study a class of uncertainty model validation invalidation problems for linear discrete time systems we consider models described by a linear fractional transformation lft of modeling uncertainties which are structured time invariant or time varying and are bounded in h or l 1 norms the experimental data available for use in invalidation are either input output time series observations or frequency response measurements we analyze the computational complexity associated with these problems while earlier work showed that for lft models with an unstructured uncertainty the invalidation problems can be reduced to one of solving linear matrix inequalities and hence may be tackled readily using well developed numerical methods in this paper we provide a simple proof to show that in the presence of structured uncertainties they are all np hard with respect to the number of uncertainty blocks suggesting that the problems are inherently intractable from a computational standpoint additionally we also demonstrate that the problems do become tractable when the lft model description is changed to an additive one leading to lmi based invalidation tests similar to those obtained elsewhere these results indicate that the main source of the computational difficulty lies in the lft description together with the structured nature of the uncertainties

computational complexity of spl mu calculation the structured singular value spl mu measures the robustness of uncertain systems numerous researchers over the last decade have worked on developing efficient methods for computing spl mu this paper considers the complexity of calculating spl mu with general mixed real complex uncertainty in the framework of combinatorial complexity theory in particular it is proved that the spl mu recognition problem with either pure real or mixed real complex uncertainty is np hard this strongly suggests that it is futile to pursue exact methods for calculating spl mu of general systems with pure real or mixed uncertainty for other than small problems

a dual craig bampton method for dynamic substructuring a novel component mode synthesis method for dynamic analysis of structures is presented it is based on free interface vibration modes and residual flexibility components although the ingredients are the same as in previously published procedures e g macneal or rubin our method is fundamentally different in that it assembles the substructures using interface forces dual assembly and enforces only weak interface compatibility the new formulation is based on a fully consistent reduction approach and the reduced matrices so obtained are exactly dual to the craig bampton reduced matrices the new free interface substructuring method proposed here is thus more natural then classical free interface synthesis procedures and leads to simpler reduced matrices we illustrate the efficiency of the dual craig bampton approach for reducing the dynamical representation on a three dimensional frame

workload models for stochastic networks value functions and performance evaluation this paper concerns control and performance evaluation for stochastic network models structural properties of value functions are developed for controlled brownian motion cbm and deterministic fluid workload models leading to the following conclusions outside of a null set of network parameters the following hold i the fluid value function is a smooth function of the initial state under further minor conditions the fluid value function satisfies the derivative boundary conditions that are required to ensure it is in the domain of the extended generator for the cbm model exponential ergodicity of the cbm model is demonstrated as one consequence ii the fluid value function provides a shadow function for use in simulation variance reduction for the stochastic model the resulting simulator satisfies an exact large deviation principle while a standard simulation algorithm does not satisfy any such bound iii the fluid value function provides upper and lower bounds on performance for the cbm model this follows from an extension of recent linear programming approaches to performance evaluation

stability and asymptotic optimality of generalized maxweight policies it is shown that stability of the celebrated maxweight or back pressure policies is a consequence of the following interpretation either policy is myopic with respect to a surrogate value function of a very special form in which the marginal disutility at a buffer vanishes for a vanishingly small buffer population this observation motivates the h maxweight policy defined for a wide class of functions h these policies share many of the attractive properties of the maxweight policy as follows i arrival rate data is not required in the policy ii under a variety of general conditions the policy is stabilizing when h is a perturbation of a monotone linear function a monotone quadratic or a monotone lyapunov function for the fluid model iii a perturbation of the relative value function for a workload relaxation gives rise to a myopic policy that is approximately average cost optimal in heavy traffic with logarithmic regret the first results are obtained for a general markovian network model asymptotic optimality is established for a general markovian scheduling model with a single bottleneck and with homogeneous servers

improved nelson s method for computing eigenvector derivatives with distinct and repeated eigenvalues t he computation of derivatives of eigenvalues and eigenvectors with respect to model parameters is crucial for many applications 1 nelson 2 proposed an approach for general real eigensystemswith distinct eigenvalueswhere only the eigenvector of interest was required ojalvo 3 mills curran 4 dailey 5 and shaw and jayasuriya 6 developed nelson s method for real symmetric eigensystems with repeated eigenvalues for computation of a particular solution themethods described in 3 5 may fail in some circumstances other methods have been suggested by millscurran 4 and song et al 7 but they are difficult to implement when a system of linear equations is solved one hopes that the calculated solution is a close representation of the true solution the computed solution for a system with a large condition number may be inexact due to extreme sensitivity of the solution to small changes in its coefficient matrix and right column vectors 8 because some diagonal elements in the coefficient matrix for particular solutions are set to units its coefficients are not all of the same order of magnitude so the coefficient matrix has a large condition number in this note nelson s method is first extended to the case of repeated eigenvalues for the symmetric real eigensystems and its improvements are then presented the condition number of the coefficient matrix of the improved method is considerably reduced

a global lojasiewicz inequality for algebraic varieties let x be the locus of common zeros of polynomials f 1 f in n complex variables a global upper bound for the distance to x is given in the form of a lojasiewicz inequality the exponent in this inequality is bounded by d min n k where d max 3 deg f i the estimates are also valid over an algebraically closed field of any characteristic

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

minimal zeros of copositive matrices abstract let a be an element of the copositive cone c n a zero u of a is a nonzero nonnegative vector such that u t a u 0 the support of u is the index set supp u 1 n corresponding to the positive entries of u a zero u of a is called minimal if there does not exist another zero v of a such that its support supp v is a strict subset of supp u we investigate the properties of minimal zeros of copositive matrices and their supports special attention is devoted to copositive matrices which are irreducible with respect to the cone s n of positive semi definite matrices i e matrices which cannot be written as a sum of a copositive and a nonzero positive semi definite matrix we give a necessary and sufficient condition for irreducibility of a matrix a with respect to s n in terms of its minimal zeros a similar condition is given for the irreducibility with respect to the cone n n of entry wise nonnegative matrices for n 5 matrices which are irreducible with respect to both s 5 and n 5 are extremal for n 6 a list of candidate combinations of supports of minimal zeros which an exceptional extremal matrix can have is provided

optimization theoretic analysis of stability optimal transmission policy for multiple antenna multiple access channel the philosophy of scheduler design in modern wireless data networks exposes the tendency towards layer spanning optimization cross layer design an important particular goal of joint design of the physical and data link layer appears to be the achievement of the entire stability region of the network in this work we provide the optimization theoretic analysis of the corresponding policy referred to as stability optimal policy in the multiple antenna multiple access channel we characterize some useful features of the policy in particular we state the conditions for optimality of link subset transmission and expose essential differences to the established scheduling approaches such as sum rate maximization this further allows for the statement of necessary and sufficient conditions for the overall stability optimality of successive interference cancellation order finally we present the approach of splitting of the multilink stability problem into the set of single link optimization problems we propose a corresponding iterative optimization method which is an extension of the known concept of iterative waterfilling from

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 new eigensolution of structures via dynamic condensation dynamic condensation or model reduction is a commonly used algorithm to fast estimate some low eigenvalues and corresponding eigenvectors of structures by reducing the order of the original structural model to a smaller one this paper proposes a new eigensolution technique via iterated dynamic condensation the technique retains all the inertia terms associated with the removed degrees of freedom in an iterated form which generates the reduced mass matrix similar to that obtained in the guyan reduction method with a frequency dependent perturbed term the corresponding eigenvalues and eigenvectors of interest are obtained as those of the guyan reduction method with perturbations by using an eigensensitivity based iterative method the effectiveness and accuracy of the proposed technique are numerically verified by using a steel frame and the garteur structure

a new bound and reduce approach of nonconvex quadratic programming problems abstract for the nonconvex quadratic programming problem a new linear programming relaxation bound and reduce algorithm is proposed and its convergence is proved in this algorithm a new hyper rectangle partition technique and a new linear programming relaxation tactics are used at the same time the hyper rectangular reduction method is used to raise its convergent speed the numerical results demonstrate the effectiveness and feasibility of the proposed algorithm

an algebraic approach to hough transforms abstract the main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical hough transform and extend them to general algebraic objects such as affine schemes the main motivation comes from problems of detection of special shapes in medical and astronomical images the classical hough transform has been used mainly to detect simple curves such as lines and circles we generalize this notion using reduced grobner bases of flat families of affine schemes to this end we introduce and develop the theory of hough regularity the theory is highly effective and we give some examples computed with cocoa see 1

an iterative substructuring approach to the calculation of eigensolution and eigensensitivity the eigensolutions and associated eigensensitivities of an analytical model are usually calculated at the global structure level which is time consuming or even prohibitive for large scale structures several substructuring approaches have been proposed that divide the global structure into some manageable substructures and assemble parts of the eigensolutions and eigensensitivities of the substructures to recover those of the global structure however these approaches are not usually accurate as only the lowest eigensolutions and eigensensitivities are retained and the higher modes are excluded in this paper a new iterative substructuring method is proposed to accurately obtain the eigensolutions and eigensensitivities of structures with this new approach the contribution of the higher modes to the reduced eigenequation is retained as a residual flexibility matrix in an iterated form which allows the eigenvalues and eigenvalue derivatives to be obtained from the previous results the eigenvectors and their derivative matrices can be calculated from a reduced eigenequation directly without iteration upon convergence the iterative scheme reproduces the eigensolutions and eigensensitivities of the original structure exactly the computational efficiency and numerical accuracy of the proposed method are verified by the applications to a cantilever plate structure and an actual super tall structure

computation of moore penrose generalized inverses of matrices with meromorphic function entries abstract in this paper given a field with an involutory automorphism we introduce the notion of moore penrose field by requiring that all matrices over the field have moore penrose inverse we prove that only characteristic zero fields can be moore penrose and that the field of rational functions over a moore penrose field is also moore penrose in addition for a matrix with rational functions entries with coefficients in a field k we find sufficient conditions for the elements in k to ensure that the specialization of the moore penrose inverse is the moore penrose inverse of the specialization of the matrix as a consequence we provide a symbolic algorithm that given a matrix whose entries are rational expression over c of finitely many meromorphic functions being invariant by the involutory automorphism computes its moore penrose inverve by replacing the functions by new variables and hence reducing the problem to the case of matrices with complex rational function entries

keypoints and local descriptors of scalar functions on 2d manifolds this paper addresses the problem of describing surfaces using local features and descriptors while methods for the detection of interest points in images and their description based on local image features are very well understood their extension to discrete manifolds has not been well investigated we provide a methodological framework for analyzing real valued functions defined over a 2d manifold embedded in the 3d euclidean space e g photometric information local curvature etc our work is motivated by recent advancements in multiple camera reconstruction and image based rendering of 3d objects there is a growing need for describing object surfaces matching two surfaces or tracking them over time considering polygonal meshes we propose a new methodological framework for the scale space representations of scalar functions defined over such meshes we propose a local feature detector meshdog and region descriptor meshhog unlike the standard image features the proposed surface features capture both the local geometry of the underlying manifold and the scale space differential properties of the real valued function itself we provide a thorough experimental evaluation the repeatability of the feature detector and the robustness of feature descriptor are tested by applying a large number of deformations to the manifold or to the scalar function

a complete characterization of the gap between convexity and sos convexity our first contribution in this paper is to prove that three natural sum of squares sos based sufficient conditions for convexity of polynomials via the definition of convexity its first order characterization and its second order characterization are equivalent these three equivalent algebraic conditions henceforth referred to as sos convexity can be checked by semidefinite programming whereas deciding convexity is np hard if we denote the set of convex and sosconvex polynomials in n variables of degree d with cn d and cn d respectively then our main contribution is to prove that cn d cn d if and only if n 1 or d 2 or n d 2 4 we also present a complete characterization for forms homogeneous polynomials except for the case n d 3 4 which is joint work with g blekherman and is to be published elsewhere our result states that the set cn d of convex forms in n variables of degree d equals the set cn d of sos convex forms if and only if n 2 or d 2 or n d 3 4 to prove these results we present in particular explicit examples of polynomials in c2 6 c2 6 and c3 4 c3 4 and forms in c3 6 c3 6 and c4 4 c4 4 and a general procedure for constructing forms in cn d 2 cn d 2 from nonnegative but not sos forms in n variables and degree d although for disparate reasons the remarkable outcome is that convex polynomials resp forms are sos convex exactly in cases where nonnegative polynomials resp forms are sums of squares as characterized by hilbert

direct method for second order sensitivity analysis of modal strain energy abstract this paper proposed a lagrange based method for calculation of the second order sensitivity of modal strain energy mse values according to scheme of the direct method a lagrange functional of the element mse which added the eigenproblem and the normalization augmented by lagrange multipliers as constraints is constructed firstly after that the lagrange multipliers can be decided by setting variations of the lagrange functional with respect to state variables to zeros and then the sensitivity of mse can be yielded by derivative of the lagrange functional easily the accuracy of the new method and the affection of normalization criterion are verified by the numerical instances of a simply supported beam and a truss structure a portal frame is employed to testify the prediction ability of both the first order and the second order sensitivities of mse values as the numerical example of the portal frame shows the computation complexity of the new method can be reduced significantly in comparison of indirect methods at similar accuracy

stability and instability of fluid models for reentrant lines reentrant lines can be used to model complex manufacturing systems such as wafer fabrication facilities as the first step to the optimal or near optimal scheduling of such lines we investigate their stability in light of a recent theorem of dai dai j g 1995 on positive harris recurrence of multiclass queueing networks a unified approach via fluid models ann appl probab 5 49 77 which states that a scheduling policy is stable if the corresponding fluid model is stable we study the stability and instability of fluid models to do this we utilize piecewise linear lyapunov functions we establish stability of first buffer first served fbfs and last buffer first served lbfs disciplines in all reentrant lines and of all work conserving disciplines in any three buffer reentrant lines for the four buffer network of lu and kumar we characterize the stability region of the lu and kumar policy and show that it is also the global stability region for this network we also study stability and instability of kelly type networks in particular we show that not all work conserving policies are stable for such networks however all work conserving policies are stable in a ring network

comparing lp bounds for queueing networks we consider performance of open multiclass queueing networks under general scheduling policies two linear program lp performance bounds are compared the achievable region method and the approximate linear program with quadratic approximation architecture the latter is shown to give tighter upper and lower bounds

a triangulation approach to asymptotically exact conditions for fuzzy summations many takagi sugeno t s fuzzy control synthesis problems in the literature are expressed as the problem of finding decision variables in a double convex sum fuzzy summation of positive definite matrices matricespsila coefficients in the summation take values in the standard simplex this paper presents a triangulation approach to the problem of generating simplicial partitions of the standard simplex in order to set up a family of sufficient conditions and in parallel another family of necessary ones for fuzzy summations the conditions proposed in this paper are asymptotically exact as the size of the involved simplices decreases its conservativeness vanishes for a sufficiently fine partition sufficiently dense mesh of vertex points the set of conditions is in the form of linear matrix inequalities lmis for which efficient software is available

the achievable region approach to the optimal control of stochastic systems summary the achievable region approach seeks solutions to stochastic optimization problems by characterizing the space of all possible performances the achievable region of the system of interest and optimizing the overall system wide performance objective over this space this is radically different from conventional formulations based on dynamic programming the approach is explained with reference to a simple two class queuing system powerful new methodologies due to the authors and co workers are deployed to analyse a general multiclass queuing system with parallel servers and then to develop an approach to optimal load distribution across a network of interconnected stations finally the approach is used for the first time to analyse a class of intensity control problems