stable numerical solution of a fractional diffusion inverse heat conduction problem the ill posed problem of attempting to recover the boundary temperature and the heat flux functions from one measured transient data temperature at some interior point of a one dimensional semi infinite conductor when the governing linear diffusion equation is of fractional type is discussed a simple algorithm based on space marching mollification techniques is introduced for the numerical solution of the discrete problem stability bounds error estimates and numerical examples of interest are also presented

a hybrid lower bound for parameter estimation of signals with multiple change points change point estimation has received much attention in the literature as it plays a significant role in several signal processing applications however the study of the optimal estimation performance in such context is a difficult task since the unknown parameter vector of interest may contain both continuous and discrete parameters namely the parameters associated with the noise distribution and the change point locations in this paper we handle this by deriving a lower bound on the mean square error of these continuous and discrete parameters specifically we propose a hybrid cramer rao weiss weinstein bound and derive its associated closed form expressions numerical simulations assess the tightness of the proposed bound in the case of gaussian and poisson observations

further relaxations of the semidefinite programming approach to sensor network localization recently a semidefinite programming sdp relaxation approach has been proposed to solve the sensor network localization problem although it achieves high accuracy in estimating the sensor locations the speed of the sdp approach is not satisfactory for practical applications in this paper we propose methods to further relax the sdp relaxation more precisely to relax the single semidefinite matrix cone into a set of small size semidefinite submatrix cones which we call a sub sdp ssdp approach we present two such relaxations although they are weaker than the original sdp relaxation they retain the key theoretical property and numerical experiments show that they are both efficient and accurate the speed of the ssdp is even faster than that of other approaches based on weaker relaxations the ssdp approach may also pave a way to efficiently solving general sdp problems without sacrificing the solution quality

distributed maximum likelihood sensor network localization we propose a class of convex relaxations to solve the sensor network localization problem based on a maximum likelihood ml formulation this class as well as the tightness of the relaxations depends on the noise probability density function pdf of the collected measurements we derive a computational efficient edge based version of this ml convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge based convex programs locally by communicating only with their close neighbors this algorithm relies on the alternating direction method of multipliers admm it converges to the centralized solution it can run asynchronously and it is computation error resilient finally we compare our proposed distributed scheme with other available methods both analytically and numerically and we argue the added value of admm especially for large scale networks

exploiting sparsity in sdp relaxation for sensor network localization a sensor network localization problem can be formulated as a quadratic optimization problem qop for qops semidefinite programming sdp relaxation by lasserre with relaxation order 1 for general polynomial optimization problems pops is known to be equivalent to the sparse sdp relaxation by waki et al with relaxation order 1 except for the size and sparsity of the resulting sdp relaxation problems we show that the sparse sdp relaxation applied to the qop is at least as strong as the biswas ye sdp relaxation for the sensor network localization problem a sparse variant of the biswas ye sdp relaxation which is equivalent to the original biswas ye sdp relaxation is also derived we compare numerically the sparse sdp relaxation applied to the qop the biswas ye sdp relaxation its sparse variant and the edge based sdp relaxation by wang et al to confirm the effectiveness of the proposed techniques for exploiting the sparsity in sdp relaxation for sensor network localization problems the sparse sdp relaxation applied to the qop is much faster than the biswas ye sdp relaxation and the sparse variant of the biswas ye sdp relaxation outperforms all other sdp relaxations in speed

brief constrained linear state estimation a moving horizon approach this article considers moving horizon strategies for constrained linear state estimation additional information for estimating state variables from output measurements is often available in the form of inequality constraints on states noise and other variables formulating a linear state estimation problem with inequality constraints however prevents recursive solutions such as kalman filtering and consequently the estimation problem grows with time as more measurements become available to bound the problem size we explore moving horizon strategies for constrained linear state estimation in this work we discuss some practical and theoretical properties of moving horizon estimation we derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate we also discuss smoothing strategies for moving horizon estimation our framework is solely deterministic

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

a general class of lower bounds in parameter estimation a general class of bayesian lower bounds on moments of the error in parameter estimation is formulated and it is shown that the cramer rao the bhattacharyya the bobrovsky zakai and the weiss weinstein lower bounds are special cases in the class the bounds can be applied to the estimation of vector parameters and any given function of the parameters the extension of these bounds to multiple parameter is discussed

fourier regularization for a backward heat equation abstract in this paper a simple and convenient new regularization method for solving backward heat equation fourier regularization method is given meanwhile some quite sharp error estimates between the approximate solution and exact solution are provided a numerical example also shows that the method works effectively

convergence behavior of interior point algorithms we show that most interior point algorithms for linear programming generate a solution sequence in which every limit point satisfies the strict complementarity condition these algorithms include all path following algorithms and some potential reduction algorithms the result also holds for the monotone complementarity problem if a strict complementarity solution exists in general the limit point is a solution that maximizes the number of its nonzero components among all solutions

decomposition optimization algorithms for distributed radar systems distributed radar systems are capable of enhancing the detection performance by using multiple widely spaced distributed antennas with prior statistic information of targets resource allocation is of critical importance for further improving the system s achievable performance in this paper the total transmitted power is minimized at a given mean square target estimation error we derive two iterative decomposition algorithms for solving this nonconvex constrained optimization problem namely the optimality condition decomposition ocd based and the alternating direction method of multipliers admm based algorithms both the convergence performance and the computational complexity of our algorithms are analyzed theoretically which are then confirmed by our simulation results the ocd method imposes a much lower computational burden per iteration while the admm method exhibits a higher per iteration complexity but as a benefit of its significantly faster convergence speed it requires less iterations therefore the admm imposes a lower total complexity than the ocd the results also show that both of our schemes outperform the state of the art benchmark scheme for the multiple target case in terms of the total power allocated at the cost of some degradation in localization accuracy for the single target case all the three algorithms achieve similar performance our admm algorithm has similar total computational complexity per iteration and convergence speed to those of the benchmark

weiss weinstein bound on multiple change points estimation in the context of multiple change points estimation performance analysis of estimators such as the maximum likelihood is often difficult to assess since the regularity assumptions are not met focusing on the estimators variance one can however use lower bounds on the mean square error in this paper we derive the so called weiss weinstein bound wwb that is known to be an efficient tool in signal processing to obtain a fair overview of the estimation behavior contrary to several works about performance analysis in the change point literature our study is adapted to multiple changes first useful formulas are given for a general estimation problem whatever the considered distribution of the data second closed form expressions are given in the cases of gaussian observations with changes in the mean and or the variance and changes in the mean rate of a poisson distribution furthermore a semidefinite programming formulation of the minimization procedure is given in order to compute the tightest wwb specifically it consists of finding the unique minimum volume covering the set constituted by hyperellipsoid elements that are generated using the derived candidate wwb matrices w r t the so called loewner partial ordering finally simulation results are provided to show the good behavior of the proposed bound

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

robust edge based semidefinite programming relaxation of sensor network localization recently wang zheng boyd and ye siam j optim 19 655 673 2008 proposed a further relaxation of the semidefinite programming sdp relaxation of the sensor network localization problem named edge based sdp esdp in simulation the esdp is solved much faster by interior point method than sdp relaxation and the solutions found are comparable or better in approximation accuracy we study some key properties of the esdp relaxation showing that when distances are exact zero individual trace is not only sufficient but also necessary for a sensor to be correctly positioned by an interior solution we also show via an example that when distances are inexact zero individual trace is insufficient for a sensor to be accurately positioned by an interior solution we then propose a noise aware robust version of esdp relaxation for which small individual trace is necessary and sufficient for a sensor to be accurately positioned by a certain analytic center solution assuming the noise level is sufficiently small for this analytic center solution the position error for each sensor is shown to be in the order of the square root of its trace lastly we propose a log barrier penalty coordinate gradient descent method to find such an analytic center solution in simulation this method is much faster than interior point method for solving esdp and the solutions found are comparable in approximation accuracy moreover the method can distribute its computation over the sensors via local communication making it practical for positioning and tracking in real time

the fractional order governing equation of levy motion a governing equation of stable random walks is developed in one dimension this fokker planck equation is similar to and contains as a subset the second order advection dispersion equation ade except that the order a of the highest derivative is fractional e g the 1 65th derivative fundamental solutions are levy s a stable densities that resemble the gaussian except that they spread proportional to time 1 a have heavier tails and incorporate any degree of skewness the measured variance of a plume undergoing levy motion would grow faster than fickian plume at a rate of time 2 a where 0 a 2 the equation is parsimonious since the parameters are not functions of time or distance the scaling behavior of plumes that undergo levy motion is accounted for by the fractional derivatives which are appropriate measures of fractal functions in real space the fractional derivatives are integrodifferential operators so the fractional ade describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space

time fractional ihcp with caputo fractional derivatives the numerical solution of the time fractional inverse heat conduction problem tfihcp on a finite slab is investigated in the presence of measured noisy data when the time fractional derivative is interpreted in the sense of caputo a finite difference space marching scheme with adaptive regularization using mollification techniques is introduced error estimates are derived for the numerical solution of the mollified problem and several numerical examples of interest are provided

the modified cramer rao bound in vector parameter estimation in this paper we extend the scalar modified cramer rao bound mcrb to the estimation of a vector of nonrandom parameters in the presence of nuisance parameters the resulting bound is denoted with the acronym mcrvb where v stands for vector as with the scalar bound the mcrvb is generally looser than the conventional crvb but the two bounds are shown to coincide in some situations of practical interest the mcrvb is applied to the joint estimation of carrier frequency phase and symbol epoch of a linearly modulated waveform corrupted by correlated impulsive noise encompassing white gaussian noise as a particular case wherein data symbols and noise power are regarded as nuisance parameters in this situation calculation of the conventional crvb is infeasible while application of the mcrvb leads to simple useful expressions with moderate analytical effort when specialized to the case of white gaussian noise the mcrvb yields results already available in the literature in fragmentary form and simplified contexts

robust localization of nodes and time recursive tracking in sensor networks using noisy range measurements simultaneous localization and tracking slat in sensor networks aims to determine the positions of sensor nodes and a moving target in a network given incomplete and inaccurate range measurements between the target and each of the sensors one of the established methods for achieving this is to iteratively maximize a likelihood function ml of positions given the observed ranges which requires initialization with an approximate solution to avoid convergence towards local extrema this paper develops methods for handling both gaussian and laplacian noise the latter modeling the presence of outliers in some practical ranging systems that adversely affect the performance of localization algorithms designed for gaussian noise a modified euclidean distance matrix edm completion problem is solved for a block of target range measurements to approximately set up initial sensor target positions and the likelihood function is then iteratively refined through majorization minimization mm to avoid the computational burden of repeatedly solving increasingly large edm problems in time recursive operation an incremental scheme is exploited whereby a new target node position is estimated from previously available node target locations to set up the iterative ml initial point for the full spatial configuration the above methods are first derived under gaussian noise assumptions and modifications for laplacian noise are then considered analytically the main challenges to overcome in the laplacian case stem from the non differentiability of l1 norms that arise in the various cost functions simulation results show that the proposed algorithms significantly outperform existing localization methods in the presence of outliers while providing comparable performance for gaussian noise

a posteriori regularization parameter choice rule for a modified kernel method for a time fractional inverse diffusion problem abstract in this paper we consider a time fractional inverse diffusion problem tfidp where the measured data is given at x 1 and the solution is required in the interval 0 x 1 we show that tfidp is severely ill posed and further apply a modified kernel method to deal with this problem based on the solution in the frequency domain the convergence estimate is obtained by using a posteriori parameter choice rule numerical examples show that the proposed method works effectively

an sdp based divide and conquer algorithm for large scale noisy anchor free graph realization we propose the disco algorithm for graph realization in mathbb r d given sparse and noisy short range intervertex distances as inputs our divide and conquer algorithm works as follows when a group has a sufficiently small number of vertices the basis step is to form a graph realization by solving a semidefinite program the recursive step is to break a large group of vertices into two smaller groups with overlapping vertices these two groups are solved recursively and the subconfigurations are stitched together using the overlapping atoms to form a configuration for the larger group at intermediate stages the configurations are improved by gradient descent refinement the algorithm is applied to the problem of determining protein moleculer structure tests are performed on molecules taken from the protein data bank database for each molecule given 20 30 of the inter atom distances less than 6a that are corrupted by a high level of noise disco is able to reliably and efficiently reconstruct the conformation of large molecules in particular given 30 of distances with 20 multiplicative noise a 13000 atom conformation problem is solved within an hour with a root mean square deviation of 1 6a

global continuation for distance geometry problems distance geometry problems arise in the determination of protein structure we consider the case where only a subset of the distances between atoms is given and formulate this distance geometry problem as a global minimization problem with special structure we show that global smoothing techniques and a continuation approach for global optimization can be used to determine global solutions of this problem reliably and efficiently the global continuation approach determines a global solution with less computational effort than is required by a standard multistart algorithm moreover the continuation approach usually finds the global solution from any given starting point while the multistart algorithm tends to fail

a distributed sdp approach for large scale noisy anchor free graph realization with applications to molecular conformation we propose a distributed algorithm for solving euclidean metric realization problems arising from large 3 d graphs using only noisy distance information and without any prior knowledge of the positions of any of the vertices in our distributed algorithm the graph is first subdivided into smaller subgraphs using intelligent clustering methods then a semidefinite programming relaxation and gradient search method are used to localize each subgraph finally a stitching algorithm is used to find affine maps between adjacent clusters and the positions of all points in a global coordinate system are then derived in particular we apply our method to the problem of finding the 3 d molecular configurations of proteins based on a limited number of given pairwise distances between atoms the protein molecules all with known molecular configurations are taken from the protein data bank our algorithm is able to reconstruct reliably and efficiently the configurations of large protein molecules from a limited number of pairwise distances corrupted by noise without incorporating domain knowledge such as the minimum separation distance constraints derived from van der waals interactions

spectral regularization method for solving a time fractional inverse diffusion problem abstract in this paper we consider an inverse problem for a time fractional diffusion equation with one dimensional semi infinite domain the temperature and heat flux are sought from a measured temperature history at a fixed location inside the body we show that such problem is severely ill posed and further apply a spectral regularization method to solve it based on the solution given by the fourier method convergence estimates are presented under a priori bound assumptions for the exact solution finally numerical examples are given to show that the proposed numerical method is effective

d map distributed maximum a posteriori probability estimation of dynamic systems this paper develops a framework for the estimation of a time varying random signal using a distributed sensor network given a continuous time model sensors collect noisy observations and produce local estimates according to the discrete time equivalent system defined by the sampling period of observations estimation is performed using a maximum a posteriori probability estimator map within a given window of interest to mediate the incorporation of information from other sensors we introduce lagrange multipliers to penalize the disagreement between neighboring estimates we show that the resulting distributed d map algorithm is able to track dynamical signals with a small error this error is characterized in terms of problem constants and vanishes with the sampling time as long as the log likelihood function which is assumed to be log concave satisfies a smoothness condition we implement the d map algorithm for a linear and a nonlinear system model to show that the performance corroborates with theoretical findings

the molecule problem exploiting structure in global optimization the molecule problem is that of determining the relative locations of a set of objects in euclidean space relying only upon a sparse set of pairwise distance measurements this np hard problem has applications in the determination of molecular conformation the molecule problem can be naturally expressed as a continuous global optimization problem but it also has a rich combinatorial structure this paper investigates how that structure can be exploited to simplify the optimization problem in particular we present a novel divide and conquer algorithm in which a large global optimization problem is replaced by a sequence of smaller ones since the cost of the optimization can grow exponentially with problem size this approach holds the promise of a substantial improvement in performance our algorithmic development relies upon some recently published results in graph theory we describe an implementation of this algorithm and report some results of its performance on a sample molecule

general classes of performance lower bounds for parameter estimation part ii bayesian bounds in this paper a new class of bayesian lower bounds is proposed derivation of the proposed class is performed via projection of each entry of the vector function to be estimated on a hilbert subspace of l2 this hilbert subspace contains linear transformations of elements in the domain of an integral transform applied on functions used for computation of bounds in the weiss weinstein class the integral transform generalizes the traditional derivative and sampling operators used for computation of existing performance lower bounds such as the bayesian cramer rao bayesian bhattacharyya and weiss weinstein bounds it is shown that some well known bayesian lower bounds can be derived from the proposed class by specific choice of the integral transform kernel a new lower bound is derived from the proposed class using the fourier transform kernel the proposed bound is compared with other existing bounds in terms of signal to noise ratio snr threshold region prediction in the problem of frequency estimation the bound is shown to be computationally manageable and provides better prediction of the snr threshold region exhibited by the maximum a posteriori probability map and minimum mean square error mmse estimators

conditions for unique graph realizations the graph realization problem is that of computing the relative locations of a set of vertices placed in euclidean space relying only upon some set of inter vertex distance measurements this paper is concerned with the closely related problem of determining whether or not a graph has a unique realization both these problems are np hard but the proofs rely upon special combinations of edge lengths if one assumes the vertex locations are unrelated then the uniqueness question can be approached from a purely graph theoretic angle that ignores edge lengths this paper identifies three necessary graph theoretic conditions for a graph to have a unique realization in any dimension efficient sequential and nc algorithms are presented for each condition although these algorithms have very different flavors in different dimensions

distributed localization with mixed measurements under switching topologies abstract this paper investigates the distributed localization problem of sensor networks with mixed measurements each node holds a local coordinate system without a common orientation and is capable of measuring only one type of information either distance bearing or relative position to near by nodes thus three types of measurements are mixed in the sensor networks moreover the communication topologies in the sensor networks may be time varying due to unreliable communications this paper develops a fully distributed algorithm called bcdl barycentric coordinate based distributed localization where each node starts from a random initial guess about its true coordinate and converges to the true coordinate via only local node interactions the key idea in bcdl is to establish a unified linear equation constraints for the sensor coordinates by using the barycentric coordinates of each node with respect to its neighbors though the sensor nodes may have different types of measurements then a distributed iterative algorithm is proposed to solve the linear equations under time varying communication networks a necessary and sufficient graphical condition is obtained to ensure global convergence of the distributed algorithm

diland an algorithm for distributed sensor localization with noisy distance measurements we present an algorithm for distributed sensor localization with noisy distance measurements diland that extends and makes the dlre more robust dlre is a distributed sensor localization algorithm in rm m 1 introduced in our previous work ieee trans signal process vol 57 no 5 pp 2000 2016 may 2009 diland operates when 1 the communication among the sensors is noisy 2 the communication links in the network may fail with a nonzero probability and 3 the measurements performed to compute distances among the sensors are corrupted with noise the sensors which do not know their locations lie in the convex hull of at least m 1 anchors nodes that know their own locations under minimal assumptions on the connectivity and triangulation of each sensor in the network we show that under the broad random phenomena described above diland converges almost surely a s to the exact sensor locations

euclidean distance geometry and applications euclidean distance geometry is the study of euclidean geometry based on the concept of distance this is useful in several applications where the input data consist of an incomplete set of distances and the output is a set of points in euclidean space realizing those given distances we survey the theory of euclidean distance geometry and its most important applications with special emphasis on molecular conformation problems

the joint map ml criterion and its relation to ml and to extended least squares the joint maximum a posteriori maximum likelihood jmap ml estimation criterion can serve as an alternative to the maximum likelihood ml criterion when estimating parameters from an observed data vector whenever another unobserved data vector is involved rather than maximize the probability of the observed data with respect to the parameters jmap ml maximizes the joint probability of the observed and unobserved data with respect to both the unknown parameters and the unobserved data in this paper we characterize the relation between the ml and jmap ml estimates in the gaussian case and provide insight into the apparent bias of jmap ml although jmap ml is an inconsistent estimator we show that with short data records it is often preferable to ml in terms of both bias and variance we also identify jmap ml as a special case of the deterministic extended least squares xls criterion we indicate a general relation between a possible maximization algorithm for jmap ml and the well known estimation maximization em algorithm

exploiting sparsity in semidefinite programming via matrix completion i general framework a critical disadvantage of primal dual interior point methods compared to dual interior point methods for large scale semidefinite programs sdps has been that the primal positive semidefinite matrix variable becomes fully dense in general even when all data matrices are sparse based on some fundamental results about positive semidefinite matrix completion this article proposes a general method of exploiting the aggregate sparsity pattern over all data matrices to overcome this disadvantage our method is used in two ways one is a conversion of a sparse sdp having a large scale positive semidefinite matrix variable into an sdp having multiple but smaller positive semidefinite matrix variables to which we can effectively apply any interior point method for sdps employing a standard block diagonal matrix data structure the other way is an incorporation of our method into primal dual interior point methods which we can apply directly to a given sdp in part ii of this article we will investigate an implementation of such a primal dual interior point method based on positive definite matrix completion and report some numerical results

distributed moving horizon estimation for linear constrained systems this paper presents a novel distributed estimation algorithm based on the concept of moving horizon estimation under weak observability conditions we prove convergence of the state estimates computed by any sensors to the correct state even when constraints on noise and state variables are taken into account in the estimation process simulation examples are provided in order to show the main features of the proposed method

two regularization methods and the order optimal error estimates for a sideways parabolic equation in this paper we consider an inverse heat conduction problem which appears in some applied subjects this problem is ill posed in the sense that the solution if it exists does not depend continuously on the data a tikhonov type s regularization method and a fourier regularization method are applied to formulate regularized solutions which are stably convergent to the exact ones with order optimal error estimates a numerical example shows that the computational effect of these methods are all satisfactory

on a registration based approach to sensor network localization we consider a registration based approach for localizing sensor networks from range measurements this is based on the assumption that one can find overlapping cliques spanning the network that is for each sensor one can identify geometric neighbors for which all inter sensor ranges are known such cliques can be efficiently localized using multidimensional scaling however since each clique is localized in some local coordinate system we are required to register them in a global coordinate system in other words our approach is based on transforming the localization problem into a problem of registration in this context the main contributions are as follows first we describe an efficient method for partitioning the network into overlapping cliques second we study the problem of registering the localized cliques and formulate a necessary rigidity condition for uniquely recovering the global sensor coordinates in particular we present a method for efficiently testing rigidity and a proposal for augmenting the partitioned network to enforce rigidity a recently proposed semidefinite relaxation of global registration is used for registering the cliques we present simulation results on random and structured sensor networks to demonstrate that the proposed method compares favourably with state of the art methods in terms of run time accuracy and scalability

on the o 1 n convergence rate of the douglas rachford alternating direction method alternating direction methods adms have been well studied in the literature and they have found many efficient applications in various fields in this note we focus on the douglas rachford adm scheme proposed by glowinski and marrocco and we aim at providing a simple approach to estimating its convergence rate in terms of the iteration number the linearized version of this adm scheme which is known as the split inexact uzawa method in the image processing literature is also discussed

well posedness for the fifth order shallow water equations abstract the cauchy problems for some kind of fifth order shallow water equations t u x 5 u x 3 u x u f u x u x 2 u 0 x t r r are considered by the fourier restriction norm method where nonlinear terms f u x u x 2 u are x u k k 2 3 u x 2 u or x u x 2 u respectively the local well posedness is established for data in h s r with s 7 4 for the kawahara equation f x u 2 and is established for data in h s r with s 1 4 for the modified kawahara equation f x u 3 respectively moreover the local result is established for data in h s r with s 0 if f u x 2 u and is established for data in h s r with s 1 4 if f x u x 2 u respectively

the fastest mixing markov process on a graph and a connection to a maximum variance unfolding problem we consider a markov process on a connected graph with edges labeled with transition rates between the adjacent vertices the distribution of the markov process converges to the uniform distribution at a rate determined by the second smallest eigenvalue lambda 2 of the laplacian of the weighted graph in this paper we consider the problem of assigning transition rates to the edges so as to maximize lambda 2 subject to a linear constraint on the rates this is the problem of finding the fastest mixing markov process fmmp on the graph we show that the fmmp problem is a convex optimization problem which can in turn be expressed as a semidefinite program and therefore effectively solved numerically we formulate a dual of the fmmp problem and show that it has a natural geometric interpretation as a maximum variance unfolding mvu problem the problem of choosing a set of points to be as far apart as possible measured by their variance while respecting local distance constraints this mvu problem is closely related to a problem recently proposed by weinberger and saul as a method for unfolding high dimensional data that lies on a low dimensional manifold the duality between the fmmp and mvu problems sheds light on both problems and allows us to characterize and in some cases find optimal solutions

solving semidefinite quadratic linear programs using sdpt3 this paper discusses computational experiments with linear optimization problems involving semidefinite quadratic and linear cone constraints sqlps many test problems of this type are solved using a new release of sdpt3 a matlab implementation of infeasible primal dual path following algorithms the software developed by the authors uses mehrotra type predictor corrector variants of interior point methods and two types of search directions the hkm and nt directions a discussion of implementation details is provided and computational results on problems from the sdplib and dimacs challenge collections are reported

wavelet and fourier methods for solving the sideways heat equation we consider an inverse heat conduction problem the sideways heat equation which is a model of a problem where one wants to determine the temperature on both sides of a thick wall but where one side is inaccessible to measurements mathematically it is formulated as a cauchy problem for the heat equation in a quarter plane with data given along the line x 1 where the solution is wanted for 0 leq x 1 the problem is ill posed in the sense that the solution if it exists does not depend continuously on the data we consider stabilizations based on replacing the time derivative in the heat equation by wavelet based approximations or a fourier based approximation the resulting problem is an initial value problem for an ordinary differential equation which can be solved by standard numerical methods e g a runge kutta method we discuss the numerical implementation of fourier and wavelet methods for solving the sideways heat equation theory predicts that the fourier method and a method based on meyer wavelets will give equally good results our numerical experiments indicate that also a method based on daubechies wavelets gives comparable accuracy as test problems we take model equations with constant and variable coefficients we also solve a problem from an industrial application with actual measured data

bayesian analysis of a poisson process with a change point summary a bayesian approach to estimation and hypothesis testing for a poisson process with a change point is developed and an example given

recovery of the solute concentration and dispersion flux in an inhomogeneous time fractional diffusion equation abstract in this paper we consider recovery of solute concentration and dispersion flux in an inhomogeneous time fractional diffusion equation we prove that the considered problem is ill posed i e the solution does not depend continuously on the data in order to obtain a regularized solution we propose a truncation regularization method the convergence estimates are established under some priori bound assumptions for the exact solution we present three numerical examples to show efficiency of the method

a computational method for a cauchy problem of laplace s equation abstract in this paper we consider the cauchy problem for the laplace s equation where the cauchy data is given at x 1 and the solution is sought in the interval 0 x 1 a spectral method together with choice of regularization parameter is presented and error estimate is obtained combining the method of lines we implement the numerical solution a numerical example shows that the method works well

joint segmentation of multivariate astronomical time series bayesian sampling with a hierarchical model astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series this paper approaches such problems using bayesian priors to represent relationships between signals with various degrees of certainty and not just rigid constraints the segmentation is conducted by using a hierarchical bayesian approach to a piecewise constant poisson rate model a gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters results obtained with synthetic and real photon counting data illustrate the performance of the proposed algorithm

molecular embedding via a second order dissimilarity parameterized approach we describe a computational approach to the embedding problem in structural molecular biology the approach is based on a dissimilarity parameterization of the problem that leads to a large scale nonconvex bound constrained matrix optimization problem the underlying idea is that an increased number of independent variables decouples the complicated effects of varying the location of individual atoms in coordinate based formulations numerical tests support this hypothesis and indicate that the optimization problem that results is relatively benign and easy to solve despite being large and nonconvex we can solve problems with millions of independent variables in a few dozen to a few score optimization iterations the nonconvexity arises due to matrix rank constraints in the problem and we focus on their efficient computational treatment we present numerical results for a number of synthetic and real protein data sets and comment on features of real experimental data that can cause computational difficulties

efficient convex relaxation methods for robust target localization by a sensor network using time differences of arrivals we consider the problem of target localization by a network of passive sensors when an unknown target emits an acoustic or a radio signal its position can be localized with multiple sensors using the time difference of arrival tdoa information in this paper we consider the maximum likelihood formulation of this target localization problem and provide efficient convex relaxations for this nonconvex optimization problem we also propose a formulation for robust target localization in the presence of sensor location errors two cramer rao bounds are derived corresponding to situations with and without sensor node location errors simulation results confirm the efficiency and superior performance of the convex relaxation approach as compared to the existing least squares based approach when large sensor node location errors are present

distributed semidefinite programming with application to large scale system analysis distributed algorithms for solving coupled semidefinite programs commonly require many iterations to converge they also put high computational demand on the computational agents in this paper we show that in case the coupled problem has an inherent tree structure it is possible to devise an efficient distributed algorithm for solving such problems the proposed algorithm relies on predictor corrector primal dual interior point methods where we use a message passing algorithm to compute the search directions distributedly message passing here is closely related to dynamic programming over trees this allows us to compute the exact search directions in a finite number of steps this is because computing the search directions requires a recursion over the tree structure and hence terminates after an upward and downward pass through the tree furthermore this number can be computed a priori and only depends on the coupling structure of the problem we use the proposed algorithm for analyzing robustness of large scale uncertain systems distributedly we test the performance of this algorithm using numerical examples

distributed wireless sensor network localization via sequential greedy optimization algorithm node localization is essential to most applications of wireless sensor networks wsns in this paper we consider both range based node localization and range free node localization with uncertainties in range measurements radio range and anchor positions first a greedy optimization algorithm named sequential greedy optimization sgo algorithm is presented which is more suitable for distributed optimization in networks than the classical nonlinear gauss seidel algorithm then a unified optimization framework is proposed for both range based localization and range free localization and two convex localization formulations are obtained based on semidefinite programming sdp relaxation techniques by applying the sgo algorithm to the edge based sdp relaxation formulation we propose a second order cone programming socp based distributed node localization algorithm two distributed refinement algorithms are also proposed by using the sgo algorithm to nonconvex localization formulations the proposed localization algorithms all can be implemented partially asynchronously in networks finally extensive simulations are conducted to demonstrate the efficiency and accuracy of the proposed distributed localization algorithms

exact reconstruction of euclidean distance geometry problem using low rank matrix completion the euclidean distance geometry problem arises in a wide variety of applications from determining molecular conformations in computational chemistry to localization in sensor networks when the distance information is incomplete the problem can be formulated as a nuclear norm minimization problem in this paper this minimization program is recast as a matrix completion problem of a low rank r gram matrix with respect to a suitable basis the well known restricted isometry property cannot be satisfied in this scenario instead a dual basis approach is introduced to theoretically analyze the reconstruction problem if the gram matrix satisfies certain coherence conditions with parameter nu the main result shows that the underlying configuration of n points can be recovered with very high probability from o nr nu log 2 n uniformly random samples computationally simple and fast algorithms are designed to solve the euclidean distance geometry problem numerical tests on different 3 d data and protein molecules validate the effectiveness and efficiency of the proposed algorithms

consensus control for linear systems with optimal energy cost in this paper we design an optimal energy cost controller for linear systems asymptotic consensus given the topology of the graph the controller depends only on relative information of the agents

simple and fast convex relaxation method for cooperative localization in sensor networks using range measurements we address the sensor network localization problem given noisy range measurements between pairs of nodes we approach the nonconvex maximum likelihood formulation via a known simple convex relaxation we exploit its favorable optimization properties to the full to obtain an approach that is completely distributed has a simple implementation at each node and capitalizes on an optimal gradient method to attain fast convergence we offer a parallel but also an asynchronous flavor both with theoretical convergence guarantees and iteration complexity analysis experimental results establish leading performance our algorithms top the accuracy of a comparable state of the art method by one order of magnitude using one order of magnitude fewer communications

a barankin type lower bound on the estimation error of a hybrid parameter vector the barankin 1949 bound is a realizable lower bound on the mean square error mse of any unbiased estimator of a nonrandom parameter vector we present a barankin type bound which is useful in problems where there is a prior knowledge on some of the parameters to be estimated that is the parameter vector is a hybrid vector in the sense that some of its entries are deterministic while other are random variables we present a simple expression for a positive definite matrix which provides bounds on the covariance of any unbiased estimator of the nonrandom parameters and an estimator of the random parameters simultaneously we show that the barankin bound for deterministic parameters estimation and the bobrovsky zakai 1976 bound for random parameters estimation are special cases of our proposed bound

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

general classes of performance lower bounds for parameter estimation part i non bayesian bounds for unbiased estimators in this paper a new class of lower bounds on the mean square error mse of unbiased estimators of deterministic parameters is proposed derivation of the proposed class is performed by projecting each entry of the vector of estimation error on a hilbert subspace of l2 this hilbert subspace contains linear transformations of elements in the domain of an integral transform of the likelihood ratio function the integral transform generalizes the traditional derivative and sampling operators which are applied on the likelihood ratio function for computation of performance lower bounds such as cramer rao bhattacharyya and mcaulay seidman bounds it is shown that some well known lower bounds on the mse of unbiased estimators can be derived from this class by modifying the kernel of the integral transform a new lower bound is derived from the proposed class using the kernel of the fourier transform in comparison with other existing bounds the proposed bound is computationally manageable and provides better prediction of the threshold region of the maximum likelihood estimator in the problem of single tone estimation

second order cone programming relaxation of sensor network localization the sensor network localization problem has been much studied recently biswas and ye proposed a semidefinite programming sdp relaxation of this problem which has various nice properties and for which a number of solution methods have been proposed here we study a second order cone programming socp relaxation of this problem motivated by its simpler structure and its potential to be solved faster than sdp we show that the socp relaxation though weaker than the sdp relaxation has nice properties that make it useful as a problem preprocessor in particular sensors that are uniquely positioned among interior solutions of the socp relaxation are accurate up to the square root of the distance error thus these sensors which are easily identified are accurately positioned in our numerical simulation the interior solution found can accurately position up to 80 90p of the sensors we also propose a smoothing coordinate gradient descent method for finding an interior solution that is faster than an interior point method

exploiting sparsity in semidefinite programming via matrix completion ii implementation and numerical results in part i of this series of articles we introduced a general framework of exploiting the aggregate sparsity pattern over all data matrices of large scale and sparse semidefinite programs sdps when solving them by primal dual interior point methods this framework is based on some results about positive semidefinite matrix completion and it can be embodied in two different ways one is by a conversion of a given sparse sdp having a large scale positive semidefinite matrix variable into an sdp having multiple but smaller positive semidefinite matrix variables the other is by incorporating a positive definite matrix completion itself in a primal dual interior point method the current article presents the details of their implementations we introduce new techniques to deal with the sparsity through a clique tree in the former method and through new computational formulae in the latter one numerical results over different classes of sdps show that these methods can be very efficient for some problems

consensus in ad hoc wsns with noisy links part i distributed estimation of deterministic signals we deal with distributed estimation of deterministic vector parameters using ad hoc wireless sensor networks wsns we cast the decentralized estimation problem as the solution of multiple constrained convex optimization subproblems using the method of multipliers in conjunction with a block coordinate descent approach we demonstrate how the resultant algorithm can be decomposed into a set of simpler tasks suitable for distributed implementation different from existing alternatives our approach does not require the centralized estimator to be expressible in a separable closed form in terms of averages thus allowing for decentralized computation even of nonlinear estimators including maximum likelihood estimators mle in nonlinear and non gaussian data models we prove that these algorithms have guaranteed convergence to the desired estimator when the sensor links are assumed ideal furthermore our decentralized algorithms exhibit resilience in the presence of receiver and or quantization noise in particular we introduce a decentralized scheme for least squares and best linear unbiased estimation blue and establish its convergence in the presence of communication noise our algorithms also exhibit potential for higher convergence rate with respect to existing schemes corroborating simulations demonstrate the merits of the novel distributed estimation algorithms