determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

a theoretical analysis of noisy sparse subspace clustering on dimensionality reduced data subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low dimensional linear subspace in many practical scenarios the dimensionality of data points to be clustered is compressed due to the constraints of measurement computation or privacy in this paper we study the theoretical properties of a popular subspace clustering algorithm named sparse subspace clustering ssc and establish formal success conditions of ssc on dimensionality reduced data our analysis applies to the most general fully deterministic model where both underlying subspaces and data points within each subspace are deterministically positioned and also a wide range of dimensionality reduction techniques e g gaussian random projection uniform subsampling and sketching that fall into a subspace embedding framework finally we apply our analysis to a differentially private ssc algorithm and established both privacy and utility guarantees of the proposed method

a fast collocation method for an inverse boundary value problem in this paper we present an implementation of a fast multiscale collocation method for boundary integral equations of the second kind and its application to solving an inverse boundary value problem of recovering a coefficient function from a boundary measurement we illustrate by numerical examples the insensitive nature of the map from the coefficient to measurement and design and test a gauss newton iteration algorithm for obtaining the best estimate of the unknown coefficient from the given measurement based on a least squares formulation

a multibody factorization method for independently moving objects the structure from motion problem has been extensively studied in the field of computer vision yet the bulk of the existing work assumes that the scene contains only a single moving object the more realistic case where an unknown number of objects move in the scene has received little attention especially for its theoretical treatment in this paper we present a new method for separating and recovering the motion and shape of multiple independently moving objects in a sequence of images the method does not require prior knowledge of the number of objects nor is dependent on any grouping of features into an object at the image level for this purpose we introduce a mathematical construct of object shapes called the shape interaction matrix which is invariant to both the object motions and the selection of coordinate systems this invariant structure is computable solely from the observed trajectories of image features without grouping them into individual objects once the matrix is computed it allows for segmenting features into objects by the process of transforming it into a canonical form as well as recovering the shape and motion of each object the theory works under a broad set of projection models scaled orthography paraperspective and affine but they must be linear so it excludes projective cameras

conjugate gradient method for the robin inverse problem associated with the laplace equation this paper studies a non linear inverse problem associated with the laplace equation of identifying the robin coefficient from boundary measurements a variational formulation of the problem is suggested thereby transforming it into an optimization problem mathematical properties relevant to its numerical computation are established the optimization problem is solved using the conjugate gradient method in conjunction with the discrepancy principle and the algorithm is implemented using the boundary element method numerical results are presented for several benchmark problems with both exact and noisy data and the convergence of the algorithm with respect to mesh refinement and decreasing the amount of noise in the data is investigated copyright 2006 john wiley sons ltd

cross term forwarding for systems with time delay this paper presents a lyapunov based control design method for nonlinear systems with time delay the key step is construction of a composite lyapunov functionalv for a stable cascade this functional consists of lyapunov functionals for the subsystems and a cross term defined by an infinite integral the ldquol g v typerdquo control law is then employed to achieve global asymptotic stability the design procedure can be applied recursively to stabilize complex feedforward structures when applied to a linear cascade it gives a formula for the control law even if some parts of the system can only be stabilized through channels with multiple non commensurate or distributed delays

detection of mines by electric measurements in a homogeneous region omega of earth with conductivity 1 a mine is possibly buried occupying a region d and having conductivity ne 1 d is unknown but meas d geqq c 0 we let electric current enter omega at some point of partial omega and exit it at another point of partial omega and we measure the resulting potential at some open portion of partial omega it is proved that if the error in the measurements is small enough then one can assert whether or not a mine d is in fact buried in omega some results on the location of d are also given

the price of robustness a robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended under this approach we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes a concern with such an approach is that it might be too conservative in this paper we propose an approach that attempts to make this trade off more attractive that is we investigate ways to decrease what we call the price of robustness in particular we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations an attractive aspect of our method is that the new robust formulation is also a linear optimization problem thus we naturally extend our methods to discrete optimization problems in a tractable way we report numerical results for a portfolio optimization problem a knapsack problem and a problem from the net lib library

subspace learning by l0 induced sparsity subspace clustering methods partition the data that lie in or close to a union of subspaces in accordance with the subspace structure such methods with sparsity prior such as sparse subspace clustering ssc elhamifar and vidal in ieee trans pattern anal mach intell 35 11 2765 2781 2013 with the sparsity induced by the ell 1 norm are demonstrated to be effective in subspace clustering most of those methods require certain assumptions e g independence or disjointness on the subspaces however these assumptions are not guaranteed to hold in practice and they limit the application of existing sparse subspace clustering methods in this paper we propose ell 0 induced sparse subspace clustering ell 0 ssc in contrast to the required assumptions such as independence or disjointness on subspaces for most existing sparse subspace clustering methods we prove that ell 0 ssc guarantees the subspace sparse representation a key element in subspace clustering for arbitrary distinct underlying subspaces almost surely under the mild i i d assumption on the data generation we also present the no free lunch theorem which shows that obtaining the subspace representation under our general assumptions can not be much computationally cheaper than solving the corresponding ell 0 sparse representation problem of ell 0 ssc a novel approximate algorithm named approximate ell 0 ssc a ell 0 ssc is developed which employs proximal gradient descent to obtain a sub optimal solution to the optimization problem of ell 0 ssc with theoretical guarantee the sub optimal solution is used to build a sparse similarity matrix upon which spectral clustering is performed for the final clustering results extensive experimental results on various data sets demonstrate the superiority of a ell 0 ssc compared to other competing clustering methods furthermore we extend ell 0 ssc to semi supervised learning by performing label propagation on the sparse similarity matrix learnt by a ell 0 ssc and demonstrate the effectiveness of the resultant semi supervised learning method termed ell 0 sparse subspace label propagation ell 0 sslp

lambertian reflectance and linear subspaces we prove that the set of all lambertian reflectance functions the mapping from surface normals to intensities obtained with arbitrary distant light sources lies close to a 9d linear subspace this implies that in general the set of images of a convex lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low dimensional linear subspace explaining prior empirical results we also provide a simple analytic characterization of this linear space we obtain these results by representing lighting using spherical harmonics and describing the effects of lambertian materials as the analog of a convolution these results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions we also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4d linear space we apply these algorithms to perform face recognition by finding the 3d model that best matches a 2d query image

on uniqueness of recovery of a discontinuous conductivity coefficient on considere le probleme de retrouver le coefficient a de l equation elliptique div a u 0 dans un domaine avec la condition aux limites u sur quand u n est donnee pour tout regulier on demontre l unicite pour a a 0 b discontinu ou est la fonction indicateur d un ensemble ouvert a o est une fonction c 2 donnee et b est une fonction c 2 inconnue

a geometric analysis of subspace clustering with outliers this paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower dimensional planes as is common in computer vision or unsupervised learning applications we do not know in advance how many subspaces there are nor do we have any information about their dimensions we develop a novel geometric analysis of an algorithm named sparse subspace clustering ssc 11 which signicantly broadens the range of problems where it is provably eective for instance we show that ssc can recover multiple subspaces each of dimension comparable to the ambient dimension we also prove that ssc can correctly cluster data points even when the subspaces of interest intersect further we develop an extension of ssc that succeeds when the data set is corrupted with possibly overwhelmingly many outliers underlying our analysis are clear geometric insights which may bear on other sparse recovery problems a numerical study complements our theoretical analysis and demonstrates the eectiveness of these methods

identification of contact regions in semiconductor transistors by level set methods in this paper we present the formulation of level set methods for the inverse problem of identifying an interface in the coefficient of an elliptic equation from a boundary measurement this problem arises from the modeling of the identification of contact regions by boundary measurements for semiconductor transistors we propose the gauss newton direction as the interface velocity and implement the scheme for a parameterized class of interfaces

fast bayesian approach for parameter estimation this paper presents two techniques i e the proper orthogonal decomposition pod and the stochastic collocation method scm for constructing surrogate models to accelerate the bayesian inference approach for parameter estimation problems associated with partial differential equations pod is a model reduction technique that derives reduced order models using an optimal problem adapted basis to effect significant reduction of the problem size and hence computational cost scm is an uncertainty propagation technique that approximates the parameterized solution and reduces further forward solves to function evaluations the utility of the techniques is assessed on the non linear inverse problem of probabilistically calibrating scalar robin coefficients from boundary measurements arising in the quenching process and non destructive evaluation a hierarchical bayesian model that handles flexibly the regularization parameter and the noise level is employed and the posterior state space is explored by the markov chain monte carlo the numerical results indicate that significant computational gains can be realized without sacrificing the accuracy

truncated predictor feedback control for exponentially unstable linear systems with time varying input delay abstract the stabilization of exponentially unstable linear systems with time varying input delay is considered in this paper we extend the truncated predictor feedback tpf design method which was recently developed for systems with all poles on the closed left half plane to be applicable to exponentially unstable linear systems assuming that the time varying delay is known and bounded the design approach of a time varying state feedback controller is developed based on the solution of a parametric lyapunov equation an explicit condition is derived for which the stability of the closed loop system with the proposed controller is guaranteed it is shown that for the stability of the closed loop system the maximum allowable time delay in the input is inversely proportional to the sum of the unstable poles in the plant the effectiveness of the proposed method is demonstrated through numerical examples

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

learning the distribution preserving semantic subspace for clustering this paper proposes a new clustering method for images called distribution preserving indexing dpi it aims to find a lower dimensional semantic space approximating the original image space in the sense of preserving the distribution of the data in the theory the intrinsic structure of the data clusters can be described by the distribution of the data effectively therefore the cluster structure of the data in a lower dimensional semantic space derived by the dpi becomes clear unlike these distance based clustering methods which reveal the intrinsic euclidean structure of data our method attempts to discover the intrinsic cluster structure of the data space that actually is the union of some sub manifolds moreover we propose a revised kernel density estimator for the case of high dimensional data which is a crucial step in dpi in addition we provide a theoretical analysis of the bound of our method finally the extensive experiments compared with other algorithms on coil20 cbcl and mnist demonstrate the effectiveness of our proposed approach

inverse problems for metal oxide semiconductor field effect transistor contact resistivity inverse problems arising from the identification of transistor contact resistivity and contact window location are studied a one point boundary measurement of the potential is shown to be sufficient to identify each from a one parameter monotone family and such identification is both stable and continuously dependent on the parameter for a nonmonotone family of locations with resistivity given similar results are obtained for measurement made on almost all boundary points

appearance characterization of linear lambertian objects generalized photometric stereo and illumination invariant face recognition traditional photometric stereo algorithms employ a lambertian reflectance model with a varying albedo field and involve the appearance of only one object in this paper we generalize photometric stereo algorithms to handle all appearances of all objects in a class in particular the human face class by making use of the linear lambertian property a linear lambertian object is one which is linearly spanned by a set of basis objects and has a lambertian surface the linear property leads to a rank constraint and consequently a factorization of an observation matrix that consists of exemplar images of different objects e g faces of different subjects under different unknown illuminations integrability and symmetry constraints are used to fully recover the subspace bases using a novel linearized algorithm that takes the varying albedo field into account the effectiveness of the linear lambertian property is further investigated by using it for the problem of illumination invariant face recognition using just one image attached shadows are incorporated in the model by a careful treatment of the inherent nonlinearity in lambert s law this enables us to extend our algorithm to perform face recognition in the presence of multiple illumination sources experimental results using standard data sets are presented

inversion of robin coefficient by a spectral stochastic finite element approach this paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the robin coefficient from boundary measurements for the steady state heat conduction the problem is formulated into an optimization problem and mathematical properties relevant to its numerical computations are investigated the spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem and its convergence is analyzed the nonlinear conjugate gradient method is derived for the optimization system numerical results for several two dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method

human motion segmentation via robust kernel sparse subspace clustering studies on human motion have attracted a lot of attentions human motion capture data which much more precisely records human motion than videos do has been widely used in many areas motion segmentation is an indispensable step for many related applications but current segmentation methods for motion capture data do not effectively model some important characteristics of motion capture data such as riemannian manifold structure and containing non gaussian noise in this paper we convert the segmentation of motion capture data into a temporal subspace clustering problem under the framework of sparse subspace clustering we propose to use the geodesic exponential kernel to model the riemannian manifold structure use correntropy to measure the reconstruction error use the triangle constraint to guarantee temporal continuity in each cluster and use multi view reconstruction to extract the relations between different joints therefore exploiting some special characteristics of motion capture data we propose a new segmentation method which is robust to non gaussian noise since correntropy is a localized similarity measure we also develop an efficient optimization algorithm based on block coordinate descent method to solve the proposed model our optimization algorithm has a linear complexity while sparse subspace clustering is originally a quadratic problem extensive experiment results both on simulated noisy data set and real noisy data set demonstrate the advantage of the proposed method

robust recovery of subspace structures by low rank representation in this paper we address the subspace clustering problem given a set of data samples vectors approximately drawn from a union of multiple subspaces our goal is to cluster the samples into their respective subspaces and remove possible outliers as well to this end we propose a novel objective function named low rank representation lrr which seeks the lowest rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary it is shown that the convex program associated with lrr solves the subspace clustering problem in the following sense when the data is clean we prove that lrr exactly recovers the true subspace structures when the data are contaminated by outliers we prove that under certain conditions lrr can exactly recover the row space of the original data and detect the outlier as well for data corrupted by arbitrary sparse errors lrr can also approximately recover the row space with theoretical guarantees since the subspace membership is provably determined by the row space these further imply that lrr can perform robust subspace clustering and error correction in an efficient and effective way

generalized principal component analysis gpca this paper presents an algebro geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points we represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point when the number of subspaces is known we show that these polynomials can be estimated linearly from data hence subspace segmentation is reduced to classifying one point per subspace we select these points optimally from the data set by minimizing certain distance function thus dealing automatically with moderate noise in the data a basis for the complement of each subspace is then recovered by applying standard pca to the collection of derivatives normal vectors extensions of gpca that deal with data in a high dimensional space and with an unknown number of subspaces are also presented our experiments on low dimensional data show that gpca outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as k subspaces and expectation maximization we also present applications of gpca to computer vision problems such as face clustering temporal video segmentation and 3d motion segmentation from point correspondences in multiple affine views

numerical estimation of piecewise constant robin coefficient this paper considers a numerical method for reconstructing piecewise constant robin coefficients from boundary measurements a novel variational formulation of the inverse problem based on the celebrated modica mortola functional is proposed and its gamma convergence to the formulation with total variation regularization is shown the differentiability of the functional is investigated based on which the concave convex procedure is justified for its numerical solution the finite element method is utilized for discretizing the functional and the convergence of the finite element approximation is established three sets of numerical experiments are presented to illustrate its distinct features

global and semi global stabilization of linear systems with multiple delays and saturations in the input this paper studies stabilization problems for linear systems with multiple delays in the input two types of delays are considered the first type of delays is constant delays which can be arbitrarily large while the second type is time varying with an arbitrarily large bound with the first type of delays under the condition that the open loop system is absolutely controllable with all its eigenvalues on the imaginary axis globally stabilizing state and output feedback laws are constructed based on the solution to a family of parametric riccati equations which can be obtained explicitly through the solution of a parametric linear matrix equation with the second type of delays under the condition that the open loop system is absolutely controllable with all its eigenvalues on the imaginary axis being zero global state and output feedback laws are explicitly constructed based on the solution to a similar family of parametric riccati equations when the input is also subject to magnitude saturation it is shown that semiglobal stabilization instead of global stabilization can still be achieved numerical examples illustrate the effectiveness of the proposed approach

inverse boundary value problems at the boundary continuous dependence we use the methods of microlocal analysis to give a new proof of a theorem of kohn and vogelius showing that the boundary values of a continuous isotropic conductivity can be recovered from voltage and current measurements at the boundary moreover we prove sharp estimates to establish the continuous dependence of the boundary values of the conductivity on the voltage to current maps

clustering partially observed graphs via convex optimization this paper considers the problem of clustering a partially observed unweighted graph i e one where for some node pairs we know there is an edge between them for some others we know there is no edge and for the remaining we do not know whether or not there is an edge we want to organize the nodes into disjoint clusters so that there is relatively dense observed connectivity within clusters and sparse across clusters we take a novel yet natural approach to this problem by focusing on finding the clustering that minimizes the number of disagreements i e the sum of the number of observed missing edges within clusters and observed present edges across clusters our algorithm uses convex optimization its basis is a reduction of disagreement minimization to the problem of recovering an unknown low rank matrix and an unknown sparse matrix from their partially observed sum we evaluate the performance of our algorithm on the classical planted partition stochastic block model our main theorem provides sufficient conditions for the success of our algorithm as a function of the minimum cluster size edge density and observation probability in particular the results characterize the tradeoff between the observation probability and the edge density gap when there are a constant number of clusters of equal size our results are optimal up to logarithmic factors

spectral curvature clustering scc this paper presents novel techniques for improving the performance of a multi way spectral clustering framework govindu in proceedings of the 2005 ieee computer society conference on computer vision and pattern recognition cvpr 05 vol 1 pp 1150 1157 2005 chen and lerman 2007 preprint in the supplementary webpage for segmenting affine subspaces specifically it suggests an iterative sampling procedure to improve the uniform sampling strategy an automatic scheme of inferring the tuning parameter from the data a precise initialization procedure for k means as well as a simple strategy for isolating outliers the resulting algorithm spectral curvature clustering scc requires only linear storage and takes linear running time in the size of the data it is supported by theory which both justifies its successful performance and guides our practical choices we compare it with other existing methods on a few artificial instances of affine subspaces application of the algorithm to several real world problems is also discussed

practical matrix completion and corruption recovery using proximal alternating robust subspace minimization low rank matrix completion is a problem of immense practical importance recent works on the subject often use nuclear norm as a convex surrogate of the rank function despite its solid theoretical foundation the convex version of the problem often fails to work satisfactorily in real life applications real data often suffer from very few observations with support not meeting the randomness requirements ubiquitous presence of noise and potentially gross corruptions sometimes with these simultaneously occurring this paper proposes a proximal alternating robust subspace minimization method to tackle the three problems the proximal alternating scheme explicitly exploits the rank constraint on the completed matrix and uses the ell 0 l 0 pseudo norm directly in the corruption recovery step we show that the proposed method for the non convex and non smooth model converges to a stationary point although it is not guaranteed to find the global optimal solution in practice we find that our algorithm can typically arrive at a good local minimizer when it is supplied with a reasonably good starting point based on convex optimization extensive experiments with challenging synthetic and real data demonstrate that our algorithm succeeds in a much larger range of practical problems where convex optimization fails and it also outperforms various state of the art algorithms

greedy feature selection for subspace clustering unions of subspaces provide a powerful generalization of single subspace models for collections of high dimensional data however learning multiple subspaces from data is challenging due to the fact that segmentation the identification of points that live in the same subspace and subspace estimation must be performed simultaneously recently sparse recovery methods were shown to provide a provable and robust strategy for exact feature selection efs recovering subsets of points from the ensemble that live in the same subspace in parallel with recent studies of efs with l1 minimization in this paper we develop sufficient conditions for efs with a greedy method for sparse signal recovery known as orthogonal matching pursuit omp following our analysis we provide an empirical study of feature selection strategies for signals living on unions of subspaces and characterize the gap between sparse recovery methods and nearest neighbor nn based approaches in particular we demonstrate that sparse recovery methods provide significant advantages over nn methods and that the gap between the two approaches is particularly pronounced when the sampling of subspaces in the data set is sparse our results suggest that omp may be employed to reliably recover exact feature sets in a number of regimes where nn approaches fail to reveal the subspace membership of points in the ensemble

high rank matrix completion this paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low rank subspaces this generalizesthe standardlow rankmatrix completion problem to situations in which the matrix rank can be quite high or even full rank since the columns belong to a union of subspaces this problem may also be viewed as a missing data version of the subspace clustering problem let x be an n n matrix whose complete columns lie in a union of at most k subspaces each of rank r 1 a constant depending on the usual incoherence conditions the geometrical arrangement of subspaces and the distribution of columns over the subspaces the result is illustrated with numerical experiments and an application to internet distance matrix completion and topology identification

a parametric lyapunov equation approach to the design of low gain feedback low gain feedback has found several applications in constrained control systems robust control and nonlinear control low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero such feedback gains can be constructed either by an eigenstructure assignment algorithm or through the solution of a parametric algebraic riccati equation are the eigenstructure assignment approach leads to feedback gains in the form of a matrix polynomial in the parameter while the are approach requires the solution of an are for each value of the parameter this note proposes an alternative approach to low gain feedback design based on the solution of a parametric lyapunov equation such an approach possesses the advantages of both the eigenstructure assignment approach and the are based approach it also avoids the possible numerical stiffness in solving a parametric are and the structural decomposition of the open loop system that is required by the eigenstructure assignment approach

stability criteria of linear systems with multiple input delays under truncated predictor feedback abstract the model reduction technique as a feedback design approach for linear systems with input delays achieves finite spectrum assignment of the closed loop system in a delay free form the resulting predictor type feedback law contains a distributed term that involves the convolution between the past input and the state transition matrix and hence causes difficulty in its implementation for the purpose of easy implementation the truncated predictor feedback tpf simplifies the predictor feedback by discarding the distributed term and delay independent truncated predictor feedback further eliminates the delay dependent exponential factor in this paper we consider the stabilization of a general linear system with multiple time varying input delays by tpf or delay independent tpf stability criteria expressed in terms of input delays and the feedback parameter are derived through lyapunov krasovskii stability analysis and then numerically studied under both feedback laws

analysis of an adaptive finite element method for recovering the robin coefficient based on a new a posteriori error estimator an adaptive finite element method is proposed for recovering the robin coefficient involved in a diffusion system from some boundary measurement the a posteriori error estimator cannot be derived for this ill posed nonlinear inverse problem as was done for the existing a posteriori error estimators for direct problems instead we shall derive the a posteriori error estimator from our convergence analysis of the adaptive algorithm we prove that the adaptive algorithm guarantees a convergent subsequence of discrete solutions in an energy norm to some exact triplet the robin coefficient state and costate variables determined by the optimality system of the least squares formulation with tikhonov regularization for the concerned inverse problem some numerical results are also reported to illustrate the performance of the algorithm

brief paper robust consensus of multi agent systems with diverse input delays and asymmetric interconnection perturbations the consensus problem of second order multi agent systems with diverse input delays is investigated based on the frequency domain analysis decentralized consensus conditions are obtained for the multi agent system with symmetric coupling weights then the robustness of the symmetric system with asymmetric perturbation is studied a bound of the largest singular value of the perturbation matrix is obtained as the robust consensus condition simulation examples illustrate the design procedure of consensus protocols and validate the correctness of the results

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

sparse subspace clustering algorithm theory and applications many real world problems deal with collections of high dimensional data such as images videos text and web documents dna microarray data and more often such high dimensional data lie close to low dimensional structures corresponding to several classes or categories to which the data belong in this paper we propose and study an algorithm called sparse subspace clustering to cluster data points that lie in a union of low dimensional subspaces the key idea is that among the infinitely many possible representations of a data point in terms of other points a sparse representation corresponds to selecting a few points from the same subspace this motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces since solving the sparse optimization program is in general np hard we consider a convex relaxation and show that under appropriate conditions on the arrangement of the subspaces and the distribution of the data the proposed minimization program succeeds in recovering the desired sparse representations the proposed algorithm is efficient and can handle data points near the intersections of subspaces another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances such as noise sparse outlying entries and missing entries by incorporating the model of the data into the sparse optimization program we demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real world problems of motion segmentation and face clustering

forwarding backstepping and finite spectrum assignment for time delay systems the nonlinear control ideas and results of forwarding and backstepping have been recently extended to systems with time delay in this paper we discuss how to apply these tools to design robust controls for linear delay systems we first show that the integral cross term forwarding produces a feedback law that achieves finite spectrum of the closed loop system combining it with backstepping provides a structured design method for a large class of systems with time delay robustness of the controller to uncertainties including uncertain time delay is illustrated by an example

global stabilization of oscillators with bounded delayed input the problem of globally asymptotically stabilizing by bounded feedback of an oscillator with an arbitrary large delay in the input is solved a first solution follows from a general result on the global stabilization of null controllable linear systems with delay in the input by bounded control laws with a distributed term next it is shown through a lyapunov analysis that the stabilization can be achieved as well when neglecting the distributed terms it turns out that this main result is intimately related to the output feedback stabilization problem

a uniqueness theorem for an inverse boundary value problem in two dimensions abstract we consider the inverse problem to determine the potential q entering the schrodinger equation u qu 0 in a bounded smooth domain in r 2 in terms of the boundary measurements dirichlet to neumann map when n 3 the uniqueness for the inverse problem was well established in this paper we prove the uniqueness in two dimensions under the assumption that the lp p 2 norm of q is small this result improves a uniqueness result of sylvester uhlmann under the assumption that the w1 norm of q is small

robust subspace clustering subspace clustering refers to the task of nding a multi subspace representation that best ts a collection of points taken from a high dimensional space this paper introduces an algorithm inspired by sparse subspace clustering ssc 25 to cluster noisy data and develops some novel theory demonstrating its correctness in particular the theory uses ideas from geometric functional analysis to show that the algorithm can accurately recover the underlying subspaces under minimal requirements on their orientation and on the number of samples per subspace synthetic as well as real data experiments complement our theoretical study illustrating our approach and demonstrating its eectiveness

properties of the parametric lyapunov equation based low gain design with applications in stabilization of time delay systems this technical note studies some properties of the recently developed parametric lyapunov equation based low gain feedback design method as applications of these new properties alternative and simpler solutions are proposed to the global stabilization problem for a class of linear systems with input delay and the semi global stabilization problem when the systems are in addition subject to actuator saturation besides the simplicity in their construction the new solutions can also be easily scheduled online to achieve global result in the presence of input saturation

noisy sparse subspace clustering this paper considers the problem of subspace clustering under noise specifically we study the behavior of sparse subspace clustering ssc when either adversarial or random noise is added to the unlabeled input data points which are assumed to be in a union of low dimensional subspaces we show that a modified version of ssc is provably effective in correctly identifying the underlying subspaces even with noisy data this extends theoretical guarantee of this algorithm to more practical settings and provides justification to the success of ssc in a class of real applications