As shown in [9, 1], signals whose wavelet coefficients exhibit a rooted tree structure can be recovered — using specially-adapted compressed sensing algorithms — from just $n=\mathcal{O}(k)$ measurements, where $k$ is the sparsity of the signal. Motivated by these results, we introduce a simplified proportional-dimensional asymptotic framework which enables the quantitative evaluation of recovery guarantees … Read more
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance the solution set of linear matrix inequalities or the Schur/Hurwitz stability domains. These sets often have very complicated shapes … Read more
In this work we study the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. We show that the sets of classical, quantum, no-signaling and unrestricted correlations can be expressed as projections of affine sections of appropriate convex cones. As a by-product, we identify … Read more
For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stff or mildly stff, and the other part is stff. Such systems can be effciently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration … Read more
Using an augmented Lagrangian matrix approach, we analytically solve in this paper a broad class of linear systems that includes symmetric and nonsymmetric problems in saddle point form. To this end, some mild assumptions are made and a preconditioning is specially designed to improve the sensitivity of the systems before the calculation of their solutions. … Read more
In this paper, driven by Behavioral applications to human dynamics, we consider the characterization of completeness in pseudo-quasimetric spaces in term of a generalization of Ekeland’s variational principle in such spaces, and provide examples illustrating significant improvements to some previously obtained results, even in complete metric spaces. At the behavioral level, we show that the … Read more
We consider multi-target,robust linear-quadratic control problem on semi-infinite interval. Using functional-analytic approach developed in [2], we reduce this problem to a convex optimization problem on the simplex. Explicit procedure for the reduced optimization problem is described. Citation Preprint, University of Notre Dame, August,2015 Article Download View Remark on multi-target,robust linear-quadratic control problem on semi-infinite interval
We propose a novel approach using shape derivatives to solve inverse optimization problems governed by Maxwell’s equations, focusing on identifying hidden geometric objects in a predefined domain. The target functional is of tracking type and determines the distance between the solution of a 3D time-dependent Maxwell problem and given measured data in an $L_2$-norm. Minimization … Read more
Thermal optimization of vertical continuous casting process is considered in the present study. The goal is to find the optimal distribution of temperature and interfacial heat transfer coefficients corresponding to the primary and secondary cooling systems, in addition to the pulling speed, such that the solidification along the main axis of strand approaches to the … Read more
We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms involve contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is also related to message passing and mean field methods. The algorithms we describe are guaranteed to converge on graphs with arbitrary topology. Moreover … Read more