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We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
We present a method that connects a well-established nonlinear (bilinear) identification method from time-domain data with neural network (NNs) advantages. The main challenge for fitting bilinear systems is the accurate recovery of the…
Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system.…
Block oriented model structure detection is quite desirable since it helps to imagine the system with real physical elements. In this work we explore experimental methods to detect the internal structure of the system, using a black box…
Pole-zero identification refers to the obtaining of the poles and zeros of a linear (or linearized) system described by its frequency response. This is usually done using optimization techniques (such as least squares, maximum likelihood…
We propose an iterative method for nonlinear semidefinite programs with box constraints. The search direction in the proposed method utilizes the distance from the current point to the boundary of a feasible set. The computation of the…
In this paper we present a new algorithm for Polynomial Linear System Solving (via evaluation/interpolation) with errors. In this scenario, errors can occur in the black box evaluation step. We improve the bound on the number of errors that…
We present a deterministic way of assigning small (log bit) weights to the edges of a bipartite planar graph so that the minimum weight perfect matching becomes unique. The isolation lemma as described in (Mulmuley et al. 1987) achieves the…
A method is presented to obtain an inner-approximation of the backward reachable set (BRS) of a given target tube, along with an admissible controller that maintains trajectories inside this tube. The proposed optimization algorithms are…
In this article, we completely describe the control sets of one-input linear control systems on solvable, nonnilpotent 3D Lie groups. We show that, if the restriction of the associate derivation to the nilradical is nontrivial, the Lie…
Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing…
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
To determine the dimension of null space of any given linearized polynomial is one of vital problems in finite field theory, with concern to design of modern symmetric cryptosystems. But, the known general theory for this task is much far…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN…
We consider the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. The problem can be solved, in principle, using real quantifier…
The Isolation Lemma of Mulmuley, Vazirani and Vazirani [Combinatorica'87] provides a self-reduction scheme that allows one to assume that a given instance of a problem has a unique solution, provided a solution exists at all. Since its…
Based on the radial basis function (RBF), non-singular general solution and dual reciprocity method (DRM), this paper presents an inherently meshless, integration-free, boundary-only RBF collocation techniques for numerical solution of…
The input domain of software systems can typically be divided into sub-domains for which the outputs are similar. To ensure high quality it is critical to test the software on the boundaries between these sub-domains. Consequently, boundary…