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We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
We study the data deletion problem for convex models. By leveraging techniques from convex optimization and reservoir sampling, we give the first data deletion algorithms that are able to handle an arbitrarily long sequence of adversarial…
We prove a removal lemma for systems of linear equations over finite fields: let $X_1,...,X_m$ be subsets of the finite field $\F_q$ and let $A$ be a $(k\times m)$ matrix with coefficients in $\F_q$ and rank $k$; if the linear system $Ax=b$…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
Permutation tests are a powerful and flexible approach to inference via resampling. As computational methods become more ubiquitous in the statistics curriculum, use of permutation tests has become more tractable. At the heart of the…
This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors, which were introduced in [3], to do reconstruction. Basic resolution and stability analysis…
This paper establishes the existence of infinitely many solutions for nonlinear problems without any symmetry, achieving three major advances. First, in the setting of semilinear elliptic PDEs, we introduce a refined variational truncation…
A useful technique for analyzing incomplete tables is to model the missing data mechanisms of the variables using log-linear models. In this paper, we use log-linear parametrization and propose estimation methods for arbitrary three-way and…
High-dimensional tests are applied to find relevant sets of variables and relevant models. If variables are selected by analyzing the sums of products matrices and a corresponding mean-value test is performed, there is the danger that the…
Cyclic reduction is a method for the solution of (block-)tridiagonal linear systems. In this note we review the method tailored to hermitian positive definite banded linear systems. The reviewed method has the following advantages: It is…
Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for…
Model order reduction is the approximation of dynamical systems into equivalent systems with smaller order. Model reduction has been studied extensively for different types of systems. In this paper, we present two methods for multi input…
We study the possibility of nullifying time-varying systems with memoryless output feedback. The systems we examine are linear single-input single-output finite-dimensional time-varying systems. For generic completely controllable and…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
Invariant sets are a key ingredient for verifying safety and other properties of cyber-physical systems that mix discrete and continuous dynamics. We adapt the elimination-theoretic Rosenfeld-Gr\"{o}bner algorithm to systematically obtain…
I discuss optimized data analysis and Monte Carlo methods. Reweighting methods are discussed through examples, like Lee-Yang zeroes in the Ising model and the absence of deconfinement in QCD. I discuss reweighted data analysis and…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
A Lie system is the non-autonomous system of differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional Lie algebra of vector fields, a so-called Vessiot--Guldberg Lie…
In the context of the variational bi-complex, we re-explain that irreducible gauge systems define a particular example of a Lie algebroid. This is used to review some recent and not so recent results on gauge, global and asymptotic…
We present a method which allows reduction of a size of a simulated system. The method can be applied to any system where one can define a finite set of possible states of the system and an elementary process which transforms one state of…