Related papers: Identification of Sparse Linear Operators

We exhibit d-dimensional limit-periodic Schrodinger operators that are uniformly localized in the strongest sense possible. That is, for each of these operators, there is a uniform exponential decay rate such that every element of the hull…

Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…

We consider the problem of learning linear operators under squared loss between two infinite-dimensional Hilbert spaces in the online setting. We show that the class of linear operators with uniformly bounded $p$-Schatten norm is online…

Let $X$ and $Y$ be separable Banach spaces and $T:X\to Y$ be a bounded linear operator. We characterize the non-separability of $T^*(Y^*)$ by means of fixing properties of the operator $T$.

This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type $1,1$ in H\"ormander's sense. Thus, it contributes to the long-standing problem of…

This paper provides a general identification approach for a wide range of nonlinear panel data models, including binary choice, ordered response, and other types of limited dependent variable models. Our approach accommodates dynamic models…

Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…

In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…

Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear transfer functions and are excited by known external excitation signals and/or unknown noise signals. A…

A continuous linear operator L defined on the space of entire functions H(C) is said to be an extended $lambda$-eigenoperator of the differentiation operator D provided DL = $lambda$LD. Here we fully characterize when an extended…

Real-world processes often contain intermediate state that can be modeled as an extremely sparse activation tensor. In this work, we analyze the identifiability of such sparse and local latent intermediate variables, which we call motifs.…

In this work, we develop a method to identify continuous-time nonlinear networked dynamics via the Koopman operator framework. The proposed technique consists of two steps: the first step identifies the neighbors of each node, and the…

This paper proposes methods for identification of large-scale networked systems with guarantees that the resulting model will be contracting -- a strong form of nonlinear stability -- and/or monotone, i.e. order relations between states are…

We study the approximation properties of pseudo-differential operators with small time-frequency dispersion, meaning that their spreading functions are supported in a small neighborhood of the origin. It is commonly assumed that for such…

This article is devoted to prove a stability result for two independent coefficients for a Schr\"odinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of…

Lasso regression is a widely employed approach within the $\ell_1$ regularization framework used to promote sparsity and recover piecewise smooth signals $f:[a,b) \rightarrow \mathbb{R}$ when the given observations are obtained from noisy,…

This paper presents a linear dynamical operator described in terms of a rational transfer function, endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end…

In this work we consider the problem of identification and reconstruction of doubly-dispersive channel operators which are given by finite linear combinations of time-frequency shifts. Such operators arise as time-varying linear systems for…

The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient…

We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark…