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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…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation…
The paper proposes a method of damage detection in elastic materials, which is based on analyzing the time-dependent (dynamic) response of the material excited by an acoustic signal. A case study is presented consisting of experimental…
The use of generalized LASSO is a common technique for recovery of structured high-dimensional signals. Each generalized LASSO program has a governing parameter whose optimal value depends on properties of the data. At this optimal value,…
Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a…
This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…
We develop a flexible framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple bootstrap algorithm. Effectively, our procedure seeks an autoencoding basis for the observed…
We propose a heuristic method to obtain the approximate groundstate for a Hamiltonian in the qubit form, based on the stabilizer formalism. These states may serve as proper initial states for further refined computation. It would be…
Double rf systems are critical for achieving the parameters of 4th-generation light sources. These systems, comprising both main and harmonic rf cavities, relax statistical collective effects but also introduce instabilities, such as…
The aim of this paper is to numerically study the performance of a method of regularization. This technique was developed to solve the illposed problem of estimating a source-dimensional Poisson equation for two dimensions from measurements…
This paper concerns the identification of continuous-time systems in state-space form that are subject to Lebesgue sampling. Contrary to equidistant (Riemann) sampling, Lebesgue sampling consists of taking measurements of a continuous-time…
To overcome the limitations of the traditional state-averaging approaches in excited state calculations, where one solves for and represents all states between the ground state and excited state of interest, we have investigated a number of…
We consider nearly-integrable Hamiltonian systems defined over a non-resonant domain. In the neighborhood of resonances, we use Nekhoroshev-like estimates to provide effective stability bounds for the action variables over long time. The…
This paper studies coefficient-level, structure-preserving output-feedback stabilization of linear port-Hamiltonian (pH) descriptor systems. Existing stabilization conditions generally require explicit pH representations, which may be…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
Harmonic stator-rotor coupling offers a promising approach for the interconnection of rotating subsystems in the simulation of electric machines. This paper studies the stability of discretization schemes based on harmonic coupling in the…
Selecting regularization parameters in penalized high-dimensional graphical models in a principled, data-driven, and computationally efficient manner continues to be one of the key challenges in high-dimensional statistics. We present…
A new algorithm for extraction of asymmetries from polarized lepton-nucleon scattering data is proposed. The algorithm is stable to set-up acceptance and/or luminosity monitor acceptance variations. A statistical test for checking the data…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…