Related papers: Sparse Differential Resultant for Laurent Differen…
We derive the Lagrangians of the higher-order Painlev\'e equations using Jacobi's last multiplier technique. Some of these higher-order differential equations display certain remarkable properties like passing the Painlev\'e test and…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
In this paper, we propose algorithms to compute differential Chow forms for prime differential ideals which are given by their characteristic sets. The main algorithm is based on an optimal bound for the order of a prime differential ideal…
In this paper, we propose two new deterministic interpolation algorithms for a sparse multivariate polynomial given as a standard black-box by introducing new Kronecker type substitutions. Let $f\in \RB[x_1,\dots,x_n]$ be a sparse black-box…
Motivated by stability analysis of large scale power systems, we describe how the Lasserre (moment-sums of squares, SOS) hierarchy can be used to generate outer approximations of the region of attraction (ROA) of sparse polynomial…
In the present work, we formulate a necessary condition for functionals with Lagrangians depending on fractional derivatives of differentiable functions to possess an extremum. The Euler-Lagrange equation we obtained generalizes previously…
We propose a two-step procedure to detect cointegration in high-dimensional settings, focusing on sparse relationships. First, we use the adaptive LASSO to identify the small subset of integrated covariates driving the equilibrium…
Composite likelihood has shown promise in settings where the number of parameters $p$ is large due to its ability to break down complex models into simpler components, thus enabling inference even when the full likelihood is not tractable.…
In this paper we show that a variational reduction procedure can be defined for Lagrangian systems subject to scaling symmetries (i.e. Lagrangian systems defined by a homogenous Lagrangian function), in such a way that the trajectories of…
The theory of spectral methods for partial differential equations leads to infinite-dimensional matrices which represent the derivative operator with respect to an underlying orthonormal basis. Favourable properties of such differentiation…
The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…
Unobserved discrete data are ubiquitous in many scientific disciplines, and how to learn the causal structure of these latent variables is crucial for uncovering data patterns. Most studies focus on the linear latent variable model or…
As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods…
This paper studies sparse nonlinear least squares problems, where the Jacobian matrices are unavailable or expensive to compute, yet have some underlying sparse structures. We construct the Jacobian models by the $ \ell_1 $ minimization…
Sparse spectral methods for solving partial differential equations have been derived in recent years using hierarchies of classical orthogonal polynomials on intervals, disks, and triangles. In this work we extend this methodology to a…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
When the model is not known and parameter testing or interval estimation is conducted after model selection, it is necessary to consider selective inference. This paper discusses this issue in the context of sparse estimation. Firstly, we…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e., solving minimal…
In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…