Related papers: Periodic Shadowing Sensitivity Analysis of Chaotic…
Spike sorting is a class of algorithms used in neuroscience to attribute the time occurences of particular electric signals, called action potential or spike, to neurons. We rephrase this problem as a particular optimization problem : Lasso…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…
Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down…
Spurious couplings and decoherence degrade the performance of solid-state quantum processors, demanding careful design, calibration, and mitigation protocols. These strategies often rely on characterization of the idling processor, but…
For nonautonomous and nonlinear differential and difference equations depending on a parameter, we formulate sufficient conditions under which they exhibit $C^k$, $k\in \N$ shadowing with respect to a parameter. Our results are applicable…
An intuitively necessary requirement of models used to provide forecasts of a system's future is the existence of shadowing trajectories that are consistent with past observations of the system: given a system-model pair, do model…
Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…
Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to…
In this paper it is reconsidered the prediction problem in time series framework by using a new non-parametric approach. Through this reconsideration, the prediction is obtained by a weighted sum of past observed data. These weights are…
We study a class of slow-fast Hamiltonian systems with any finite number of degrees of freedom, but with at least one slow one and two fast ones. At $% \epsilon =0$ the slow dynamics is frozen. We assume that the frozen system (i.e. the…
Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, e.g., identifiability and asymptotic properties of statistical estimation are still obscure. This paper…
This paper proposes a unified sparsity-aware robust recursive least-squares RLS (S-RRLS) algorithm for the identification of sparse systems under impulsive noise. The proposed algorithm generalizes multiple algorithms only by replacing the…
Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a…
Recently, machine learning techniques, particularly deep learning, have demonstrated superior performance over traditional time series forecasting methods across various applications, including both single-variable and multi-variable…
Self-adjusting, or adaptive systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these…