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A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…

Differential Dynamic Programming (DDP) is an efficient trajectory optimization algorithm relying on second-order approximations of a system's dynamics and cost function, and has recently been applied to optimize systems with time-invariant…

Clinical oriented applications of computational electrocardiology require efficient and reliable identification of patient-specific parameters of mathematical models based on available measures. In particular, the estimation of cardiac…

Mathematical models of cardiac electrical activity are one of the most important tools for elucidating information about the heart diagnostic. Even though it is one of the major problems in biomedical research, an efficient mathematical…

Nonadiabatic ring-polymer molecular dynamics employs the mapping approach to describe nonadiabatic effects within the ring-polymer ansatz. In this paper, it is generalized to allow for the nuclear and electronic degrees of freedom to be…

Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

This study proposes an end-to-end unsupervised diffeomorphic deformable registration framework based on moving mesh parameterization. Using this parameterization, a deformation field can be modeled with its transformation Jacobian…

Deformation modeling of cardiac muscle is an important issue in the field of cardiac analysis. For this reason, many approaches have been developed to best estimate the cardiac muscle deformation, and to obtain a practical model to use in…

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…

The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…

The circadian rhythm plays a crucial role in regulating biological processes, and its disruption is linked to various health issues. Identifying small molecules that influence the circadian period is essential for developing targeted…

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential,…

In this paper we start a global study of the parameter space (dissipation, perturbation, frequency) of the dissipative spin-orbit problem in Celestial Mechanics with the aim of delimiting regions where the dynamics, or at least some of its…

In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…

Deformation modeling of cardiac muscle is an important issue in the field of cardiac analysis. Many approaches have been developed to better estimate the cardiac muscle deformation, and to obtain a practical model to be used in diagnostic…

This study focuses on extending the concept of weak signal enhancement from dynamical systems based on vibrational resonance of nonlinear systems, to non-smooth systems. A Van der Pol- Duffing oscillator with a one-sided barrier, subjected…

We present formulations and numerical algorithms for solving diffeomorphic shape matching problems. We formulate shape matching as a variational problem governed by a dynamical system that models the flow of diffeomorphism $f_t \in…

Many real-world data sets, especially in biology, are produced by complex nonlinear dynamical systems. In this paper, we focus on brain calcium imaging (CaI) of different organisms (zebrafish and rat), aiming to build a model of joint…

A new approach called Flow Curvature Method has been recently developed in a book entitled Differential Geometry Applied to Dynamical Systems. It consists in considering the trajectory curve, integral of any n-dimensional dynamical system…