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We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…

Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…

During the past few years the development of experimental techniques has allowed the quantitative analysis of biological systems ranging from neurobiology and molecular biology. This work focuses on the quantitative description of these…

We investigate the performance of various methods of symplectic integration, which are based on two part splitting of the integration operator, for the numerical integration of multidimensional Hamiltonian systems. We implement these…

In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…

In continuation to our recent work on noncommutative polynomial factorization, we consider the factorization problem for matrices of polynomials and show the following results. (1) Given as input a full rank $d\times d$ matrix $M$ whose…

Mathematical models of protein-protein dynamics, such as the heterodimer model, play a crucial role in understanding many physical phenomena. This model is a system of two semilinear parabolic partial differential equations describing the…

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic…

In this paper, we propose a constructive algorithm to dynamically linearize two-input control systems via successive one-fold prolongations of a control that has to be suitably chosen at each step of the algorithm. Linearization via…

Stochastic differential equations play an important role in various applications when modeling systems that have either random perturbations or chaotic dynamics at faster time scales. The time evolution of the probability distribution of a…

In nature, biological organisms jointly evolve both their morphology and their neurological capabilities to improve their chances for survival. Consequently, task information is encoded in both their brains and their bodies. In robotics,…

We introduce a novel longitudinal mixed model for analyzing complex multidimensional functional data, addressing challenges such as high-resolution, structural complexities, and computational demands. Our approach integrates dimension…

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…

This paper discusses an approach for incorporating prior physical knowledge into the neural network to improve data efficiency and the generalization of predictive models. If the dynamics of a system approximately follows a given…

We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…

When brain signals are recorded in an electroencephalogram or some similar large-scale record of brain activity, oscillatory patterns are typically observed that are thought to reflect the aggregate electrical activity of the underlying…

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and…

We combine stochastic control methods, white noise analysis and Hida-Malliavin calculus applied to the Donsker delta functional to obtain new representations of semimartingale decompositions under enlargement of filtrations. The results are…

A hallmark of biological intelligence and control is combinatorial generalization: animals are able to learn various things, then piece them together in new combinations to produce appropriate outputs for new tasks. Inspired by the ability…

The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is…