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Biological networks provide insight into the complex organization of biological processes in a cell at the system level. They are an effective tool for understanding the comprehensive map of functional interactions, finding the functional…

This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…

There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…

This thesis contains three main parts, which are largely independent. In the first part we deal with the boundary bootstrap in supersymmetric factorized scattering theory. We give a description of supersymmetry in the case when the space is…

We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…

The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather…

Spikes and rhythms organize control and communication in the animal world, in contrast to the bits and clocks of digital technology. As continuous-time signals that can be counted, spikes have a mixed nature. This paper reviews ongoing…

We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…

The linearization method builds a bridge from mature methods for linear systems to nonlinear systems and has been widely used in various areas. There are currently two main linearization methods: Jacobian linearization and feedback…

This is the first in a series of papers in which we describe explicit structural properties of spaces of diagonal rectangular harmonic polynomials in $k$ sets of $n$ variables, both as $GL_k$-modules and $S_n$-modules, as well as some of…

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…

We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a…

In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-order case, we propose a framework of transition from deterministic or…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

This PhD thesis has the following structure: Chapter 1 - General introduction; Chapter 2 - Preliminaries; Chapter 3 - The Replicated Transfer Matrix; Chapter 4 - Finite Size Corrections On Random Graphs; Chapter 5 - The Random Field Ising…

The combination of protrusions and retractions in the movement of polarized cells leads to understand the effect of possible synchronisation between the two ends of the cells. This synchronisation, in turn, could lead to different dynamics…

Neuromorphic control is receiving growing attention due to the multifaceted advantages it brings over more classical control approaches, including: sparse and on-demand sensing, information transmission, and actuation; energy-efficient…

We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…

This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by…

Fishing quotas are unpleasant but efficient to control the productivity of a fishing site. A popular model has a stochastic differential equation for the biomass on which a stochastic dynamic programming or a Hamilton-Jacobi-Bellman…