Related papers: Recent Topics on Linear Dynamics
These notes overlap with lectures given at the TASI summer schools in 2014 and 2011, as well as at the European School of High Energy Physics in 2013. This is primarily an attempt at transcribing my hand-written notes, with emphasis on…
This document presents the contents of three lectures delivered by the author at the Erd\H{o}s Center School ``Optimal Transport on Quantum Structures'', Septemer 19-23, 2022 in Budapest, Hungary. It presents a fairly self contained account…
The aim of these lecture notes is a description of the statics and dynamics of zero-range processes and related models. After revisiting some conceptual aspects of the subject, emphasis is then put on the study of the class of zero-range…
We give a review of some recent developments in embeddings of time series and dynamic networks. We start out with traditional principal components and then look at extensions to dynamic factor models for time series. Unlike principal…
Short comment for a recent paper, suggesting for some directions related to previous studies in chaotic dynamics.
The recent progresses in Machine Learning opened the door to actual applications of learning algorithms but also to new research directions both in the field of Machine Learning directly and, at the edges with other disciplines. The case…
This thesis explores how deep learning models learn over time, using ideas inspired by force analysis. Specifically, we zoom in on the model's training procedure to see how one training example affects another during learning, like…
Those notes rest on the Samuel Eilenberg Lectures I gave at Columbia University, NY, in the fall 2022. I thank all the mathematicians who participated in their elaboration, directly or indirectly. They are meant to be published as a…
Chapters 1 to 4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5 to 8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9 and…
This file is composed of questions that emerged or were of interest during the workshop "Interactions between Descriptive Set Theory and Smooth Dynamics" that took place in Banff, Canada on 2022.
This volume contains a selection of papers presented at Linearity/TLLA 2018: Joint Linearity and TLLA workshops (part of FLOC 2018) held on July 7-8, 2018 in Oxford. Linearity has been a key feature in several lines of research in both…
This thesis is entitled Dynamic programming systems for modeling and control of the traffic in transportation networks. Two parts are distinguished in this dissertation: 1) methods and approaches based on min-plus or max-plus algebra, where…
Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…
The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential dichotomy and its corresponding spectral theory. The second…
I will present here my perception on the status of Deep Inelastic Scattering physics, as I have further developed it during this Workshop, together with a number of comments on the results that have impressed me most during this week. I…
This paper gives an overview of a Workshop on Chiral Dynamics: Theory and Experiment which was held at MIT July 25-29, 1994; its unique feature was the equal mixture of theory and experiment. The purpose of the workshop was to bring…
This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.
These are notes prepared for presentation at the workshop "Challenges in Granular Matter" at the Abdus Salam Institute for Theoretical Physics, Trieste, August 2001. Revisions and figures will be added at a later date. Many features of real…
These notes are an extended version of the course "Introduction to rough paths theory" given at the XXV Brazilian School of Probability in Campinas in August 2022. Their aim is to give a consise overview to Lyon's theory of rough paths with…
These are the extended lecture notes of my lecture about ``Linear Operators on Polynomials, $K$-Positivity Preserver, and their Generators''. The lecture was given at the University of Konstanz in the winter semester 2025/26.