Related papers: Recent Topics on Linear Dynamics

Notes on algebraic stacks, prepared for an 11-lecture course at the NCTS, Taipei, during the fall of 2022.

These are notes from elementary lectures given in the summer of 2013 at the YMSC center at Tsinghua University in Beijing.

The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…

We consider concepts centered around modal analysis, data science, network science, and machine learning to reveal the essential dynamics from high-dimensional fluid flow data and operators. The presentation of the material herein is…

These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…

This expository survey is dedicated to recent developments in the area of linear dynamics. Topics include frequent hypercyclicity, $\mathcal{U}$-frequent hypercyclicity, reiterative hypercyclicity, operators of C-type, Li-Yorke and…

This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…

I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics…

These notes are the outgrowth of a series of lectures given at MSRI in January 1995 at the beginning of the special semester in complex dynamics and hyperbolic geometry. In these notes, the primary aim is to motivate the study of complex…

These notes are for the proceedings of the NATO Advanced Study Insitutue on "Scale Invariance, Interfaces, and Non--Equilibrium Dynamics", held at the Isaac Newton Institute, 20--30 June 1994. The four lectures address a number of issues…

These are the lecture notes of a course given by the first author on December 27, 2012 - January 4, 2013, held at the Academy of Mathematics and Systems Science Chinese Academy of Sciences in Beijing.

I review the basic ideas of "trace dynamics", as formulated in my 2004 Cambridge University Press book "Quantum Theory as an Emergent Phenomenon", and then discuss how they have influenced much of my work of the last two decades.

These notes are based on a series of three lectures given at the Les Houches summer school on 'Integrability in Atomic and Condensed Matter Physics' in August 2018. They provide an introduction into the unusual transport properties of…

Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations,…

Notes from 11 October 2004 lecture presented at the Joint Institute for Nuclear Astrophysics R-Matrix School at Notre Dame University.

These notes are based on a lecture delivered by NC on March 2021, as part of an advanced course in Princeton University on the mathematical understanding of deep learning. They present a theory (developed by NC, NR and collaborators) of…

These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…

This article gathers notes of two lectures given at Grenoble's University in June $2023$, and is an introduction to recent works on shear layers, in collaboration with D. Bian, Y. Guo, T. Nguyen and B. Pausader.

We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…

This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of…