Related papers: Recent Topics on Linear Dynamics
This is a write-up of the lectures given by the author during the Master Class "Categorification" at {\AA}rhus University, Denmark in October 2010.
Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.
Changes in the number of publications in a certain field might reflect the dynamic of scientific progress in this field, since an increase in the number of publications can be interpreted as an increase in the field-specific knowledge. In…
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion revolves around complex ordinary differential equations and…
We review recent experimental and theoretical progress in spin physics, as presented in the spin parallel session of DIS2006. In particular, we discuss the status of the nucleon spin structure, transverse polarized asymmetries, and recent…
In this closing talk of the DIS 2021 Workshop, I review some of the lessons we've learned about quantum chromodynamics, and reflect on what we may hope to learn in the coming years.
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…
We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…
Lattice simulations of hadronic structure are now reaching a level where they are able to not only complement, but also provide guidance to current and forthcoming experimental programmes at, e.g. Jefferson Lab, COMPASS/CERN and FAIR/GSI.…
This is a list of unsolved problems given at the Conformal Dynamics Conference which was held at SUNY Stony Brook in November 1989. Problems were contributed by the editor and the other authors.
Linearization of the dynamics of recurrent neural networks (RNNs) is often used to study their properties. The same RNN dynamics can be written in terms of the ``activations" (the net inputs to each unit, before its pointwise nonlinearity)…
A short lecture given at the Summer School on "Modern perspectives in lattice QCD", Les Houches, August 3-28, 2009.
This manuscript is an edited and refined version of the lecture script for a one-semester graduate course given originally at the PhD school in the Institute of Physics of Polish Academy of Sciences in the Spring/Summer semester of 2022.…
Despite the phenomenal success of deep learning in recent years, there remains a gap in understanding the fundamental mechanics of neural nets. More research is focussed on handcrafting complex and larger networks, and the design decisions…
This is a brief and updated summary of a talk given at the International Conference on Gravitation and Cosmology that took place in Poona in December 1995. It is very brief and is mostly intended as a guide to current literature, or to keep…
These notes were originally prepared as additional material for the lessons I have given at the summer school Gamma-ray Astrophysics and Multifrequency: Data analysis and astroparticle problems, organized by the Department of Physics of the…
I review the most important objectives of the physics program of a next-generation e+e- linear collider. (Introductory theory lecture presented at the 1999 International Workshop on Linear Colliders, Sitges, Barcelona, Spain.)
This extended abstract was presented at the Nectar Track of ECML PKDD 2024 in Vilnius, Lithuania. The content supplements a recently published paper "Laws of Macroevolutionary Expansion" in the Proceedings of the National Academy of…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
The past decade has witnessed two important new developments in the study of linear series on algebraic varieties. First, vector bundles have emerged as powerful tools for analyzing linear series on curves and surfaces. More recently, the…