Related papers: Computable Integrability
This book provides a compact, derivation-oriented introduction to the mathematical foundations of modern generative artificial intelligence. Rather than surveying every recent architecture or implementation detail, it develops a coherent…
A few remarks on integrable dynamical systems inspired by discussions with Jurgen Moser and by his work.
The subject of our discussion is the theory of differential equations as set out in two classical Euler's textbooks "Institutiones Calculi Differentialis" and "Institutiones Calculi Integralis".
This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals…
Computational reproducibility of scientific results, that is, the execution of a computational experiment (e.g., a script) using its original settings (data, code, etc.), should always be possible. However, reproducibility has become a…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
This habilitation thesis is cumulative and, therefore, is collecting and connecting research that I (together with several co-authors) have conducted over the last few years. Thus, the absolute core of the work is formed by the ten…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
This special volume of Statistical Sciences presents some innovative, if not provocative, ideas in the area of reliability, or perhaps more appropriately named, integrated system assessment. In this age of exponential growth in science,…
No matter how much the world of computing changes, system design remains crucial. While most people try to learn it through quick tutorials or AI-generated summaries, there is no better way to master the field than by studying the original…
This is my working paper on a proposed logical framework for the practice of mathematics, which is paralleled by philosophical considerations and a computer implementation (a variant of Automath). Updated 10/27/2016 with a version from…
Additional material for the original paper "Automated Verification of Interactive Rule-Based Configuration Systems".
This is a mainly expository sketch showing how some integrable systems (e.g. KP or KdV) can be viewed as quantum mechanical in nature.
An updated version of this paper is available at http://arxiv.org/abs/1505.01131
Book Chapter from "Coarse-Grained Modeling of Biomolecules" part of the submitted "Series in Computational Biophysics"
This work describes the development of a robotic system that acquires knowledge incrementally through human interaction where new tools and motions are taught on the fly. The robotic system developed was one of the five finalists in the…
Executable scientific papers contain not just layouted text for reading. They contain, or link to, machine-comprehensible representations of the scientific findings or experiments they describe. Client-side players can thus enable readers…
This paper provides interested beginners with an updated and detailed introduction to the field of Intelligent Tutoring Systems (ITS). ITSs are computer programs that use artificial intelligence techniques to enhance and personalize…
Some contemporary views of the universe assume information and computation to be key in understanding and explaining the basic structure underpinning physical reality. We introduce the Computable Universe exploring some of the basic…
Computational scientists are facing a new era where the old ways of developing and reusing code have to be left behind and a few daring steps are to be made towards new horizons. The present work analyzes the needs that drive this change,…