Related papers: Lecture notes on descriptional complexity and rand…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
This manuscript contains an outline of lectures course "Evolutionary Algorithms" read by the author. The course covers Canonic Genetic Algorithm and various other genetic algorithms as well as evolutionary strategies, genetic programming,…
Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of…
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
There is no single definition of complexity (Edmonds 1999; Gershenson 2008; Mitchell 2009; De Domenico, et al., 2019), as it acquires different meanings in different contexts. A general notion is the amount of information required to…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…
This progress report covers recent developments in the area of quantum randomness, which is an extraordinarily interdisciplinary area that belongs not only to physics, but also to philosophy, mathematics, computer science, and technology.…
In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
These lecture notes focus on the recent advancements in neural information retrieval, with particular emphasis on the systems and models exploiting transformer networks. These networks, originally proposed by Google in 2017, have seen a…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
The progress of machine learning over the past decade is undeniable. In retrospect, it is both remarkable and unsettling that this progress was achievable with little to no rigorous theory to guide experimentation. Despite this fact,…
The digital transformation is turning archives, both old and new, into data. As a consequence, automation in the form of artificial intelligence techniques is increasingly applied both to scale traditional recordkeeping activities, and to…
Informatics studies all aspects of the structure of natural and artificial information systems. Theoretical and abstract approaches to information have made great advances, but human information processing is still unmatched in many areas,…
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…
The theory of random real numbers is exceedingly well-developed, and fascinating from many points of view. It is also quite challenging mathematically. The present notes are intended as no more than a gateway to the larger theory. They…
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…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
Inference of causal relations from data now has become an important field in artificial intelligence. During the past 16 years, causality analysis (in a quantitative sense) has been developed independently in physics from first principles.…