Related papers: Dragons and Kasha
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…
What are the functions of curiosity? What are the mechanisms of curiosity-driven learning? We approach these questions about the living using concepts and tools from machine learning and developmental robotics. We argue that…
``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words…
Dots-and-Boxes is a child's game which remains analytically unsolved. We implement and evolve artificial neural networks to play this game, evaluating them against simple heuristic players. Our networks do not evaluate or predict the final…
The Mizar language aims to capture mathematical vernacular by providing a rich language for mathematics. From the perspective of a user, the richness of the language is welcome because it makes writing texts more "natural". But for the…
Evolution and learning have historically been interrelated topics, and their interplay is attracting increased interest lately. The emerging new factor in this trend is morphological evolution, the evolution of physical forms within…
These notes are a brief introduction to the RSA algorithm and modular arithmetic. They are intended for an undergraduate audience.
A suite of impressive scientific discoveries have been driven by recent advances in artificial intelligence. These almost all result from training flexible algorithms to solve difficult optimization problems specified in advance by teams of…
K. Kato has recently defined and studied heights of mixed motives and proposed some interesting questions. In this paper, we relate the study of heights to the study of Tamagawa numbers of motives. We also partially answer one of Kato's…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has two objectives. The first is to reconcile the way of…
Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain…
Problems for the graduate students who want to improve problem-solving skills in geometry. Every problem has a short elegant solution -- this gives a hint which was not available when the problem was discovered.
In the last decades we have witnessed the success of applications of Artificial Intelligence to playing games. In this work we address the challenging field of games with hidden information and card games in particular. Jass is a very…
We describe a new arithmetic system for the Magma computer algebra system for working with $p$-adic numbers exactly, in the sense that numbers are represented lazily to infinite $p$-adic precision. This is the first highly featured such…
The study examines the relationship between Ball's magic numbers and reverses divisors. These numbers are the source of beautiful and curious properties. Activities related to numbers can be a fun way to motivate mathematics students, while…
Computers have already changed the way that humans do mathematics: they enable us to compute efficiently. But will they soon be helping us to reason? And will they one day start reasoning themselves? We give an overview of recent…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
High school science classrooms across the United States are answering calls to make computation a part of science learning. The problem is that there is little known about the barriers to learning that computation might bring to a science…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…