Related papers: Homogeneous length functions on Groups: Intertwine…
In this talk I would like to illustrate with examples taken from Quantum Field Theory and Biophysics how an intelligent exploitation of the unprecedented power of today's computers could led not only to the solution of pivotal problems in…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
Excellent computer simulations are done for a purpose. The most valid purposes are to explore uncharted territory, to resolve a well-posed scientific or technical question, or to make a design choice. Stand-alone modeling can serve the…
A rising vision for AI in the open world centers on the development of systems that can complement humans for perceptual, diagnostic, and reasoning tasks. To date, systems aimed at complementing the skills of people have employed models…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
Simple memorizing tasks have been chosen such as a binary code on a matrix. After the establishment of an appropriate protocol, the codified matrices were individually presented to 150 university students who had to memorize them. A…
Large Language Models (LLMs) are capable of displaying a wide range of abilities that are not directly connected with the task for which they are trained: predicting the next words of human-written texts. In this article, I review recent…
Understanding how to engage users is a critical question in many applications. Previous research has shown that unexpected or astonishing events can attract user attention, leading to positive outcomes such as engagement and learning. In…
In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computer-assisted proofs will be give a special…
The Web has made it possible to harness human cognition en masse to achieve new capabilities. Some of these successes are well known; for example Wikipedia has become the go-to place for basic information on all things; Duolingo engages…
Modifiable combining functions are a synthesis of two common approaches to combining evidence. They offer many of the advantages of these approaches and avoid some disadvantages. Because they facilitate the acquisition, representation,…
In human computer interaction (HCI), it is common to evaluate the value of HCI designs, techniques, devices, and systems in terms of their benefit to users. It is less common to discuss the benefit of HCI to computers. Every HCI task allows…
Large language models (LLMs) are advanced artificial intelligence (AI) systems that can perform a variety of tasks commonly found in human intelligence tests, such as defining words, performing calculations, and engaging in verbal…
Complex machine learning algorithms are used more and more often in critical tasks involving text data, leading to the development of interpretability methods. Among local methods, two families have emerged: those computing importance…
Given the recent successes of Deep Learning in AI there has been increased interest in the role and need for explanations in machine learned theories. A distinct notion in this context is that of Michie's definition of Ultra-Strong Machine…
Human cognitive performance is enhanced by the use of tools. For example, a human can produce a much greater, and more accurate, volume of mathematical calculation in a unit of time using a calculator or a spreadsheet application on a…
Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as alternatives to physical experiments. Design and analysis of computer experiments have attracted great attention in past…
While Artificial Intelligence has successfully outperformed humans in complex combinatorial games (such as chess and checkers), humans have retained their supremacy in social interactions that require intuition and adaptation, such as…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
As an intrinsic and fundamental property of big data, data heterogeneity exists in a variety of real-world applications, such as precision medicine, autonomous driving, financial applications, etc. For machine learning algorithms, the…