Related papers: The Mathematics of Artificial Intelligence
In the decade since 2010, successes in artificial intelligence have been at the forefront of computer science and technology, and vector space models have solidified a position at the forefront of artificial intelligence. At the same time,…
Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main…
This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…
Artificial intelligence is gaining strength and materials science can both contribute to and profit from it. In a simultaneous progress race, new materials, systems and processes can be devised and optimized thanks to machine learning…
The discussions around Artificial Intelligence (AI) and medical imaging are centered around the success of deep learning algorithms. As new algorithms enter the market, it is important for practicing radiologists to understand the pitfalls…
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…
The paper reflects on the future role of AI in scientific research, with a special focus on turbulence studies, and examines the evolution of AI, particularly through Diffusion Models rooted in non-equilibrium statistical mechanics. It…
In recent years, the field of statistics has experienced a surge in interest and application, largely due to significant advances in computer technology. This progress has led to remarkable developments in statistics methods and algorithms,…
The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We…
The application of "machine learning" and "artificial intelligence" has become popular within the last decade. Both terms are frequently used in science and media, sometimes interchangeably, sometimes with different meanings. In this work,…
Artificial intelligence (AI) raises expectations of substantial increases in rates of technological and scientific progress, but such anticipations are often not connected to detailed ground-level studies of AI use in innovation processes.…
Creating learning models that can exhibit sophisticated reasoning skills is one of the greatest challenges in deep learning research, and mathematics is rapidly becoming one of the target domains for assessing scientific progress in this…
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…
Artificial Intelligence is rapidly transforming materials science and engineering, offering powerful tools to navigate complexity, accelerate discovery, and optimize material design in ways previously unattainable. Driven by the…
Artificial intelligence (AI) advancements over the past few years have had an unprecedented and revolutionary impact across everyday application areas. Its significance also extends to technical challenges within science and engineering,…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
We aim to demonstrate the value of mathematical models for policy debates about technological progress in cybersecurity by considering phishing, vulnerability discovery, and the dynamics between patching and exploitation. We then adjust the…
The purpose of this article is to review the achievements made in the last few years towards the understanding of the reasons behind the success and subtleties of neural network-based machine learning. In the tradition of good old applied…
Artificial Intelligence is a field that lives many lives, and the term has come to encompass a motley collection of scientific and commercial endeavours. In this paper, I articulate the contours of a rather neglected but central scientific…
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…