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This tutorial is based on lecture notes written for a class taught in the Statistics Department at Stanford in the Winter Quarter of 2017. The objective was to provide a working knowledge of some of the techniques developed over the last 40…

Statistics Theory · Mathematics 2024-01-29 Andrea Montanari , Subhabrata Sen

The 2024 Nobel Prize in Physics was awarded for pioneering contributions at the intersection of artificial neural networks (ANNs) and spin-glass physics, underscoring the profound connections between these fields. The topological…

Disordered Systems and Neural Networks · Physics 2025-12-09 Zongrui Pei

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…

The ubiquitous presence of computer simulations in all kinds of research areas evidence their role as the new driving force for the advancement of science and engineering research. Nothing seems to escape the image of success that computer…

Other Computer Science · Computer Science 2019-04-03 Juan M. Durán

Biological, linguistic, sociological and economical applications of statistical physics are reviewed here. They have been made on a variety of computers over a dozen years, not only at the NIC computers. A longer description can be found in…

Popular Physics · Physics 2007-05-23 D. Stauffer

With the advent of high-level programming languages capable of quickly rendering three-dimensional simulations, the inclusion of computers as a learning tool in the classroom has become more prevalent. Although work has begun to study the…

Physics Education · Physics 2015-11-18 Michael J. Obsniuk , Paul W. Irving , Marcos D. Caballero

We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…

Computational Complexity · Computer Science 2008-02-04 Florent Krzakala , Lenka Zdeborová

The design of new devices and experiments in science and engineering has historically relied on the intuitions of human experts. This credo, however, has changed. In many disciplines, computer-inspired design processes, also known as…

Quantum Physics · Physics 2020-10-28 Mario Krenn , Manuel Erhard , Anton Zeilinger

Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…

History and Overview · Mathematics 2025-02-14 Michael R. Douglas , Kyu-Hwan Lee

Our understanding of supercooled liquids and glasses has lagged significantly behind that of simple liquids and crystalline solids. This is in part due to the many possibly relevant degrees of freedom that are present due to the disorder…

Machine Learning · Statistics 2018-08-01 Samuel S. Schoenholz

This paper reviews connections between physics and computation, and explores their implications. The main topics are computational "hardness" of physical systems, computational status of fundamental theories, quantum computation, and the…

Logic · Mathematics 2007-05-23 Joseph Shipman

Theoretical computer science discusses foundational issues about computations. It asks and answers questions such as "What is a computation?", "What is computable?", "What is efficiently computable?","What is information?", "What is…

Logic in Computer Science · Computer Science 2017-10-10 Noson S. Yanofsky

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication…

Physics and Society · Physics 2015-05-30 Chi Ho Yeung , David Saad

This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an efficient way to describe an important class of…

Quantum Physics · Physics 2013-11-12 Keisuke Fujii

Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…

Quantum Physics · Physics 2007-05-23 O. E. Barndorff-Nielsen , R. D. Gill , P. E. Jupp

Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this…

Disordered Systems and Neural Networks · Physics 2012-01-10 David Sherrington

Economies are fundamentally complex and becoming more so, but the new discipline of data science-which combines programming, statistics, and domain knowledge-can help cut through that complexity, potentially with productivity benefits to…

General Economics · Economics 2025-02-06 Arthur Turrell

Physicists study a wide variety of phenomena creating new interdisciplinary research fields by applying theories and methods originally developed in physics in order to solve problems in economics, social science, biology, medicine,…

Popular Physics · Physics 2007-07-24 D. Volchenkov , Ph. Blanchard

Quantitative social science is not only about regression analysis or, in general, data inference. Computer simulations of social mechanisms have a 60-year long history. They have been used for many different purposes -- to test scenarios,…

Physics and Society · Physics 2021-10-01 Petter Holme , Fredrik Liljeros

The world faces two interlinked crises: climate change and loss of biodiversity. Forest restoration on degraded lands and surplus croplands can play a significant role both in sequestering carbon and re-establishing bio-diversity. There is…

Computers and Society · Computer Science 2021-09-17 Gemma Gordon , Amelia Holcomb , Tom Kelly , Srinivasan Keshav , Jon Ludlum , Anil Madhavapeddy