Related papers: Introduction to Phase Transitions in Random Optimi…

These notes are based on a series of six lectures, given during my stay at the CRC 701 in June/July 2008. The lecture series intended to give a survey of some of the results for the almost Mathieu operator that have been obtained since the…

This is a set of lecture notes used in a graduate topic class in applied mathematics called ``Quantum Algorithms for Scientific Computation'' at the Department of Mathematics, UC Berkeley during the fall semester of 2021. These lecture…

These proceedings collect the presentations given at the first three meetings of the INFN "Workshop on Monte Carlo's, Physics and Simulations at the LHC", held at the Frascati National Laboratories in 2006. The first part of these…

For Encyclopedia of Complexist and System Science No abstract given I. Definition and Introduction II. Ising Model III. Fractals IV. Diffusion on Fractals V. Ising Model on Fractals VI. Other Subjects ? VII. Networks VIII. Future Directions

We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase…

This is a status report on a companion subject to extremal combinatorics, obtained by replacing extremality properties with emergent structure, `phases'. We discuss phases, and phase transitions, in large graphs and large permutations,…

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…

Hybrid systems are complex dynamical systems that combine discrete and continuous components. Reachability questions, regarding whether a system can run into a certain subset of its state space, stand at the core of verification and…

This volume contains the post-proceedings of PLACES 2014, the seventh Workshop on Programming Language Approaches to Concurrency and Communication-cEntric Software, which was held in Grenoble, France, on April 12th 2014, and co-located with…

These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…

Lecture notes in french of the lecture on surface tension given in 2015 and 2016 at the preparation to "Agr\'egation de physique" in the Ecole Normale Sup\'erieure de Lyon

Numerical methods play an ever more important role in astrophysics. This is especially true in theoretical works, but of course, even in purely observational projects, data analysis without massive use of computational methods has become…

Notes of five lectures given at the 2003 European School of High-Energy Physics, Tsakhkadzor, Armenia, September 2003

Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. The lectures covered quantum mechanics for closed systems like the universe, generalized quantum mechanics, time in…

I present an analytic approach to establishing the presence of phase transitions in a large set of decision problems. This approach does not require extensive computational study of the problems considered. The set -- that of all paddable…

We present computer simulations run with a stochastic cellular automaton which describes $d=1$ particle systems connected to reservoirs which keep two different densities at the endpoints. We fix the parameters so that there is a phase…

It is a working version of a lecture on the theory of enlargement of filtration, given at the African Mathematic School in Marrakech, October 19-23, 2015.

These are notes for a set of 7 two-hour lectures given at the 2010 Summer School on Quantitative Evolutionary and Comparative Genomics at OIST, Okinawa, Japan. The emphasis is on understanding how biological systems process information. We…

This material was presented in a series of lectures at the Santa Fe Institute, the Los Alamos National Laboratory, and the University of New Mexico, during a one-month visit to the Santa Fe Institute, April 1995.

This document collects the lecture notes from my course "Communication Complexity (for Algorithm Designers),'' taught at Stanford in the winter quarter of 2015. The two primary goals of the course are: 1. Learn several canonical problems…