Challenges in computational statistical mechanics

Statistical mechanics of classical and quantum computational complexity

The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous framework for classifying the hardness of problems according to the computational resources, most notably time, needed to solve them. Its extension to quantum comput...

Introduction. Statistical and computational challenges in molecular phylogenetics and evolution

1. INTRODUCTION Since the widespread acceptance of Darwin's theory of evolution (Darwin 1859), scientists have been interested in reconstructing the evolutionary relationships of living (and extinct) organisms. Evolution occurs too slowly to be experimented upon in situ in any but the most extreme cases, and scientists must look for information in the contemporary world that can lead to insight...

Dependence models in high dimensions: Statistical and computational challenges

Complexity in Ecology and Conservation: Mathematical, Statistical, and Computational Challenges

E communities comprise complex networks of individuals interacting with each other and with their environment. Two major challenges for scientists, managers, and policymakers are (1) understanding the forces that organize these heterogeneous systems across space and time (Levin 1992, Levin et al. 1997, Brown et al. 2002) and (2) using this understanding to address environmental problems at loca...

Justification in Statistical Mechanics

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low entropy macrostates are less probable than high entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law of thermodynamics is fun...