Statistical, Nonlinear, and Soft Matter Physics Commons^™

The Grasshopper's Journey To The Bloch Sphere, David Llamas

Graduate Doctoral Dissertations

The Grasshopper Problem asks a simple geometric question. A grasshopper lands on a lawn of fixed area and jumps a fixed distance in a random direction. What shape of lawn maximizes the probability that the grasshopper remains on the lawn after jumping? The jump rule is rotationally symmetric, but the best lawns do not have to be. This dissertation studies how that symmetry breaking occurs, maps the continuum problem to a novel constrained spin system, and uses the spherical Grasshopper Problem to compare quantum singlet correlations with classical local models.

For planar lawns, boundary-integral and perturbative calculations explain why the …

A Statistical Mechanics Approach To Reinforcement Learning, Jacob Adamczyk

Graduate Doctoral Dissertations

Reinforcement learning (RL), the study of optimal decision-making over long timescales in stochastic systems, has recently seen remarkable advances due in large part to the efforts of the deep learning community. RL has witnessed great success in solving problems in video games, robotics, biological control, and language modeling. However, a unified statistical mechanics framework to understand and develop the corresponding algorithms is lacking. To address this issue, we begin by showing that the reinforcement learning problem can be formulated and solved using the tools of statistical mechanics. Drawing on physical principles of free energy minimization and invariance, we address important …

Application Of Graphical Models In Protein-Protein Interactions And Dynamics, Amir Vajdi Hoojghan

Graduate Doctoral Dissertations

Every organism contains a few hundred to thousands of proteins. A protein is made of a sequence of molecular building blocks named amino acids. Amino acids will be referred to as residues. Every protein performs one or more functions in the cell. In order for a protein to do its job, it requires to bind properly to other partner proteins. Many genetic diseases such as cancer are caused by mutations (changes) of specific residues which cause disturbances in the functions of those proteins.

The problem of prediction of protein binding site is a crucial topic in computational biology. A protein …