Non-affine fluctuations and the Statistics of Defect Precursors in the Planar Honeycomb Lattice

Certain localised displacement fluctuations in the planar honeycomb lattice may be identified as precursors to topological defects. We show that these fluctuations are among the most pronounced {\em non-affine} distortions of an elemental coarse graining volume of the honeycomb structure at non zero temperatures. We obtain the statistics of these precursor modes in the canonical ensemble, evaluating exactly their single point and two-point spatio-temporal distributions, for a lattice with harmonic nearest neighbour and next near neighbour bonds. As the solid is destabilised by tuning interactions, the precursor fluctuations diverge and correlations become long-lived and long-ranged.Comment: 14 pages, 7 figures, IOP forma

LEAD: Least-Action Dynamics for Min-Max Optimization

Adversarial formulations such as generative adversarial networks (GANs) have rekindled interest in two-player min-max games. A central obstacle in the optimization of such games is the rotational dynamics that hinder their convergence. Existing methods typically employ intuitive, carefully hand-designed mechanisms for controlling such rotations. In this paper, we take a novel approach to address this issue by casting min-max optimization as a physical system. We leverage tools from physics to introduce LEAD (Least-Action Dynamics), a second-order optimizer for min-max games. Next, using Lyapunov stability theory and spectral analysis, we study LEAD's convergence properties in continuous and discrete-time settings for bilinear games to demonstrate linear convergence to the Nash equilibrium. Finally, we empirically evaluate our method on synthetic setups and CIFAR-10 image generation to demonstrate improvements over baseline methods

Invasive fish disrupt host-pathogen dynamics leading to amphibian declines

Sudden disease outbreaks may not necessarily reflect a recent pathogen introduction but may instead arise from the disruption of a host-pathogen equilibrium. Together with invasive species, emerging pathogens pose significant threats to biodiversity. The dynamics of each stressor have been studied separately, yet rarely when interacting. Using a 40-year dataset, we tested the hypothesis that the introduction of an invasive fish leads to such a disruption, manifested by ranavirosis outbreaks on amphibian hosts. MCP sequencing revealed the historical presence of two major Ranavirus clades, with low prevalence. The introduction of fish was not followed by the emergence of new viruses, but rather by an increase in the prevalence of the strains already present, fitting the ‘endemic pathogen hypothesis’. Two decades after the first die-offs, one amphibian species persists in extremely low numbers, but Ranavirus prevalence is closer to the enzootic phase that preceded the outbreaks. Models show that host population collapse and lack of recovery are best explained by the concerted interaction of Ranavirus and invasive fish. We provide robust evidence that invasive species can impact naïve communities by disrupting the host-pathogen balance, exacerbating health threats. This study emphasizes the importance of exploring the historical interactions between multiple stressors to understand population declines.info:eu-repo/semantics/publishedVersio

Topics in Quantum-Hall Physics, Game-Optimization and Generalization in Neural Networks

This thesis contains research conducted on various topics in quantum Hall physics and deep learning theory. The first chapter studies a particular aspect of quantum Hall systems, namely their behavior around the $\nu = 1/2$ Landau level (LL) state. This work is motivated by the need to understand better this particular state in light of the two proposed distinct theoretical descriptions existing for the same. Specifically, we analyze quantum oscillations around the $\nu = 1/2$ LL state using one of the propositions to support the latter. The second and third chapters study two distinct domains in deep learning, multi and single-objective models. In particular, the second considers a specific type of multi-objective model, zero-sum games, to demonstrate existing issues in training such setups and develop an efficient optimization scheme. The final chapter involves studying a particular aspect of the generalization behavior of deep neural networks (DNNs). Specifically, it attempts to provide a theoretical framework to explain the recently observed phenomenon of "epoch-wise double descent" in such DNNs