Abstract: Natural selection favors traits that improve fitness: the ability to survive and reproduce. But how many traits matter? We show that recovery after catastrophe can reveal the answer. When selection acts on abundant existing variation in a population, the gap between average and highest fitness shrinks inversely with time. Interestingly, the prefactor of this decay is proportional to the number of traits under selection. This law is a dynamical analog of the equipartition principle in statistical mechanics, with time playing the role of inverse temperature and the relevant trait axes acting as effective degrees of freedom. It therefore allows us to count these axes in two large experimental fitness landscapes measured in E. coli under antibiotic stress. We further show that, rather than following gradient ascent on a fitness landscape, adaptation follows a common optimization algorithm, the Levenberg-Marquardt method. Near fitness peaks, the adaptation trajectories become increasingly biased against greediness: from an optimization perspective, post-catastrophic selection becomes progressively optimistic over time. The pace and path of recovery from catastrophe thus quantitatively probe the underlying fitness landscape geometry.

Abstract: I will discuss phase diagrams for non equilibrium steady states of relativistic systems. I will argue that the theoretical prediction agree with the behavior of dynamical black holes.

Abstract: Although chaotic dynamics limits our ability to predict individual trajectories, it may still be possible to make accurate statistical predictions. The Newtonian three-body problem offers a fascinating setting in which to explore this distinction, combining a rich history, fundamental questions in dynamical systems, and considerable astrophysical importance. In this colloquium, I will present a novel statistical theory that expresses predictions in terms of phase-space flux. Validated against extensive numerical simulations, this flux-based theory provides the most accurate statistical predictions to date for the three-body problem. I will also describe a novel dynamical reduction, introducing dynamical variables that significantly simplify the formulation of the problem. Finally, I will show how a related flux-based theory successfully predicts statistical properties of another paradigmatic chaotic system—the double pendulum—including its mean flip rate.

Abstract: TBA