Abstract: In this talk, I will present our recent results on the statistical properties of the non-hierarchical planar three-body problem, relevant to astrophysical systems with nearly planar dynamics. Using the Flux-based statistical theory of the three-body problem, previously studied in three dimensions, we derive theoretical predictions for several statistical observables in the planar case. We compare these predictions directly with numerical simulations and contrast the results with the corresponding unconstrained three-dimensional case. Our analysis is based on one million simulations for each of eight distinct mass sets. We examine escape probabilities, properties of marginal escape events, eccentricity distributions, lifetime distributions, and relative prevalence of prograde and retrograde escapes. While several of the theoretical predictions are in good agreement with the simulations, others exhibit unexpected discrepancies.

Abstract: TBA

Abstract: Many processes at the LHC produce energetic b-quarks that hadronize into b-hadrons. Identifying which b-hadron is produced is important for many analyses, yet most infer it from a single exclusive decay channel, usually a decay into fully charged final particles. This approach is limited by small branching ratios and an irreducible background from competing decays with the same final state. We instead propose an inclusive fragmentation tagger based on machine learning.

The central challenge is the training data. A model trained on simulation inherits the poor modelling of low-energy, non-perturbative QCD. Training on real collisions removes that dependence but introduces a bias toward the small subset of reconstructible decay topologies.

We address this with BLIND (Bias-free Labeling for INclusive Decays), a two-stage algorithm. It builds on the fact that the particles produced during fragmentation at the primary vertex have some correlation with the b-hadron's identity, regardless of the decay channel. A first network infers the b-hadron species from primary-vertex information alone, assigning pseudo-labels to a fully inclusive sample. A second, weakly supervised network then trains directly on this sample, learning to separate species from the decay. The two outputs may be combined to exploit both the fragmentation and decay views for the final prediction. The result is a tagger trained entirely on data, free of simulation and of decay-selection bias, that leverages the full jet information.

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: TBA