Integrating evidence under uncertainty: from sensory perception to reward-guided predictions

Adaptive behavior requires organisms to infer the state of the environment from information that is incomplete, noisy, and distributed across multiple sources and timescales. Although perception, learning, and decision-making are often studied as separate cognitive functions, they can also be viewed as manifestations of a common inferential problem: constructing and continuously updating internal models of the world to guide behavior under uncertainty. This thesis investigates how humans and ...

Relativistic Magnetohydrodynamic Modelling of Gamma-ray Burst Jets: From Early Propagation to Afterglow Emission

Gamma-ray bursts are among the most energetic transient phenomena in the Universe. Since their discovery, a dedicated branch of research has been developed to understand their origin and the physics involved. They are thought to arise from ultra-relativistic jets, launched by at least two distinct classes of progenitors: a binary neutron star merger, and the core collapse of a rotating, strongly magnetised massive star. In both cases, the jet is launched by a central engine, harbouring a rot...

The Statistics of Alternative Attractors in Microbial Communities

Representations of Atomic Environments and effects on Body-Ordering and Electrostatics on Machine-Learning Potentials

Machine learning interatomic potentials (MLIPs) achieve DFT-level accuracy by replacing rigid functional forms with neural network architectures that allow for much more effective regression at the cost of less intuitive representations. This thesis explores how representations of atomic environments used by MLIPs behave in two regimes: at short range in how body-ordered expansions converge with respect to their basis functions, and at long range, in improving modeling the electronic response...

Data-driven models for RNA: physical and statistical approaches to secondary structure, RNA–protein interactions, and siRNA potency

RNA structures and interactions are often accessible only through indirect, noisy measurements. Principled models of how observations arise allow data-driven regression to infer not only measured labels but also latent biological quantities. This thesis develops such physical and statistical frameworks for RNA secondary structure, RNA--protein interactions, and siRNA potency. MERGE-RNA describes RNA structural ensembles by modelling the physics of dimethyl sulfate (DMS) probing. It lear...

Molecular Dynamics Simulations of Flexible Biomolecules: Development of Enhanced Sampling Methods and Integration of Experimental Data

Molecular dynamics (MD) simulations act as molecular microscopes, giving access to the position of every atom at every instant of time. This access comes at a price: the reliability of the result is limited by the accuracy of the underlying force field, and by the amount of conformational space that the simulation is actually able to explore. This thesis addresses both sides of this problem, by developing techniques that make the exploration of conformational space more efficient and by integ...

Theory of Learning in High-Dimensional Neural Networks: Generalization, Transfer Learning, and Neural Scaling Laws

This thesis develops predictive theories for neural networks in high-dimensional settings, focusing on three problems of particular relevance to modern machine learning: generalization, transfer learning, and neural scaling laws. We first study the generalization error of two-layer neural networks with generic activation functions in a setting closer to empirical risk minimization, rather than restricting the analysis to an optimal statistical benchmark, and we characterize how the regulariza...

Mechanical instabilities in soft active materials: Flutter in electroactive structures and surface instability in magnetoelastic solids

Soft active materials deform in response to external fields, a feature enabling their untethered actuation. Of particular interest in this context are actuation strategies that exploit mechanical instabilities, whereby the loss of stability of an equilibrium at a critical value of the external stimulus triggers large-amplitude deformations or motions. This thesis explores this opportunity through the analysis of three model systems, under a restriction maintained throughout the study: the...

Reflection Positivity, Magnetic Lattice Laplacians and Emergent Phases in Lattice Fermionic Systems

Emergent phenomena in interacting fermionic systems often arise as collective many-body effects whose formation can be understood by studying the interplay between geometry and symmetry. Understanding such phenomena from first principles remains one of the central challenges of Mathematical Physics, particularly in regimes where perturbative methods fail and non-trivial phases emerge through strongly correlated dynamics. This thesis investigates a class of lattice fermionic systems exhibi...