Related papers: How model sets can be determined by their two-poin…

We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means…

Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…

The non-Hermitian dynamics of open systems deal with how intricate coherent effects of a closed system intertwine with the impact of coupling to an environment. The system-environment dynamics can then lead to so-called exceptional points,…

In this project we show the existence of arbitrary length arithmetic progressions in model sets and Meyer sets in the Euclidean $d$-space. We prove a van der Waerden type theorem for Meyer sets. We show that pure point subsets of Meyer sets…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

Nonlinearity and non-Hermiticity, for example due to environmental gain-loss processes, are a common occurrence throughout numerous areas of science and lie at the root of many remarkable phenomena. For the latter, parity-time-reflection…

We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and are defined by a probability density and a two-form. This…

We show an approach to automated control of machine vision systems based on incremental creation and evaluation of a particular family of influence diagrams that represent hypotheses of imagery interpretation and possible subsequent…

Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…

In segmentation problems, inference on change-point position and model selection are two difficult issues due to the discrete nature of change-points. In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable formulae…

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate (N+1)-point correlation functions with a…

Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through…

Minimizing the Euclidean distance to a set arises frequently in applications. When the set is algebraic, a measure of complexity of this optimization problem is its number of critical points. In this paper we provide a general framework to…

For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…

Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…

We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with…

The performance of machine learning models is determined by the quality of their learned features. They should be invariant under irrelevant data variation but sensitive to task-relevant details. To visualize whether this is the case, we…

The objective of change-point detection is to discover abrupt property changes lying behind time-series data. In this paper, we present a novel statistical change-point detection algorithm based on non-parametric divergence estimation…

The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as…

Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…