Related papers: How model sets can be determined by their two-poin…
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time…
Large language models can exhibit unexpected behavior in the blink of an eye. In a recent computer use demo, a language model switched from coding to Googling pictures of Yellowstone, and these sudden shifts in behavior have also been…
The problem of determining three-dimensional density fields from single two-dimensional projections is hopelessly underdetermined without additional assumptions. While parameterized inversions are typically used to solve this problem, we…
In an era characterized by advancements in artificial intelligence and robotics, enabling machines to interact with and understand their environment is a critical research endeavor. In this paper, we propose Answerability Fields, a novel…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
We study the variance in the number of points contained within a window $\Omega$ of arbitrary size, and to further illuminate our understanding of {\it hyperuniform} systems, i.e., point patterns that do not possess long-wavelength…
We employ the microcanonical inflection-point analysis method, developed for the systematic identification and classification of phase transitions in systems of any size, to study the two-dimensional Ising model at various lattice sizes and…
The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict…
We introduce and demonstrate two linear inverse modelling methods for systems of stochastic ODE's with accuracy that is independent of the dimensionality (number of elements) of the state vector representing the system in question.…
We propose dynamical collapse models in which the stochastic collapse terms affect only photons and/or gravitons. In principle, isolated systems comprising only massive particles could evolve unitarily indefinitely in such models. In…
We develop theory to understand an intriguing property of diffusion models for image generation that we term critical windows. Empirically, it has been observed that there are narrow time intervals in sampling during which particular…
This paper addresses the classical problem of determining the set of possible states of a linear discrete-time system subject to bounded disturbances from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…
Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection.…
Is it possible to understand the intricacies of a dynamical system not solely from its input/output pattern, but also by observing the behavior of other systems within the same class? This central question drives the study presented in this…
One of the main challenges in identifying structural changes in stochastic processes is to carry out analysis for time series with dependency structure in a computationally tractable way. Another challenge is that the number of true change…
We address the problem of finding reliable dense correspondences between a pair of images. This is a challenging task due to strong appearance differences between the corresponding scene elements and ambiguities generated by repetitive…
The requirement of generating predictions that exactly fulfill the fundamental symmetry of the corresponding physical quantities has profoundly shaped the development of machine-learning models for physical simulations. In many cases,…