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We review a number a recent advances in the study of two-dimensional statistical models with strong geometrical constraints. These include folding problems of regular and random lattices as well as the famous meander problem of enumerating…
Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
From an optimizer's perspective, achieving the global optimum for a general nonconvex problem is often provably NP-hard using the classical worst-case analysis. In the case of Cox's proportional hazards model, by taking its statistical…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
Slender structures, such as rods, often exhibit large nonlinear geometrical deformations even under moderate external forces (e.g., gravity). This characteristic results in a rich variety of morphological changes, making them appealing for…
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
Autonomous systems operate in environments that may change over time. An example is the control of a self-driving vehicle among pedestrians and human-controlled vehicles whose behavior may change based on factors such as traffic density,…
This paper shows that the mass-sheet degeneracy and other degeneracies in lensing have simple geometrical interpretations: they are mostly rescalings of the arrival-time surface. Different degeneracies appear in Local Group lensing and in…
Quasi-Bayesian theory uses convex sets of probability distributions and expected loss to represent preferences about plans. The theory focuses on decision robustness, i.e., the extent to which plans are affected by deviations in subjective…
The goal of this article is to discuss a recent conjecture of the two authors, which aims to describe the long time behavior of solutions to one-dimensional dispersive equations with cubic and higher nonlinearities. These problems arguably…
Optimized sensing is important for computational imaging in low-resource environments, when images must be recovered from severely limited measurements. In this paper, we propose a physics-constrained, fully differentiable, autoencoder that…
Defects dictate the properties of many functional materials. To understand the behaviour of defects and their impact on physical properties, it is necessary to identify the most stable defect geometries. However, global structure searching…
{\em Algorithms with predictions} incorporate machine learning predictions into algorithm design. A plethora of recent works incorporated predictions to improve on worst-case optimal bounds for online problems. In this paper, we initiate…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…