Related papers: Reflect-Push Methods Part I: Two Dimensional Techn…
We study a large family of Riesz-type singular interaction potentials with anisotropy in two dimensions. Their associated global energy minimizers are given by explicit formulas whose supports are determined by ellipses under certain…
We study the Lorentzian Calder\'on problem, where the objective is to determine a globally hyperbolic Lorentzian metric up to a boundary fixing diffeomorphism from boundary measurements given by the hyperbolic Dirichlet-to-Neumann map. This…
Many Bayesian statistical inference problems come down to computing a maximum a-posteriori (MAP) assignment of latent variables. Yet, standard methods for estimating the MAP assignment do not have a finite time guarantee that the algorithm…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
Deep neural networks have delivered remarkable performance and have been widely used in various visual tasks. However, their huge size causes significant inconvenience for transmission and storage. Many previous studies have explored model…
We consider conformal defects joining two conformal field theories along a line. We define two new quantities associated to such defects in terms of expectation values of the stress tensors and we propose them as measures of the…
Over the recent past data-driven algorithms for solving stochastic optimal control problems in face of model uncertainty have become an increasingly active area of research. However, for singular controls and underlying diffusion dynamics…
We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ…
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured…
Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…
Over the years a number of topologies for the set of laws of stochastic processes have been proposed. Building on the weak topology they all aim to capture more accurately the temporal structure of the processes. In a parallel paper we show…
Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
$D$-optimal designs originate in statistics literature as an approach for optimal experimental designs. In numerical analysis points and weights resulting from maximal determinants turned out to be useful for quadrature and interpolation.…
We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine,…
Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus…
This paper presents a geometric approach to the classical isoperimetric problem by analysing the efficiency of regular polygons in enclosing maximum area for a fixed perimeter. Using efficiency metrics, it proves that regular polygons…
We prove existence and uniqueness for semimartingale reflecting diffusions in 2-dimensional piecewise smooth domains with varying, oblique directions of reflection on each "side", under geometric, easily verifiable conditions. Our…
We propose a novel approach to dimensionality reduction combining techniques of metric geometry and distributed persistent homology, in the form of a gradient-descent based method called DIPOLE. DIPOLE is a dimensionality-reduction…
We theoretically demonstrate that an external magnetic field can be used to control quantum reflection of matter waves in graphene due to its extraordinary magneto-optical properties. We calculate the quantum reflection probabilities in…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…