Related papers: On Procrustes Analysis in Hyperbolic Space
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
Instead of testing solely a precise hypothesis, it is often useful to enlarge it with alternatives that are deemed to differ from it negligibly. For instance, in a bioequivalence study one might consider the hypothesis that the…
We investigate the problem of finding complete strictly convex hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of curvature functions.
This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…
This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…
In critical applications, including search-and-rescue in degraded environments, blockages can be prevalent and prevent the effective deployment of certain sensing modalities, particularly vision, due to occlusion and the constrained range…
Contrast set consistency is a robustness measurement that evaluates the rate at which a model correctly responds to all instances in a bundle of minimally different examples relying on the same knowledge. To draw additional insights, we…
Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques such as $k$-center clustering and agglomerative hierarchical clustering. These techniques…
Optimal estimation of signal amplitude, background level, and photocentre location is crucial to the combined extraction of astrometric and photometric information from focal plane images, and in particular from the one-dimensional…
This paper considers the problem of recovering the delays and amplitudes of a weighted superposition of pulses. This problem is motivated by a variety of applications such as ultrasound and radar. We show that for univariate and bivariate…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and…
The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted area with minimum weighted perimeter. According to Chambers' recent proof of the Log Convex Density Conjecture, for many densities on $\mathbb{R}^n$…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
We propose a Procrustean entanglement concentration scheme for continuous variable states inspired by the scheme proposed in Fiurasek et. al. Phys. Rev. A 67, 022304, (2003). We show that the eight-port homodyne measurement of Fiurasek et.…
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.…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…