Related papers: Fermat Distances: Metric Approximation, Spectral C…

We proposed a novel approach to coherent imaging of dynamic samples. The inter-frame similarity of the sample's local structures is found to be a powerful constraint in phasing a sequence of diffraction patterns. We devised a new image…

Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance…

The determination of exponentially stable equilibria and their basin of attraction for a dynamical system given by a general autonomous ordinary differential equation can be achieved by means of a contraction metric. A contraction metric is…

To construct dispersion relations for diffusion or oscillation processes on random networks, it is necessary to obtain effective length scales for the eigenvectors of a graph Laplacian matrix, whose eigenvalues represent inverse time…

In this paper, we systematically develop the $m$-contiguity distance between simplicial maps as a discrete approximation framework for homotopical complexity in the category of simplicial complexes. We construct an increasing sequence of…

In this paper, we present a new self-supervised scene flow estimation approach for a pair of consecutive point clouds. The key idea of our approach is to represent discrete point clouds as continuous probability density functions using…

The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic…

We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…

We introduce the Frustrated Distance Matrix (FDM) model, a dynamic extension of the static distance-matrix ensemble on S^2 analyzed by Bogomolny, Bohigas, and Schmit (BBS). Its entries are pairwise geodesic distances between N Brownian…

Distance matrices are matrices whose elements are the relative distances between points located on a certain manifold. In all cases considered here all their eigenvalues except one are non-positive. When the points are uncorrelated and…

We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…

We introduce a rigorous, physically appealing, and practical way to measure distances between exchange-only correlations of interacting many-electron systems, which works regardless of their size and inhomogeneity. We show that this…

Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…

Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent a substantively important form of acyclic digraphs. For example, the study of such networks includes the spread of…

Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…

This paper presents a deep relational metric learning (DRML) framework for image clustering and retrieval. Most existing deep metric learning methods learn an embedding space with a general objective of increasing interclass distances and…

Predicting human trajectories is a challenging task due to the complexity of pedestrian behavior, which is influenced by external factors such as the scene's topology and interactions with other pedestrians. A special challenge arises from…

Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…