Related papers: Computing the luminosity distance via optimal homo…
The cosmic distance duality relation (DDR), which links the angular diameter distance and the luminosity distance, is a cornerstone in modern cosmology. Any deviation from DDR may indicate new physics beyond the standard cosmological model.…
Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein…
We propose a new practical algorithm for computing the Feigenbaum constants {\alpha} and {\delta}, having significantly lower time and space complexity than previously used methods. The algorithm builds upon well-known linear algebra…
The most recent Hubble constant ($H_0)$ estimates from local methods (z << 1), $H_0=73.8\pm 2.4$ km s$^{-1}$ Mpc$^{-1}$, and the one from high redshifts $H_0=67.3\pm 1.2$ km s$^{-1}$ Mpc$^{-1}$, are discrepant at $2.4 \sigma$ confidence…
The discrete Fr{\'e}chet distance is a measure of similarity between point sequences which permits to abstract differences of resolution between the two curves, approximating the original Fr{\'e}chet distance between curves. Such distance…
We compare various approaches to find the most efficient method for the practical computation of the lightcurves (integrated brightnesses) of irregularly shaped bodies such as asteroids at arbitrary viewing and illumination geometries. For…
In Optimal Transport (OT) on a finite metric space, one defines a distance on the probability simplex that extends the distance on the ground space. The distance is the value of a Linear Programming (LP) problem on the set of…
The method of stable random projections is a tool for efficiently computing the $l_\alpha$ distances using low memory, where $0<\alpha \leq 2$ is a tuning parameter. The method boils down to a statistical estimation task and various…
We present a cosmographic study designed to test the simplest type of accelerating cosmology: a flat universe with matter and a cosmological constant ($\Lambda$). Hubble series expansions are fit to the SCP Union2.1 supernova data set to…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
I present general analytic expressions for distance calculations (comoving distance, time coordinate, and absorption distance) in the standard $\Lambda$CDM cosmology, allowing for the presence of radiation and for non-zero curvature. The…
We present a cosmological model-independent determination of the Hubble constant, $H_0$, by combining time-delay measurements from seven TDCOSMO systems, Einstein radius measurements, and Type Ia Supernovae data sourced from the Pantheon+…
Illumination estimation remains a pivotal challenge in image processing, particularly for robotics, where robust environmental perception is essential under varying lighting conditions. Traditional approaches, such as RGB histograms and…
This paper presents a new model-independent constraint on the Hubble constant ($H_0$) by anchoring relative distances from Type Ia supernovae (SNe Ia) observations to absolute distance measurements from time-delay strong Gravitational…
This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…
The abundant spatial and angular information from light fields has allowed the development of multiple disparity estimation approaches. However, the acquisition of light fields requires high storage and processing cost, limiting the use of…
Consider a compact $M \subset \mathbb{R}^d$ and $l > 0$. A maximal distance minimizer problem is to find a connected compact set $\Sigma$ of the length (one-dimensional Hausdorff measure $\mathcal H$) at most $l$ that minimizes \[ \max_{y…
The \emph{Skorokhod distance} is a natural metric on traces of continuous and hybrid systems. For two traces, from $[0,T]$ to values in a metric space $O$, it measures the best match between the traces when allowed continuous bijective…
All known algorithms for the Fr\'echet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values.…
A homogeneous set of $n$ points in the $d$-dimensional Euclidean space determines at least $\Omega(n^{2d/(d^2+1)} / \log^{c(d)} n)$ distinct distances for a constant $c(d)>0$. In three-space, we slightly improve our general bound and show…