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The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…
We present far-infrared spectral line observations of five galaxies from the LITTLE THINGS sample: DDO 69, DDO 70, DDO 75, DDO 155, and WLM. While most studies of dwarfs focus on bright systems or starbursts due to observational…
Correlations between electrons and the effective dimensionality are crucial factors that shape the properties of an interacting electron system. For example, the onsite Coulomb repulsion, U, may inhibit, or completely block the intersite…
When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…
The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…
Linear complementary dual codes (LCD) intersect trivially with their dual. In this paper, we develop a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level. Further,…
The 2-Wasserstein distance (or RMS distance) is a useful measure of similarity between probability distributions that has exciting applications in machine learning. For discrete distributions, the problem of computing this distance can be…
Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…
To achieve multi-Gb/s data rates in 6G optical wireless access networks based on narrow infrared (IR) laser beams, a high-speed receiver with two key specifications is needed: a sufficiently large aperture to collect the required optical…
Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance…
For each $d \in {1,2,3,7,11}$, let $T_d$ be the nearest-integer complex continued fraction map associated with the Euclidean ring $\mathcal{O}*d$, and let $(a_n)$ be its digit sequence. We prove two metric results for this five-system…
The Gaia data release 2 (DR2) contains $>$6000 objects with parallaxes $(Plx+3\times{e\_Plx})>50$mas placing them within 20pc from the Sun. Since the expected numbers extrapolating the well-known 10pc census are much lower, nearby Gaia…
Attributes such as the Radiative Decay Rate (RDR) and the Radiation Pattern (RP) of Quantum Dots (QDs) are highly sensitive to their nearby surrounding material. To enhance the RDR and shape the RP, interspacing between the QDs and their…
The Radon cumulative distribution transform (R-CDT), is an easy-to-compute feature extractor that facilitates image classification tasks especially in the small data regime. It is closely related to the sliced Wasserstein distance and…
We study infinite Euclidean distance discriminants of algebraic varieties, defined as the loci of data points whose fibers under the second projection from the Euclidean distance correspondence are positive-dimensional. In particular, these…
A two-dimensional grid with dots is called a \emph{configuration with distinct differences} if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many…
Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…
Products of MDS codes are of major practical importance; for a recent example, they are used in Data Availability Sampling (DAS) in blockchain networks such as Celestia and as part of the Ethereum roadmap. This motivates us to consider…
Low-disorder two-dimensional electron systems in the presence of a strong, perpendicular magnetic field terminate at very small Landau level filling factors in a Wigner crystal (WC), where the electrons form an ordered array to minimize the…
Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…