Related papers: Optimal Bounds for Weak Consistent Digital Rays in…
The goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of compressible complete Euler system in the full space $ \mathbb{R}^d,\; d=2,3 $ is a weak solution of the system then eventually the…
Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles…
In general, it is difficult to measure distances in the Weil-Petersson metric on Teichm\"uller space. Here we consider the distance between strata in the Weil-Petersson completion of Teichm\"uller space of a surface of finite type. Wolpert…
Deep Convolutional Neural Networks (CNNs) have achieved remarkable results on Single Image Super-Resolution (SISR). Despite considering only a single degradation, recent studies also include multiple degrading effects to better reflect…
We investigate the box dimensions of compact sets in $\mathbb{R}^2$ that contain a unit distance in every direction (such sets may have zero Hausdorff dimension). Among other results, we show that the lower box dimension must be at least…
Charge-density wave (CDW) order is a key property of high-Tc cuprates, but its boundaries in the phase diagram and potential connections to other phases remain controversial. We report nuclear magnetic resonance (NMR) measurements in the…
We study range spaces, where the ground set consists of either polygonal curves in $\mathbb{R}^d$ or polygonal regions in the plane that may contain holes and the ranges are balls defined by an elastic distance measure, such as the…
We study linear codes that maximize minimum distance subject to arbitrary support constraints on the parity-check matrix. Such constraints arise naturally in the design of LDPC codes, locally repairable codes, and hardware-constrained…
To save energy and alleviate interferences in a wireless sensor network, the usage of virtual backbone was proposed. Because of accidental damages or energy depletion, it is desirable to construct a fault tolerant virtual backbone, which…
While Signed Distance Fields (SDF) are well-established for modeling watertight surfaces, Unsigned Distance Fields (UDF) broaden the scope to include open surfaces and models with complex inner structures. Despite their flexibility, UDFs…
In the Hausdorff Voronoi diagram of a set of clusters of points in the plane, the distance between a point t and a cluster P is the maximum Euclidean distance between t and a point in P. This diagram has direct applications in VLSI design.…
We study the presence of tidal features associated with ultra diffuse galaxies (UDGs) in galaxy clusters. Specifically, we stack deep Subaru images of UDGs in the Coma cluster to determine whether they show position angle twists at large…
Low-dimensional materials are susceptible to electronic instabilities such as charge density waves (CDWs), originating from a divergence in the Lindhard electron response function, combined with a finite electron-phonon coupling strength.…
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…
In object detection, a well-defined similarity metric can significantly enhance model performance. Currently, the IoU-based similarity metric is the most commonly preferred choice for detectors. However, detectors using IoU as a similarity…
We prove some geometric properties of sets in the first Heisenberg group whose Heisenberg Hausdorff dimension is the minimal or maximal possible in relation to their Euclidean one and the corresponding Hausdorff measures are positive and…
We present a catalogue of 5306 new ultracool dwarf (UCD) candidates in the three Euclid Deep Fields in the Q1 data release. They range from late M to late T dwarfs, and include 1200 L and T dwarfs. A total of 546 objects have been…
A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann--Tzeng (HT) bound is formulated…
Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations, bit mapping and coding. Earlier results obtained for the AWGN channel are extended to…
$\delta$-Covering, for some covering range $\delta>0$, is a continuous facility location problem on undirected graphs where all edges have unit length. The facilities may be positioned on the vertices as well as on the interior of the…