Related papers: Two-Dimensional Patterns with Distinct Differences…
Graph Edit Distance (GED) is a fundamental, albeit NP-hard, metric for structural graph similarity. Recent neural graph matching architectures approximate GED by first encoding graphs with a Graph Neural Network (GNN) and then applying…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
This paper extends the problem of 2-dimensional palindrome search into the area of approximate matching. Using the Hamming distance as the measure, we search for 2D palindromes that allow up to $k$ mismatches. We consider two different…
An $m$-distance set is a collection of points such that the distances between any two points have $m$ possible values. We use two different methods to construct large $m$-distance sets on the triangular lattices. One is to use the first m…
Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent…
In this article we prove that locally Griffiths' horizontal distribution on the period domain is given by a generalized version of the familiar contact differential system. As a consequence of this description we obtain strong local…
Maximum distance separable (MDS) codes are optimal error-correcting codes in the sense that they provide the maximum failure-tolerance for a given number of parity nodes. Suppose that an MDS code with $k$ information nodes and $r=n-k$…
In this paper, we explore the design and analysis of regular bipartite graphs motivated by their application in low-density parity-check (LDPC) codes specifically with constrained girth and in the high-rate regime. We focus on the relation…
We construct families of symmetric, antisymmetric, and asymmetric solitary modes in one-dimensional bichromatic lattices with the second-harmonic-generating ($\chi ^{(2)}$) nonlinearity concentrated at a pair of sites placed at distance…
Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the…
A theoretical investigation is made of the dispersion characteristics of plasmons in a two-dimensional periodic system of semiconductor (dielectric) cylinders embedded in a dielectric (semiconductor) background. We consider both square and…
We confirm a conjecture by Everett, Sinclair, and Dankelmann~[Some Centrality results new and old, J. Math. Sociology 28 (2004), 215--227] regarding the problem of maximizing closeness centralization in two-mode data, where the number of…
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
The distributions of the random distances associated with hexagons, rhombuses and triangles have been derived and verified in the existing work. All of these geometric shapes are related to each other and have various applications in…
MRD codes are maximum codes in the rank-distance metric space on $m$-by-$n$ matrices over the finite field of order $q$. They are diameter perfect and have the cardinality $q^{m(n-d+1)}$ if $m\ge n$. We define switching in MRD codes as…
For a linear code $C$ over a finite field, if its dual code $C^{\perp}$ is equivalent to itself, then the code $C$ is said to be {\it isometry-dual}. In this paper, we first confirm a conjecture about the isometry-dual MDS elliptic codes…
We provide a geometric solution to the problem of optimal relay positioning to maximize the multicast rate for low-SNR networks. The networks we consider, consist of a single source, multiple receivers and the only intermediate and…
The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the correlation structure among different functionals such as nodal…
Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in…
Decompositional parameters such as treewidth are commonly used to obtain fixed-parameter algorithms for NP-hard graph problems. For problems that are W[1]-hard parameterized by treewidth, a natural alternative would be to use a suitable…