相关论文: Novel Constructions of 2-D Golay Complementary Arr…

Graph contrastive learning (GCL) has become a hot topic in the field of graph representation learning. In contrast to traditional supervised learning relying on a large number of labels, GCL exploits augmentation strategies to generate…

The study of optical orthogonal codes has been motivated by an application in an optical code-division multiple access system. This paper focuses on optimal two-dimensional optical orthogonal codes with autocorrelation and cross-correlation…

Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…

Two-dimensional (2D) graphene-like layered semiconductors provide a new platform for materials research because of their unique mechanical, electronic and optical attributes. Their in-plane covalent bonding and dangling-bond-free surface…

We determine the symmetries of four different theories: I) Galilean Electrodynamics (GED), II) GED coupled to 5 free static scalar fields, III) Galilean Yang-Mills (GYM), and IV) GYM coupled to 5 interacting scalar fields. We correct some…

CCS can be considered as a most natural extension of finite state automata in which interaction is made possible thanks to parallel composition. We propose here a similar extension for top-down tree automata. We introduce a parallel…

Using transfer matrices up to next-nearest-neighbour (NNN) interactions, we examine the structural correlations of quasi-one-dimensional systems of hard disks confined by two parallel lines and hard spheres confined in cylinders.…

In this letter, we propose a (2+1)-dimensional generalized Camassa-Holm (2dgCH) hierarchy with both quadratic and cubic nonlinearity. The Lax representation and peakon solutions for the 2dgCH system are derived.

This is the fourth paper in the CayleyPy project, which applies AI methods to the exploration of large graphs. In this work, we suggest the existence of a new discrete version of holographic string dualities for this setup, and discuss…

Let $G$ be a finite simple graph on a vertex set $V(G)=\{x_{11}, \ldots, x_{n1}\}$. Also let $m_1, \ldots,m_n \geq 2$ be integers and $G_1, \ldots, G_n$ be connected simple graphs on the vertex sets $V(G_i)=\{x_{i1}, \ldots, x_{im_i}\}$. In…

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…

Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are…

Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\mathbb{R}^d$. We consider…

One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…

A linear code with parameters $[n, k, n - k + 1]$ is called maximum distance separable (MDS), and one with parameters $[n, k, n - k]$ is called almost MDS (AMDS). A code is near-MDS (NMDS) if both it and its dual are AMDS. NMDS codes…

This paper presents a "two-dimensional Fourier Continuation" method (2D-FC) for construction of bi-periodic extensions of smooth non-periodic functions defined over general two-dimensional smooth domains. The approach can be directly…

We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is…

A new realization of extended quantum-mechanical supersymmetry (QM SUSY) with central extension is investigated. We first show that two different sets of $d+2$ ($d+1$) supercharges for $d=$ even (odd), each of which satisfies an…

This is an overview about a method of constructing ccc forcings: Suppose first that a continuous, commutative system of complete embeddings between countable forcings indexed along $\omega_1$ is given. Then its direct limit satisfies ccc by…

We propose to consider ensembles of cycles (quadrics), which are interconnected through conformal-invariant geometric relations (e.g. "to be orthogonal", "to be tangent", etc.), as new objects in an extended Moebius--Lie geometry. It was…