相关论文: Intriguing symmetry in statistical structures of S…

We use binary trees to study the Bratteli diagram of Sylow 2-subgroups of symmetric groups. We show that it is simple, has a recursive structure, and self-similarities at all scales. We contrast its subgraph of one-dimensional…

We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…

Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…

Consider the number of permutations in the symmetric group on n letters that contain c copies of a given pattern. As c varies (with n held fixed) these numbers form a sequence whose properties we study for the monotone patterns and the…

We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…

Processing of symbolic sequences represented by mapping of symbolic data into numerical signals is commonly used in various applications. It is a particularly popular approach in genomic and proteomic sequence analysis. Numerous mappings of…

The regular structures of a generic 4D symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1D-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of…

In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…

Recent works have developed samples of blazars from among the Fermi-LAT unassociated sources via machine learning comparisons with known blazar samples. Continued analysis of these new blazars tests the predictions of the blazar sequence…

I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…

We review here our study of a supersymmetric left-right model (SLRM). In the model the $R$-parity is spontaneously broken. Phenomenologically novel feature of the model is the occurrance of the doubly charged particles in the Higgs sector,…

Leptoquarks extending the Standard Model (SM) are attracting an increasing attention in the recent literature. Hence, the identification of 4D SM-like models and the classification of allowed leptoquarks from strings is an important step in…

I discuss the usefulness of lattice supersymmetry in relation to string phenomenology. I suggest how lattice results might be incorporated into string phenomenology. I outline difficulties and describe some constructions that contain an…

Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…

The classification procedure of streaming data usually requires various ad hoc methods or particular heuristic models. We explore a novel non-parametric and systematic approach to analysis of heterogeneous sequential data. We demonstrate an…

Spatial transcriptomics is a modern sequencing technology that allows the measurement of the activity of thousands of genes in a tissue sample and map where the activity is occurring. This technology has enabled the study of the so-called…

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…

A model of genomic sequence evolution on a species tree should include not only a sequence substitution process, but also a coalescent process, since different sites may evolve on different gene trees due to incomplete lineage sorting.…

The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has…

Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized…