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In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…

We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…

The degree sequence of a graph is a numerical method to characterize the properties of graphs. Generalized forms of degree sequences exist for complete graphs and complete graphs. Nikolopolus et al. characterized the number of spanning…

FinInG is a package for computation in Finite Incidence Geometry. It provides users with the basic tools to work in various areas of finite geometry from the realms of projective spaces to the flat lands of generalised polygons. The…

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

Motivation: Bacteriophages (aka phages), which mainly infect bacteria, play key roles in the biology of microbes. As the most abundant biological entities on the planet, the number of discovered phages is only the tip of the iceberg.…

Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network…

Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple…

With the rapid growth of large-scale single-cell omic datasets, omic foundation models (FMs) have emerged as powerful tools for advancing research in life sciences and precision medicine. However, most existing omic FMs rely primarily on…

Machine learning has emerged as a powerful tool for time series analysis. Existing methods are usually customized for different analysis tasks and face challenges in tackling practical problems such as partial labeling and domain shift. To…

Coordination sequences of periodic and quasiperiodic graphs are analysed. These count the number of points that can be reached from a given point of the graph by a number of steps along its bonds, thus generalising the familiar coordination…

While many good textbooks are available on Protein Structure, Molecular Simulations, Thermodynamics and Bioinformatics methods in general, there is no good introductory level book for the field of Structural Bioinformatics. This book aims…

We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…

These are lecture notes for a short course about spectral sequences that was held at M\'alaga, October 18--20 (2016), during the "Fifth Young Spanish Topologists Meeting". The approach was to illustrate the basic notions via fully computed…

Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg's proof of Szemer\'edi's Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost…

Information extraction methods proved to be effective at triple extraction from structured or unstructured data. The organization of such triples in the form of (head entity, relation, tail entity) is called the construction of Knowledge…

{\sc Combine} is an add-on to {\sc SigSpec} and {\sc Cinderella}. A {\sc SigSpec} result file or a file generated by {\sc Cinderella} contains the significant sinusoidal signal components in a time series. In this file, {\sc Combine} checks…

Manifold learning techniques for dynamical systems and time series have shown their utility for a broad spectrum of applications in recent years. While these methods are effective at learning a low-dimensional representation, they are often…

Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…

Textual graphs (TGs) are graphs whose nodes correspond to text (sentences or documents), which are widely prevalent. The representation learning of TGs involves two stages: (i) unsupervised feature extraction and (ii) supervised graph…