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Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…

Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a…

The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…

Recently, a lot of effort has been dedicated to developing next-generation optoelectronic devices based on two-dimensional materials, thanks to their unique optical properties that are significantly different from those of their bulk…

This document is an informal bibliography of the papers dealing with distributed approximation algorithms. A classic setting for such algorithms is bounded degree graphs, but there is a whole set of techniques that have been developed for…

In this paper, we gave some properties of binomial coefficient.

This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of…

Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of…

The $N$th power of a polynomial matrix of fixed size and degree can be computed by binary powering as fast as multiplying two polynomials of linear degree in~$N$. When Fast Fourier Transform (FFT) is available, the resulting complexity is…

Binary Parseval frames share many structural properties with real and complex ones. On the other hand, there are subtle differences, for example that the Gramian of a binary Parseval frame is characterized as a symmetric idempotent whose…

In this paper, we describe a novel shape classification method which is embedded in the Bayesian paradigm. We discuss the modelling and the resulting shape classification algorithm for two and three dimensional data shapes. We conclude by…

In previous work on Clebsch-Gordan coefficients, certain remarkable hexagonal arrays of integers are constructed that display behaviors found in Pascal's Triangle. We explain these behaviors further using the binomial transform and discrete…

A new family of binary linear completely transitive (and, therefore, completely regular) codes is constructed. The covering radius of these codes is growing with the length of the code. In particular, for any integer r > 1, there exist two…

The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of…

We calculate the differential, total, and transport cross-sections for scattering of two-dimensional massless Dirac electrons by a circular barrier. For scatterer of a small radius, the cross-sections are dominated by quantum effects such…

A special type of binomial splitting process is studied. Such a process can be used to model a high-dimensional corner parking problem, as well as the depth of random PATRICIA tries (a special class of digital tree data structures). The…

Two-dimensional (2D) materials have been proposed, among many other applications, as a efficient tool for the separation of atomic and molecular species and their corresponding isotopes, given the confinement provided by their subnanometric…

We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse…

We establish a novel connection between the central binomial coefficients $\binom{2n}{n}$ and Gould's sequence through the construction of a specialized multivariate polynomial quotient ring. Our ring structure is characterized by ideals…

In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…