Related papers: Linear $k$-Chord Diagrams
This paper presents an approach to the modeling of degree-degree correlation in complex networks. Thus, a simple function, \Delta(k', k), describing specific degree-to- degree correlations is considered. The function is well suited to…
The rise of deep learning technologies has quickly advanced many fields, including that of generative music systems. There exist a number of systems that allow for the generation of good sounding short snippets, yet, these generated…
Very recently planar collections of Feynman diagrams were proposed by Borges and one of the authors as the natural generalization of Feynman diagrams for the computation of $k=3$ biadjoint amplitudes. Planar collections are one-dimensional…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
We introduce and study multiple partition structures which are sequences of probability measures on families of Young diagrams subjected to a consistency condition. The multiple partition structures are generalizations of Kingman's…
We introduce the $k$-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding $k$ consecutive $1$'s, also called generalized $k$-bonacci words. The polyominoes are very entrancing objects, considered in…
A big challenge in algorithmic composition is to devise a model that is both easily trainable and able to reproduce the long-range temporal dependencies typical of music. Here we investigate how artificial neural networks can be trained on…
We describe recent achievements in the theory of weight systems, which are functions on chord diagrams satisfying so-called $4$-term relations. Our main attention is devoted to constructions of weight systems. The two main sources of these…
In this paper, we count acyclic and strongly connected uniform directed labeled hypergraphs. For these combinatorial structures, we introduce a specific generating function allowing us to recover and generalize some results on the number of…
We study asymptotic behaviour of the correlation functions of bipartite sparse random $N\times N$ matrices. We assume that the graphs have $N$ vertices, the ratio of parts is $\displaystyle\frac{\alpha}{1-\alpha}$ and the average number of…
This work investigates structural and computational aspects of list-based graph coloring under interval constraints. Building on the framework of analogous and p-analogous problems, we show that classical List Coloring, $\mu$-coloring, and…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
We give an efficient construction of a reasonably small dominating set in a circulant graph on $n$ notes and $k$ distinct chord lengths. This result is based on bounds on some double exponential sums. .
We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the…
We generalize the problem of reconstructing strings from their substring compositions first introduced by Acharya et al. in 2015 motivated by polymer-based advanced data storage systems utilizing mass spectrometry. Namely, we see strings as…
k-nearest neighbor graph is a fundamental data structure in many disciplines such as information retrieval, data-mining, pattern recognition, and machine learning, etc. In the literature, considerable research has been focusing on how to…
The purpose of this article is to study the relation between combinatorial equivalence and topological conjugacy, specifically how a certain type of combinatorial equivalence implies topological conjugacy. We introduce the concept of…
The generalized composition graph is used by Cardoso and some researchers for factorization of the adjacency spectrum and Laplacian of a simple graph. Because the generalized composition graph is an example of a set-theoretic linear operad,…
Precise estimation of cross-correlation or similarity between two random variables lies at the heart of signal detection, hyperdimensional computing, associative memories, and neural networks. Although a vast literature exists on different…
We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and…