Related papers: Analysis of Prime Reciprocal Sequences in Base 10
For lossless periodic structures with a proper symmetry, the transmission and reflection spectra often have peaks and dips that are truly $100\%$ and $0\%$, respectively. The full peaks and zero dips typically appear near resonant…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
The reciprocity principle is that, when an emitted wave gets scattered on an object, the scattering transition amplitude does not change if we interchange the source and the detector - in other words, if incoming waves are interchanged with…
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the…
In this paper, we give recurrence relations and identities for some integer sequences related to Ward numbers such as Ward-Lah numbers, varied Ward numbers and binomial Ward numbers. Most of the sequences are entered in the On-Line…
In this work, we propose a deep neural network architecture motivated by primal-dual splitting methods from convex optimization. We show theoretically that there exists a close relation between the derived architecture and residual…
Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as…
Recently, there has been a sharp rise of interest in properties of digits primes. Here we study yet another question of this kind. Namely, we fix an integer base $g \ge 2$ and then for every infinite sequence $${\mathcal D} =…
Induction benefits from useful priors. Penalized regression approaches, like ridge regression, shrink weights toward zero but zero association is usually not a sensible prior. Inspired by simple and robust decision heuristics humans use, we…
In this paper, we study a class of functions defined recursively on the set of natural numbers in terms of the greatest common divisor algorithm of two numbers and requiring a minimality condition. These functions are permutations, products…
Group interactions are prevalent in a variety of areas. Many of them, including email exchanges, chemical reactions, and bitcoin transactions, are directional, and thus they are naturally modeled as directed hypergraphs, where each hyperarc…
Given a Fractional Repetition code, finding the reconstruction and repair degree in a distributed storage system is an important problem. In this work, we present algorithms for computing the reconstruction and repair degree of fractional…
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
A modified Lagrange Polynomial is introduced for polynomial extrapolation, which can be used to estimate the equally spaced values of a polynomial function. As an example of its application, this article presents a prime-generating…
Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). The recovered period for the sequence of the first 10000 prime numbers is equal to…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
Prevailing accounts in both multi-agent AI and the social sciences explain social structure through top-down abstractions-such as institutions, norms, or trust-yet lack simulateable models of how such structures emerge from individual…
In the context of the genome rearrangement problem, we analyze two well known models, namely the reversal and the prefix reversal models, by exploiting the connection with the notion of permutation pattern. More specifically, for any $k$,…
In this article, we explore the concept of spectral redundancy within the class of pineapple graphs, denoted as $\mathcal{P}(\alpha,\beta)$. These graphs are constructed by attaching $\beta$ pendent edges to a single vertex of a complete…
The notion of chiral prime concatenations is studied as a recursive construction of prime numbers starting from a seed set and with appropriate blocks to define the primality growth, generation by generation, either from the right or from…