相关论文: Golden Ratio Nets and Sequences

We introduce and study norms in the space of hermitian operators, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum…

Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally…

The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a…

For an integer $n\geq 1$, consider the $n$-th metallic number $\phi_n=\frac{n+\sqrt{n^2+4}}{2}$ (e.g. $\phi_1$ is the golden number) and denote by $[\phi_n]_q$ its $q$-deformation in the sense of S. Morier-Genoud and V. Ovsienko. This is an…

Adaptive systems must strike a balance between prediction and surprise to thrive in uncertain environments. We propose an information-theoretic balance function, $ f(p) = -(1 - p)\ln(1 - p) + \ln p $, which quantifies the net informational…

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context, with a training objective that makes them approximately sample in proportion to a given reward…

The golden ratio and Fibonacci numbers are found to occur in various aspects of nature. We discuss the occurrence of this ratio in an interesting physical problem concerning center of masses in two dimensions. The result is shown to be…

For fitness preferential attachment random networks, we define the empirical degree and pair measure, which counts the number of vertices of a given degree and the number of edges with given fits, and the sample path empirical degree…

Let $\varphi : S = k[y_0,..., y_n] \to R = k[y_0,...,y_n]$ be given by $y_i \to f_i$ where $f_0,...,f_n$ is an $R$-regular sequence of homogeneous elements of the same degree. A recent paper shows for ideals, $I_\Delta \subseteq S$, of…

We introduce a random hypergraph model for core-periphery structure. By leveraging our model's sufficient statistics, we develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is…

We study the distribution P(\omega) of the random variable \omega = x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution \Psi(x)…

A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…

It has been known since Vinogradov that, for irrational $\alpha$, the sequence of fractional parts $\{\alpha p\}$ is equidistributed in $\mathbb{R}/\mathbb{Z}$ as $p$ ranges over primes. There is a natural second-order equidistribution…

Two power series models are proposed to represent self-similarity and they are compared to the Zipf and Benford distributions. Since evolution of a social network is associated with replicating self-similarity at many levels, the nature of…

We study the quasi-uniformity properties of digital nets, a class of quasi-Monte Carlo point sets. Quasi-uniformity is a space-filling property used for instance in experimental designs and radial basis function approximation. However, it…

We derive interesting arctangent identities involving the golden ratio, Fibonacci numbers and Lucas numbers. Binary BBP-type formulas for the arctangents of certain odd powers of the golden ratio are also derived, for the first time in the…

In this paper, a Neural network is derived from first principles, assuming only that each layer begins with a linear dimension-reducing transformation. The approach appeals to the principle of Maximum Entropy (MaxEnt) to find the posterior…

Curie's principle states that "when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them". We demonstrate that symmetry equivariant neural networks uphold Curie's principle and can be used to…

This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…

In this paper, we study commutative Krasner hyperring with nonzero identity. $\phi$-prime, $\phi$-primary and $\phi$-$\delta$-primary hyperideals are introduced. We intend to extend the concept of $\delta$-primary hyperideals to…