相关论文: Golden Ratio Nets and Sequences

Given a dataset consisting of a single realization of a network, we consider conducting inference on a parameter selected from the data. In particular, we focus on the setting where the parameter of interest is a linear combination of the…

We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth,…

The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…

Szemer\'edi's regularity lemma is a powerful tool in graph theory. It states that for every large enough graph, there exists a partition of the edge set with bounded size such that most induced subgraphs are quasirandom. When the graph is a…

We propose a statistical model for graphs with a core-periphery structure. To do this we define a precise notion of what it means for a graph to have this structure, based on the sparsity properties of the subgraphs of core and periphery…

Basic principles of set theory have been applied in the context of probability and binary computation. Applying the same principles on inequalities is less common but can be extremely beneficial in a variety of fields. This paper formulates…

Parity binomial edge ideals of simple undirected graphs are introduced. Unlike binomial edge ideals, they do not have square-free Gr\"obner bases and are radical if only if the graph is bipartite or the characteristic of the ground field is…

In this paper we devise a generative random network model with core-periphery properties whose core nodes act as sublinear dominators, that is, if the network has $n$ nodes, the core has size $o(n)$ and dominates the entire network. We show…

This paper introduces Haros graphs, a construction which provides a graph-theoretical representation of real numbers in the unit interval reached via paths in the Farey binary tree. We show how the topological structure of Haros graphs…

In this paper we show discrepancy bounds for index-transformed uniformly distributed sequences. From a general result we deduce very tight lower and upper bounds on the discrepancy of index-transformed van der Corput-, Halton-, and…

We explore the space of matrix-generated (0, m, 2)-nets and (0, 2)-sequences in base 2, also known as digital dyadic nets and sequences. In computer graphics, they are arguably leading the competition for use in rendering. We provide a…

This paper studies the zero-divisor graphs attached to several finite chain-ring families and computes the homological invariants of their edge ideals by using cochordal constructible systems. We begin with a general layered graph $C(q,L)$,…

Asymptotic normality is frequently observed in large combinatorial structures, rigorously established for many quantities such as cycles or inversions in random permutations, the number of prime factors of random integers, and various…

In the course of studies of the measure of chaos for the distribution of the prime numbers among the positive integers N arched structures have been found. It is given a brief description of the fine structure of the positive integers…

Consider a network of agents that all want to guess the correct value of some ground truth state. In a sequential order, each agent makes its decision using a single private signal which has a constant probability of error, as well as…

In a base phi representation a natural number is written as a sum of powers of the golden mean $\varphi$. There are many ways to do this. How many? Even if the number of powers of $\varphi$ is finite, then any number has infinitely many…

We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…

Interval analysis (or interval bound propagation, IBP) is a popular technique for verifying and training provably robust deep neural networks, a fundamental challenge in the area of reliable machine learning. However, despite substantial…

We write out relations between the base of natural logarithms ($e$), the ratio of the circumference of a circle to its diameter ($\pi$), the golden ratios ($\Phi_p$) of the additive $p$-sequences, and the ratio of the diagonal of a square…

A set of fixed points of the Hopfield type neural network is under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…