Related papers: The rigorous solution for the average distance of …
We investigate a relationship network of humans located in a metric space where relationships are drawn according to a distance-dependent probability density. The obtained spatial graph allows us to calculate the average separation of…
In this article we investigate the existence of a solution to a semilinear, elliptic, partial differential equation with distributional coefficients and data. The problem we consider is a generalization of the Lichnerowicz equation that one…
We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by…
This paper presents an algorithm which solves exponentially fast the average consensus problem on strongly connected network of digital links. The algorithm is based on an efficient zooming-in/zooming-out quantization scheme.
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
A concept of higher order neighborhood in complex networks, introduced previously (PRE \textbf{73}, 046101, (2006)), is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each…
Let $D$ be a strongly connected digraph. The average distance $\bar{\sigma}(v)$ of a vertex $v$ of $D$ is the arithmetic mean of the distances from $v$ to all other vertices of $D$. The remoteness $\rho(D)$ and proximity $\pi(D)$ of $D$ are…
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…
In this paper, we define a stochastic Sierpinski gasket, on the basis of which we construct a network called random Sierpinski network (RSN). We investigate analytically or numerically the statistical characteristics of RSN. The obtained…
In this paper, we propose an evolving Sierpinski gasket, based on which we establish a model of evolutionary Sierpinski networks (ESNs) that unifies deterministic Sierpinski network [Eur. Phys. J. B {\bf 60}, 259 (2007)] and random…
In this paper, we study the distance problem in the setting of finite p-adic rings. In odd dimensions, our results are essentially sharp. In even dimensions, we clarify the conjecture and provide examples to support it. Surprisingly,…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…
We give an analogy between non-reversible Markov chains and electric networks much in the flavour of the classical reversible results originating from Kakutani, and later Kem\'eny-Snell-Knapp and Kelly. Non-reversibility is made possible by…
Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…
We propose the Distance-informed Neural Process (DNP), a novel variant of Neural Processes that improves uncertainty estimation by combining global and distance-aware local latent structures. Standard Neural Processes (NPs) often rely on a…
We present the simulation of the time evolution of the distance matrix. The result is the node-node distance distribution for various kinds of networks. For the exponential trees, analytical formulas are derived for the moments of the…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…