Related papers: The rigorous solution for the average distance of …
Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…
Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…
Many real-world networks exhibit the so-called small-world phenomenon: their typical distances are much smaller than their sizes. One mathematical model for this phenomenon is a long-range percolation graph on a $d$-dimensional box $\{0, 1,…
Average consensus algorithms compute the global average of sensor data in a distributed fashion using local sensor nodes. Simple execution, decentralized philosophy make these algorithms suitable for WSN scenarios. Most of the researchers…
The paper considers various formalisms based on Automata, Temporal Logic and Regular Expressions for specifying queries over sequences. Unlike traditional binary semantics, the paper presents a similarity based semantics for thse…
Findings: We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain. As a consequence, the average and median distances in any such network are smaller than or equal to those of a chain. Research…
We propose a method of constructing a network, in which its time structure is directly incorporated, based on a deterministic model from a time series. To construct such a network, we transform a linear model containing terms with different…
We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to…
A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…
Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…
Predicting missing links in real networks is an important problem in network science to which considerable efforts have been devoted, giving as a result a vast plethora of link prediction methods in the literature. In this work, we take a…
Generalized Wasserstein distances allow to quantitatively compare two continuous or atomic mass distributions with equal or different total mass. In this paper, we propose four numerical methods for the approximation of three different…
Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general,…
We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated…
We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…
We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical…