Related papers: Approximate conditional distributions of distances…
This paper is concerned by the problem of selecting an optimal sampling set of sensors over a network of time series for the purpose of signal recovery at non-observed sensors with a minimal reconstruction error. The problem is motivated by…
The diameter of a graph measures the maximal distance between any pair of vertices. The diameters of many small-world networks, as well as a variety of other random graph models, grow logarithmically in the number of nodes. In contrast, the…
A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of…
Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…
Proximity catch digraphs (PCDs) are based on proximity maps which yield proximity regions and are special types of proximity graphs. PCDs are based on the relative allocation of points from two or more classes in a region of interest and…
We derive the probability that a randomly chosen NL-node over $S$ gets localized as a function of a variety of parameters. Then, we derive the probability that the whole network of NL-nodes over $S$ gets localized. In connection with the…
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing…
In large networks, using the length of shortest paths as the distance measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs and directed graphs is controversial. The second shortcoming is that a…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…
We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
Wireless Sensor Networks (WSNs) are composed of nodes that gather metrics like temperature, pollution or pressure from events generated by external entities. Localization in WSNs is paramount, given that the collected metrics must be…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
We proposed a new criterion \textit{noise-stability}, which revised the classical rigidity theory, for evaluation of MDS algorithms which can truthfully represent the fidelity of global structure reconstruction; then we proved the…
An equidistant set in the Euclidean space consists of points having equal distances to both members of a given pair of sets, called focal sets. Since there is no effective formula to compute the distance of a point and a set, it is hard to…
Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into…