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We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…

This letter proposes a novel random medium access control (MAC) based on a transmission opportunity prediction, which can be measured in a form of a conditional success probability given transmitter-side interference. A transmission…

Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…

We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…

Recent research has demonstrated the importance of boundary effects on the overall connection probability of wireless networks but has largely focused on convex deployment regions. We consider here a scenario of practical importance to…

This paper presents an unusual view of interference wireless networks based on complex system thinking. To proceed with this analysis, a literature review of the different applications of complex systems is firstly presented to illustrate…

We consider a random geometric graph with vertices sampled from a probability measure supported on $\mathbb R^d$, and study its connectivity. We show the graph is typically disconnected, unless the sampling density has superexponential…

We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…

The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…

We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…

This paper considers a multimessage network where each node may send a message to any other node in the network. Under the discrete memoryless model, we prove the strong converse theorem for any network whose cut-set bound is tight, i.e.,…

Location-based services in a wireless network require nodes to know their locations accurately. Conventional solutions rely on contention-based medium access, where only one node can successfully transmit at any time in any neighborhood. In…

This paper develops a stochastic geometry-based approach for the modeling and analysis of finite millimeter wave (mmWave) wireless networks where a random number of transmitters and receivers are randomly located inside a finite region. We…

Link residual closeness is a newly proposed measure for network vulnerability. In this model, vertices are perfectly reliable and the links fail independently of each other. It measures the vulnerability even when the removal of links does…

In this paper, we investigate the geometric structure of activation spaces of fully connected layers in neural networks and then show applications of this study. We propose an efficient approximation algorithm to characterize the convex…

In this note we define and study graph invariants generalizing to higher dimension the maximum degree of a vertex and the vertex-connectivity (our $0$-dimensional cases). These are known to coincide almost surely in any regime for…

We develop a convex analytic approach to analyze finite width two-layer ReLU networks. We first prove that an optimal solution to the regularized training problem can be characterized as extreme points of a convex set, where simple…

We study problems related to connecting multi-interface networks of wireless devices. These problems are modeled using graphs, where vertices represent the devices and edges represent potential communication links. Each vertex can activate…

Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distance between cells. In order to comprehend the role of these…

Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…