Related papers: Propagation rules for (u,m,e,s)-nets and (u,e,s)-s…
We discuss the generalization of recently discovered BPS configurations, corresponding to the planar string networks, to non-planar ones by considering the U-duality symmetry of type II string theory in various dimensions. As an explicit…
We examine Bayesian methods for learning Bayesian networks from a combination of prior knowledge and statistical data. In particular, we unify the approaches we presented at last year's conference for discrete and Gaussian domains. We…
We study numerically statistical properties and dynamical disease propagation using a percolation model on a one dimensional small world network. The parameters chosen correspond to a realistic network of school age children. We found that…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
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…
Link prediction in complex networks has attracted considerable attention from interdisciplinary research communities, due to its ubiquitous applications in biological networks, social networks, transportation networks, telecommunication…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of…
A model for the spreading of online information or "memes" on multiplex networks is introduced and analyzed using branching-process methods. The model generalizes that of [Gleeson et al., Phys.Rev. X., 2016] in two ways. First, even for a…
Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have…
The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to…
The radio wave propagation channel is central to the performance of wireless communication systems. In this paper, we introduce a novel machine learning-empowered methodology for wireless channel modeling. The key ingredients include a…
This paper presents a unified algebraic, topological, and logical framework for electrical one-port networks based on \v{S}are's $m$-theory. Within this formalism, networks are represented by $m$-words (jorbs) over an ordered alphabet,…
In this paper, we deal with distributed estimation problems in diffusion networks with heterogeneous nodes, i.e., nodes that either implement different adaptive rules or differ in some other aspect such as the filter structure or length, or…
In this work, extension theorems are generalized to self-dual codes over rings and as applications many new binary self-dual extremal codes are found from self-dual codes over F_2^m+uF_2^m for m = 1, 2. The duality and distance preserving…
We propose a novel method for network inference from partially observed edges using a node-specific degree prior. The degree prior is derived from observed edges in the network to be inferred, and its hyper-parameters are determined by…
Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted…
Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats…
Unidirectional pulse propagation equations [UPPE, Phys. Rev. E 70, 036604 (2004)] have provided a theoretical underpinning for computer-aided investigations into dynamics of high-power ultrashort laser pulses and have been successfully…
Inferring the network topology from the dynamics is a fundamental problem with wide applications in geology, biology and even counter-terrorism. Based on the propagation process, we present a simple method to uncover the network topology.…