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The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…
We present a brief introduction to a flexible, general network inference framework which models data as a network space, sampled to optimize network structure to a particular task. We introduce a formal problem statement related to…
With the phenomenal growth in the Internet, network security has become an integral part of computer and information security. In order to come up with measures that make networks more secure, it is important to learn about the…
We discuss several interesting random network models which exhibit (provable) explosive transitions and their applications.
Network analysis is currently used in a myriad of contexts: from identifying potential drug targets to predicting the spread of epidemics and designing vaccination strategies, and from finding friends to uncovering criminal activity.…
We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide a guide to available methodology and…
Proposal for contribution to the quantum field theory section in "Encyclopedia of Mathematical Physics".
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
In this paper, we present the outer product decomposition of a product of compatible linked networks. It provides a foundation for the fractional approach in network analysis. We discuss the standard and Newman's normalization of networks.…
Infectious disease remains, despite centuries of work to control and mitigate its effects, a major problem facing humanity. This paper reviews the mathematical modelling of infectious disease epidemics on networks, starting from the…
The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic…
Submitted to F. Schweitzer (ed.), Microscopic Models for Economic Dynamics, Lecture notes in physics, Springer, Berlin-Heidelberg 2002.kiel.tex
Comparative graph and network analysis play an important role in both systems biology and pattern recognition, but existing surveys on the topic have historically ignored or underserved one or the other of these fields. We present an…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges. The number of research papers in the literature concerning these models is growing rapidly due to their impressive performance on…
Over the past years, embedding learning on networks has shown tremendous results in link prediction tasks for complex systems, with a wide range of real-life applications. Learning a representation for each node in a knowledge graph allows…
Draft of textbook chapter on neural machine translation. a comprehensive treatment of the topic, ranging from introduction to neural networks, computation graphs, description of the currently dominant attentional sequence-to-sequence model,…
Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…
The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…
Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…