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This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…
This is an introductory article to the theory of multiple gaps.
This article reviews and presents various solved and open problems in the development, analysis, and control of epidemic models. We are interested in presenting a relatively concise report for new engineers looking to enter the field of…
We introduce a novel approach to description of networks/graphs. It is based on an analogue physical model which is dynamically evolved. This evolution depends on the connectivity matrix and readily brings out many qualitative features of…
Expanded lecture notes. Preliminary version, comments are welcome.
In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…
Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic…
Given the unprecedented availability of data and computing resources, there is widespread renewed interest in applying data-driven machine learning methods to problems for which the development of conventional engineering solutions is…
Review article of various complexity measures of networks
What is a complex network? How do we characterize complex networks? Which systems can be studied from a network approach? In this text, we motivate the use of complex networks to study and understand a broad panoply of systems, ranging from…
These notes provide a systematic mathematical treatment of the subject of data assimilation.
We analyze a science collaboration network, i.e. a network whose nodes are scientists with edges connecting them for each paper published together. Furthermore we develop a model for the simulation of discontiguous small-world networks that…
This paper provides an entry point to the problem of interpreting a deep neural network model and explaining its predictions. It is based on a tutorial given at ICASSP 2017. It introduces some recently proposed techniques of interpretation,…
In this chapter, we present a review of latent position models for networks. We review the recent literature in this area and illustrate the basic aspects and properties of this modeling framework. Through several illustrative examples we…
An introduction to Hyperbolic Analysis is presented.
This text is based on a translation of a chapter in a handbook about network analysis (published in German) where we tried to make beginners familiar with some basic notions and recent developments of network analysis applied to…
In recent times, the functioning of various aspects of modern society---ranging from the various infrastructural utilities such as electrical power, water to socio-economical aspects such as telecommunications, business, commerce,…
Understanding the causes and consequences of, and devising countermeasures to, global warming is a profoundly complex problem. Network representations are sometimes the only way forward, and sometimes able to reduce the complexity of the…
In this short paper, we explore relationship between various models of complex networks with pinning controllers.