Network Dynamics as an Inverse Problem

Reconstruction, Design and Optimality

by Jose Luis Casadiego Bastidas
Doctoral thesis
Date of Examination:2016-01-13
Date of issue:2016-12-16
Advisor:Prof. Dr. Marc Timme
Referee:Prof. Dr. Reiner Kree
Referee:Prof. Dr. Ulrich Parlitz
Referee:Prof. Dr. Stephan Herminghaus
Referee:Prof. Dr. Theo Geisel
Referee:Prof. Dr. Patrick Cramer
Persistent Address: http://dx.doi.org/10.53846/goediss-6042

 

 

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Abstract

English

In this thesis, we take a general view on the study of networks from inverse perspectives. By proposing a general representation for the dynamics of networks in terms of explicit dependencies among units, we develop new concepts for understanding, among other things, (i) how disparate networks achieve identical dynamics, and (ii) how we may reconstruct the structural connectivity of networks regardless of the type of network under study (e.g. gene regulatory networks, metabolic networks or neural networks). Specifically, here we heavily rely on concepts and tools coming from nonlinear dynamics and linear algebra to introduce physics-inspired inverse approaches for explaining the fundamental mechanisms for revealing connections in networks. Furthermore, the content and results of this thesis are self-sufficient, such that the reader may not need to refer to additional scientific sources.
Keywords: network + inference + reconstruction + inverse + dynamics + inferring + revealing + reconstructing + dynamical + systems + correlations + transfer + entropy + synaptic + connectivity + neural + connections + links + reveal + discover + ARNI + event + space; explict + dependencies
 
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