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Tools for a critical analysis of network criticality and beyond

Applicant Stoop Rudolf
Number 153542
Funding scheme Project funding
Research institution Institut für Neuroinformatik Universität Zürich Irchel und ETH Zürich
Institution of higher education University of Zurich - ZH
Main discipline Other disciplines of Physics
Start/End 01.03.2015 - 28.02.2018
Approved amount 191'007.00
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Keywords (1)

Network analysis, meso-structure, criticality, bra

Lay Summary (German)

Lead
Die Theorie der Zufallsnetzwerke hat sich im letzten Jahrzehnt radikal verändert, wobei Konzepte der statistischen Physik (insbesondere das von ‘Kritikalität’) eine zentrale Rolle spielen. Im Projekt wird die Verwendung dieses Begriffes kritisch hinterfragt und Methoden für eine fundamental gesicherte Verwendung entwickelt. 
Lay summary

Das Interesse an nichtlinearen Systemen hat sich in den letzten Jahren stark von Einzelsystemen zu Netzwerken solcher Einzelsysteme verschoben. Dieser Forschungszweig ist unter dem (etwas weiter gefassten) Begriff ‘Komplexe Netzwerke’ bekannt geworden. Diese Systeme zeigen typischerweise Verteilungen charakteristischer lokaler Netzwerkkenngrössen welche einem Potenzgesetzgesetz folgen. Aus der Sicht des Physikers wirft dies die Frage auf, ob wir es hier mit kritischen Systemen zu tun haben, und wie Kritikalität in diesem Zusammenhang genauer zu definieren wäre. Eine Hoffnung ist dabei, so genannte Universalitätsklassen von Netzwerken definieren zu können, welche die Eigenschaften der Mitglieder solcher Klassen genauer als das bisher möglich war und für alle gleichermassen gültig festlegen würden.

Wir werden die Fragestellung aus der Sicht von neu entwickelten und zu entwickelnden mathematischen Hilfsmittel der Netzwerkanalyse von Grunde aus angehen. Wir lassen uns dabei von durch uns bereits analysierten realen komplexen Netzwerken aus der Biologie leiten und untersuchen, wo und in welchem Sinne selbst-organisierte Kritikalität behauptet werden kann. Insbesondere interessiert uns, wie in neuronalen Netzen diese Eigenschaft durch Lernen zerstört wird (dies eine unserer Hypothesen). 

Die einschlägigen Experimente stammen hauptsächlich aus dem Bereich biologischer neuronaler Netze (kortikale Slices, neuronale Zellkulturen) und ihrer Simulation. Durch diese enge Bindung an biologische Netzwerke kommt unserer Fragestellung wegen der unbezweifelbaren Optimalität biologischer Signalverarbeitung, über die Möglichkeit der Verwendung ihrer Grundregeln für biologisch motivierte alternative Methoden der Informationsverarbeitung, eine grosse Tragweite zu. Dabei wird sich auch zeigen, wie sich mesoskopische Strukturen in den Netzwerkdaten, welche von besonderem Interesse auch im Zusammenhang mit ‘big data’ sind, im betrachteten biologischen computationellen Kontext manifestieren.

 

Direct link to Lay Summary Last update: 26.02.2015

Responsible applicant and co-applicants

Employees

Publications

Publication
Frequency sensitivity in mammalian hearing from a fundamental nonlinear physics model of the inner ear
Karlis Kanders, Tom Lorimer, Florian Gomez, Ruedi Stoop (2017), Frequency sensitivity in mammalian hearing from a fundamental nonlinear physics model of the inner ear, in Scientific Reports, 7(9931), 1-8.
Clustering: How much bias do we need?
Tom Lorimer, Jenny Held, Ruedi Stoop (2017), Clustering: How much bias do we need?, in Philosophical Transactions A, 375(20160293), 1-18.
Avalanche and edge-of-chaos criticality do not necessarily co-occur in neural networks
Karlis Kanders, Tom Lorimer, Ruedi Stoop (2017), Avalanche and edge-of-chaos criticality do not necessarily co-occur in neural networks, in Chaos, 27(047408), 1-9.
Complex Structures and Behavior from Elementary Adaptive Network Automata
Daniel Wechsler, Ruedi Stoop (2017), Complex Structures and Behavior from Elementary Adaptive Network Automata, in Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences, Como.
Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences
Giorgio Mantica, Ruedi Stoop, Sebastiano Stramaglia (ed.) (2017), Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences, Springer, Cham, Switzerland.
Hebbian Learning Clustering with Rulkov Neurons
Jenny Held, Tom Lorimer, Carlo Albert, Ruedi Stoop (2017), Hebbian Learning Clustering with Rulkov Neurons, in Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences, Como.
Nonparametric clustering approach towards big data
Tom Lorimer, Jenny Held, Carlo Albert, Ruedi Stoop (2017), Nonparametric clustering approach towards big data, in Proceedings of NOLTA 2016.
Nonparametric clustering approach towards big data
Tom Lorimer, Jenny Held, Carlo Albert, Ruedi Stoop (2017), Nonparametric clustering approach towards big data, in Springer Proceedings in Physics, 191, 127-141.
Phase Response Properties of Rulkov Neurons
Karlis Kander, Ruedi Stoop (2017), Phase Response Properties of Rulkov Neurons, in Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences, Como.
Power laws in neuronal culture activity from limited availability of a shared resource
Damian Berger, Tom Lorimer, S Yoo, Yoonkey Nam, Ruedi Stoop (2017), Power laws in neuronal culture activity from limited availability of a shared resource, in Springer Proceedings in Physics, 191, 209-220.
Recent Advances in Nonlinear Dynamics and Synchronization
Wolfgang Mathis, Zhong Li, Ruedi Stoop, Kyandoghere Kyamakya, Jean Chamberlain (ed.) (2017), Recent Advances in Nonlinear Dynamics and Synchronization, Springer, Cham, Schweiz.
Clustered Multidimensional Scaling with Rulkov Neurons T
Thomas Ott, Martin Schüle, Jenny Held, Carlo Albert, Ruedi Stoop (2016), Clustered Multidimensional Scaling with Rulkov Neurons T, in Proceedings of the Nolta 2016, Yugawara, Japan.
Neural avalanches at the edge-of-chaos?
Karlis Kanders (2016), Neural avalanches at the edge-of-chaos?, in Proceedings of NOLTA2016, Yugawara, JapanIECIE, Tokyo, Japan.
Novel insights into cochlear information processing
Ruedi Stoop, Karlis Kanders, Leonardo Novelli (2016), Novel insights into cochlear information processing, in Proceedings of the Nolta 2016.
Synchronization in Dynamical Polygonal Oscillatory Networks with Switching Topology
Yoko Uwate, Yoshifumi Nishio (2016), Synchronization in Dynamical Polygonal Oscillatory Networks with Switching Topology, in Proceedings of the Nolta 2016, Yugawara, JapanIECIE, Tokyo, Japan.
Auditory power-law activation avalanches exhibit a fundamental computational ground state
Ruedi Stoop, Florian Gomez (2016), Auditory power-law activation avalanches exhibit a fundamental computational ground state, in Physical Review Letters, 117, 1-7.
Big data naturally rescaled
Ruedi Stoop, Karlis Kanders, Tom Lorimer, Jenny Held, Carlo Albert (2016), Big data naturally rescaled, in Chaos Solitons and Fractals, 90, 81-90.
Signal-coupled subthreshold Hopf-type systems show a sharpened collective response
Florian Gomez, Tom Lorimer, Ruedi Stoop (2016), Signal-coupled subthreshold Hopf-type systems show a sharpened collective response, in Physical Review Letters, 116, 1-5.
Two universal principles shape the topological statistics of real-world networks
Tom Lorimer, Florian Gomez, Ruedi Stoop (2015), Two universal principles shape the topological statistics of real-world networks, in Scientific Reports, 5(12353), 1-8.

Collaboration

Group / person Country
Types of collaboration
Prof. L.A. Bunimovich, Georgia Institute of Technology United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Exchange of personnel

Abstract

“Tools for critically revisiting network criticality and beyond”The analysis of networks for their structures and how the latter may evolve is currently a strongly emphasized focus within the physics community. There are strong tendencies to relate the evolution of such networks to well-understood processes in physics. Partially, this is driven by the hope of being able to find universality classes among the networks.One of the most important concepts in this context is the notion of criticality. A dynamical system is in a critical state if the physical model of the system would imply that the system is at a phase-transition state (often making reference to some external parameter). A self-organized critical system achieves this state without the need of external parameter monitoring, i.e., the critical state emerges as the attractor of some dynamics operating on the system. Whereas today many scientists would subscribe to a statement like “The brain, as most biological networks, is at a critical state” with little hesitation, we believe that the criticality assumption is essentially the result of a first order network approximation. Such approximations have recently been deduced from the network microstructure, where criticality was obtained from purely local descriptors, like node degree, by means of a preferential attachment rule. Our claim is that in reality networks depart from criticality to achieve their performance, but that presently we do not have the appropriate tools for working out the important meso-structures present in those networks that would allow us to analyze and classify the networks on a more refined level. This claim is strongly supported by preliminary studies of networks artificially constructed on two scaling processes, and by the preliminary analysis of real-world networks. During our project, we will develop efficient mathematical methods for the detection of sub-structures in realistic networks. This will teach us the extent to which the induced deviations depart from assumed or claimed network criticality and elucidate which networks may faithfully be described by a probably generalized notion of criticality. Regarding the real-world data to be used we will focus on sensory, cortical, and behavioral networks, down to the networks defined by musical compositions. Whereas our research will mostly work with medium-size data, the methods to be developed will be also of great interest for the analysis of ‘big data’, by providing mathematically well-defined methods to systematically dissect data and to structure it according to well-chosen data aspects. The obtained mesoscopic structures will tell us what we need to know about the inner network structure (contained but hidden when we look at the data from a purely local or global perspective) and allow us to build synthetic networks on these structures, to overcome finite size limitations. We hope that with this approach, we will be able in the long term to relate the current proliferation of connectome data to expressed behavior, having in mind Drosophila as the first example.
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