Differential Equivalence Yields Network Centrality View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2018-10-31

AUTHORS

Stefano Tognazzi , Mirco Tribastone , Max Tschaikowski , Andrea Vandin

ABSTRACT

One of the most distinctive features of collective adaptive systems (CAS) is the presence of many individuals which interact with each other and with the environment, giving rise to a system-level behaviour that cannot be analyzed by studying the single agents in isolation. The interaction structure among the individuals of CAS is often captured by networks where nodes denote individuals and edges interactions. Understanding the interplay between the network topology and the CAS dynamics calls for tools from network theory in order, for instance, to identify the most important nodes of a network. Centrality measures address this task by assigning an importance measure to each node, a possible example being the famous PageRank algorithm of Google. In this paper we investigate the relationship between centrality measures and model reduction techniques, such as lumpability of Markov chains, which seek to reduce a model into a smaller one that can be processed more efficiently, while preserving information of interest. In particular, we focus on the relation between network centrality and backward differential equivalence, a generalization of lumpability to general dynamical systems. We show that any two backward differential equivalent nodes enjoy identical centrality measures. By efficiently obtaining substantial reductions of real-world networks from biochemistry, social sciences and computer engineering, we demonstrate the applicability of the result. More... »

PAGES

186-201

References to SciGraph publications

  • 2015. Differential Bisimulation for a Markovian Process Algebra in MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE 2015
  • 2012. Exact Fluid Lumpability for Markovian Process Algebra in CONCUR 2012 – CONCURRENCY THEORY
  • 2004. The Enron Corpus: A New Dataset for Email Classification Research in MACHINE LEARNING: ECML 2004
  • 2016-04. Noise Reduction in Complex Biological Switches in SCIENTIFIC REPORTS
  • 2005. Role Assignments in NETWORK ANALYSIS
  • 2016. Efficient Syntax-Driven Lumping of Differential Equations in TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS
  • 2010. Simple O(m logn) Time Markov Chain Lumping in TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS
  • 2017. ERODE: A Tool for the Evaluation and Reduction of Ordinary Differential Equations in TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS
  • 2001-05. Lethality and centrality in protein networks in NATURE
  • Book

    TITLE

    Leveraging Applications of Formal Methods, Verification and Validation. Distributed Systems

    ISBN

    978-3-030-03423-8
    978-3-030-03424-5

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-030-03424-5_13

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    DIMENSIONS

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