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Insights into Information Dissipation in Complex Systems: Research Overview and Future Directions

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This document provides an update on our research regarding information dissipation (ID) within complex systems, including networks and their dynamics. We explore ID in various contexts such as the immune response to HIV and financial markets. Key tasks addressed include understanding the time and length of information dissipation, as well as their effects on system behavior. Our findings illustrate how nodes in a network influence each other and how information dynamics can serve as indicators of system stability and susceptibility. We discuss collaboration opportunities in these research areas.

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Insights into Information Dissipation in Complex Systems: Research Overview and Future Directions

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  1. March 2013 Rick Quax, Peter M.A. Sloot TOPDRIM: Update WP2

  2. Outline • Our research so far (bird’seye view) • Information dissipation (ID) in networks • ID in immune response to HIV • ID in financial market • Addressing WP2 tasks • Ideasforcollaboration

  3. Our view of a complex system • node dynamics + complex network = complex system + = Each node has a statewhich it changes over time The system behavior is complexcompared to an individual node Nodes interact with each otheri.e., their states influence each other

  4. Our view of a complex system • node dynamics + complex network = complex system problem + = Each node has a statewhich it changes over time The system behavior is complexcompared to an individual node Nodes interact with each otheri.e., their states influence each other

  5. Information processing in complex systems • Let’s say the state of A influences the state of B… state state interaction Node A Node B

  6. Information processing in complex systems • We wouldliketo ‘see’ influencespreading state state interaction Node A Node B

  7. Information processing in complex systems state • Different influences spread through the networksimultaneously Node C state state interaction Node A Node B state Howto makemakethisquantitative? Node D

  8. Solution: information theory? How much informationis stored in A? Entropy: state state How much informationin A is also in B? state Node A Node A Mutual information Node B (pitfall: MI = causality + correlation)

  9. Information dissipation How long is the informationabout a node’s stateretained in the network? Information dissipation time measures of influence of a single nodeto the behavior of the entirenetwork! How farcan the informationabout a node’s state reachbeforeit is lost? Information dissipationlength

  10. Our research #1

  11. Information dissipation time • Node dynamics: (local) Gibbs measure • I.e., edgesrepresentaninteractionpotentialtowhich a node can quasi-equilibrate • Network structure • Large • Randomizedbeyonddegreedistribution • growslessthanlinear in

  12. Results: analyticalandnumerical Information dissipation time D(s)of a node s Number of interactionsof a node proof: D(s) willeventuallybea decreasingfunction of ks

  13. Our research #2

  14. Cell types in immune responseandtheirinteractions Susceptibility of HIV immuneresponse toperturbation Agent-basedsimulations IDT Susceptibility of immune system

  15. Our research #3

  16. Leadingindicatorin financialmarkets We are nowworking onan agent-based model ofbanksthatcreate a dynamicnetwork of IRS contracts, tostudycriticaltransitions

  17. How this fit the Tasks in WP2

  18. Task 2.1 • “(…) In particular, UvA will derive an analytical expression for the information dissipation.” • We have definedandanalyzedboth information dissipationtime as well as information dissipationlength • IDT in review process at J. R. Soc. Interface • IDL in review process at ScientificReports

  19. Cell types in immune responseandtheirinteractions Task 2.2 • “UvA will study the decay rate of information as function of noise to identify it as a universal measure of how susceptible the system is to noise (…) for a variety of network topologies” • We didnotyet start this exact task • Possiblecollaboration: comparethismeasurewith the ‘barcode’ of the network • We are exploringanimplementation in the ComputationalExploratory (Sophocles) • However, we are studyinga more specificproblem: • “How susceptible is the HIV immune response to perturbations (such as therapy) over time?” • Application: at which moment in time should HIV-treatment bestarted? • ‘Complex’ network in the sense that thenode dynamics are complex, not the networktopology Susceptibility of immune system

  20. Task 2.3 • “UvA will develop a critical dissipation threshold which any system must exceed before it can transition as a whole.” • We do not (yet) have ananalyticalexpressionfor a threshold • We havestudied the use of ‘information dissipationlength’ todetect a criticaltransition(Lehman Brothers) in the financial derivatives market (real data) • In revisionprocess at ScientificReports

  21. Task 2.4 • Refineandintegrate • …

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