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

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Outline Our research so far (birds eye view) Information dissipation (ID) in networks ID in immune response to HIV ID in financial market Addressing WP2 tasks Ideas for collaboration

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Our view of a complex system node dynamics + complex network = complex system += Each node has a state which it changes over time Nodes interact with each other i.e., their states influence each other The system behavior is complex compared to an individual node

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Our view of a complex system node dynamics + complex network = complex system += Each node has a state which it changes over time Nodes interact with each other i.e., their states influence each other The system behavior is complex compared to an individual node problem

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Information processing in complex systems Node ANode B state interaction Lets say the state of A influences the state of B…

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Information processing in complex systems Node ANode B state interaction We would like to see influence spreading

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Information processing in complex systems Different influences spread through the network simultaneously Node A state interaction Node B Node C state Node D state How to make make this quantitative?

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

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Information dissipation Information dissipation time Information dissipation length measures of influence of a single node to the behavior of the entire network! How long is the information about a nodes state retained in the network? How far can the information about a nodes state reach before it is lost?

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Our research #1

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Information dissipation time Node dynamics: (local) Gibbs measure I.e., edges represent an interaction potential to which a node can quasi-equilibrate Network structure Large Randomized beyond degree distribution grows less than linear in

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Results: analytical and numerical Number of interactions of a node Information dissipation time D(s) of a node s proof: D(s) will eventually be a decreasing function of k s

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Our research #2

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Susceptibility of HIV immune response to perturbation Cell types in immune response and their interactions Susceptibility of immune system Agent-based simulations IDT

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Our research #3

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Leading indicator in financial markets We are now working on an agent-based model of banks that create a dynamic network of IRS contracts, to study critical transitions

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How this fit the Tasks in WP2

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Task 2.1 (…) In particular, UvA will derive an analytical expression for the information dissipation. We have defined and analyzed both information dissipation time as well as information dissipation length IDT in review process at J. R. Soc. Interface IDL in review process at Scientific Reports

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Task 2.2 Susceptibility of immune system Cell types in immune response and their interactions 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 did not yet start this exact task –Possible collaboration: compare this measure with the barcode of the network –We are exploring an implementation in the Computational Exploratory (Sophocles) However, we are studying a more specific problem: How susceptible is the HIV immune response to perturbations (such as therapy) over time? Application: at which moment in time should HIV- treatment be started? Complex network in the sense that the node dynamics are complex, not the network topology

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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 an analytical expression for a threshold We have studied the use of information dissipation length to detect a critical transition (Lehman Brothers) in the financial derivatives market (real data) In revision process at Scientific Reports

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Task 2.4 Refine and integrate …

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4. PREFERENTIAL ATTACHMENT The rich gets richer. Empirical evidences Many large networks are scale free The degree distribution has a power-law behavior.

4. PREFERENTIAL ATTACHMENT The rich gets richer. Empirical evidences Many large networks are scale free The degree distribution has a power-law behavior.

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