TOPDRIM: Update WP2

March 2013

Rick Quax, Peter M.A. Sloot

Outline

• Our research so far (bird’s eye view)

• Information dissipation (ID) in networks

• ID in immune response to HIV

• ID in financial market• Addressing WP2 tasks• Ideas for collaboration

Our view of a complex system

node dynamics + complex network = complex system

+ =

Each node has a statewhich it changes over time

Nodes interact with each otheri.e., their states influence each other

The system behavior is complexcompared to an individual node

Our view of a complex system

node dynamics + complex network = complex system

+ =

Each node has a statewhich it changes over time

Nodes interact with each otheri.e., their states influence each other

The system behavior is complexcompared to an individual node

problem

Information processing in complex systems

Node A Node B

state state

interaction

• Let’s say the state of A influences the state of B…

Information processing in complex systems

Node A Node B

state state

interaction

• We would like to ‘see’ influence spreading

Information processing in complex systems

• Different influences spread through the network simultaneously

Node A

state state

interactionNode B

Node C

state

Node D

state

How to makemake this quantitative?

Solution: information theory?

Node A

state

Entropy:

( ) logA i A ii

H A p p (H )

Mutual information

( ; ) ( ) ( | )I A B H B H B A (I Node A

state

Node B

state

; )

How much informationis stored in A?

How much informationin A is also in B?

(pitfall: MI = causality + correlation)

Information dissipation

Info

rmat

ion

diss

ipat

ion

time

Information dissipation length

measures of influence of a single nodeto the behavior of the entire network!

How long is the informationabout a node’s state

retained in the network?

How far can the informationabout a node’s state reach

before it is lost?

Our research #1

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

1( | ,...) exp ( , )t t ti j j

j

p s x s E x s

maxk N

Results: analytical and numerical

Number of interactionsof a node

Info

rmat

ion

diss

ipat

ion

time

D(s

)of

a n

ode

s

proof: D(s) will eventually bea decreasing function of ks

Our research #2

Susceptibility of HIV immuneresponse to perturbation

Cell types in immune responseand their interactions

Susceptibility of immune system

0 0provirus( );CD4( )I t t t

Agent-based simulations

IDT

Our research #3

Leadingindicatorin financialmarkets

We are now working onan agent-based model ofbanks that create a dynamic network of IRS contracts, to studycritical transitions

How this fit the Tasks in WP2

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

1

1

log log( ) , wherelog

( ) .1 ( )

i

k

ki i

i s

ID sI

k p k IIk H i

1

1

( ) ( ), where

( ) ( | )j

k

t tj i k

I U k k T k

T k I s s

( 1) ( ) where a 1.T k a T k

Task 2.2

Susceptibility of immune system

Cell types in immune responseand 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 thenode dynamics are complex, not the network topology

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

Task 2.4

• Refine and integrate• …