topdrim: update wp2
DESCRIPTION
March 2013. Rick Quax, Peter M.A. Sloot. TOPDRIM: Update WP2. 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. - PowerPoint PPT PresentationTRANSCRIPT
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• …