TOPDRIM: Update WP2 March 2013 Rick Quax, Peter M.A. Sloot.
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Transcript of TOPDRIM: Update WP2 March 2013 Rick Quax, Peter M.A. Sloot.
![Page 1: TOPDRIM: Update WP2 March 2013 Rick Quax, Peter M.A. Sloot.](https://reader036.fdocuments.in/reader036/viewer/2022062620/5519d20e5503468b0c8b4852/html5/thumbnails/1.jpg)
TOPDRIM: Update WP2
March 2013
Rick Quax, Peter M.A. Sloot
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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
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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
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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
![Page 5: TOPDRIM: Update WP2 March 2013 Rick Quax, Peter M.A. Sloot.](https://reader036.fdocuments.in/reader036/viewer/2022062620/5519d20e5503468b0c8b4852/html5/thumbnails/5.jpg)
Information processing in complex systems
Node A Node B
state state
interaction
• Let’s say the state of A influences the state of B…
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Information processing in complex systems
Node A Node B
state 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 state
interactionNode B
Node C
state
Node D
state
How to makemake this quantitative?
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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)
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Information dissipation
Info
rmat
ion
dis
sip
atio
n t
ime
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?
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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
1( | ,...) exp ( , )t t ti j j
j
p s x s E x s
maxk N
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Results: analytical and numerical
Number of interactionsof a node
Info
rma
tion
dis
sipa
tion
time
D(s
)of
a n
ode
s
proof: D(s) will eventually bea decreasing function of ks
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Our research #2
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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
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Our research #3
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Leadingindicatorin financialmarkets
We are now working onan agent-based model ofbanks that create a dynamic network of IRS contracts, to studycritical 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
1
1
log log( ) , where
log
( ).
1 ( )
i
k
ki i
i s
ID s
I
k p k II
k 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
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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
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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• …