Laurea Specialistica
Telecommunications Engineering
19 July 2010
A Signal Processing Approach
to the Analysis of
Chemical Networking Protocols
Author
Massimo Monti
Supervisors
Prof. Marco Luise
Prof. Filippo Giannetti
Prof. Christian Tschudin
Thomas Meyer
(University of Pisa)
(University of Pisa)
(University of Basel)
(University of Basel)
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Chemically Inspired Communication System
19 July 2010
Communication Model
Ack1
Sender 1
Receiver 1
Ch
OUT
IN1
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Chemical Model
IN2
Sender 2
Ack2
Receiver 2
Loss
Congestion Avoidance CNP (T.Meyer, to be published)
Dynamics
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2
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Laurea specialistica
19 July 2010
Concept of Chemical Networking Protocols (CNPs)
Equilibrium
Robustness
Self-Healing
Self-Optimization
Self-Protection
Goal
Life-like properties observed in nature
Chemical Metaphor......
Molecules
Chemical vessel
Chemical reactions
Chemical virtual machines




Chemical model implementation:
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Packets
Communication network nodes
Communication links
Computers with standard CPU
Fraglets simulator.
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
CNP Information Encoding
19 July 2010
User Information
User information is encoded inside packets.
A certain type of molecules (species) contain the same string of symbols.
e.g. [node2 HELLO WORLD]
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System State Information
System state information is encoded in the packet rate itself.
• Concentration of a chemical species
≡
Number of molecules of that species.
• Reactions happen according to the «Law of mass action»:
Reaction Rate
Species concentration
Randomize queue entries
Schedule the service
Forwarding as fast as possible
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Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
CNP Properties
Laurea specialistica
19 July 2010
Dynamics Forecast
• Communication protocol implementations
mapped
Abstract chemical models
• Chemical model dynamics are analyzable
• Dynamics analysis
lead to
Chemical model optimization
lead to
Protocol implementation optimization
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5
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Standard Analysis of Network Dynamics (1/2)
19 July 2010
The Chemical Master Equation (CME)
The chemical model as
a continuous time discrete space Markov jump process
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(System state equals species concentration)
Dynamics of the system probability distribution
governed by the CME
Features:
Exact analysis of the stochastic dynamical behavior of a model
Very high computational complexity
Solution not always possible
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6
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Standard Analysis of Network Dynamics (2/2)
Laurea specialistica
19 July 2010
The Differential Rate Equations Approximation (DREs)
Deterministic approximation of the exact stochastic behavior.
Features:
Decrease of the computational complexity (still high)
High concentration systems required
Dependence on initial condition
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Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
The New Signal Processing Approach
19 July 2010
Concept
Chemical networks as systems of blocks and interconnections.
Concentration seen as a continuos-time continuos-value signal.
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Features
•
Transfer function description
Generality of results
•
Based on Differential Rate Equations (DREs) approximation
(DREs model description
Laplace transform solution)
Low computational complexity
Deterministic approximation
Dependence on initial condition
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Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Our Analysis Approach of Linear CNPs
Series of N-Node
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19 July 2010
The Disperser CNP
Parallel of N-Node
Connections
Typology
Loop Network
Disperser Features:
1 Output
Species ≡ Vessels ≡ Nodes
Impulse input ≡ Injenction of molecules
Distributed average computation
Molecules equally distributed over the network
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Elementary
Reactions
N Output
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Laurea specialistica
19 July 2010
Simulink Schematic
Node 1
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Node 2
Node 3
10
Node 4
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Analysis Results (1/2)
Laurea specialistica
19 July 2010
Frequency
Transforms
The Disperser CNP
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11
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Analysis Results (2/2)
Laurea specialistica
19 July 2010
Impulse
Responses
The Disperser CNP
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Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Laurea specialistica
19 July 2010
System Control Theory (1/2)
State Variable Representation
•
State matrix
•
Input matrix
•
Output matrix
•
Direct transmission matrix
Block Diagram
Analyzed systems must be Linear Time Invariant (LTI)
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13
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Laurea specialistica
19 July 2010
System Control Theory (2/2)
Frequency Transform
Frequency characterization of species concentration
Step Response
Dynamical behavior of the network
Analyzed systems must be Linear Time Invariant (LTI)
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Transmission and Communication Systems
14
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Laurea specialistica
19 July 2010
A Non-Linear CNP
DREs with Non-Linearities
Non-Linear Chemical Model






 Species
 Molecules
 Reactions
• Chemical Homeostasis
• Species Dilution Flow
 Reaction Coefficients
Traffic Generation of Tx.1
Tx.1 Output Rate
Tx.2 Output Rate
Channel Limitation
Actual Network Output Rate
Selective Feedbacks
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Transmission and Communication Systems
15
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Laurea specialistica
19 July 2010
Metabolic Control Analysis to Non-Linear CNPs
DREs with Non-Linearities
Non-Linear Chemical Model
Concept: System linearization around a fixed point (steady states)
State Variable
Representation
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Transmission and Communication Systems
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Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Analysis Results (1/2)
(n)
19 July 2010
Frequency Transform W (s)
Ack1
Tx 1
Vout
‘
R
Rx 1
Vout
Vin
Ack2
Rx 2
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Tx 2
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Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Analysis Results (2/2)
19 July 2010
Step Response
Ack1
Tx 1
Vout
‘
R
Rx 1
Vout
Vin
Ack2
Rx 2
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Tx 2
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Transmission and Communication Systems
18
Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
Laurea specialistica
19 July 2010
Discussion
!
Conclusion
Protocol behavior was not easily predictable.
• Now, all linear chemical networks are analyzable, with
similar procedures to those shown.
• Non-linear networks are linearizable (MCA), with the
side effect of a high computational complexity.
• Even links with delay have been analyzed (not shown).
Limits & Future
• Bi-stable systems.
• Fixed point near the saddle point.
• Stochasticity of CNPs briefly introduced.
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Massimo Monti
A Signal Processing Approach to the Analysis of Chemical Networking Protocols
End
End
Specialistic Degree
19 July 2010
Thank You
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Transmission and Communication Systems
Massimo Monti