Laurea Specialistica Telecommunications Engineering 19 July 2010 A Signal Processing Approach to the Analysis of Chemical Networking Protocols Supervisors Prof. Marco Luise (University of Pisa) Author Prof. Filippo Giannetti (University of Pisa) Massimo Monti Prof. Christian Tschudin (University of Basel) Thomas Meyer (University of Basel)
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Chemically Inspired Communication System Communication Model Chemical Model 19 July 2010 Ack1 Receiver 1 Sender 1 Ch OUT IN1 Laurea specialistica IN2 Sender 2 Receiver 2 Ack2 Loss Congestion Avoidance CNP (T.Meyer, to be published) Dynamics Telecommunications Engineering Massimo Monti Transmission and Communication Systems 2
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Concept of Chemical Networking Protocols (CNPs) Goal Equilibrium 19 July 2010 Robustness Self-Healing Life-like properties observed in nature Self-Optimization Self-Protection Laurea specialistica Chemical Metaphor...... Molecules Packets Communication network nodes Chemical vessel Chemical reactions Communication links Chemical virtual machines Computers with standard CPU Chemical model implementation: Fraglets simulator . Telecommunications Engineering Massimo Monti Transmission and Communication Systems 3
A Signal Processing Approach to the Analysis of Chemical Networking Protocols CNP Information Encoding User Information User information is encoded inside packets . 19 July 2010 A certain type of molecules ( species ) contain the same string of symbols. e.g. [node2 HELLO WORLD] System State Information Laurea specialistica 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 Forwarding as fast as possible Schedule the service Telecommunications Engineering Massimo Monti Transmission and Communication Systems 4
A Signal Processing Approach to the Analysis of Chemical Networking Protocols CNP Properties Dynamics Forecast 19 July 2010 mapped • Communication protocol implementations Abstract chemical models • Chemical model dynamics are analyzable Laurea specialistica lead to • Dynamics analysis Chemical model optimization lead to Protocol implementation optimization Telecommunications Engineering Massimo Monti Transmission and Communication Systems 5
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Standard Analysis of Network Dynamics (1/2) The Chemical Master Equation (CME) 19 July 2010 The chemical model as a continuous time discrete space Markov jump process (System state equals species concentration) Laurea specialistica 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 Telecommunications Engineering Massimo Monti Transmission and Communication Systems 6
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Standard Analysis of Network Dynamics (2/2) The Differential Rate Equations Approximation (DREs) 19 July 2010 Deterministic approximation of the exact stochastic behavior. Laurea specialistica Features : Decrease of the computational complexity (still high ) High concentration systems required Dependence on initial condition Telecommunications Engineering Massimo Monti Transmission and Communication Systems 7
A Signal Processing Approach to the Analysis of Chemical Networking Protocols The New Signal Processing Approach Concept 19 July 2010 Chemical networks as systems of blocks and interconnections. Concentration seen as a continuos-time continuos-value signal. Features Transfer function description • Laurea specialistica 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 Telecommunications Engineering Massimo Monti Transmission and Communication Systems 8
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Our Analysis Approach of Linear CNPs Series of N- Node The Disperser CNP 19 July 2010 Parallel of N- Node Connections Typology Laurea specialistica Loop Network Disperser Features: 1 Output Species ≡ Vessels ≡ Nodes Impulse input ≡ Injenction of molecules Elementary N Output Distributed average computation Reactions Molecules equally distributed over the network Telecommunications Engineering Massimo Monti Transmission and Communication Systems 9
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Simulink Schematic 19 July 2010 Laurea specialistica Node 1 Node 2 Node 3 Node 4 Telecommunications Engineering Massimo Monti Transmission and Communication Systems 10
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Analysis Results (1/2) Frequency 19 July 2010 Transforms Laurea specialistica The Disperser CNP Telecommunications Engineering Massimo Monti Transmission and Communication Systems 11
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Analysis Results (2/2) Impulse 19 July 2010 Responses Laurea specialistica The Disperser CNP Telecommunications Engineering Massimo Monti Transmission and Communication Systems 12
A Signal Processing Approach to the Analysis of Chemical Networking Protocols System Control Theory (1/2) State Variable Representation Block Diagram 19 July 2010 Laurea specialistica • State matrix • Input matrix • Output matrix • Direct transmission matrix Analyzed systems must be Linear Time Invariant (LTI) Telecommunications Engineering Massimo Monti Transmission and Communication Systems 13
A Signal Processing Approach to the Analysis of Chemical Networking Protocols System Control Theory (2/2) Frequency Transform 19 July 2010 Frequency characterization of species concentration Laurea specialistica Step Response Dynamical behavior of the network Analyzed systems must be Linear Time Invariant (LTI) Telecommunications Engineering Massimo Monti Transmission and Communication Systems 14
A Signal Processing Approach to the Analysis of Chemical Networking Protocols A Non-Linear CNP 19 July 2010 DREs with Non-Linearities Non-Linear Chemical Model Laurea specialistica Traffic Generation of Tx.1 Species Tx.1 Output Rate Molecules Tx.2 Output Rate Reactions Channel Limitation • Chemical Homeostasis Actual Network Output Rate • Species Dilution Flow Selective Feedbacks Reaction Coefficients Telecommunications Engineering Massimo Monti Transmission and Communication Systems 15
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Metabolic Control Analysis to Non-Linear CNPs 19 July 2010 DREs with Non-Linearities Non-Linear Chemical Model Laurea specialistica Concept: System linearization around a fixed point ( steady states ) State Variable Representation Telecommunications Engineering Massimo Monti Transmission and Communication Systems 16
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Analysis Results (1/2) (n) Frequency Transform W (s) Ack1 19 July 2010 Rx 1 Tx 1 R V ‘ V out out V in Tx 2 Rx 2 Ack2 Laurea specialistica Telecommunications Engineering Massimo Monti Transmission and Communication Systems 17
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Analysis Results (2/2) Step Response Ack1 19 July 2010 Rx 1 Tx 1 R V ‘ V out out V in Tx 2 Rx 2 Ack2 Laurea specialistica Telecommunications Engineering Massimo Monti Transmission and Communication Systems 18
A Signal Processing Approach to the Analysis of Chemical Networking Protocols Discussion Conclusion ! Protocol behavior was not easily predictable. 19 July 2010 • Now, all linear chemical networks are analyzable, with similar procedures to those shown. • Non-linear networks are linearizable (MCA), with the Laurea specialistica 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. Telecommunications Engineering Massimo Monti Transmission and Communication Systems 19
A Signal Processing Approach to the Analysis of Chemical Networking Protocols End End Specialistic Degree 19 July 2010 Thank You Telecommunications Engineering Massimo Monti Transmission and Communication Systems
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