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Theoretical foundations: Architecture, control, networks, robustness, and complexity John Doyle John G Braun Professor Control and Dynamical Systems BioEngineering, Electrical Engineering Caltech math NetSE: Network Science and Engineering Good news and bad news: Spectacular recent progress in (more integrated) • foundations for a mathematical theory of • network robustness, control, and architecture Spectacular continued confusion and errors in • various “new sciences” of • “networks” • “complexity” • Etc, etc,.. math NetSE: Network Science and Engineering Good news and bad news: Spectacular recent progress in (more integrated) • foundations for a mathematical theory of • network robustness, control, and architecture Are there lessons to be learned in trying to create a theory of impossible things (e.g. security)? NetME: Progress and promise • Internet theory: layering, control, traffic, topology, architecture (?) • Unifying theories of hard limits and optimal synthesis (Shannon, Bode, Carnot, Turing/Godel) • Comparative physiology of successful network architectures • Universal architectural features (layering, hourglass, bowtie) in technology and biology • Duality and optimization as unifying framework (algorithms, distributed, dynamic, layered, nested relaxations, etc…) Diverse case studies • • • • • Internet and extensions Cell/systems biology Ecosystems (e.g. CA coastal wildfire) Biomedical and physiology Toy example: Lego • Earthquake dynamics and statistics • Disasters statistics • Infrastructure: Electric power, Transportation, Manufacturing • Multiscale physics (Turbulence, Foundations of Statistical mechanics, Friction, Fracture, Granular Flows) Early Internet “pre-theory” • Principles • …but no math “theory” per se • Good engineers always lead theory (and science) • Theory adds depth, rigor, scalability, etc Early theory (post deployment) • Measurement • Statistics • Packet-level dynamic simulation Theory and the Internet Levels of understanding Topics Verbal/cartoon Traffic Data and statistics Modeling and simulation Topology Control and dynamics Analysis Layering Synthesis Architectures “The Matrix” - subfields of networking, and progress therein.. ARCHITECTURE Traffic Topology Verbal Data/stat Mod/sim Analysis Synthesis C&D Layering ??? Traffic (1993-2000) Traffic Verbal Data/stat Mod/sim Analysis Synthesis • Heavy tails (HT) in net traffic??? • Careful measurements • Appropriate statistics • Connecting traffic to application behavior • “optimal” web layout HT files HT traffic Unnecessary confusion (and its resolution) Traffic Topology Verbal Data/stat Mod/sim Analysis Synthesis 2 10 High degree hublike core Low degree mesh-like core 1 identical power-law degrees 10 Completely different networks can have the same node degrees. 0 10 0 10 1 10 2 10 3 10 • Low degree core • High performance and robustness • Efficient, economic • High degree “hubs” • Poor performance and robustness • Wasteful, expensive Nothing like the real Internet. See PNAS, Sigcomm, TransNet papers for details. Network technology Yet One of the most-read papers ever on the Internet! Network science? Why is this “science” not? Much “network science” and “complex systems” literature is equally specious Huge and recent progress Traffic Verbal Data/stat Mod/sim Analysis Synthesis Topology C&D Layering Architect. The Internet hourglass my computer router router HTTP TCP IP LINK web server my computer Diverse router router web server HTTP TCP IP LINK Diverse Diverse Application Highly conserved core control processes TCP/AQM IP Layered MAC Physical Diverse Diverse Application TCP/AQM Highly conservedHidden to most core usersIPand control technologies processes Layered MAC Physical Diverse Application Highly conserved core control processes Hardware Diverse Operating system Layered Diverse Operating system Diverse Hardware Layered Layered Application Diverse Conserved core control TCP IP Diverse function Physical Universal Control Diverse Hourglass components Diverse Layering as optimization decomposition • Each layer is abstracted as an optimization problem • Operation of a layer is a distributed solution • Results of one problem (layer) are parameters of others • Operate at different timescales Application: utility application transport network link physical max x0 U ( x ) i i i Phy: power subj to Rx c( p ) x X IP: routing Link: scheduling Architecture as optimization decomposition System constraints: utility • reflect real human behavior • real-time control of physical systems U ( x ) U i i 0 i subj to x X Component constraints • heterogeneous, physical infrastructure • realistic dynamics • robustness to uncertainties Architecture as optimization decomposition Emergent constraints: • Integrated • Control • Energy • Materials • Computation U ( x ) U i i 0 i subj to x X Protocol constraints: • distributed • layered? • real-time control rate form/activity level rate form/activity level rate Reaction rate Enzyme form/activity Proteins Enzyme level/ Translation rate form/activity RNAs RNA level/ Transcription rate DNAs Academic stovepipes EE, CS, ME, MS, APh, ChE, Bio, Geo, Eco, … Apps Tools/ tech Apps Apps Apps Tools/ tech Tools/ tech Apps Tools/ tech Tools/ tech New applications Funding twine Apps Apps Apps AppsApps Tools/ Tools/Tools/ tech Tools/ Tools/ tech tech tech tech “Multidisciplinary cross-sterilization” New applications Layering academia? ????? Apps Apps Apps Apps Tools/ Tools/ Tools/ Apps Tools/ tech tech tech tech Tools/ tech fan-in of diverse inputs universal carriers Bowties: flows within layers fan-out of diverse outputs Diverse function Universal Control Diverse components Hourglass: layering of control and interfaces Constraints that deconstrain Variety of files • • • packets Variety of files Main bowtie in Internet S All advanced technologies have protocols specifying “knot” of carriers, building blocks, interfaces, etc Facilitates control, enabling robustness and evolvability Creates fragilities to hijacking and cascading failure Variety of files packets Applications TCP IP Link Variety of files Many bowties in Internet fan-in of diverse inputs universal carriers Internet is very special Diverse function Universal Control Diverse components fan-out of diverse outputs • • • • • Pure communication Simple dynamics No “metabolism” No assembly No autocatalysis Electric power network Variety of producers Variety of consumers • Good designs transform/manipulate energy • Subject (and close) to hard limits Standard interface Energy carriers Variety of producers • • • • • 110 V, 60 Hz AC (230V, 50 Hz AC) Gasoline ATP, glucose, etc Proton motive force Variety of consumers Architecture Biology Evolution of the Internet Circuits, Pathways, Molecules, Two foci: • Components (VLSI, optics, web apps …) – Rapid change, diversity, and rearrangement • Architecture (TCP/IP) – Largely fixed and universal Architecture of the cell Network elements Components Architecture • Well understood • Changes rapidly • Takes architecture for granted • Focus of most research and innovation in both science and engineering • Widely viewed as most important • Poorly understood • Changes rarely • If well-designed is largely invisible • Source of most confusion • Most essential? • Growing importance? The dangers of naïve biomemetics Feathers and flapping? Or lift, drag, propulsion, and control? Getting it (W)right, 1901 • “We know how to construct airplanes.” (lift and drag) • “..and to build engines.” (propulsion) • “Inability to balance/steer [is the] problem.” (control) • “When this one feature has been worked out, the age of flying will have arrived, for all other difficulties are of minor importance.” Wilbur Wright on Control, 1901 Getting it right, 2010, Control++ Architecture, networks, robustness, and complexity • • • • Words we use all the time Often as their own antonym Thus potential sources of confusion Today: discuss a few basic ideas that seem necessary • Illustrate with familiar examples • Should be at the heart of NetSE Essential ideas Robust yet fragile Constraints that deconstrain local global Human complexity Robust Yet Fragile Efficient, flexible metabolism Obesity and diabetes Rich microbial symbionts and Parasites, infection Immune systems Inflammation, Auto-Im. Regeneration & renewal Cancer Complex societies Epidemics, war, … Advanced technologies Catastrophic failures Robust Implications/ Generalizations Efficient, flexible metabolism Rich microbial symbionts and Immune systems Regeneration & renewal Complex societies Advanced technologies Yet Fragile Obesity and diabetes Parasites, infection Inflammation, Auto-Im. Cancer Epidemics, war, … Catastrophic failures • Complexity driven by control and robust/fragile • More than minimal functionality • Easy to create robustness, harder to avoid fragility • Hijacking and side effects of mechanisms evolved for robustness • New robust/fragile conservation laws Robust yet fragile Biology (and advanced tech) show extremes • Robust Yet Fragile • Simplicity and complexity • Unity and diversity • Evolvable and frozen What makes this possible and/ or inevitable? Architecture (= constraints) Let’s dig deeper. Hard limits and tradeoffs On systems and their components • Thermodynamics (Carnot) • Communications (Shannon) • Control (Bode) • Computation (Turing/Gödel) No networks Assume different architectures a priori. Hard limits and tradeoffs On systems and their components • Thermodynamics (Carnot) • Communications (Shannon) • Control (Bode) • Computation (Turing/Gödel) • Fragmented and incompatible • Cannot be used as a basis for comparing architectures • New unifications are encouraging No dynamics or feedback Hard limits and tradeoffs On systems and their components • Thermodynamics (Carnot) • Communications (Shannon) • Control (Bode) • Computation (Turing/Gödel) • Include dynamics and feedback • Extend to networks • New unifications are encouraging Robust/ fragile is unifying concept [a system] can have [a property] robust for [a set of perturbations] Fragile Yet be fragile for Robust [a different property] Or [a different perturbation] [a system] can have [a property] robust for [a set of perturbations] • Some fragilities are inevitable in robust complex systems. Fragile Robust • But if robustness/fragility are conserved, what does it mean for a system to be robust or fragile? Emergent Fragile • Some fragilities are inevitable in robust complex systems. Robust • But if robustness/fragility are conserved, what does it mean for a system to be robust or fragile? • Robust systems systematically manage this tradeoff. • Fragile systems waste robustness. Hard limits RHP z and p z z p ln S j 2 d ln 2 0 z z p 1 Nominal Variable Process Value? q autocatalysis 1 inhibition 1 k 2nd enzyme 1 z p 1 2 1 z p hk 0q 1 1 2 1 2 2 2 2.41 rate form/activity level rate form/activity level rate Reaction rate Enzyme form/activity Proteins Enzyme level/ Translation rate form/activity RNAs RNA level/ Transcription rate DNAs Catabolism Precursors Inside every cell Carriers Nucleotides Catabolism Precursors Core metabolism Carriers Nucleotides Precursors Catabolism Carriers Gly G1P G6P Catabolism F6P F1-6BP Gly3p ATP 13BPG 3PG 2PG NADH Oxa PEP Pyr ACA TCA Cit Gly Precursors G1P G6P F6P metabolites F1-6BP Gly3p 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA Cit Gly G1P G6P Enzymatically catalyzed reactions F6P F1-6BP Gly3p 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA Cit Gly Precursors G1P G6P F6P Autocatalytic F1-6BP Gly3p Carriers ATP 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA NADH Cit Gly G1P G6P Regulatory F6P F1-6BP Gly3p ATP 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA NADH Cit Gly G1P G6P F6P F1-6BP Gly3p 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA Cit If we drew the feedback loops the diagram would be unreadable. Gly G1P G6P F6P F1-6BP Gly3p ATP 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA NADH Cit Stoichiometry or mass and energy balance Biology is not a graph. dx Sv( x) dt Mass & Reaction Energy flux Balance Interna l Nutrients Products dx Sv( x) dt Stoichiometry plus regulation Mass & Reaction d Mass&Energy Energy flux dt Balance Matrix of integers “Simple,” can be known exactly Amenable to high throughput assays and manipulation Bowtie architecture Vector of (complex?) functions Difficult to determine and manipulate Effected by stochastics and spatial/mechanical structure Hourglass architecture Can be modeled by optimal controller (?!?) dx S Sv( x) dt Mass & Reaction Energy flux Balance Gly G1P G6P F6P F1-6BP Gly3p ATP Stoichiometry matrix 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA NADH Cit dx Sv( x) dt Mass & Reaction Energy flux Balance Gly G1P G6P F6P F1-6BP Gly3p Regulation of enzyme levels by transcription/translation/degradation 13BPG 3PG 2PG Oxa PEP level Pyr ACA TCA Cit dx Sv( x) dt Mass & Reaction Energy flux Balance Gly G1P G6P F6P F1-6BP form/activity Gly3p ATP 13BPG Allosteric regulation of enzymes 3PG 2PG Oxa PEP Pyr ACA TCA NADH Cit Mass & Reaction dx Sv( x) Energy flux dt Balance Gly G1P G6P rate F6P form/activity F1-6BP Gly3p level ATP 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA NADH Cit Mass & Reaction dx Sv( x) Energy rate dt Balance Gly G1P G6P rate F6P Layered F1-6BP architecture Gly3p form/activity level ATP 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA NADH Cit rate form/activity level Control of protein levels Reaction rate Enzyme form/activity Proteins Enzyme level/ Translation rate RNAs DNAs rate form/activity level rate form/activity level rate Reaction rate Enzyme form/activity Proteins Enzyme level/ Translation rate form/activity RNAs RNA level/ Transcription rate DNAs Transcription RNA Transc. RNAp Gene xRNA RNA level/ Transcription rate DNA level RNA level product Enz Controlled, dynamic RNA Transc. RNAp Gene xRNA RNA level/ Transcription rate DNA level Precursors AA tRNA trans. mRNA RNA Transc. RNAp Enzyme level/ Enzymes Translation rate Gene xRNA ncRNA RNA level/ Transcription rate DNA level reactions S Enz1 reaction3 AA trans. products Reaction P rate Enzyme form/activity Enz2 Enzyme level/ Enzymes Translation rate mRNA Ribosome tRNA RNA Transc. RNAp ncRNA xRNA Gene RNA form/activity RNA level/ Transcription rate What to call the sublayers? Reaction rate Enzyme form/activity rate form/activity level What is where Enzyme level/ Translation rate RNA form/activity RNA level/ Transcription rate Catabolism Precursors Nutrients Taxis and transport Same 12 in all Core metabolism cells Nucleotides Carriers Same 8 in all cells Taxis and transport Autocatalytic feedback 12 Polymerization and complex assembly Precursors Catabolism Co-factors Genes Carriers DNA replication Huge Variety 8 100 Trans* Proteins Nutrients Core metabolism 104 to ∞ in one organisms Autocatalytic feedback Polymerization and complex assembly Huge Variety Proteins Genes DNA replication Trans* 104 to ∞ in one organisms Precursors Biosynthesis Massively autocatalytic Co-factors RNA Transc. xRNA RNA level/ Transcription rate RNAp Gene DNA level Precursors Catabolism AA RNA Transc. Gene xRNA RNAp Precursors Catabolism AA transl. tRNA Enzymes Ribosome ncRNA mRNA RNA Transc. Gene xRNA RNAp Precursors Catabolism AA transl. Enzymes tRNA Autocatalysis everywhere Ribosome RNA transc. xRNA RNAp S reactions P Enz1 reaction3 tRNA ncRNA AA trans. products Reaction rate Enzyme form/activity Enz2 Enzyme level/ Translation rate Enzymes Enz2 RNA form/activity mRNA RNA Transc. Gene RNAp xRNA RNA level/ Transcription rate Ribosome reactions All products feedback everywhere products reaction3 Proteins trans. These won’t be drawn in detail Transc. ncRNA S reactions P Enz1 reaction3 tRNA ncRNA AA trans. products Reaction rate Enzyme form/activity Enz2 Enzyme level/ Translation rate Enzymes Enz2 RNA form/activity mRNA RNA Transc. Gene RNAp xRNA RNA level/ Transcription rate Ribosome S reactions P Enz1 reaction3 tRNA ncRNA AA trans. Reaction rate Enz2 Enzymes Enzyme form/activity Enzyme level/ Translation rate RNA form/activity mRNA RNA Transc. Gene RNAp xRNA RNA level/ Transcription rate Ribosome S reactions Enz1 reaction3 P products Reaction rate Enz2 Enzyme form/activity Running only the top layers Mature red blood cells live 120 days Diverse Application Diverse application s and genomes Genome Diverse Horizontal gene transfer HGT and Shared Protocols Bacteria Eukaryotes Animals Archaea Fungi Plants Algae What is locus of early evolution? Horizontal gene transfer HGT and Shared Protocols Bacteria Eukaryotes Animals Archaea Gene Fungi Plants Algae DNA level Controlled, dynamic reactions S HGT and Shared Protocols Bacteria products Reaction P rate Eukaryotes Enz1 reaction3 Enz2 Animals Fungi Plants Archaea AA trans. Enzyme form/activity Enzyme level/ Enzymes Translation rate Algae mRNA Ribosome tRNA RNA Transc. RNAp ncRNA xRNA Gene RNA form/activity RNA level/ Transcription rate Gly G1P G6P F6P F1-6BP Gly3p ATP 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA NADH Cit Gly G1P G6P F6P F1-6BP Gly3p ATP ATP 13BPG 3PG 2PG Oxa PEP Pyr ACA TCA NADH Cit Autocatalytic x 1 0 kx x Control q Vx q 1 1 xh F6P F1-6BP Gly3p ATP 13BPG 3PG y 1 q 1 k y y Autocatalytic x 1 0 kx x Control q Vx q 1 1 xh F6P F1-6BP Gly3p 13BPG 3PG ATP y 1 q 1 k y y Autocatalytic x 1 0 kx x Control q Vx q 1 1 xh Minimal metabolism model • x = ultimate product (ATP) • y = intermediate metabolite • Two feedbacks of x: – Autocatalytic – Control y 1 q 1 k y y Hard limits RHP z and p z z p ln S j 2 d ln 2 0 z z p 1 Nominal Variable Process Value? q autocatalysis 1 inhibition 1 k 2nd enzyme 1 z p 1 2 1 z p hk 0q 1 1 2 1 2 2 2 2.41 Autocatalytic q Vx q 1 1 xh x Control y 1 0 (1 ) 1 q 1 k y y x produced ky y y consumed k y ( y) y Autocatalytic x Control k1 ( x) y consumed produced k1 ( x) x x 1 0 (1 ) consumed x q 1 q 1 y 1 k x x 1 ky 0 (1 ) Autocatalytic q Vx q 1 1 xh 1 0 (1 ) x y k y ( y) y 1 q 1 k y y Autocatalytic q Vx q 1 1 xh x Control y 1 0 (1 ) 1 q 1 k y y k y ( y) k1 ( x) Autocatalytic q Vx q 1 1 xh x Control y 1 0 (1 ) 1 q 1 k y y Robust Yet Fragile Strong inhibition Enzyme complexity, Oscillations Low autocatalysis High reaction rates Inefficiency, metabolic load [ATP] 1.05 Ideal 1 h >>1 0.95 Time response 0.9 Sh = F( x) h h=1 0.8 0 5 10 15 20 Time (minutes) 0.8 h >>1 0.6 Log(|Sn/S0|) Fourier Transform of error 0.85 0.4 0.2 Spectrum h=1 0 log S h log S1 -0.2 -0.4 -0.6 -0.8 0 2 4 Frequency 6 8 10 [ATP] 1.05 1 h >> 1 0.95 Time response 0.9 0.85 Yet fragile h=1 0.8 0 5 10 15 20 Time (minutes) 0.8 h >>1 Robust Log(Sn/S0) 0.6 0.4 0.2 Spectrum h=1 0 -0.2 ln Sh j ln S0 j -0.4 -0.6 -0.8 0 2 4 Frequency 6 8 10 ln S j d 0 0 Yet fragile 0.8 h=3 Robust Log(Sn/S0) 0.6 0.4 0.2 h=0 0 -0.2 -0.4 -0.6 -0.8 0 2 4 Frequency 6 8 10 0 ln S j d 0 ln S j d 0 Yet fragile 0.8 Robust Log(Sn/S0) 0.6 0.4 0.2 h=0 0 -0.2 -0.4 -0.6 -0.8 0 2 4 Frequency 6 8 10 This tradeoff is a law. log|S | Transients, Oscillations x ) d constant log F(Biological complexity is n Tighter regulation dominated by the evolution of mechanisms to more finely tune this robustness/fragility tradeoff. Hard limits RHP p 1 ln S j d 0 Re p 0 z p ln z p 0 RHP z 1 z ln S j 2 d 2 0 z 1 z d 1 2 2 0 z Benefits must be “paid for” within bandwidth z Necessity, not accident z z p ln S j 2 d ln 2 0 z z p 1 “Optimal” controller 1 0 1 x “Optimal” enzyme y 1 q 1 ky q=α=0 q=α=1 Necessity, not accident hˆ 2 hˆ 10 hˆ 1.5 hˆ .5 hˆ 1.5 hˆ 1.25 0 10 0 10 • Necessity or accident? • Alternative designs Synthesis challenges Robust Yet Fragile large hˆ small Enzyme complexity, Oscillations large k small q Inefficiency, metabolic load • Other rates and uncertainty • Computational complexity – Higher order dynamics – Global, nonlinear – Comparisons with data • Robustness is key Hard limits and tradeoffs On systems and their components • Thermodynamics (Carnot) • Communications (Shannon) • Control (Bode) • Computation (Turing/Gödel) • Include dynamics and feedback • Extend to networks • New unifications are encouraging Robust/ fragile is unifying concept cost = amplification goal: make this small log S d log S d • benefits = attenuation of disturbance • goal: make this as negative as possible Constraint: log S d log S d benefits costs Bode e=d-u Plant -u d S E D a u delay Control log S d log S d benefits costs a stabilize Bode e=d-u Plant -u d S E D a u delay Control log S d log S d benefits costs a stabilize - e=d-u Plant u CC Control Channel Control log S d log( a ) d Disturbance d Remote Sensor CS Sensor Channel r Encode CC log S d CS Nuno C Martins and Munther A Dahleh, Feedback Control in the Presence of Noisy Channels: “Bode-Like” Fundamental Limitations of Performance. Nuno C. Martins, Munther A. Dahleh and John C. Doyle Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information (Both in IEEE Transactions on Automatic Control) http://www.glue.umd.edu/~nmartins/ Electric power network Variety of producers Variety of consumers • Good designs transform/manipulate energy • Subject (and close) to hard limits Standard interface Energy carriers Variety of producers • • • • • 110 V, 60 Hz AC (230V, 50 Hz AC) Gasoline ATP, glucose, etc Proton motive force Variety of consumers d e=d-u Plant Disturbance Fragile d Remote Sensor Control Channel Control log( a ) Sensor Channel benefits r Robust Encode stabilize log S d log(a) costs CC remote control feedback log S d CS remote sensing • Robust designs transform/manipulate robustness • Subject (and close) to hard limits • Fragile designs are far away from hard limits and waste robustness. Hard limits and tradeoffs On systems and their components • Thermodynamics (Carnot) • Communications (Shannon) • Control (Bode) • Computation (Turing/Gödel) • Include dynamics and feedback • Extend to networks • New unifications are encouraging Robust/ fragile is unifying concept [a system] can have [a property] robust for [a set of perturbations] Fragile Yet be fragile for Robust [a different property] Or [a different perturbation] [a system] can have [a property] robust for [a set of perturbations] • Some fragilities are inevitable in robust complex systems. Fragile Robust • But if robustness/fragility are conserved, what does it mean for a system to be robust or fragile? Emergent Fragile • Some fragilities are inevitable in robust complex systems. Robust • But if robustness/fragility are conserved, what does it mean for a system to be robust or fragile? • Robust systems systematically manage this tradeoff. • Fragile systems waste robustness.
