Fat tails, hard limits, thin layers John Doyle, Caltech

Transcription

1 Fat tails, hard limits, thin layers John Doyle, Caltech Rethinking fundamentals* Parameter estimation and goodness of fit measures for fat tail distributions Hard limits on robust, efficient networks integrating comms, controls, energy, materials Essentials of layered architectures, naming and address, pub-sub, control, coding, latency, and implications for wireless Implications for control over networks Try to get you to read some papers you might otherwise not *really simple so we can move fast

2 Fundamentals! A rant A series of obvious observations (hopefully)

3 Case studies Networking and clean slate architectures wireless end systems info or content centric application layer integrate routing, control, scheduling, coding, caching control of cyber-physical Lots from cell biology glycolytic oscillations for hard limits bacterial layering for architecture Neuroscience PC, OS, VLSI, etc (IT components) Earthquakes Medical physiology Smartgrid, cyber-phys Physics: turbulence, stat mech (QM?) Wildfire ecology Lots of aerospace Fundamentals!

4 Existing design frameworks Sophisticated components Poor integration Limited theoretical framework ictio Goa n ls Acti ons error s layers Meta- Phys iolog Acti oon rgs ans Fast, Limited scope y Control Remote Sensor Sensor Actuator Disturba nce Pred Comms Cort Slow, Broad scope Interface ex Fix? Plant

5 ictio Goa n ls Acti ons error s laye Meta- rs Phys iolog Acti oon rgs ans Fast, Limited scope y Control Remote Sensor Sensor Actuator Disturba nce Pred Comms Cort Slow, Broad scope Interface ex Layered architectures Plant

6 This paper aims to bridge progress in neuroscience involving sophisticated quantitative analysis of behavior, including the use of robust control, with other relevant conceptual and theoretical frameworks from systems engineering, systems biology, and mathematics. Doyle and Csete, Proc Nat Acad Sci USA, online JULY

7 accessible accountable accurate adaptable administrable affordable auditable autonomy available credible process capable compa?ble composable configurable correctness customizable debugable degradable determinable demonstrable dependable deployable discoverable distributable durable effec?ve efficient evolvable extensible failure transparent fault- tolerant fidelity flexible inspectable installable Integrity interchangeable interoperable learnable maintainable manageable mobile modifiable modular nomadic operable orthogonality portable precision predictable producible provable recoverable relevant reliable repeatable reproducible resilient responsive reusable robust safety scalable seamless self- sustainable serviceable supportable securable simplicity stable standards compliant survivable sustainable tailorable testable?mely traceable ubiquitous understandable upgradable usable Requirements on systems and architectures

8 accessible accountable accurate adaptable administrable affordable auditable autonomy available credible process capable compa?ble composable configurable correctness customizable debugable degradable determinable demonstrable dependable deployable discoverable distributable durable effec?ve efficient evolvable extensible failure transparent fault- tolerant fidelity flexible inspectable installable Integrity interchangeable interoperable learnable maintainable manageable mobile modifiable modular nomadic operable orthogonality portable precision predictable producible provable recoverable relevant reliable repeatable reproducible resilient responsive reusable robust safety scalable seamless self- sustainable serviceable supportable securable simplicity stable standards compliant survivable sustainable tailorable testable?mely traceable ubiquitous understandable upgradable usable Simplified, minimal requirements

9 accessible accountable accurate adaptable administrable affordable auditable autonomy available credible process capable compa?ble composable configurable correctness customizable debugable degradable determinable demonstrable dependable deployable discoverable distributable durable effec?ve efficient evolvable extensible failure transparent fault- tolerant fidelity flexible inspectable installable Integrity interchangeable interoperable learnable maintainable manageable mobile modifiable modular nomadic operable orthogonality portable precision predictable producible provable recoverable relevant reliable repeatable reproducible resilient responsive reusable robust safety scalable seamless self- sustainable serviceable supportable securable simplicity stable standards compliant survivable sustainable tailorable testable?mely traceable ubiquitous understandable upgradable usable Requirements on systems and architectures wasteful fragile efficient robust

10 Robust to uncertainty in environment and components Efficient in use of real physical resources fragile robust Want robust efficiency efficient wasteful

11 2.5d space of systems and architectures fragile robust efficient wasteful

12 Want to understand the space of systems/architectures fragile Case studies? Strategies? robust Want robust and efficient systems and architectures efficient wasteful Architectures?

13 Control, OR Bode Pontryagin Kalman Shannon Comms Nash Von Neumann Theory? Deep, but fragmented, incoherent, incomplete Carnot Turing Compute Godel Heisenberg Einstein Boltzmann Physics

14 Control Bode Shannon Comms fragile? slow? Each theory one dimension Tradeoffs across dimensions Assume architectures a priori Progress is encouraging, but? Turing Compute wasteful? Godel Heisenberg Einstein Carnot Boltzmann Physics

15 Technology? fragile At best we get one robust efficient wasteful

16 ??? fragile Often neither robust efficient wasteful

17 fragile??? Bad architectures?? gap? robust Bad theory?? efficient wasteful

18 Conservation laws? fragile Sharpen hard bounds Case studies wasteful

19 Control Bode Comms Shannon fragile? slow? wasteful?

20 Control Familiar pictures Comms e=d-u Plant - u Control d e=d-u - u Decode d delay Capacity C Sense channel Disturbance Sense/ Encode Sensitivity Circa 1950? Entropy Bode Shannon Assume favorable delays

21 Shannon e=d-u - d delay Disturbance Decode Capacity C S Sense channel Sense/ Encode Entropy Assume favorable delays

22 Bode e=d-u Plant - u d unstable pole p Control Sensitivity Simplified and dropped constants, slight differences between cont and disc time

23 Control Comms e=d-u Plant - u Control d e=d-u - u Decode d delay Capacity C Sense channel Disturbance Sense/ Encode Circa 1950? So, anything happened since?

24 Layered architectures Diverse applications TCP IP MAC Switch MAC Pt to Pt MAC Pt to Pt Physical

25 This paper aims to bridge progress in neuroscience involving sophisticated quantitative analysis of behavior, including the use of robust control, with other relevant conceptual and theoretical frameworks from systems engineering, systems biology, and mathematics. Doyle and Csete, Proc Nat Acad Sci USA, online JULY

26 Proceedings of the IEEE, Jan 2007 Chang, Low, Calderbank, and Doyle

27 Too clever? Diverse applications TCP IP Diverse Physical

28 Layered architectures Deconstrained (Applications) Networks TCP IP Constrained Deconstrained (Hardware) constraints that deconstrain (Gerhart and Kirschner)

29 Original design challenge? Deconstrained (Applications) Networked OS Constrained TCP/ IP Deconstrained (Hardware) Trusted end systems Unreliable hardware Facilitated wild evolution Created whole new ecosystem complete opposite

30 Layered architectures Deconstrained (Applications) Essentials Few global variables Constrained OS Don t cross layers Control, share, virtualize, and manage resources Deconstrained (Hardware) Processing Memory I/O

31 Catabolism AA ATP Layered architectures Precursors Deconstrained (diverse) Environments ATP Building Blocks RNA AA DNA Enzymes transl. transc. Repl. Proteins xrna Gene Ribosome Shared protocols RNAp DNAp Bacterial biosphere Architecture = Constraints that Deconstrain Deconstrained (diverse) Genomes

32 Catabolism Precursors AA ATP Inside every cell almost Enzymes Crosslayer autocatalysis Building Blocks Macro-layers AA ATP RNA DNA transl. transc. Repl. Proteins Ribosome xrna RNAp Gene DNAp

33 Catabolism AA ATP What makes the bacterial biosphere so adaptable? Deconstrained phenotype Environment Action Precursors ATP Layered architecture Building Blocks AA RNA Enzymes Proteins transl. Ribosome transc. xrna Core conserved constraints facilitate tradeoffs RNAp DNA Repl. Gene DNAp Deconstrained genome Active control of the genome (facilitated variation)

34 Layered architectures Deconstrained (Applications) Few global variables Don t cross layers Direct access Constrained OS Control, to share, virtualize, physical and manage resources memory? Processing Memory Deconstrained I/O (Hardware)

35 Catabolism AA ATP Deconstrained (diverse) Environments Bacterial biosphere Precursors ATP Building Blocks AA RNA DNA Enzymes transl. transc. Repl. Proteins Few global variables Shared protocols Architecture = Constraints Ribosome that xrna RNAp Don t cross layers Gene DNAp Deconstrain Deconstrained (diverse) Genomes

36 Problems with leaky layering Modularity benefits are lost Global variables? Poor portability of applications Insecurity of physical address space Fragile to application crashes No scalability of virtual/real addressing Limits optimization/control by duality?

37 Fragilities of layering/virtualization Hijacking, parasitism, predation Universals are vulnerable Universals are valuable Breakdowns/failures/unintended/ not transparent Hyper-evolvable but with frozen core

38 Original design challenge? Deconstrained (Applications) Networked OS Constrained TCP/ IP Deconstrained (Hardware) Trusted end systems Unreliable hardware Facilitated wild evolution Created whole new ecosystem complete opposite

39 Layered architectures Deconstrained (Applications) Few global variables? Constrained TCP/ IP Don t cross layers? Control, share, virtualize, and manage resources Deconstrained (Hardware) I/O Comms Latency? Storage? Processing?

40 App Robust? Secure Scalable Verifiable Evolvable Maintainable Designable IPC IP addresses interfaces (not nodes) DNS App Global and direct access to physical address!

41 Naming and addressing need to be resolved within layer translated between layers not exposed outside of layer Related issues VPNs NATS Firewalls Multihoming Mobility Routing table size Overlays Application TCP IP Physical

42 Next layered architectures Deconstrained (Applications) Few global variables Constrained? Don t cross layers Control, share, virtualize, and manage resources Deconstrained (Hardware) Comms Memory, storage Latency Processing Cyber-physical

43 Persistent errors and confusion ( network science ) Architecture is least graph topology. Every layer has different diverse graphs. Application TCP IP Architecture facilitates arbitrary graphs. Physical

44 What happened to this picture? - d Source Decode Source coding Code 1. Hard limits 2. Achievability 3. Decomposition/Layering Channel coding Decode Channel Code

45 Under certain assumptions Decoupled Hides details Virtualizes channel Decode Rcv Channel coding Physical layer Channel Code Xmit

46 - d Source Decomp Source coding Compress Decoupled Hides details Virtualizes source Under certain assumptions

47 Rate distortion (backwards) error gap? Hard tradeoffs Architecture = separation + coding R data rate

48 Rate distortion (backwards) error gap? delay? Hard tradeoffs Architecture = separation + coding R data rate

49 - d Source Decomp Data compression Compress Internet= Distributed OS Layered architecture Control theory Decode Link layer Code Rcv Channel Xmit

50 - d Decomp Application layer Source Compress Control/optimization theory needed for Routing Congestion control Scheduling Caching? Distributed control of cyber-physical Still incomplete, needs more integration, with OS, languages Info theory, particularly for wireless Decode Rcv Physical layer Channel Code Xmit

51 Control Comms e=d-u Plant - u Control d e=d-u - u Decode d delay Capacity C Sense channel Disturbance Sense/ Encode Sensitivity Circa 1950? Entropy What next?

52 Bode e=d-u Plant - u d ω Control benefits causality stabilize costs unstable pole p

53 Bode e=d-u Plant - u d ω Control benefits stabilize causality unstable pole p costs

54 Bode e=d-u Plant - u d Control benefits stabilize causality unstable pole p costs

55 e=d-u - d Martins and Dahleh, IEEE TAC, 2008 Plant Control Channel benefits Control stabilize remote control max costs feedback

56 Shannon e=d-u - d delay Disturbance Decode Capacity C S Sense channel Sense/ Encode Entropy Assume favorable delays

57 Shannon e=d-u - d delay Disturbance Decode C S Sense/ Encode benefits -C S

58 e=d-u - d delay Disturbance Plant Control C S Sense/ Encode benefits stabilize remote control -C S Martins, Dahleh, Doyle IEEE TAC, 2007 costs causality

59 0 d delay Disturbance delay?? Benefits? -C S benefits stabilize -C S costs causality

60 e=d-u - d delay Disturbance Plant Physical implementation? Control C S Sense/ Encode Abstract models of resource use Foundations, origins of noise dissipation amplification catalysis

61 Chandra, Buzi, and Doyle

62 CSTR, yeast extracts Experiments K Nielsen, PG Sorensen, F Hynne, H- G Busse. Sustained oscillafons in glycolysis: an experimental and theore?cal study of chao?c and complex periodic behavior and of quenching of simple oscilla?ons. Biophys Chem 72:49-62 (1998).

63 4 3 2 Standard SimulaFon v= v= v= Figure S4. Simula?on of two state model (S7.1) qualita?vely recapitulates experimental observa?on from CSTR studies [5] and [12]. As the flow of material in/out of the system is increased, the system enters a limit cycle and then stabilizes again. For this simula?on, we take q=a=vm=1, k=0.2, g=1, u=0.01, h=2.5.

64 4 3 2 Experiments Why? SimulaFon v= v= v= Figure S4. Simula?on of two state model (S7.1) qualita?vely recapitulates experimental observa?on from CSTR studies [5] and [12]. As the flow of material in/out of the system is increased, the system enters a limit cycle and then stabilizes again. For this simula?on, we take q=a=vm=1, k=0.2, g=1, u=0.01, h=2.5.

65 Glycoly?c circuit and oscilla?ons Most studied, persistent mystery in cell dynamics End of an old story (why oscilla?ons) side effect of hard robustness/efficiency tradeoffs no purpose per se just needed a theorem Beginning of a new one robustness/efficiency tradeoffs complexity and architecture need more theorems and applica?ons

66 fragile? Robust =maintain energy charge w/fluctuating cell demand robust? Tradeoffs? efficient? PFK? autocatalytic? a? h? x? control? y? PK? g? rate k? Rest? wasteful? Efficient=minimize metabolic overhead

67 Theorem! Fragility z and p func?ons of enzyme complexity and amount simple enzyme complex enzyme Savageaumics Enzyme amount

68 Catabolism Precursors AA ATP Inside every cell almost Enzymes Crosslayer autocatalysis Building Blocks Macro-layers AA ATP RNA DNA transl. transc. Repl. Proteins Ribosome xrna RNAp Gene DNAp

69 Energy Catabolism Precursors AA ATP Enzymes Crosslayer autocatalysis Building Blocks Macro-layers AA ATP RNA DNA transl. transc. Repl. Proteins Protein biosyn xrna Gene Ribosome RNAp DNAp

70 Energy Catabolism Precursors ATP

71 Minimal model Metabolic flux intermediate metabolite Reaction 1 ( PFK ) x Reaction 2 ( PK ) energy ATP Rest of cell Efficient metabolic overhead

72 Reaction 1 ( PFK ) enzymes catalyze reactions Rest of cell Reaction 2 ( PK ) enzymes enzymes enzymes Protein biosyn Efficient metabolic overhead enzyme amount

73 Fluorescence histogram (fluorescence vs. cell count) of GFP- tagged Glyceraldehyde- 3- phosphate dehydrogenase (TDH3). Cells grown in ethanol has lower mean and median of fluorescence, and also higher variability.

74 Metabolic Overhead

75 highly variable 10 1 g=0 Fragility 10-1 g= Metabolic Overhead g=0 is implausibly fragile

76 Reaction 1 ( PFK ) enzymes autocatalytic feedback: energy energy ATP Rest of cell Reaction 2 ( PK ) Protein biosyn enzymes enzymes Efficient metabolic overhead enzyme amount

77 Metabolic flux Inherently unstable Reaction 1 ( PFK ) x ATP Rest of cell Reaction 2 ( PK ) Efficient metabolic overhead enzyme amount

78 control feedback Fragile Reaction 1 ( PFK ) x Reaction 2 ( PK ) h control g ATP disturbance energy Rest of cell Robust Robust = Maintain energy despite demand fluctuation

79 Fragile Reaction 1 ( PFK ) x Reaction 2 ( PK ) h control g ATP disturbance energy Rest of cell Robust Efficient metabolic overhead enzyme amount

80 Theorem! Fragile Reaction 1 ( PFK ) h control x Reaction 2 ( PK ) g ATP energy disturbance Rest of cell Robust Efficient metabolic overhead enzyme amount

81 Theorem! Fragile simple enzyme Reaction 1 ( PFK ) h control x Reaction 2 ( PK ) g ATP energy disturbance Rest of cell Robust complex enzyme Efficient metabolic overhead enzyme amount

82 Fragile Reaction 1 ( PFK ) h control x Reaction 2 ( PK ) g ATP energy disturbance Rest of cell Robust complex enzyme Efficient metabolic overhead enzyme amount

83 y = WS δ weighed sensitivity H WS [P W] y=atp δ Reaction 1 ( PFK ) x Reaction 2 ( PK ) h g energy ATP control disturbance Rest of cell

84 Architecture fragile Good architectures allow for effective tradeoffs Alternative systems with shared architecture wasteful

85 Theorem z and p are func?ons of enzyme complexity and amount standard biochemistry models phenomenological first principles?

86 Fragility hard limits General Rigorous First principle complex simple Overhead, waste? Plugging in domain details Domain specific Ad hoc Phenomenological

87 Control Wiener Comms Kalman Bode robust control Shannon General Rigorous First principle? Fundamental mul?scale physics Founda?ons, origins of noise dissipa?on amplifica?on catalysis Heisenberg Boltzmann Carnot Physics

88 Control Compute Complex networks Comms doesn t work Alderson &Doyle, Contrasting Views of Complexity and Their Implications for Network-Centric Infrastructure, IEEE TRANS ON SMC, JULY 2010 New sciences of complexity and networks edge of chaos, self- organized cri?cality, scale- free, Stat physics Heisenberg Carnot Boltzmann Physics

89 Control Compute Complex networks Comms doesn t work Alderson &Doyle, Contrasting Views of Complexity and Their Implications for Network-Centric Infrastructure, IEEE TRANS ON SMC, JULY 2010 Sandberg, Delvenne, & Doyle, On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurement, IEEE TRANS ON AC, FEBRUARY, 2011 Stat physics Heisenberg Carnot Boltzmann Physics

90 Control Comms Complex networks Compute orthophysics Sandberg, Delvenne, & Doyle, On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurement, IEEE TRANS ON AC, FEBRUARY, 2011 Stat physics, fluids, QM Heisenberg Boltzmann Carnot Physics

91 J. Fluid Mech (2010) Streamlined Laminar Flow Flow Turbulence and drag? Turbulent Flow

92 Physics of Fluids (2011) z y Flow x Coherent structures and turbulent drag high- speed region downflow upflow 3D coupling low speed streak y z x Blunted turbulent velocity profile Turbulent Laminar

93 fragile Laminar Turbulent Laminar robust? Control? Turbulent efficient wasteful

94 Control Wiener Comms Kalman Bode robust control Shannon General Rigorous First principle Founda?ons, origins of noise dissipa?on amplifica?on catalysis Heisenberg Carnot Boltzmann Physics

95 Smart Antennas (Javad Lavaei) Security, co- channel interference, power consump?on Conven?onal Antenna Smart Antenna 1) MulFple acfve elements: Easy to program Hard to implement Smart Antennas 2) MulFple passive elements: Easy to implement Hard to program

96 Passively Controllable Smart (PCS) Antenna PCS Antenna: One ac?ve element, reflectors and several parasi?c elements This type of antenna is easy to program and easy to implement but hard to solve (e.g. 4 weeks offline computa?on). We solved the problem in 1 sec with huge improvement:

97 Decentralized control Partial bibliography (Lamperski) Triaged today Great topic

98 In press, available online Really fat tails How big is big?

99 Note: rare example (in science) involving power laws that isn t obviously ridiculous smaller log(rank) Gutenberg- Richter slope = - 1 Persistent controversy characteris?c earthquake??? largest bump magnitude log(power)?

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102 Randomly sampled G- R magnitudes Distribu?on of max event No bump s?ll might look like a bump

103 Order sta?s?cs P( (k of n) > x) p=- dp/dx More data, but Tail stays highly variable More samples

104 Fault traces and epicenters

105 Number of earthquakes per fault 155 faults Synthe?c GR Number of earthquakes per fault Mag of largest quake

106 3 biggest quakes Mag of largest quake

107 3 biggest quakes p=.03 p=.01 p=.002

108 Magnitude binned by distance to faults 3.6

109 Randomly sampled G- R magnitudes Distribu?on of max event No bump s?ll might look like a bump

110 Los Padres Na?onal Forest Truncated pareto model P(>x) 10 3 Wildfires LPNF data (decimated)

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113 Comparison of model n P(>x) with cumula?ve raw data (decimated) LPNF data (decimated)

114 Comparison of varia?ons in LPNF data versus that of pseudo- random samples. LPNF data (black) plus 4 pseudo- random samples from P(>x) (colors) LPNF data and pseudo- random samples have similar varia?ons

115 MLE as WLS Exponen?al Pareto

116 MLE as WLS Exponen?al

117 Pareto Distribu?on α=1 n=100 K- S p- value: 0.34

118 MATLAB s ksstest func?on with the null hypothesis Pareto alpha=1 Pareto Distribu?on α=1 n=100 p= x

119 MATLAB s ksstest func?on with the null hypothesis Pareto alpha= Test Distribution Null Distribution need weighted KS, but what weight? Rank 10 1 α=1 n=100 p=0.34!!! makes no difference x

120 Order sta?s?cs P( (k of n) > x) p=- dp/dx But this is so easy and is (apparently) advocated by many sta?s?cians. More samples