Fat tails, hard limits, thin layers - PowerPoint Presentation

Fat tails, hard limits, thin layersJohn Doyle, Caltech Rethinking fundamentals*Parameter estimation and goodness of fit measures for fat tail distributionsHard limits on robust, efficient networks integrating comms, controls, energy, materialsEssentials of layered architectures, naming and address, pub-sub, control, coding, latency, and implications for wirelessImplications for control over networksTry to get you to read some papers you might otherwise not * really simple so we can move fast

Fundamentals! A rant A series of “obvious” observations (hopefully) Systems

Case studies Networking and clean slate architectures wireless end systemsinfo or content centric application layerintegrate routing, control, scheduling, coding, caching control of cyber-physicalLots from cell biologyglycolytic oscillations for hard limitsbacterial layering for architectureNeurosciencePC, OS, VLSI, etc (IT components)EarthquakesMedical physiology Smartgrid , cyber-phys Physics: turbulence, stat mech (QM?) Wildfire ecologyLots of aerospace Fundamentals!

Meta-layers Physiology Organs Prediction Goals Actions errors Actions Cortex Fast, Limited scope Slow, Broad scope Comms Disturbance Plant Remote Sensor Sensor Actuator Interface Control Existing design frameworks Sophisticated components Poor integration Limited theoretical framework Fix?

Meta-layers Physiology Organs Prediction Goals Actions errors Actions Cortex Fast, Limited scope Slow, Broad scope Comms Disturbance Plant Remote Sensor Sensor Actuator Interface Control Layered architectures

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 25 2011

accessible accountableaccurateadaptableadministrableaffordableauditableautonomyavailablecredibleprocess capable compatible composable configurable correctness customizable debugabledegradabledeterminabledemonstrable dependable deployable discoverable distributable durable effective efficient evolvable extensible failure transparent fault-tolerant fidelity flexible inspectable installable Integrity interchangeable interoperable learnable maintainablemanageablemobilemodifiablemodular nomadicoperableorthogonality portableprecisionpredictable producibleprovablerecoverable relevantreliablerepeatablereproducible resilientresponsivereusable robust safety scalableseamlessself-sustainable serviceablesupportablesecurable simplicitystable standards compliantsurvivable sustainabletailorabletestable timelytraceable ubiquitousunderstandableupgradableusable Requirements on systems and architectures

accessible accountableaccurateadaptableadministrableaffordableauditableautonomy available credible process capable compatible composable configurablecorrectnesscustomizable debugable degradable determinable demonstrable dependable deployable discoverable distributable durable effective efficient evolvable extensible failure transparent fault-tolerant fidelity flexible inspectable installable Integrityinterchangeableinteroperable learnablemaintainable manageablemobile modifiablemodularnomadicoperable orthogonalityportable precisionpredictableproducibleprovable recoverablerelevantreliablerepeatable reproducible resilientresponsivereusable robust safety scalableseamlessself-sustainable serviceablesupportable securablesimplicitystable standards compliantsurvivable sustainabletailorabletestabletimely traceableubiquitousunderstandable upgradableusable Simplified, minimal requirements

accessible accountableaccurateadaptableadministrableaffordableauditableautonomy available credible process capable compatible composable configurablecorrectnesscustomizabledebugabledegradable determinabledemonstrable dependable deployable discoverable distributable durable effective efficient evolvable extensible failure transparent fault-tolerant fidelity flexible inspectable installable Integrity interchangeable interoperable learnablemaintainablemanageable mobilemodifiablemodularnomadicoperable orthogonalityportableprecision predictableproducible provablerecoverablerelevantreliable repeatablereproducibleresilientresponsive reusable robustsafety scalable seamlessself-sustainableserviceable supportablesecurablesimplicity stable standards compliantsurvivablesustainable tailorabletestable timelytraceableubiquitousunderstandable upgradableusable Requirements on systems and architectures wasteful fragile efficient robust

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

2.5d space of systems and architectures wasteful fragile efficient robust simple complex

wasteful fragile efficient robust Want to understand the space of systems/architectures Want robust and efficient systems and architectures Hard limits on robust efficiency? Case studies? Strategies? Architectures?

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

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

wasteful fragile robust efficient At best we get one Technology?

wasteful fragile robust efficient Often neither  ??? 

Bad theory? ???  ? ? Bad architectures? wasteful fragile gap? robust efficient

Case studies wasteful fragile Sharpen hard bounds Hard limit Conservation “laws”?

Control CommsShannonBode wasteful? fragile? slow?

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

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

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

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

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

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 25 2011

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

TCP IP Physical Diverse applications Diverse Too clever?

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

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

OS Deconstrained (Hardware) Deconstrained (Applications) Layered architectures Constrained Control, share, virtualize , and manage resources Processing Memory I/O Few global variables Don’t cross layers Essentials

CatabolismAA Ribosome RNA RNAp transl. Proteins xRNA transc . Precursors Nucl. AA DNA D NAp Repl. Gene ATP ATP Enzymes Building Blocks Shared protocols Deconstrained (diverse) Environments Deconstrained (diverse) Genomes Bacterial biosphere Architecture = Constraints that Deconstrain Layered architectures

CatabolismAA Ribosome RNA RNAp transl. Proteins xRNA transc . Precursors Nucl. AA DNA D NAp Repl. Gene ATP ATP Enzymes Building Blocks Crosslayer autocatalysis Macro-layers Inside every cell almost

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

OS Deconstrained (Hardware) Deconstrained (Applications) Layered architectures Constrained Control, share, virtualize , and manage resources Processing Memory I/O Few global variables Don’t cross layers Direct access to physical memory?

CatabolismAA Ribosome RNA RNAp transl. Proteins xRNA transc . Precursors Nucl. AA DNA D NAp Repl. Gene ATP ATP Enzymes Building Blocks Shared protocols Deconstrained (diverse) Environments Deconstrained (diverse) Genomes Bacterial biosphere Architecture = Constraints that Deconstrain Few global variables Don’t cross layers

Problems with leaky layeringModularity benefits are lostGlobal variables? @$%*&!^%@& Poor portability of applicationsInsecurity of physical address spaceFragile to application crashesNo scalability of virtual/real addressing Limits optimization/control by duality?

Fragilities of layering/virtualization Hijacking, parasitism, predationUniversals are vulnerableUniversals are valuableBreakdowns/failures/unintended/… not transparentHyper-evolvable but with frozen core

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

TCP/ IP Deconstrained (Hardware) Deconstrained (Applications) Layered architectures Constrained Control, share, virtualize , and manage resources I/O Comms Latency? Storage? Processing? Few global variables? Don’t cross layers?

CPU/ Mem Dev2 CPU/ Mem Dev CPU/ Mem Dev2 Dev2 App App IPC Global and direct access to physical address! Robust? Secure Scalable Verifiable Evolvable Maintainable Designable … DNS IP addresses interfaces (not nodes)

Physical IP TCP Application 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 …

? Deconstrained (Hardware) Deconstrained (Applications) Next layered architectures Constrained Control, share, virtualize , and manage resources Comms Memory, storage Latency Processing Cyber-physical Few global variables Don’t cross layers

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

Source -Decode Channel Code d Hard limits Achievability Decomposition/Layering Code Decode Channel coding Source coding What happened to this picture?

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

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

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

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

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

Decode Channel Code Physical layer Rcv Xmit Source - d Compress Decomp Application layer 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

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

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

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

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

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

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

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

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

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

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

Chandra, Buzi, and Doyle

K Nielsen, PG Sorensen, F Hynne, H-G Busse. Sustained oscillations in glycolysis: an experimental and theoretical study of chaotic and complex periodic behavior and of quenching of simple oscillations. Biophys Chem 72:49-62 (1998). Experiments CSTR, yeast extracts

Figure S4 . Simulation of two state model (S7.1) qualitatively recapitulates experimental observation 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 simulation, we take q=a=Vm=1, k=0.2, g=1, u=0.01, h=2.5. 0 20 40 60 80 100 120 140 160 180 200 0 1 2 3 4 v=0.03 0 20 40 60 80 100 120 140 160 180 200 0 0.5 1 1.5 2 v=0.1 0 20 40 60 80 100 120 140 160 180 200 0.2 0.4 0.6 0.8 1 v=0.2 “Standard” Simulation

Figure S4 . Simulation of two state model (S7.1) qualitatively recapitulates experimental observation 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 simulation, we take q=a=Vm=1, k=0.2, g=1, u=0.01, h=2.5. 0 20 40 60 80 100 120 140 160 180 200 0 1 2 3 4 v=0.03 0 20 40 60 80 100 120 140 160 180 200 0 0.5 1 1.5 2 v=0.1 0 20 40 60 80 100 120 140 160 180 200 0.2 0.4 0.6 0.8 1 v=0.2 Simulation Experiments Why?

Glycolytic “circuit” and oscillations Most studied, persistent mystery in cell dynamicsEnd of an old story (why oscillations)side effect of hard robustness/efficiency tradeoffsno purpose per sejust needed a theoremBeginning of a new one robustness/efficiency tradeoffscomplexity and architecture need more theorems and applications

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

simple enzyme Fragility Enzyme amount complex enzyme Theorem! z and p functions of enzyme complexity and amount Savageaumics

CatabolismAA Ribosome RNA RNAp transl. Proteins xRNA transc . Precursors Nucl. AA DNA D NAp Repl. Gene ATP ATP Enzymes Building Blocks Crosslayer autocatalysis Macro-layers Inside every cell almost

CatabolismAA Ribosome RNA RNAp transl. Proteins xRNA transc . Precursors Nucl. AA DNA D NAp Repl. Gene ATP ATP Enzymes Building Blocks Crosslayer autocatalysis Macro-layers Energy Protein biosyn

CatabolismPrecursors ATP Energy

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

enzymes catalyze reactions Rest of cell Reaction 2 (“PK”) Reaction 1 (“PFK”) Protein biosyn enzymes enzymes enzymes metabolic overhead  e nzyme amount Efficient

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.

Metabolic Overhead 10 1 10 2 10 3

g =0 is implausibly fragilehighly variable Fragility 10 -1 10 0 10 1 10 -1 1 10 g = 0 g = 1 Metabolic Overhead

ATP autocatalytic feedback: energy Rest of cell Reaction 2 (“PK”) Reaction 1 (“PFK”) Protein biosyn energy enzymes enzymes enzymes metabolic overhead  e nzyme amount Efficient

ATP Metabolic flux Rest of cell energy x ATP Reaction 2 (“PK”) Reaction 1 (“PFK”) metabolic overhead  e nzyme amount Efficient Inherently unstable

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

ATP Rest of cell energy x ATP h g control Reaction 2 (“PK”) Reaction 1 (“PFK”) disturbance Fragile Robust metabolic overhead  e nzyme amount Efficient

Fragile Robust ATP Rest of cell energy x ATP h g control Reaction 2 (“PK”) Reaction 1 (“PFK”) disturbance metabolic overhead  e nzyme amount Efficient Theorem!

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

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

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

Architecture “Conservation laws” Good architectures allow for effective tradeoffs wasteful fragile Alternative systems with shared architecture

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

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

Control CommsPhysicsWiener Bode Kalman Heisenberg Carnot Boltzmann robust control Fundamental multiscale physics Foundations, origins of noise dissipation amplification catalysis General Rigorous First principle ? Shannon

doesn’t work Stat physicsComplex networks Physics Heisenberg Carnot Boltzmann Control Comms Compute 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 criticality, scale-free,…

doesn’t work Stat physicsComplex networks Physics Heisenberg Carnot Boltzmann Control Comms Compute 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, Complex networksPhysics Heisenberg Carnot Boltzmann Control Comms Compute Sandberg , Delvenne, & Doyle, On Lossless Approximations, the Fluctuation-Dissipation Theorem, and Limitations of Measurement, IEEE TRANS ON AC, FEBRUARY, 2011 fluids, QM “ orthophysics ”

J. Fluid Mech (2010)Transition to Turbulence Flow Streamlined Laminar Flow Turbulent Flow Increasing Drag , Fuel/Energy Use and Cost Turbulence and drag?

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

wasteful fragile Laminar Turbulent efficient robust Laminar Turbulent ? Control?

Control CommsPhysicsWiener Bode Kalman Heisenberg Carnot Boltzmann robust control Foundations, origins of noise dissipation amplification catalysis General Rigorous First principle Shannon

Smart Antennas (Javad Lavaei) Security, co-channel interference, power consumption Conventional Antenna Smart Antenna 1) Multiple active elements: Easy to program Hard to implement 2 ) Multiple passive elements: Easy to implement Hard to program Smart Antennas

Passively Controllable Smart (PCS) Antenna PCS Antenna: One active element, reflectors and several parasitic elements This type of antenna is easy to program and easy to implement but “hard” to solve (e.g. 4 weeks offline computation). We solved the problem in 1 sec with huge improvement:

Decentralized control Partial bibliography(Lamperski) Triaged today Great topic

In press, available online Really fat tailsHow big is “big”?

Persistent controversy log(rank)largest smaller magnitude  log(power) Gutenberg-Richter ? “bump”  “characteristic earthquake”??? Note: rare example (in science) involving power laws that isn’t obviously ridiculous slope = -1

Randomly sampled G-R magnitudes Distribution of max eventNo bump still might look like a “bump”

Order statistics More data, but…Tail stays highly variableMore samples P( (k of n) > x) p=- dP / dx

Fault traces and epicenters

Number of earthquakes per fault Mag of largest quakeSynthetic GRNumber of earthquakes per fault 155 faults

Mag of largest quake3 biggest quakes

p=.03 p=.01p=.0023 biggest quakes

Magnitude binned by distance to faults 3.6

Randomly sampled G-R magnitudes Distribution of max eventNo bump still might look like a “bump”

Truncated pareto model •P(>x) 10 -1 10 0 10 1 10 2 10 3 10 0 10 1 10 2 10 3 LPNF data (decimated) Wildfires Los Padres National Forest

10 -1 10 0 10 1 10 2 10 3 10 0 10 1 10 2 10 3 10 -2 10 -1 10 0 10 1 10 2 10 0 10 1 10 2 10 3 LPNF data (decimated) Comparison of model n•P (> x ) with cumulative raw data (decimated).

LPNF data (black) plus 4 pseudo-random samples from P (>x) (colors). LPNF data and pseudo-random samples have similar variations. Comparison of variations in LPNF data versus that of pseudo-random samples. 10 -1 10 0 10 1 10 2 10 3 10 0 10 1 10 2 10 3 10 -2 10 -1 10 0 10 1 10 2 10 0 10 1 10 2 10 3

MLE as WLS Exponential Pareto

MLE as WLS Exponential

Pareto Distribution α=1n=100K-S p-value: 0.34

Pareto Distribution α=1n=100p=0.34MATLAB’s ksstest function with the null hypothesis Pareto alpha=1 10 0 10 2 10 4 10 6 10 8 x

α=1 n=100p=0.34!!! 10 0 10 2 10 4 10 6 10 8 10 0 10 1 10 2 x Rank Test Distribution Null Distribution MATLAB’s ksstest function with the null hypothesis Pareto alpha=1 makes no difference need weighted KS, but what weight?

Order statistics But this is so easy and is (apparently) advocated by many statisticians.More samplesP( (k of n) > x) p=- dP / dx