John Doyle 道陽 Jean-Lou Chameau Professor Control and Dynamical Systems, EE, & BioE

Universal las and architectures: Theory and lessons from brains, hearts, cells, grids, nets, bugs, fluids, bodies, planes, docs, fire, fashion, earthquakes, music, buildings, cities, art, running, cycling, throing, Synesthesia, spacecraft, statistical mechanics John Doyle 道陽 Jean-Lou hameau rofessor ontrol and Dynamical Systems, EE, & BioE a # 1tech https://.cds.caltech.edu/~doyle

Universal las and architectures: The videos The folloing previe is approved for all audiences. https://rigorandrelevance.ordpress.com/author/doyleatcaltech/ https://.cds.caltech.edu/~doyle

SDN, IOT, IOE, S, etc.. ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Bipedalism Maternal care Warm blood Flight Mitochondria Oxygen Translation (ribosomes) Glycolysis Major transitions

SDN, IOT, IOE, S, etc.. ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Bipedalism Maternal care Warm blood Major Flight transitions Mitochondria Oxygen Translation (ribosomes) Glycolysis Theory of Evolution Architecture omplexity Netorks Evolution Our heroes omplexity Architecture

SDN, IOT, IOE, S, etc. ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Bipedalism Maternal care Warm blood Flight Mitochondria Oxygen Translation (ribosomes) Glycolysis U Theorems+ {case study} Brains Bugs (microbes, ants) Nets/Grids (cyberphys) Medical physiology Lots of aerospace Wildfire ecology Earthquakes hysics: turbulence, stat mech (QM?) Toy : Lego clothing, fashion Buildings, cities Synesthesia

recursors in 1940s U Theorems+ {case study} Brains Bugs (microbes, ants) Nets/Grids (cyberphys) Medical physiology Lots of aerospace Wildfire ecology Earthquakes hysics: turbulence, stat mech (QM?) Toy : Lego clothing, fashion Buildings, cities Synesthesia

1980s recursors in 1940s 2012 U Theorems+ {case study} Brains Bugs (microbes, ants) Nets/Grids (cyberphys) Medical physiology Lots of aerospace Wildfire ecology Earthquakes hysics: turbulence, stat mech (QM?) Toy : Lego clothing, fashion Buildings, cities Synesthesia

Gary Balas @UMN 1990-2014 2006-2014: Department Head Aerospace Engineering and Mechanics 2001-2014: rofessor AEM and ontrol Science & Dynamical Systems enter 1996-2001: Associate rofessor AEM and SDS 1995-2014: o-director ontrol Science and Dynamical Systems rogram 1992-2004: Director of Grad Studies SDS Department 1990-1996: Assistant rofessor AEM 1989 : h.d. Aeronautics, alifornia Institute of Technology

ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Bipedalism/balance Theorems+ U {case study} Brains Familiar, accessible Live demos! heap, reproducible Open Unavoidable

aveats and Issues Bad scholarship, cinematography, diplomacy, organization Badly organized (Videos, slides, papers in Dropbox) More questions than ansers Trailer for videos But Applicable Accessible (even latest theory research is relatively ) Almost undergrad for almost everything Obvious (if in retrospect) Eager for feedback (and also ne material)

Las as Tradeoffs fragile Function= Locomotion robust Ideal efficient costly

>2x fragile Tradeoffs 4x robust Ideal efficient costly

fragile Similar Tradeoffs Las Mechanisms But simpler Models? Experiments? robust efficient costly

fragile crash harder hard Similar Tradeoffs Las Mechanisms But simpler Models Experiments robust short efficient long costly

Simplified inverted pendulum l Act

Simplified inverted pendulum y θ l l g v length (to OM) gravity control (acceleration) l v x Act

Simplified inverted pendulum y θ l l g v length (to OM) gravity control (acceleration) l v x Act x = v l θ + gsinθ = vcosθ y = x+ l sin O θ

Simplified inverted pendulum y g p = l Instability l x θ Act l v l length (to OM) g gravity v control (acceleration) x = v l θ + gsinθ = vcosθ y = x+ l sin O θ

Simplified sensorimotor control E error N noise eye vision p = g l l T ( j ) ω = E delay ontrol? N Instability Act

E error N noise Simplified sensorimotor control brain eye vision p = g l l T ( j ) ω = E slo delay τ.3s Instability N ontrol Act

Amplification (noise to error)? T ( j ) ω = E N E N eye vision p = g l l delay τ.3s Instability ontrol Act

Amplification (noise to error) theorem: Entropy rate Energy (L2) exp ( ln T ) exp( pτ ) T T E jω = ( ) E N N eye vision p = g l l delay ontrol τ.3s Necessary! Act

Entropy rate Energy (L2) exp ( ln T ) exp( pτ ) T Intuition state 1 exp( pt) p l Before you can react τ.3s delay τ time

error T roof? + noise jω = ( ) E N Undergrad math { } T = sup T( jω ) = sup T( s) Re( s) 0 ω Max modulus T() s = M() s Θ() s Θ ( jω) = 1 ( s) exp ( τ s) Θ = ( ) ( ) p = T p = 1 ( s) ( s) exp ( τ s) = M 1 ( τ p) ( τ ) T = M M( p) Θ( p) exp p T exp 1 p M( p) =Θ( )

T noise error fragility exp( pτ ) 10 8 6 4 x = v l θ + gsinθ = vcosθ y = x+ l sin O θ g p = l τ =.3s Length l τ = delay.3s 2 0 Shorter? 0.2 0.4 0.6 0.8 1 Length l, m

noise error T fragility exp( pτ ) 10 8 6 4 exp( pτ ) x = v l θ + gsinθ = vcosθ y = x+ l sin O θ g p = l τ =.3s Length l τ = delay.3s 2 0 Shorter 0.2 0.4 0.6 0.8 1 Length l, m

exp ( ln T ) exp( pτ ) T Theory 10 8 6 noise 4 error Length l delay 2 0 0.2 0.4 0.6 0.8 1 Length l, m

exp ( ln T ) exp( pτ ) T 10 8 noise Theory & Data 6 4 Harder Hard error Length l delay 2 0 0.2 0.4 0.6 0.8 1 Length l, m

Robust to noise model Entropy rate Energy (L2) exp ( ln T ) exp( pτ ) T T jω = ( ) E N N E eye vision p = g l l delay ontrol τ.3s Necessary! Act

La #1 : Mechanics La #2 : Gravity La #3 : Light/vision La #4 : T exp ( pτ ) crash fragile harder hard robust short long Yoke eng Leong

Mechanics+ Gravity + Light + Universal las exp ( ln T ) exp( pτ ) T fragile robust crash harder hard E N eye vision short long p = g l l T jω = ( ) E N delay ontrol τ.3s Necessary! Act

l l O hard harder???

l l O l l O l O harder???

exp ( ln ) exp( pτ ) T T z+ p z p Simple analytic formulas g g z = p = l lo l z+ p l + l lo = z p l l l lo z+ p 1+ 1 α α = = = l z p 1 1 α O ( 1+ 1 α ) 2 α Unstable zeros

roof? error + noise { } T = sup T( jω ) = sup T( s) Re( s) 0 ω T() s = M() s Θ() s Θ ( jω) = 1 s z Θ ( s) = exp ( τ s) s + z Undergrad math s z = ( ) ( ) exp ( τ ) s M s s s + z 1 z+ p T M M( p) ( p) = Θ exp( τ p) z p z+ p T exp ( τ p) z p

τ =.3s 100 z+ p exp( pτ ) z p exp ( ln T ) z+ p exp( pτ ) exp( pτ ) T z p hardest! 10 Theory 2.1.2.5 1 Length, m l O l = 1

τ =.3s 100 exp ( ln T ) z+ p exp( pτ ) exp( pτ ) T z+ p exp( pτ ) z p z p hard hardest! 10 2 exp pτ ( ) p 1 l.1.2.5 1 Length, m

What is sensed matters. l0 l l0 l hard harder hardest! Unstable pole Unstable zero

fragile robust.1 1 1g short mass 10kg

fragile robust Robust to mass don short long Fragile to Up Length l Length l o (sense) Noise Medial direction lose one eye Stand one leg Alcohol Age delay Instability Sensors/ actuators Delay

Robust to noise model Spiking neurons? Discrete axons? Distributed control? Entropy rate Energy (L2) exp ( ln T ) T Quantized exp pτ ( ) E eye vision p = g l l delay ontrol τ.3s Necessary! Act

Robust to noise model Spiking neurons? Discrete axons? Distributed control? E Entropy rate Energy (L2) eye exp Quantized vision ( ln T ) T Quantized exp pτ ( ) p = g l l delay ontrol τ.3s Necessary! Act

hardest! fragile crash crash harder robust short Theory & data long hard

Gratuitously fragile fragile Example of sparse/bad sensing robust short long

Gratuitously fragile fragile Look up & shorten robust short long

fragile Just add a bike? robust efficient costly

Learn fragile robust efficient costly

Learn fragile Learn robust efficient costly

Major transitions ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Bipedalism/balance unstable fragile robust efficient costly

Major transitions ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Bipedalism/balance fragile crash harder robust hard short efficient long costly

Similar Tradeoffs Las Mechanisms fragile crash But simpler Models Experiments robust short efficient harder hard long costly

Efficiency/instability/layers/feedback ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Balance (biped) Maternal care Warm blood Flight (streamlining) Mitochondria Oxygen Translation (ribosomes) Glycolysis Efficient but unstable

apers Biology + tutorial videos 1. handra, Buzi, Doyle (2011) Glycolytic oscillations and limits on robust efficiency. Science 2. Gayme, McKeon, Bamieh, apachristodoulou, Doyle (2011) Amplification and Nonlinear Mechanisms in lane ouette Flo, hysics of Fluids 3. Li, ruz, hien, Sojoudi, Recht, Stone, sete, Bahmiller, Doyle (2014) Robust efficiency and actuator saturation explain healthy heart rate control and variability, NAS Robust efficiency Undergrad (mostly) Obvious (in retrospect) Extreme bimodal revies hysics Medicine Very universal

handra, Buzi, and Doyle UG biochem, math, control theory Insight Accessible Verifiable Very universal

Efficient but unstable Needs complex/active control With associated las? Specific La #1 La #2 La #3 Balancing Specific robust La #1 La #2 La #3 Glycolysis robust short too fragile complex cheap

Efficient but unstable Needs complex/active control With associated las? fragile robust efficient Universal asteful La #4 z + p T z p Specific Specific La #1 La #2 La #3 Balancing robust La #1 La #2 La #3 Glycolysis robust short too fragile complex cheap

Universal Balancing fragile La #4 z + p T z p robust short robust efficient asteful Glycolysis robust too fragile complex cheap

Efficient but unstable Needs complex/active control With associated las? Specific Money/finance/lobbyists Industrialization Universal Society/agriculture Weapons La #4 Balancing z + p T Maternal care z p Warm blood Flight Specific Mitochondria Oxygen Translation (ribosomes) Glycolysis La #1 La #2 La #3 Balancing robust La #1 La #2 La #3 Glycolysis robust short too fragile complex cheap

Flight Money/finance/lobbyists Industrialization Society/agriculture Weapons Balancing Maternal care Warm blood Flight Mitochondria Oxygen Translation (ribosomes) Glycolysis unstable

Flight and simming (streamlining) Specific? Universal? u 1 + u Ñ u + Ñ p = D u t R

Turbulent Universal fragile u 1 + u Ñ u + Ñ p = D u t R robust efficient asteful

fragile robust Laminar efficient Turbulent asteful Turbulent Universal y z Turbulent Laminar x u 1 + u Ñ u + Ñ p = D u t R Flo U U u Blunted turbulent velocity profile

hysics of Fluids (2011) fragile robust Laminar efficient Turbulent asteful y z Turbulent Laminar x u 1 + u Ñ u + Ñ p = D u t R Flo U U u Blunted turbulent velocity profile

fragile Laminar robust Sharks Dolphins efficient Turbulent asteful

Efficient but unstable Needs complex/active control With associated las? Money/finance/lobbyists Industrialization Society/agriculture Weapons Balancing Maternal care Warm blood Flight (streamlining)? Mitochondria Oxygen Translation (ribosomes) Glycolysis Specific Balancing robust Specific robust Specific Glycolysis robust short Sharks Dolphins efficient too fragile complex No tradeoff cheap Flo u Turbulent

Efficient but unstable Needs complex/active control With associated las? Money/finance/lobbyists Industrialization Society/agriculture Weapons Balancing Maternal care Warm blood Flight (streamlining)? Mitochondria Oxygen Translation (ribosomes) Glycolysis Universal Robust efficiency Balancing robust robust Glycolysis robust short Sharks Dolphins efficient too fragile complex No tradeoff cheap Flo u Turbulent

Efficient but unstable Needs complex/active control With associated las? Money/finance/lobbyists Industrialization Society/agriculture Weapons Balancing (running) Maternal care Warm blood Flight (streamlining)? Mitochondria Oxygen Translation (ribosomes) Glycolysis (metabolism) Universal Robust efficiency Specific Running Specific Metabolism robust too fragile complex No tradeoff cheap

Efficient but unstable Needs complex/active control With associated las? Money/finance/lobbyists Industrialization Society/agriculture Weapons Balancing (running) Maternal care Warm blood Flight (streamlining)? Mitochondria Oxygen Translation (ribosomes) Glycolysis (metabolism) Universal Robust efficiency Specific Running ardiovascular physiology Metabolism robust too fragile complex No tradeoff cheap

Li, ruz, hien, Sojoudi, Recht, Stone, sete, Bahmiller, Doyle robust Robust efficiency and actuator saturation explain healthy heart rate control and variability roc. Nat. Acad. Sci. LUS 2014 efficient controls heart rate ventilation vasodilation High coagulation inflammation digestion storage external disturbances High ardiophysiology errors O2 B phlo Glucose Energy store Blood volume internal nois

robust robust 10 1 too fragile complex No tradeoff 10 0 10-1 10 0 10 1 k Neuro efficient 100 10 2 Biology robust Robust efficiency expensive Tradeoffs, mechanisms.1.2 1 efficient controls heart rate ventilation vasodilation High coagulation inflammation digestion storage external disturbances High Flo u Turbulent hysics Medicine errors O2 B phlo Glucose Energy store Blood volume internal nois

robust Neuro robust 10 1 too fragile complex No tradeoff 10 0 10-1 10 0 10 1 100 10 2 k efficient Biology Foundational Huge literatures robust expensive Data, models, simulation Yet persistent mysteries.1.2 1 efficient controls heart rate ventilation vasodilation High coagulation inflammation digestion storage external disturbances Robust efficiency Tradeoffs, mechanisms High Flo u Turbulent hysics Medicine errors O2 B phlo Glucose Energy store Blood volume internal nois

So far Universal las and architectures: Theory and lessons from brains, hearts, cells, grids, nets, bugs, fluids, bodies, planes, docs, fire, fashion, earthquakes, music, buildings, cities, art, running, cycling, throing, Synesthesia, spacecraft, statistical mechanics https://rigorandrelevance.ordpress.com/author/doyleatcaltech/

Major transitions ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons BipedalismBalance Maternal care Warm blood Flight Turbulence Mitochondria Oxygen Translation (ribosomes) Glycolysis Glycolysis ardiophysiology Efficient but unstable Needs complex control rash robust efficient Similar Tradeoffs Las Mechanisms But simpler Models Experiments

ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Balance (biped) Maternal care Warm blood Flight (streamlining) Mitochondria Oxygen Translation (ribosomes) Glycolysis Weapons Bad Mass extinction Warfare ( up ) rey ( back ) rash

ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Balance (biped) Maternal care Warm blood Flight (streamlining) Mitochondria Oxygen Translation (ribosomes) Glycolysis Slavery Famine forard back rashes back can hurt everyone rashes forard benefit those (fe) that cause and maintain them Systematic study is missing

Major transitions ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Bipedalism Maternal care Warm blood Flight Mitochondria Oxygen Translation (ribosomes) Glycolysis Efficient but unstable Needs complex control Fast Gene Apps ortex Flexible robust efficient Next Trans* OS erebellum rotein HW Reflex

Next Universal las and architectures: Theory and lessons from brains, hearts, cells, grids, nets, bugs, fluids, bodies, planes, docs, fire, fashion, earthquakes, music, buildings, cities, art, running, cycling, throing, Synesthesia, spacecraft, statistical mechanics https://rigorandrelevance.ordpress.com/author/doyleatcaltech/

100 Speed 1/τ noise exp( pτ ) 10 Theory Length l o error 2 Length l.1.2.5 1 delay? Speed 1/τ T exp ( ) z + pτ p z p

Fast Flexible robust + efficient

accessible accountable accurate adaptable administrable affordable auditable autonomy available credible process capable compatible composable configurable correctness customizable debugable degradable determinable demonstrable dependable deployable discoverable distributable durable effective evolvable extensible fail transparent fast 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 safety scalable seamless self-sustainable serviceable supportable securable simple stable standards survivable tailorable testable timely traceable ubiquitous understandable upgradable usable efficient robust sustainable robust + efficient efficient Fast Flexible

Hard Limits on Robust ontrol Over Delayed and Quantized ommunication hannels With Applications to Sensorimotor ontrol IEEE onference on Decision and ontrol December 2015 Osaka, Japan

Li, ruz, hien, Sojoudi, Recht, Stone, sete, Bahmiller, Doyle Robust efficiency and actuator saturation explain healthy heart rate control and variability NAS LUS 2014 180 160 140 120 100 80 60 40 0 100 200 300 sec 400 c = Q F c = F Q c = Q F as as l s vs vs s r ap ap r p ( + + p ap ) s ([ ] [ ] ) c = V c c c vp vp total as as vs vs a v [ O ] = M + F O O TO, 2 2 v 2 a 2 v q q O O q H H dt 2 2 2 2 * 2 * 2 * min as as o H ( ) + ( ) ( ) 2 2 + 2

Slo Data Fast

Slo Fast Ho? Why? Mechanism Tradeoff Architecture Speed Flexibility Robustness Virtualization Diversity

Object motion + eye Act Error slo vision delay ortex Slo vision Fast Flexible High Res Inflexible

Object motion + eye Error vision Head motion Act Does not ortex use vision? delay Slo vision VOR fast slo Fast Flexible VOR Inflexible Lo Res Vestibular Ocular Reflex (VOR)

Mechanism Object motion Head motion + eye Act Error vision delay ortex Slo vision Tradeoff VOR fast slo Fast VOR Minimal cartoon Flexible High Res Inflexible Lo Res

Object motion Head motion + eye Act Error vision delay ortex VOR fast slo These signals must match Next important piece?

Object motion Head motion + fast eye Act Error vision ortex slo delay VOR gain Tune gain? VOR and visual gain must match

Object motion Head motion + fast eye Act Error vision ortex slo delay VOR gain Tune gain AOS Error erebellum AOS = Accessory Optical system

Object motion Head motion + direct, fast fast eye Act Error slo slo vision delay ortex VOR This fast forard path is necessary gain Tune gain feedback AOS Error erebellum AOS = Accessory Optical system

Object motion Head motion + direct, fast fast eye Act Error slo slo vision delay ortex VOR This fast forard path gain Tune gain sloest feedback AOS Error Needs erebellum feedback tuning AOS = Accessory Optical system

Grey boxes vision ortex VOR gain AOS delay erebellum distributed compute (& control)

White cables VOR fast sparse communication, heterogeneous delays gain Act sloest AOS erebellum vision delay ortex sloer sloer

Mechanism Object motion Head motion + eye Act Error vision delay ortex Slo vision Tradeoff VOR fast slo Fast VOR Flexible High Res Inflexible Lo Res Minimal cartoon

extreme heterogeneity Slo Tune Vision Fast VOR Flexible High Res Inflexible Lo Res

extreme heterogeneity delay log 10 hours secs msecs Vision Ideal high res (flexible) Tune hy? VOR lo res

hours These dimensions Tradeoff Extreme heterogeneity Tune delay log 10 secs msecs Vision Ideal high res (flexible) hy? VOR lo res

Motion Vision High resolution vision robust /motion Object motion Self motion

High resolution vision robust /motion Object motion Self motion

hours delay log 10 secs lan navigate Tune msecs lo error Reflex high heterogeneous delays

8 > 10 hours delay log 10 secs lan navigate Tune msecs lo error Reflex high heterogeneous delays

Tune lan navigate Reflex

Robust

Fragile Robust

Tune lan navigate Reflex

Robust

Fragile Robust

8 > 10 hours delay log 10 secs lan navigate Tune msecs lo error heterogeneous delays and errors 11 > 10 Reflex high

X D Q T Y F R H O B A U K Z M V Q N A M B W T G J Y L K A

FAST X D Q T Y F R H O B A U K Z M V Q N A HIGH M RES B W T G J Y L K A

FAST delay log 10 hours secs Vision X A U D K F Z M H R O V Q N A HIGH Q M RES B W T G A J B Y L T Y K msecs high res (flexible) VOR lo res?

FAST delay log 10 hours X A lo resolution noisy Y K secs msecs Vision high res (flexible) VOR lo res?

8 > 10 hours delay log 10 secs lan navigate Tune exp ( ln G ) G g 1 exp pτ ( ) msecs heterogeneous Ideal lo error? delays and errors 12 10 > Reflex high

Tune exp ( ln G ) G g 1 exp pτ ( ) x 2 x error?

Extreme system level heterogeneity hours delay log 10 secs msecs lan navigate error Tune Reflex Object Head VOR + fast gain Tune eye Act Error erebellum vision ortex slo delay Why?

log10 axons per nerve Olfactory 6 Optic 4 2 cranial Auditory Vestibular Sciatic spinal 0-1 0 1 log10 axon diameter Aα Extreme component level heterogeneity

Olfactory 10 6 Optic axons per 10 4 nerve 6 > 10 10 2 10 0 cranial Auditory Vestibular spinal Sciatic 10-1 10 0 10 1 mean axon diameter (microns) Aα

Olfactory 10 6 Optic axons per 10 4 nerve 6 > 10 10 2 10 0 cranial Auditory Vestibular spinal Sciatic 10-2 10 0 10 2 mean axon area Aα

log10 axons per nerve Olfactory 6 Optic 4 2 cranial Auditory Vestibular Sciatic spinal 0-1 0 1 log10 axon diameter Aα Extreme component level heterogeneity Why?

Object Head VOR log10 axons per nerve Olfactory 6 Optic 4 2 + fast gain Tune cranial eye Act Error erebellum vision ortex slo Auditory Vestibular Sciatic spinal 0-1 0 1 log10 axon diameter delay Aα hours delay log 10 secs Extreme heterogeneity msecs onnect scales lan navigate error Tune Reflex

Assume: resource (cost) (to build and maintain nerve) area α α

Assume: resource (cost) (to build and maintain nerve) area α Assume lengths and areas are given α

area α resource (cost) area α log axons per nerve 7 bits 3 bits 1 bit log axon diam µm

resource (cost) area α axons per nerve Olfactory 6 Optic 4 2 cranial Auditory Vestibular spinal 0-1 0 1 axon diameter too big Sciatic Aα

resource (cost) area α N= axons per nerve 6 4 2 0 ρ = nerve area = α = 0 1 axon radius (µm) Nπρ 2

Why not make axon radius small? (Maximize mutual information.) axons per nerve Olfactory 6 Optic 4 2 Ideal? cranial 7 bits Auditory Vestibular spinal 0-1 0 1 axon radius Sciatic 3 bits Aα 1 bit

Why not make axon radius small? (Maximize mutual information.) Tradeoffs axons per nerve Olfactory 6 Optic 4 2 Ideal? cranial Auditory Vestibular Sciatic spinal 0-1 0 1 axon radius Aα

spike rate ρ spike speed ρ (propagation) N= axons per nerve 6 4 2 0 Ideal? nerve area = α = ρ = 0 1 Nπρ 2 axon radius (µm) Tradeoffs in spiking neurons

spike rate ρ R (bits/time) Nρ N= axons per nerve 6 4 2 0 nerve area = α = ρ = 0 1 Nπρ 2 axon radius (µm) R α α ρ 2 ρ ρ N α ρ 2

spike rate ρ R (bits/time) Nρ spike speed delay T s ρ 1 ρ N= axons per nerve 6 4 2 0 nerve area = α = ρ = 0 1 Nπρ 2 axon radius (µm) R α α 2 ρ ρ ρ αt R =λ α T

slo R T λ α R T = λ α delay T s 1 ρ feasible infeasible fast lo res R high res R =λ α T

resource = nerve area = α = Nπρ 2 slo R T = λ α delay T s 1 ρ delay slo fast lo res R high res fast R T = λ α 1/R

resource = nerve area = α = Nπρ 2 delay slo R = λ α ( T)? fast slo high res 1/R lo res delay fast R T = λ α 1/R

Assuming fixed length and area slo delay feasible 3 bits fast high res infeasible 1/R R lo res T = λ α 1 bit

slo delay lan navigate Tune slo fast Ideal lo error Reflex high feasible Extreme heterogeneity delay onnect scales infeasible Mechanistic physiology R = λ T fast α Ideal Integrated high 1/R lo Quantitative res res Tradeoffs as las

reflex (delayed) K L K L Reflex controller (VOR: Motion compensation) Q L Q Quantizer x T Delay of T v (head motion) u state Q L hannel (neural signaling)

reflex (delayed) K L K L Reflex controller (VOR: Motion compensation) x Q L Q T Quantizer Delay of T R = λ T α v (head motion) u state Q L hannel (neural signaling)

reflex (delayed) K L u K L Q Q Quantizer L Reflex controller (VOR: Motion compensation) x T Delay of T v (head motion) state [ ] xt ( + 1) = axt () Qut ( T) + vt () L

reflex (delayed) KL KH remote sensing advanced arning high level planning QL QH x v (head motion) u delay r (target motion)

reflex (delayed) K H Q H remote sensing advanced arning high level planning x K L [ ( )] Qut T H r (target motion) r 1 delay x =? [ ] xt ( + 1) = axt ( ) Qut ( T ) + rt ( T) H r

reflex (delayed) x L u H r arned v v δ r 1 xt ( + 1) = axt ( ) + x =?

reflex (delayed) x L u H r arned v v δ r 1 Theorem xt ( + 1) = axt ( ) + TL i 1 L min sup = δ δ 2 2 v δ, r 1 i= 1 a 0, T T H r 1 1 ( ) ( ) T R R x a + a a + a delayed delay cost delayed quant cost arned quant cost

arned, plan, tune Extremely different delayed, fast, reflex diverse, small axons small errors 10 cost 1 ctrl total state quant fe uniformly large axons large errors.1 delay 10 value delay Ts total delay delay >>1 bits >>1 1 quant small, constant bits & delay.1 4 2 0-2 -4 Warned (T) Delayed (Tc)

arned, plan, tune 10 ctrl total state delayed, fast, reflex ost 1 (system).1 delay quant Optimal value (parts) 10 1 delay Ts quant (bits) total delay.1 6 4 2 Warned (T) 0 0-2 -4 Delayed (Tc) -6

ost ctrl constant 10 total state ctrl 1 total state quant << 1 delay 0.1 6 4 2 0 Warned (T) ost = size of signal ith orst-case disturbance

ost 10 ctrl Extremely different total state total state delay >> 1 1 total state quant << 1.1 6 delay 4 2 Warned (T) 0 0 quant -2-4 Delayed (Tc) -6 ctrl constant ost = size of signal ith orst-case disturbance

ost 10 1.1 ctrl total state delay arned, planning, tuning, precision 10 Optimal value 1.1 6 delay Ts quant (bits) 4 2 0 delay >>1 bits >>1 diverse small axons small errors Warned (T)

Extremely different Optimal value 10 1 delay Ts quant (bits) total delay.1 6 4 2 0 0-2 -4-6 Warned (T) Delayed (Tc)

arned, plan, tune 10 ctrl total state delayed, fast, reflex ost 1 (system).1 delay quant Optimal value (parts) 10 1 delay Ts quant (bits) total delay.1 6 4 2 Warned (T) 0 0-2 -4 Delayed (Tc) -6

slo delay lan navigate Tune fast lo Reflex error high

cost (error) 10 1.1 total state quant << 1 ctrl quant delay diverse, small axons small errors slo delay fast lan navigate lo Tune Reflex error high

slo delay R T = λ α fast high res 1/R lo res

slo delay fast diverse, small axons small errors high res R 1/R value T = λ α 10 1.1 lo res delay Ts quant total delay 4 2 Warned (T) 0

10 cost 1 total state ctrl slo delay plan nav Tune.1 10 value quant delay Ts delay fast lo error Reflex high slo delay R T = λ α 1.1 quant total delay 4 2 0 fast high res 1/R lo res Warned (T)

slo delay plan nav Tune slo delay R x T = λ α v L u H r fast lo error Reflex high fast high res 1/R lo res

slo delay plan nav Tune fast reflex lo high error slo delay R T = λ α fast high res 1/R reflex lo res

slo R T = λ α 10 cost 1.1 10 value 1 total state slo delay delay quant fast total delay delay Ts quant plan nav lo error Tune reflex high delay fast high res 1/R.1 reflex lo res 0-2 -4 Delayed (Tc)

slo delay plan nav Tune fast lo error reflex high

Olfactory 6 Optic axons per nerve 4 2 cranial Auditory Vestibular spinal 0-1 0 1 axon diameter Sciatic Aα 10 value 1 total delay delay Ts quant.1 0-2 -4 Delayed (Tc)

delayed, fast, reflex Olfactory 6 Optic axons per nerve 4 2 cranial Auditory Vestibular 0-1 0 1 axon diameter Sciatic spinal Aα 10 cost 1.1 10 value 1.1 total state ctrl quant total delay delay Ts quant 0-2 -4 Delayed (Tc)

10 value 1.1 delay Ts quant total delay 4 2 Warned (T) 0 Olfactory 6 Optic axons per nerve 4 2 cranial Auditory Vestibular Sciatic spinal 0-1 0 1 axon diameter Aα

arned, plan, tune, precision 10 cost 1.1 10 value 1.1 total state ctrl quant delay delay Ts quant total delay 4 2 Warned (T) 0 Olfactory 6 Optic axons per nerve 4 2 cranial Auditory Vestibular Sciatic spinal 0-1 0 1 axon diameter Aα

8 > 10 hours delay log 10 secs lan navigate Tune msecs lo error Reflex high heterogeneous delays

slo delay plan nav Tune fast lo error Reflex high

slo delay plan nav Tune slo delay R x T = λ α v L u H r fast lo error Reflex high fast high res 1/R lo res

From: Understanding Vision: theory, models, and data, by Li Zhaoping, Oxford University ress, 2014

From: Understanding Vision: theory, models, and data, by Li Zhaoping, Oxford University ress, 2014 Layered feedback Eye muscle

Distributed/local control ommunications sparse delayed, quantized Localized control (Ls) layered scalable local model, synthesis, implement brains cortex reflex R R R R R grey boxes and hite cables

Distributed/local control brains sensors + muscles body + tools + environment act/ sense R cortex reflex R R physical sense R plant disturbance R act/ sense

Distributed/local control body + tools + environment hysical plant unstable dynamics distributed sparse Disturbance () orst case advanced arning T act/ sense physical sense plant disturbance act/ sense

Distributed/local control ommunications sparse delayed, quantized Actuation and sensing saturates sparse delayed, quantized hysical plant unstable dynamics distributed sparse Disturbance () orst case advanced arning T act/ sense R physical sensors + muscles R sense plant disturbance R act/ sense

Distributed/local control ommunications sparse delayed, quantized Actuation and sensing saturates sparse delayed, quantized hysical plant unstable dynamics distributed sparse Disturbance () orst case advanced arning T act/ sense Localized control (Ls) layered scalable local model, synthesis, implement R R physical cortex reflex R sense R plant disturbance R act/ sense

ommunications sparse delayed, quantized Actuation and sensing saturates sparse delayed, quantized hysical plant unstable dynamics distributed sparse Disturbance () orst case advanced arning T Scalability?

Localized control model, synthesis, implement layered ommunications sparse delayed, quantized Actuation and sensing saturates sparse delayed, quantized hysical plant unstable dynamics distributed sparse Disturbance () orst case advanced arning T R Scalable cortex R R reflex R R

Distributed/local control ommunications sparse delayed, quantized Actuation and sensing saturates sparse delayed, quantized hysical plant unstable dynamics distributed sparse Disturbance () orst case advanced arning T act/ sense Localized control (Ls) layered scalable local model, synthesis, implement R R physical cortex reflex R sense R plant disturbance R act/ sense

Distributed/local control Robust Robust Fast act/ sense R cortex reflex R R sense R physical plant R act/ sense Flexible disturbance

Distributed/local control ommunications sparse delayed, quantized Fast Flexible act/ sense Localized control (Ls) layered scalable local model, synthesis, implement R R physical cortex reflex R sense R plant disturbance R act/ sense

Distributed/local control ommunications sparse delayed, quantized cortex reflex R R R R R Fast Flexible Delay vs resolution tradeoff.

X D Q T Y F R H O B A U K Z M V Q N A M B W T G J Y L K A

Motion olor? Object Head + fast eye Act slo vision ortex delay Reflex gain AOS Slo Motion vision Tune gain Error erebellum Fast VOR Flexible Inflexible

Stare at the intersection color vision Marge Livingstone

Stare at the intersection.

Stare at the intersection

Stare at the intersection.

olor? Motion Slo Motion Fast vision VOR Object Head Reflex + gain fast Tune gain eye Act AOS slo Error erebellum vision ortex delay Flexible Inflexible

olor Motion Slo color vision Object + eye vision Slo vision color vision Act slo ortex delay Motion Fast VOR Flexible Inflexible

OK, color decisions are rarely urgent. Slo Slo Motion Fast vision color vision VOR Flexible Inflexible

Linux OS Object motion Head motion Reflex + gain fast eye vision Act AOS slo Sensorimotor ortex delay Tune gain Error erebellum Vastly more different than similar RNA rpoh σ mrna Bacterial σ cell σ Other operons DnaK ftsh σ DnaK DnaK Heat Lon σ RNA DnaK FtsH Lon

ortex eye vision Act slo delay fast Object motion Head motion erebellum + Error Tune gain gain AOS Reflex RNA DnaK σ RNA σ DnaK rpoh FtsH Lon Heat σ σ mrna Other operons σ DnaK DnaK ftsh Lon Mechanisms Linux OS Bacterial cell Universals are profound Fast Slo Flexible Inflexible Apps OS HW Gene Trans* rotein erebellum ortex Reflex

Universals are profound Tradeoffs Evolvability Gene Slo Fast Apps ortex Trans* OS erebellum rotein HW Reflex Flexible Inflexible

Slo Fast Diverse Not Diverse Tradeoffs Gene Apps Trans* ortex OS erebellum rotein HW Reflex Flexible Inflexible Universals are profound Tradeoffs Evolvability Hourglass diversity onstraints that deconstrain

Diverse Universals are profound Slo Fast Horizontal Transfer Gene Apps ortex Illusion Flexible Not Diverse Trans* OS erebellum Tradeoffs rotein HW Reflex Horizontal Transfer Inflexible Tradeoffs Evolvability Hourglass diversity Horizontal transfer Tunable (illusion)

Diverse Universals are profound Slo Fast Horizontal Transfer Diverse Gene Apps ortex Illusion Flexible Not Trans* Virtual internal OS hidden erebellum Tradeoffs rotein HW Reflex Horizontal Transfer Inflexible Tradeoffs Evolvability Hourglass diversity Horizontal transfer Tunable (illusion) Virtual/Internal Hijacking

Diverse/Digital Universals are profound Slo Fast Horizontal Transfer Diverse Gene Apps ortex Illusion Flexible Not Trans* Virtual internal OS hidden erebellum Tradeoffs rotein HW Reflex Horizontal Transfer Inflexible Tradeoffs Evolvability Hourglass diversity Horizontal transfer Tunable (illusion) Virtual/Internal Hijacking Digital Robustness

SDN, NFV, IOT, IOE, S ompute/control technology Industrialization Money/finance/lobbyists/etc Society/agriculture/states Weapons Bipedalism (balance, cardiovascular physiology) Maternal care Warm blood Flight (turbulence) Mitochondria Oxygen Translation (ribosomes) Glycolysis ells Universals are profound Tradeoffs Evolvability Hourglass diversity Horizontal transfer Tunable (illusion) Virtual/Internal Hijacking Digital Robustness

https://www.cds.caltech.edu/~doyle John Doyle 道陽 Jean-Lou Chameau Professor Control and Dynamical Systems, EE, & BioE