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

Transcription

1 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

2 Universal las and architectures: The videos The folloing previe is approved for all audiences.

3 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

4 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

5 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

6 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

7 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

8 Gary : Department Head Aerospace Engineering and Mechanics : rofessor AEM and ontrol Science & Dynamical Systems enter : Associate rofessor AEM and SDS : o-director ontrol Science and Dynamical Systems rogram : Director of Grad Studies SDS Department : Assistant rofessor AEM 1989 : h.d. Aeronautics, alifornia Institute of Technology

9 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

10 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)

11 Las as Tradeoffs fragile Function= Locomotion robust Ideal efficient costly

12 >2x fragile Tradeoffs 4x robust Ideal efficient costly

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

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

15 Simplified inverted pendulum l Act

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

17 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

18 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

19 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

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

21 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

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

23 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

24 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

25 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( )

26 T noise error fragility 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? Length l, m

27 noise error T fragility exp( pτ ) 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 Length l, m

28 exp ( ln T ) exp( pτ ) T Theory noise 4 error Length l delay Length l, m

29 exp ( ln T ) exp( pτ ) T 10 8 noise Theory & Data 6 4 Harder Hard error Length l delay Length l, m

30 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

31 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

32 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

33 l l O hard harder???

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

35 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

36 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

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

38 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 Length, m

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

40 fragile robust.1 1 1g short mass 10kg

41 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

42 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

43 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

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

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

46 Gratuitously fragile fragile Look up & shorten robust short long

47 fragile Just add a bike? robust efficient costly

48 Learn fragile robust efficient costly

49 Learn fragile Learn robust efficient costly

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

51 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

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

53 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

54 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 Needs control omplex Distributed Layered Active Las/tradeoffs Ho universal?

55 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

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

57 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

58 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

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

60 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

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

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

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

64 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

65 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

66 fragile Laminar robust Sharks Dolphins efficient Turbulent asteful

67 fragile Laminar robust Sharks Dolphins efficient Turbulent asteful

68 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

69 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

70 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

71 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

72 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

73 robust robust 10 1 too fragile complex No tradeoff k Neuro efficient Biology robust Robust efficiency expensive Tradeoffs, mechanisms 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

74 robust Neuro robust 10 1 too fragile complex No tradeoff k efficient Biology Foundational Huge literatures robust expensive Data, models, simulation Yet persistent mysteries 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

75 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

76 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

77 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

78 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 Bad rash

79 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

80 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

81 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

82 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

83 100 Speed 1/τ noise exp( pτ ) 10 Theory Length l o error 2 Length l delay? Speed 1/τ T exp ( ) z + pτ p z p

84 Fast Flexible robust + efficient

85 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

86 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

87 Li, ruz, hien, Sojoudi, Recht, Stone, sete, Bahmiller, Doyle Robust efficiency and actuator saturation explain healthy heart rate control and variability NAS LUS sec 400 Old story

88 Li, ruz, hien, Sojoudi, Recht, Stone, sete, Bahmiller, Doyle Robust efficiency and actuator saturation explain healthy heart rate control and variability NAS LUS 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 * min as as o H ( ) + ( ) ( )

89 Li, ruz, hien, Sojoudi, Recht, Stone, sete, Bahmiller, Doyle Robust efficiency and actuator saturation explain healthy heart rate control and variability NAS LUS sec

90 Slo Data Fast

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

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

93 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)

94 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

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

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

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

98 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

99 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

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

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

102 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

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

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

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

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

107 High resolution vision robust /motion Object motion Self motion

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

109 8 > 10 hours delay log 10 secs lan navigate Tune msecs lo error Reflex high heterogeneous delays

110 Tune lan navigate Reflex

111 Robust

112 Fragile Robust

113 Fragile Robust

114 Tune lan navigate Reflex

115 Robust

116 Fragile Robust

117 8 > 10 hours delay log 10 secs lan navigate Tune msecs lo error heterogeneous delays and errors 11 > 10 Reflex high

118 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

119 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

120 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

121 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?

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

123 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 > Reflex high

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

125 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?

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

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

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

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

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

131 Object Head VOR log10 axons per nerve Olfactory 6 Optic fast gain Tune cranial eye Act Error erebellum vision ortex slo Auditory Vestibular Sciatic spinal log10 axon diameter delay Aα hours delay log 10 secs Extreme heterogeneity msecs onnect scales Mechanistic physiology Integrated Quantitative Tradeoffs as las lan navigate error Tune Reflex

132 Object Head VOR log10 axons per nerve Olfactory 6 Optic fast gain Tune cranial eye Act Error erebellum vision ortex slo Auditory Vestibular Sciatic spinal log10 axon diameter delay Aα hours delay log 10 secs msecs lan navigate error Tune Reflex

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

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

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

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

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

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

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

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

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

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

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

144 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

145 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

146 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

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

148 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

149 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)

150 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)

151 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

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

153 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

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

155 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

156 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 Warned (T) Delayed (Tc)

157 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 Warned (T) Delayed (Tc) -6

158 ost ctrl constant 10 total state ctrl 1 total state quant << 1 delay Warned (T) ost = size of signal ith orst-case disturbance

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

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

161 Extremely different Optimal value 10 1 delay Ts quant (bits) total delay Warned (T) Delayed (Tc)

162 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 Warned (T) Delayed (Tc) -6

163 slo delay lan navigate Tune fast lo Reflex error high

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

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

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

167 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 fast high res 1/R lo res Warned (T)

168 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 fast high res 1/R lo res Warned (T)

169 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

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

171 slo R T = λ α 10 cost 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 Delayed (Tc)

172 slo delay plan nav Tune fast lo error reflex high

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

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

175 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 axon diameter Aα

176 arned, plan, tune, precision 10 cost 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 axon diameter Aα

177 8 > 10 hours delay log 10 secs lan navigate Tune msecs lo error Reflex high heterogeneous delays

178 slo delay plan nav Tune fast lo error Reflex high

179 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

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

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

182 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

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

184 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

185 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

186 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

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

188 ommunications sparse delayed, quantized Actuation and sensing saturates sparse delayed, quantized hysical plant unstable dynamics distributed sparse Disturbance () orst case advanced arning T Localized control modeling, synthesis implementation Scalable

189 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

190 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

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

192 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

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

194 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

195 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

196 Stare at the intersection color vision Marge Livingstone

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198 Stare at the intersection.

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200 Stare at the intersection

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206 Stare at the intersection.

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211 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

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

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

214 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

215 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

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

217 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

218 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)

219 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

220 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

221 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