John Doyle

1

• John Doyle
• Control and Dynamical Systems
• Caltech

2
Research interests

• Complex networks applications
• Ubiquitous, pervasive, embedded control,
  computing, and communication networks
• Biological regulatory networks
• New mathematics and algorithms
• robustness analysis
• systematic design
• multiscale physics

3
Collaboratorsand contributors(partial list)

• Biology Csete,Yi, Borisuk, Bolouri, Kitano,
  Kurata, Khammash, El-Samad,
• Alliance for Cellular Signaling Gilman, Simon,
  Sternberg, Arkin,
• HOT Carlson, Zhou,
• Theory Lall, Parrilo, Paganini, Barahona,
  DAndrea,
• Web/Internet Low, Effros, Zhu,Yu, Chandy,
  Willinger,
• Turbulence Bamieh, Dahleh, Gharib, Marsden,
  Bobba,
• Physics Mabuchi, Doherty, Marsden,
  Asimakapoulos,
• Engineering CAD Ortiz, Murray, Schroder,
  Burdick, Barr,
• Disturbance ecology Moritz, Carlson, Robert,
• Power systems Verghese, Lesieutre,
• Finance Primbs, Yamada, Giannelli,
• and casts of thousands

4
Background reading online

• On website accessible from SFI talk abstract
• Papers with minimal math
• HOT and power laws
• Chemotaxis, Heat shock in E. Coli
• Web Internet traffic, protocols, future issues
• Thesis Structured semidefinite programs and
  semialgebraic geometry methods in robustness and
  optimization
• Recommended books
• A course in Robust Control Theory, Dullerud and
  Paganini, Springer
• Essentials of Robust Control, Zhou, Prentice-Hall
• Cells, Embryos, and Evolution, Gerhart and
  Kirschner

5
Biochemical Network E. Coli Metabolism
Regulatory Interactions
Complexity ? Robustness
Supplies Materials Energy
Supplies Robustness
From Adam Arkin
from EcoCYC by Peter Karp
6
Robustness
Complexity
7
An apparent paradox
Component behavior seems to be gratuitously
uncertain, yet the systems have robust
performance.
Mutation
Selection
Darwinian evolution uses selection on random
mutations to create complexity.
8
Component behavior seems to be gratuitously
uncertain, yet the systems have robust
performance.

• Such feedback strategies appear throughout
  biology (and advanced technology).
• Gerhart and Kirschner (correctly) emphasis that
  this exploratory behavior is ubiquitous in
  biology
• but claim it is rare in our machines.
• This is true of primitive, but not advanced,
  technologies.
• Robust control theory provides a clear
  explanation.

Transcription/ translation Microtubules Neurogenes
is Angiogenesis Immune/pathogen Chemotaxis .
Regulatory feedback control
9
Overview

• Without extensive engineering theory and math,
  even reverse engineering complex engineering
  systems would be hopeless. (Let alone actual
  design.)
• Why should biology be much easier?
• With respect to robustness and complexity, there
  is too much theory, not too little.

10
Overview

• Two great abstractions of the 20th Century
• Separate systems engineering into control,
  communications, and computing
• Theory
• Applications
• Separate systems from physical substrate
• Facilitated massive, wildly successful, and
  explosive growth in both mathematical theory and
  technology
• but creating a new Tower of Babel where even the
  experts do not read papers or understand systems
  outside their subspecialty.

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Any sufficiently advanced technology is
indistinguishable from magic. Arthur C. Clarke
13
Any sufficiently advanced technology is
indistinguishable from magic. Arthur C. Clarke

• Those who say do not know, those who know do not
  say.
• Zen saying

14
Todays goal

• Introduce basic ideas about robustness and
  complexity
• Minimal math
• Hopefully familiar (but unconventional) example
  systems
• Caveat the real thing is much more complicated
• Perhaps any such story is necessarily
  misleading
• Hopefully less misleading than existing popular
  accounts of complexity and robustness

15
Complexity and robustness

• Complexity phenotype robust, yet fragile
• Complexity genotype internally complicated
• New theoretical framework HOT (Highly optimized
  tolerance, with Jean Carlson, Physics, UCSB)
• Applies to biological and technological systems
• Pre-technology simple tools
• Primitive technologies use simple strategies to
  build fragile machines from precision parts.
• Advanced technologies use complicated
  architectures to create robust systems from
  sloppy components
• but are also vulnerable to cascading failures

16
Robust, yet fragile phenotype

• Robust to large variations in environment and
  component parts (reliable, insensitive,
  resilient, evolvable, simple, scaleable,
  verifiable, ...)
• Fragile, often catastrophically so, to cascading
  failures events (sensitive, brittle,...)
• Cascading failures can be initiated by small
  perturbations (Cryptic mutations,viruses and
  other infectious agents, exotic species, )
• There is a tradeoff between
• ideal or nominal performance (no uncertainty)
• robust performance (with uncertainty)
• Greater pheno-complexity more extreme robust,
  yet fragile

17
Robust, yet fragile phenotype

• Cascading failures can be initiated by small
  perturbations (Cryptic mutations,viruses and
  other infectious agents, exotic species, )
• In many complex systems, the size of cascading
  failure events are often unrelated to the size of
  the initiating perturbations
• Fragility is interesting when it does not arise
  because of large perturbations, but catastrophic
  responses to small variations

18
Complicated genotype

• Robustness is achieved by building barriers to
  cascading failures
• This often requires complicated internal
  structure, hierarchies, self-dissimilarity,
  layers of feedback, signaling, regulation,
  computation, protocols, ...
• Greater geno-complexity more parts, more
  structure
• Molecular biology is about biological simplicity,
  what are the parts and how do they interact.
• If the complexity phenotypes and genotypes are
  linked, then robustness is the key to biological
  complexity.
• Nominal function may tell little.

19
An apparent paradox
Component behavior seems to be gratuitously
uncertain, yet the systems have robust
performance.
Mutation
Selection
Darwinian evolution uses selection on random
mutations to create complexity.
20
Cell
Temp cell
Temp environ
21
Cell
How does the cell build barriers (in state
space) to stop this cascading failure event?
Temp cell
Temp environ
22
Temp cell
Folded Proteins
Temp environ
23
Temp cell
Folded Proteins
Temp environ
24
More robust ( Temp stable) proteins
Unfolded Proteins
Aggregates
Temp cell
Folded Proteins
Temp environ
25

• Key proteins can have multiple (allelic or
  paralogous) variants
• Allelic variants allow populations to adapt
• Regulated multiple gene loci allow individuals
  to adapt

Unfolded Proteins
Aggregates
Temp cell
Folded Proteins
Temp environ
26
37o
42o
Log of E. Coli Growth Rate
46o
21o
-1/T
27
Robustness/performance tradeoff?
37o
42o
Log of E. Coli Growth Rate
46o
21o
-1/T
28
Heat shock response involves complex feedback and
feedforward control.
Unfolded Proteins
Temp cell
Folded Proteins
Temp environ
29
Alternative strategies
Why does biology (and advanced technology)
overwhelmingly opt for the complex control
systems instead of just robust components?

• Robust proteins
• Temperature stability
• Allelic variants
• Paralogous isozymes
• Regulate temperature
• Thermotax
• Heat shock response
• Up regulate chaperones and proteases
• Refold or degraded denatured proteins

30
E. Coli Heat Shock (with Kurata, El-Samad,
Khammash, Yi)
31
Heater
Thermostat
32
Thus stabilizing forward flight.
At the expense of extra weight and drag.
33
For minimum weight drag, (and other performance
issues) eliminate fuselage and tail.
34
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35
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36
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38
Why do we love building robust systems from
highly uncertain and unstable components?
39
P
-

• Assumptions on components
• Everything just numbers
• Uncertainty in P
• Higher gain more uncertain

40
P
-

G
-

Negative feedback
K
41

• Design recipe
• 1 gtgt K gtgt 1/G
• G gtgt 1/K gtgt 1
• G maximally uncertain!
• K small, low uncertainty

• Results for y? (1/K )r
• high gain
• low uncertainty
• d attenuated

S sensitivity function
42

• Design recipe
• 1 gtgt K gtgt 1/G
• G gtgt 1/K gtgt 1
• G maximally uncertain!
• K small, low uncertainty

• Results for y? (1/K )r
• high gain
• low uncertainty
• d attenuated

• Extensions to
• Dynamics
• Multivariable
• Nonlinear
• Structured uncertainty
• All cost more computationally.

43
G
-
Uncertain high gain
K
Transcription/translation Microtubule
formation Neurogenesis Angiogenesis Antibody
production Chemotaxis .
44
Summary

• Primitive technologies build fragile systems from
  precision components.
• Advanced technologies build robust systems from
  sloppy components.
• There are many other examples of regulator
  strategies deliberately employing uncertain and
  stochastic components
• to create robust systems.
• High gain negative feedback is the most powerful
  mechanism, and also the most dangerous.
• In addition to the added complexity, what can go
  wrong?

45
G
-


F
K
46

If y, d and F are just numbers
F
S measures disturbance rejection.
S sensitivity function
Its convenient to study ln(S).
47
F gt 0 ln(S) gt 0
ln(S)
amplification
F
F lt 0 ln(S) lt 0
ln( S )
attenuation
48
F ? 1 ln(S) ? ?
ln(S)
extreme sensitivity
F
extreme robustness
F ? ?? ln(S) ? ??
49

• Assume
• F (and S) random variables
• Prob( F -1 ) gt 0

F
Increase F
? 1
50
If these model physical processes, then d and y
are signals and F is an operator. We can still
define S(?? Y(?? /D(?? where E and D are
the Fourier transforms of y and d. ( If F is
linear, then S is independent of D.)

F
Under assumptions that are consistent with F and
d modeling physical systems (in particular,
causality), it is possible to prove that
?he amplification (Fgt0) must at least balance the
attenuation (Flt0).
(Bode, 1940)
51
Positive feedback
?
lnS
logS
Negative feedback
F
52
yet fragile
Positive feedback
?
?
lnS
logS
Negative feedback
Robust
F
53
Robustness of HOT systems
Fragile
Fragile (to unknown or rare perturbations)
Robust (to known and designed-for uncertainties)
Uncertainties
Robust
54
Feedback and robustness

• Negative feedback is both the most powerful and
  most dangerous mechanism for robustness.
• It is everywhere in engineering, but appears
  hidden as long as it works.
• Biology seems to use it even more aggressively,
  but also uses other familiar engineering
  strategies
• Positive feedback to create switches (digital
  systems)
• Protocol stacks
• Feedforward control
• Randomized strategies
• Coding

55
Robustness
Complexity
56
Current research

• So far, this is all undergraduate level material
• Current research involves lots of math not
  traditionally thought of as applied
• New theoretical connections between robustness,
  evolvability, and verifiability
• Beginnings of a more integrated theory of
  control, communications and computing
• Both biology and the future of ubiquitous,
  embedded networking will drive the development of
  new mathematics.

57
Robustness of HOT systems
Fragile
Fragile (to unknown or rare perturbations)
Robust (to known and designed-for uncertainties)
Uncertainties
Robust
58
Robustness of HOT systems
Fragile
Humans
Chess
Meteors
Robust
59
Robustness of HOT systems
Fragile
Humans
Archaea
Chess
Meteors
Machines
Robust
60
Diseases of complexity
Fragile

• Cancer
• Epidemics
• Viral infections
• Auto-immune disease

Uncertainty
Robust
61
Sources of uncertainty

• In a system
• Environmental perturbations
• Component variations
• In a model
• Parameter variations
• Unmodeled dynamics
• Assumptions
• Noise

Fragile
Robust
62
Sources of uncertainty
Fragile
?
Robust
63
Typically NP hard.
?
64
Typically coNP hard.

• Fundamental asymmetries
• Between P and NP
• Between NP and coNP

?

• More important problem.
• Short proofs may not exist.

Unless theyre the same
65
How do we prove that

• Standard techniques include relaxations, Grobner
  bases, resultants, numerical homotopy, etc
• Powerful new method based on real algebraic
  geometry and semidefinite programming (Parrilo,
  Shor, )
• Nested series of polynomial time relaxations
  search for polynomial sized certificates
• Exhausts coNP (but no uniform bound)
• Relaxations have both computational and physical
  interpretations
• Beats gold standard algorithms (eg MAX CUT)
  handcrafted for special cases
• Completely changes the P/NP/coNP picture

66
Bacterial chemotaxis
67
Bacterial chemotaxis (Yi, Huang, Simon, Doyle)
Random walk
Ligand
Motion
Motor
68
Biased random walk
gradient
Ligand
Motion
Motor
Signal Transduction
69
High gain (cooperativity)
ultrasensitivity
References Cluzel, Surette, Leibler
Motor
Ligand
Motion
Signal Transduction
70
Motor
References Cluzel, Surette, Leibler Alon,
Barkai, Bray, Simon, Spiro, Stock, Berg,
Signal Transduction
71
ligand binding
motor
FAST
ATT
-ATT
flagellar
motor
R
CH
3
MCPs
MCPs
SLOW
CW
W
W
P
P
-CH
3
A
A


Y
B

P
Z
ATP
ADP
ATP
P
P
Y
B
i
i
72
Fast (ligand and phosphorylation)
ligand binding
motor
FAST
ATT
-ATT
flagellar
motor
MCPs
MCPs
CW
W
W
P
A
A

Y

P
Z
ATP
ADP
ATP
P
Y
i
73
Short time Yp response
1
Ligand
0
0
1
2
3
4
5
6
Che Yp
Barkai, et al
No methylation
Extend run (more ligand)
0
1
2
3
4
5
6
Time (seconds)
74
Slow (de-) methylation dynamics
R
CH
3
MCPs
MCPs
SLOW
W
W
P
-CH
3
A
A

B

P
ATP
ADP
ATP
P
B
i
75
ligand binding
motor
FAST
ATT
-ATT
flagellar
motor
R
CH
3
MCPs
MCPs
SLOW
CW
W
W
P
P
-CH
3
A
A


Y
B

P
Z
ATP
ADP
ATP
P
P
Y
B
i
i
76
Long time Yp response
5
3
1
0
0
1000
2000
3000
4000
5000
6000
7000
No methylation
B-L
0
1000
2000
3000
4000
5000
6000
7000
Time (seconds)
77
Tumble (less ligand)
Ligand
Extend run (more ligand)
78
Biologists call this perfect adaptation

• Methylation produces perfect adaptation by
  integral feedback.
• Integral feedback is ubiquitous in both
  engineering systems and biological systems.
• Integral feedback is necessary for robust perfect
  adaptation.

79
Perfect adaptation is necessary
ligand
80
Tumbling bias
Perfect adaptation is necessary
to keep CheYp in the responsive range of the
motor.
ligand
81
Fine tuned or robust ?

• Maybe just not the right question.
• Fine tuned for robustness
• with resource costs and new fragilities as the
  price.

82
Biochemical Network E. Coli Metabolism
Regulatory Interactions
Complexity ? Robustness
Supplies Materials Energy
Supplies Robustness
From Adam Arkin
from EcoCYC by Peter Karp
83
What about ?

• Not really about complexity
• These concepts themselves are robust, yet
  fragile
• Powerful in their niche
• Brittle (break easily) when moved or extended
• Some are relevant to biology and engineering
  systems
• Comfortably reductionist
• Remarkably useful in getting published

• Information entropy
• Fractals self-similarity
• Chaos
• Criticality and power laws
• Undecidability
• Fuzzy logic, neural nets, genetic algorithms
• Emergence
• Self-organization
• Complex adaptive systems
• New science of complexity

84
Criticality and power laws

• Tuning 1-2 parameters ? critical point
• In certain model systems (percolation, Ising, )
  power laws and universality iff at criticality.
• Physics power laws are suggestive of criticality
• Engineers/mathematicians have opposite
  interpretation
• Power laws arise from tuning and optimization.
• Criticality is a very rare and extreme special
  case.
• What if many parameters are optimized?
• Are evolution and engineering design different?
  How?
• Which perspective has greater explanatory power
  for power laws in natural and man-made systems?

85
6
Data compression (Huffman)
WWW files Mbytes (Crovella)
5
4
Cumulative
3
Frequency
Forest fires 1000 km2 (Malamud)
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Decimated data Log (base 10)
Size of events
86
Size of events x vs. frequency
log(Prob gt size)
log(rank)
log(size)
87
6
Web files
5
Codewords
4
Cumulative
3
Frequency
Fires
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
Size of events
Log (base 10)
88
The HOT view of power laws

• Engineers design (and evolution selects) for
  systems with certain typical properties
• Optimized for average (mean) behavior
• Optimizing the mean often (but not always) yields
  high variance and heavy tails
• Power laws arise from heavy tails when there is
  enough aggregate data
• One symptom of robust, yet fragile

89
Source coding for data compression
90
Shannon coding

• Ignore value of information, consider only
  surprise
• Compress average codeword length (over stochastic
  ensembles of source words rather than actual
  files)
• Constraint on codewords of unique decodability
• Equivalent to building barriers in a zero
  dimensional tree
• Optimal distribution (exponential) and optimal
  cost are

91
Data
6
DC
5
How well does the model predict the data?
4
3
2
1
0
-1
0
1
2
92
Data Model
6
DC
5
How well does the model predict the data?
4
3
Not surprising, because the file was compressed
using Shannon theory.
2
1
0
-1
0
1
2
Small discrepancy due to integer lengths.
93
Web layout as generalized source coding

• Keep parts of Shannon abstraction
• Minimize downloaded file size
• Averaged over an ensemble of user access
• But add in feedback and topology, which
  completely breaks standard Shannon theory
• Logical and aesthetic structure determines
  topology
• Navigation involves dynamic user feedback
• Breaks standard theory, but extensions are
  possible
• Equivalent to building 0-dimensional barriers in
  a 1- dimensional tree of content

94
A toy website model( 1-d grid HOT design)
document
95
links files
96
Forest fires dynamics
Intensity Frequency Extent
97
A HOT forest fire abstraction
Fire suppression mechanisms must stop a 1-d front.
Optimal strategies must tradeoff resources with
risk.
98
Generalized coding problems

• Optimizing d-1 dimensional cuts in d dimensional
  spaces
• To minimize average size of files or fires,
  subject to resource constraint.
• Models of greatly varying detail all give a
  consistent story.
• Power laws have ? ? 1/d.
• Completely unlike criticality.

Data compression
Web
99
Theory
d 0 data compression d 1 web layout d
2 forest fires
100
Data
6
DC
5
WWW
4
3
FF
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
101
Data Model/Theory
6
DC
5
WWW
4
3
FF
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
102
Forest fires?
Fire suppression mechanisms must stop a 1-d front.
103
Forest fires?
Geography could make d lt2.
104
California geographyfurther irresponsible
speculation

• Rugged terrain, mountains, deserts
• Fractal dimension d ? 1?
• Dry Santa Ana winds drive large (? 1-d) fires

105
Data HOT Model/Theory
6
5
California brushfires
4
3
FF (national) d 2
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
106
Data HOTSOC
6
5
4
3
2
1
0
-1
-6
-5
-4
-3
-2
-1
0
1
2
107
Critical/SOC exponents are way off
Data ? gt .5
SOC ? lt .15
108
18 Sep 1998
Forest Fires An Example of Self-Organized
Critical Behavior Bruce D. Malamud, Gleb Morein,
Donald L. Turcotte
4 data sets
109
HOT FF d 2
2
10
1
10
0
10
-2
-1
0
1
2
3
4
10
10
10
10
10
10
10
Additional 3 data sets
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111
Fires 1930-1990
Fires 1991-1995
112
HOT
SOC and HOT have very different power laws.
d1
SOC
d1

• HOT ? decreases with dimension.
• SOC?? increases with dimension.

113

• HOT yields compact events of nontrivial size.
• SOC has infinitesimal, fractal events.

HOT
SOC
large
infinitesimal
size
114
SOC and HOT are extremely different.
HOT
SOC
115
SOC and HOT are extremely different.
HOT
SOC
116
Robust
Log(freq.) cumulative
yet fragile
Log(event sizes)
117
Power laws are inevitable.
Gaussian
log(probgtsize)
log(size)
118
Power laws summary

• Power laws are ubiquitous
• HOT may be a unifying perspective for many
• Criticality, SOC is an interesting and extreme
  special case
• but very rare in the lab, and even much rarer
  still outside it.
• Viewing a complex system as HOT is just the
  beginning of study.
• The real work is in new Internet protocol design,
  forest fire suppression strategies, etc

119
Universal network behavior?
Congestion induced phase transition.
throughput

• Similar for
• Power grid?
• Freeway traffic?
• Gene regulation?
• Ecosystems?
• Finance?

demand
120
Web/Internet?
121
Networks

• Making a random network
• Remove protocols
• No IP routing
• No TCP congestion control
• Broadcast everything
• ? Many orders of magnitude slower

log(thru-put)
log(demand)
122
Networks
HOT
log(thru-put)
log(demand)
123
Turbulence
flow
HOT
pressure drop
124
streamlined pipes
flow
HOT
HOT turbulence? Robust, yet fragile?
random pipes
pressure drop

• Through streamlined design
• High throughput
• Robust to bifurcation transition (Reynolds
  number)
• Yet fragile to small perturbations
• Which are irrelevant for more generic flows

125
Shear flow turbulence summary

• Shear flows are ubiquitous and important
• HOT may be a unifying perspective
• Chaos is interesting, but may not be very
  important for many important flows
• Viewing a turbulent or transitioning flow as HOT
  is just the beginning of study

126
The yield/density curve predicted using random
ensembles is way off.
designed

• Similar for
• Power grid
• Freeway traffic
• Gene regulation
• Ecosystems
• Finance?

HOT
Yield, flow,
random
Densities, pressure,
127
Turbulence in shear flows
Kumar Bobba, Bassam Bamieh
wings
channels
Turbulence is the graveyard of theories. Hans
Liepmann Caltech
pipes
128
Chaos and turbulence

• The orthodox view
• Adjusting 1 parameter (Reynolds number) leads to
  a bifurcation cascade to chaos
• Turbulence transition is a bifurcation
• Turbulent flows are chaotic, intrinsically
  nonlinear
• There are certainly many situations where this
  view is useful.

129
velocity
high
low
equilibrium
periodic
chaotic
130
random pipe
131
bifurcation
laminar
flow (average speed)
turbulent
pressure (drop)
132
Random pipes are like bluff bodies.
133
flow
Typical flow
pressure
134
wings
Streamline
channels
pipes
135
theory
laminar
log(flow)
experiment
turbulent
Random pipe
log(pressure)
136
log(flow)
Random pipe
log(Re)
137
This transition is extremely delicate (and
controversial).
Random pipe
It can be promoted (or delayed!) with tiny
perturbations.
log(Re)
138
Transition to turbulence is promoted (occurs at
lower speeds) by
Surface roughness Inlet distortions Vibrations The
rmodynamic fluctuations? Non-Newtonian effects?
139
None of which makes much difference for random
pipes.
Random pipe
140
Shark skin delays transition to turbulence
141
log(flow)
It can be reduced with small amounts of polymers.
log(pressure)
142
streamlined pipes
flow
HOT
HOT turbulence? Robust, yet fragile?
random pipes
pressure drop

• Through streamlined design
• High throughput
• Robust to bifurcation transition (Reynolds
  number)
• Yet fragile to small perturbations
• Which are irrelevant for more generic flows

143
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144
streamwise
Couette flow
145
high-speed region
From Kline
146
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147
Streamwise constant perturbation
Spanwise periodic
148
Streamwise constant perturbation
Spanwise periodic
149
y
flow
position
z
x
150
y
v
flow
flow
x
u
position
velocity
z
w
151
y
v
flow
flow
x
u
position
velocity
z
w
152
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153
y
flow
x
position
z
2 dimensions
2d-3c model
154
These equations are globally stable! Laminar flow
is global attractor.
2d-3c model
155
energy
(Bamieh and Dahleh)
t
156
energyN10R1000t1000alpha2
5
10
Total energy
0
10
energy
vortices
-5
10
-10
10
0
200
400
600
800
1000
t
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What youll see next.
Log-log plot of time response.
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Random initial conditions on
concentrated at lower boundary.
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Streamwise streaks.
Long range correlation.
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streamlined pipes
flow
HOT
HOT turbulence? Robust, yet fragile?
random pipes
pressure drop

• Through streamlined design
• High throughput
• Robust to bifurcation transition (Reynolds
  number)
• Yet fragile to small perturbations
• Which are irrelevant for more generic flows

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Complexity, chaos and criticality

• The orthodox view
• Power laws suggest criticality
• Turbulence is chaos
• HOT view
• Robust design often leads to power laws
• Just one symptom of robust, yet fragile
• Shear flow turbulence is noise amplification
• Other orthodoxies
• Dissipation, time irreversibility, ergodicity and
  mixing
• Quantum to classical transitions
• Quantum measurement and decoherence

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Epilogue

• HOT may make little difference for explaining
  much of traditional physics lab experiments,
• So if youre happy with orthodox treatments of
  power laws, turbulence, dissipation, quantum
  measurement, etc then you can ignore HOT.
• Otherwise, the differences between the orthodox
  and HOT views are large and profound,
  particularly for
• Forward or reverse (eg biology) engineering
  complex, highly designed or evolved systems,
• But perhaps also, surprisingly, for some
  foundational problems in physics