Guiding questions

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Brief review of last week
Guiding questions
New Terminology
Alan Turing
What is Complexity ?
What is Intelligence ?
2
Dreams about understaning the Universe
Dark Matter
Dark Energy
Dreams about understaning Life
New physics?
3
What is Life ? Schrödinger 1945
4
Vortices-based self-organization of bacteria
8.8cm
5
Emergence
Patterning via Competition
Alan Turing 1952
Macro-level ?? Micro-level
Entropy production, Irregular
Local equilibrium, Length scales, Symmetries
6
Blueprint Engineering vs.Self-engineered
organization

• An old man ,
• sitting by a pile of rocks,
• is chiseling one into a block.

Passer by what are you doing?
Old Man "Can't you see? I'm building a
cathedral!"
What would a mound-building termite, carrying a
ball of mud, reply to this question?
Ben Jacob, Nature 2002
7
The role of information collective information
processing ?
Termites Cathedral
8
From Complexity to Perplexity
Horgan Sci. Am June 1995
Can science achieve a unified theory of complex
system?
Even at the Santa Fe institute, some researchers
have their doubts.
???????????

Steven Hawking
I think the next century will be the century of
complexity
9
What is Complexity? -Characterization
???????
????????
Complicated
Complex
???????
??????
Temperature
Entropy
10
The commonly accepted naïve picture
Hubberman and Hogg, Physica D 1986, Gellmann
The Quark and the Jaguar
11
Our requirements
Complexity-Regularity plane
Recorded
Shuffled
12
Guiding Questions
What is Complexity ?
New Biology ?
Characterization, Emergence, Universal
Principles, Why biological systems are complex,
Functional Complexity, Complexity Information
connection
Non-DNA information, Genome cybernetics, More
is different on all levels, Swarming intelligence
What is Information ?
What is Life ?
New Physics ?
Shannon information, Relevant information, Crypto
graphy, Correlations,
Self-organization, More is different, Physical
information
Schrödinger 1942
New Mathematics ?
What is Intelligence ?
Biological computing, Machine intelligence,
Natural intelligence, Are we Turing's machines ?
Distributed information processing,
Digital-analogue computation, Beyond Turing's
machine,
13
"Let the Complex be Simple"
My group motto
Teaching Strategy
New facts, Terminology, Concepts,
Mathematics Physics, Numerical
methods, Perspective.
"Top down" vs. "Bottom up"
Zooming in by iterations
The rational "Lack of Background"
Mixed audience
14
Following two advices
Francis Bacon It would be an unsound fancy
and self-contradictory to expect, that things
which have never yet been done can be done
except by means which never have yet been tried
Everything should be made as simple as possible,
but no simpler than that.
15
As early as 1901 (age 22) Einstein wrote "It
is a glorious feeling to recognize the
unification of a complex of phenomena that
appear to direct sense experience as completely
separate things".
He stated his criteria for judging a physical
theory "A theory is the more impressive the
greater the simplicity of its premises, the
more different kinds of things it relates, and
the more extended its area of applicability".
In 1932 Einstein wrote that "The goal of my
research has always been the simplification and
unification of the system of theoretical
physics".
16
The structure of the course
8. The human brain 9. Let the Complex be
Simple   10. Information Processing 11. Swarming
Intelligence    12. Gene-networks Dynamics   13.
Hidden Genetics 14. What is the Role of Physics
in The Emergence of New Biology?
1. Introduction 2. Dynamical Systems   3.
Emergence   4. Information Theory   5. Networks T
heory 6. Neural Networks   7. Functional
complexity    
17
Today
Introduction to Dynamical Systems
Motivation Neural networks
Individual neuron as a dynamical system
Phase space analysis the lovers game
Physical Pendulum
BBC 2
18
The brain
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Brains in a Nutshell
A lesson from Cultured Neural Networks
Regulated spontaneous activity the basic
templates for computability?
Segev et al Phy Rev lett 2000,2001,2002,2003 Baruc
hi et al, Complexity 2005
20
What is a neuron
21
What is an action potential Pump out positively
charged sodium ions. In addition, pump in
positively charged potassium ions
22

• Propagation along the axon
• When an action potential depolarises the
  membrane, the leading edge activates other
  adjacent sodium channels.
• A wave of depolarisation spreads from the point
  of initiation.

23

• Neurons communication - Synapses
• When an action potential reaches a synapse,
  pores in the cell membrane are opened allowing an
  influx of calcium ions (positively charged
  calcium atoms) into the pre-synaptic terminal.
  This causes a small 'packet' of a chemical
  neurotransmitter to be released into a small gap
  between the two cells, known as the synaptic
  cleft. The neurotransmitter diffuses across the
  synaptic cleft and interacts with specialized
  proteins called receptors that are embedded in
  the post-synaptic membrane. These receptors are
  ion channels that allow certain types of ions
  (charged atoms) to pass through a pore within
  their structure. The pore is opened following
  interaction with the neurotransmitter allowing an
  influx of ions into the post-synaptic terminal,
  which is propagated along the dendrite towards
  the soma.

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• Inhibitory neurons

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Modeling the neuron
We will start with simpler examples
27
Dynamical Systems Formal Definition
A dynamical system is a concept in mathematics
where a fixed rule describes the time
dependence of a point in a geometrical space.
The mathematical models used to describe the
swinging of a clock pendulum, the flow of water
in a pipe, or the number of fish each spring in
a lake are examples of dynamical systems.
28
Phase Space Analysis

• When do we understand a dynamical system?
• Is an analytical solution better?
• Often no analytical solution to nonlinear systems.

29
Fixed point
Y
x
30
Love Affairs

• Romeo loves Juliet. The more Juliet loves him the
  more he wants her
• Juliet is a fickle lover. The more Romeo loves
  her, the more she wants to run away.

31

• Study with flow field the forecast for lovers
  governed by the general linear system

• Consider combinations of different types of
  lovers, e.g.
• The eager beaver (agt0,bgt0), who gets excited by
  Juliets love and is spurred by his own
  affectionate feelings.
• The cautious lover (alt0,bgt0). Can he find true
  love with an eager beaver?
• What about two identical cautious lovers?

32
Fixed point
33

• Dynamics of Romeo and Juliet

34

• Romeo loves Juliet. The more Juliet loves him the
  more he wants her. Juliet is the same.

Saddle point
35

• Romeo loves Juliet. The more Juliet loves him the
  more he wants her. But Juliets love is
  independent of his, he has to adjust

Saddle point
36

• The more Juliet loves him the more he wants her,
  but his love is fed by his own feeling also.

Stable fixed point
37

• Adding some kids to the same equations

Stable fixed point
38

• When adding non linear terms phase space can get
  more complex

Unstable
Stable
39
Damped driven pendulum
?


- ??
- sin
q

40
f0 1.35
f0 1.45
f0 1.47
f0 1.48
f0 1.49
f0 1.50
41
Rabbit vs. Sheep

• We begin with the classic Lotka-Volterra model of
  competion between two species competing for the
  same (limited) food supply.

• Each species would grow to its carrying
  capacity in the absence of the other. (Assume
  logistic growth!)
• Rabbits have a legendary ability to reproduce,
  so we should assign them a higher intrinsic
  growth rate.
• When rabbits and sheep encounter each other,
  trouble starts. Sometimes the rabbit gets to eat
  but more usually the sheep nudges the rabbit
  aside. We assume that these conflicts occur at a
  rate proportional to the size of each population
  and reduce the growth rate for each species
  (more severely for the rabbits!).

Principle of Competitive Exclusion Two species
competing for the same limited resource typically
cannot coexist.
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Poincaré Section
44
Strange Attractors

• Chaotic attractors of dissipative systems
  (strange attractors) are fractals
• Our Pendulum 2 lt dim lt 3
• The fine structure is quite complex and similar
  to the gross structure self-similarity.

non-integer dimension
45
Attractors

• The surfaces in phase space along which the
  pendulum follows (after transient motion decays)
  are called attractors
• Examples
• for a damped undriven pendulum, attractor is just
  a point at ???0. (0D in 2D phase space)
• for an undamped pendulum, attractor is a curve
  (1D attractor)

46
Poincaré Section Examples
47
f0 1.07
f0 1.48
f0 1.50
f0 1.15 q 0.25
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Logistic Map Part I

• The logistic map describes a simpler system that
  exhibits similar chaotic behavior
• Can be used to model population growth
• For some values of ?, x tends to a fixed point,
  for other values, x oscillates between two points
  (period doubling) and for other values, x becomes
  chaotic.

50
Logistic Map Part II

• To demonstrate

x
n
x
n
-
1
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Feigenbaum Number

• The ratio of spacings between consecutive values
  of ? at the bifurcations approaches a universal
  constant, the Feigenbaum number.
• This is universal to all differential equations
  (within certain limits) and applies to the
  pendulum. By using the first few bifurcation
  points, one can predict the onset of chaos.

-
m
m


d
-
k
k
...
669201
.
4
lim
1
-
m
m


k

k
k
1
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Trivial Example Point, Line, Surface,
57
What is Dimension?

• Capacity dimension of a line and square

e

d
d
)
/
1
(
)
(
e
L
N
e
e

)
/
1
log(

/
)
(
log

lim
N
d
c
e

0
58
Non-Trivial Example Cantor Set

• The Cantor set is produced as follows

N ?
1 1
59
Bifurcation Diagrams Part I

• Bifurcation a change in the number of solutions
  to a differential equation when a parameter is
  varied
• To observe bifurcatons, plot long term values of
  ?, at a fixed value of ?Dt mod 2? as a function
  of the force term f0

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Simpler example Forced Mixing
Water
Air
Glycerin
2
In the Glycerin
64
The principle of singular feedback
Universality I
A snowflake
?????? ???? ?????
(CNN)
Engineered Self-Organization of air bubbles
65
Universality II
Bacterial Self-organization
(Nature 2001, Trends in Microbiology 2004
Physical Biology 2004)
8.8cm
1011 bacteria
66
Branching out for food
Bacterial solution to starvation on hard surface
67
Bacterial solution to Turing's competition
Hard substrate
Low nutrients
Collective lubrication for swimming
Branching low average density
68
Bacterial Mathematical Ingenuity

From diffusion to non-linear diffusion - a
mathematical singular perturbation
b
Bacterial density
Self-engineered singular perturbation
Adjustment of the value of ? as needed
Hints about a new mathematics Functional
Solvability
69
Universality II
Bacterial Colonies
70
Guiding Questions
What is Complexity ?
Characterization, Emergence, Universal
Principles, Why biological systems are complex,
Functional Complexity, Complexity Information
connection
What is Information ?
What is Intelligence ?
71
Functional Complexity
Self-regulated Variability with Reproducibility
The Complexity Flexibility Adaptability
Principle
Ben-Jacob Nobel Symposium 2002 (paper available)
72
Self-Engineered Organization? Regulated
Complexity? Functional Variability?
73
Reproducible Complexity
The Generating Dot
Two colonies of 1010 P. vortex bacteria.
Both inoculated from the same parent colony.
Growth time 3 days
74
Self-Generation of Vortices
SIMULATIONS
UTILIZATION of ATTRACTIVE CHEMOTAXIS
(Czirok, Cohen et al)
75
Fig 6
76
The idea of Functional (healthy) complexity
Normal growth
Response to non-lethal levels of antibiotic
The effect of Septrin
Second growth - learning
77
The effect of Ampicillin
Learning
78

• Do termites have a sense of participating in a
  group task?
• Is self-organization executed on the basis of
  purely local information?
• Or can the individuals gather global information
  (colonial level)?

We will learn from bacteria
79
There is no genetically stored blueprint dealing
with each condition.
1011 bacteria
Information is cooperatively generated as
self-organization proceeds. Thus, the bacteria
need only have genetically stored guidelines for
producing the tools that are needed to generate
new information as required
80
Can bacteria guide us also to new physics ?
Can bacteria teach us about ourselves?
81
Clues about
Self-Organization based Information Processing
Computation in the space of correlations
Non-local in time and space quantum-mechanic-lik
e
82
A New Biology for a New Century
MICROBIOLOGY AND MOLECULAR BIOLOGY REVIEWS, June
2004, p. 173186 Vol. 68, No. 2 Carl R. Woese
Science is an endless search for truth. Any
representation of reality we develop can be only
partial. There is no finality, sometimes no
single best representation
Bacterial colony
The genome
83
Guiding Questions
What is Complexity ?
Why Biological systems are complex? Complexity
Information connection,
What is Information ?
Shannon information, Relevant information, Crypto
graphy, Correlations,
What is Intelligence ?
84
Clashes of Intelligence
Intracellular Information Processing
William Loomis
85
Shannon Information
(1949)
iehfeirggjfkhregejgqhjrwffhrekjeruhdsnkhggjgrn
? Pi ln(Pi)
I
i
It is not a measure of information !
Can we measure relevant information ?
86
Information Correlations and Cryptography
The September 11 Metaphor
?? ????????
Aoccdrnig to a rscheearch at Cmabrigde
Uinervtisy, it deosn't mttaer in waht oredr the
ltteers in a wrod are, the olny iprmoetnt tihng
is taht the frist and lsat ltteer be at the
rghit pclae. The rset can be a toatl mses and
you can sitll raed it wouthit porbelm. Tihs is
bcuseae the huamn mnid deos not raed ervey lteter
by istlef, but the wrod as a wlohe.
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Dreams about new mathematics
Functional solvability
Nested phase field models
Bringing information into the models
Modeling distributed information processing
Dreams about natural bioinformatics
Intracellular self-organization
Self-organization based computation
89
Guiding Questions
What is Complexity ?
Why Biological systems are complex? Complexity
Information connection,
What is Information ?
Shannon information, Relevant information, Crypto
graphy, Correlations,
What is Intelligence ?
90
Is intelligence an essential requirement for life
?
How can we test if bacteria are intelligent ?
91
Multi-Faces of Intelligence
What is intelligence? Turing 1950
Beyond a Turing machine?
Alan Turing
Artificial Intelligence vs. Natural Intelligence
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Learning from Bacterial Self-Organization about
Nested Information Processing
94
What are Bacteria
The most fundamental organisms.
Microns in size

• paved the way for life on earth.
• contributed 10 of our genes.
• comprise about 90 (in number)
• of our body cells.
• are essential to our existence.
• help us to produce food, drugs
• and to clean the mess
• we make on earth.

95
Some facts about bacteria
96
Bacterial Mathematical Ingenuity II
Using chemical communication for
front
Self-engineered genomic switching
Active bacteria
Stationary (pre-spore) bacteria
back
97
Bacteria take control
Self-Engineered Organization Chemotactic
Signaling
High
Medium
Low
Food level
98
Chemotactic communication
Bacteria take more control
Chemotaxis Bias of cell movements according
to the concentration gradient of chemical
agents Chemotactic communication Chemotaxis in
response to chemical agents produced by the
bacteria
99
Testing the idea in model simulations
Ben Jacob et al., Nature 1994
Repulsive chemotaxis
Food chemotaxis
Attractive Repulsive
Gene-regulations and switching
Nested information processing
100
Collective genome-wide switching
The Paenibacillus dendritiformis bacteria
The Physicist's bacteria
Branching Morphotype
Chiral Morphotype
101
Broken Chiral (handedness) Symmetry
Ben-Jacob and Levine Sci. Am. 98 Nature 2001
102
The Chiral Branching Patterns
Longer Bacteria Liquid crystal-like orientation
interaction
Quasi-1D Random Walk Limited tumbling with
specific handedness
103
Modeling the Chiral Patterning
Each bacterium is described as a spinor with
orientation ?i ??i/?t ? (?- ?)Modp ?? ?
Mean field orientation
Fixed rotation
Noise
104
Spontaneous Morphotype Transitions
Inheritable genome-wide switching
harder
Substrate
soft
Low
Food
higher
105
Simulations of morphotype transitions
106
Harnessing the model
Auto-catalytic or collective gene-expression
107
Self-Engineered Genome-Wide Switching
Started after time delay
Growth direction
Encountered obstacle
during the growth
108
Precursors of cell differentiation
Genome-wide switching between Epigenetic
gene-network states
Autocatalytic and Inheritable
Dreams about natural bioinformatics
Beyond the current system biology paradigm?
Possible role of small RNA?
Hybrid information processing?
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Vortex formation
bacteria
Humans
Ameba (Levine et al)
Ants (Cuzin et al
Fish
111
Engineered organization A Non-Living Analogue
Kudrolli et al, 2003
Cooper rods
Shaken up and down
112
X-Rated Movies of Bacteria during life in
bio-films
Not today
Do not reproduce by sex
Use sex for distribution of knowledge
For example, resistance to antibiotic
113
Generation of new information and Genome
Cybernetics
The genome is beyond a universal Turing Machine
114
Beyond Modeling
The parent colony
Differentiated and inherited identity
Inoculation from the center
Inoculation from the front
115
Beyond modeling Inheritable cell differentiation
116
Colonial identity
Beyond current understanding
Linguistic elements Semantic Pragmatic
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119

• 3. MACROSCOPIC SOLVABILITY (Ben-Jacob and
  Garik, Nature 1990)
• Macro-level Singular Feedback

• SELF-CONSISTENCY (Ben-Jacob and Levine,
  Nature 2001)
• SINGULAR PERTURBATION ? SINGULAR FEEDBACK
• LEADING TO THE FORMATION OF COMPLEX HIERARCHIC
  SPATIO-TEMPORAL PATTERNS

120

• THE FASTEST GROWING MORPHOLOGY SELECTION
• (Ben-Jacob, Garik,Nature 1990)
• Morphology?Rate correspondence
• Morphology Transitions
• Morphology Diagram

fig3
121
ABIOTIC (ECD)
Morphology selection
Morphology transition
Morphotype transition
Macro micro self-consistency
Ben Jacob and Garik Nature 1990
122
Engineered Self-Organization
Forcing the system to express its hidden
abilities
Engineered growth of air bubbles
Ben-Jacob, Levine, et al Phys Rev Let. (1985)
123
4-fold
air into glycerine
10-fold
6-fold
124
(Ben-Jacob and Garik Nature 1990)
Micro-Macro Interplay Hierarchical
Self-Consistency
(Ben-Jacob and Levine nature 2001)
1cm
Electro-chemical-deposition
10?m
125
Electro-chemical-deposition
Bacteria
But, Avoid the reminiscence syndrome!
126
Learning from Bacteria Self-Organization
Eshel Ben-Jacob School of Physics Tel Aviv
University
UCSD October-May
What is Self-Organization?
Living Systems
Non living systems
127
What are Bacteria

• paved the way for life on earth.
• contributed 10 of our genes.
• comprise about 90 (in number)
• of our body cells.
• are essential to our existence.
• help us to produce food, drugs
• and to clean the mess
• we make on earth.

128
Prologue - The world is Complex
Bacterial colony
The universe
A Galaxy
The genome

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Lifting the Perplexity off the Complexity
Eshel Ben-Jacob
Eyal Hulata et al Phys Rev lett. 2004
We do not propose The world best definition of
Complexity
Quantitative observables associated with the
intuitive notion
Inspired from the activity of Neural Networks
Brain in a Nutshell
The Time-frequency domain
The Complexity-Regularity plane
Functional Complexity
Recorded Brain Activity
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Abiotic vs. Biotic Self-Organization (Complexity)
Is there a fundamental difference?
Living systems
Non-living systems