Complexity Research Why and How

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Complexity Research Why and How
Sorin Solomon Racah Institute of Physics HUJ
Israel Director, Complex Multi-Agent Systems
Division, ISI TurinDirector, Lagrange
Interdisciplinary Laboratory for Excellence In
Complexity
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Complexity
Sorin Solomon, Racah Institute of Physics HUJ
Israel Director, Complex Multi-Agent Systems
Division, ISI Turin
Director, Lagrange Interdisciplinary Lab for
Excellence In Complexity
MORE IS DIFFERENT (Anderson 72)(more is more
than more) Complex Macroscopic properties are
often the collective effect of many simple
microscopic components (and independent on
their details)

• Phil Anderson Real world is controlled
• by the exceptional, not the mean
• by the catastrophe, not the steady drip
• by the very rich, not the middle class.
  we need to free ourselves from
  average thinking.

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Misfit was always assigned to the neglect of
specific details.We show it was rather due to
the neglect of the discreteness. Once taken in
account gt complex adaptive collective objects.
emerge
even in the worse conditions
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Complexity
Sorin Solomon, Racah Institute of Physics HUJ
Israel andDirector of the Complex Multi-Agent
Systems Division, ISI Turin
Lagrange Laboratory for Excellence In Complexity
at ISI Torino support for students
and researchers General Integration Action in
Complexity Science 12 Specific Targeted
Research Projects in Complexity (CO3)
MORE IS DIFFERENT (Anderson 72)(more is more
than more) Complex Macroscopic properties may
be the collective effect of many simple
microscopic components (and independent on
their details)
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The Multi-Agent Complex Systems Paradigm MICRO -
the relevant microscopic degrees of
freedom         INTER - their fundamental
interactions         MACRO - the macroscopic
emerging collective objects

• Intrinsically (3x) interdisciplinary
• MICRO belongs to one science
• MACRO to another science
• Mechanisms statistical mechanics (?)
  phase transitions, scale
  invariance,

The challenge
transcend traditional disciplinary research
Complexity Research More than a juxtaposition
of expertises a new grammar with new
interrogative forms allowing
the formulation of new questions. Grow a new
generation of bi- or multi-lingual scientists.
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MORE IS DIFFERENT Complex Systems Paradigm
MICRO - the relevant elementary
agents         INTER - their basic, simple
interactions         MACRO - the emerging
collective objects

• Intrinsically (3x) interdisciplinary
• MICRO belongs to one science
• MACRO to another science
• Mechanisms a third science

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Complexity
Sorin Solomon, Racah Institute of Physics HUJ
Israel Complex Multi-Agent Systems Division, ISI
TurinLagrange Interdisciplinary Lab for
Excellence In Complexity
MORE IS DIFFERENT (Anderson 72)(more is more
than more) Complex Macroscopic properties may
be the collective effect of many simple
microscopic components (and independent on
their details)

• Phil Anderson Real world is controlled
• by the exceptional, not the mean
• by the catastrophe, not the steady drip
• by the very rich, not the middle class.
  we need to free ourselves from average
  thinking.

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Simplest Example of a More is Different
Transition
Water level vs. temperature
1cm
1Kg
950C
BOILING PHASE
TRANSITIONMore is different a single molecule
does not boil at 100C0
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Example of MORE IS DIFFERENT transition in
Finance Instead of Water Level -economic
index(Dow-Jones etc)
Crash result of collective behavior of
individual traders
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Systems, Organisms health,
perception self-non-self recognition
Cells
chemotaxis, metabolism
DNA chains, proteins reproduction,evolution,syn
thesis
Chemicals
almost free particles
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Meaning
Cells,life
Social groups
Words
people
Chemicals
Markets
WWW
Customers
E-pages
Anderson abstractization
Herds, Crashes
Cognition, perception
Traders
Neurons
Statistical Mechanics Phase Transition
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Instead of temperature (energy /
matter) Exchange rate/interest rate Value At
Risk / liquid funds Equity Price /
Dividends Equity Price / fundamental
value Taxation (without representation)/ Tea
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Product Propagation
Bass extrapolation formula vs microscopic
representation
VCR
Actual sales
Extrapolation
CARS in USA 1895-1930
DVD
Reality curves
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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Microscopic view of a water drop a network of
linked water molecules
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The water drop becomes vapors the network splits
in small clusters
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The water drop becomes vapors the network splits
in small clusters
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The water drop becomes vapors the network splits
in small clusters
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The water drop becomes vapors the network splits
in small clusters
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The water drop becomes vapors the network splits
in small clusters
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Boiling is not a physical property of particular
molecules but a generic property
of the cluster geometry
To understand, one does not need the details of
the interactions.
Rather one can prove theorems on what is the
density of links that ensures
the emergence or
disintegration of clusters
Phase Transition
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Product Propagation
Bass extrapolation formula vs microscopic
representation
VCR
VCR
Actual sales
SALES
Extrapolation
BASS
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Product Propagation
Bass extrapolation formula vs microscopic
representation
VCR
VCR
Actual sales
SALES
Extrapolation
BASS
Also Belief Propagation
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Product Propagation
Bass extrapolation formula vs microscopic
representation
VCR
Actual sales
Extrapolation
Also Belief Propagation
CARS in USA 1895-1930
DVD
Reality curves
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- Microscopic Customers and Macroscopic
Sales      MICRO Customers, products / ideas /
information     INTER purchase, inform, learn,
hear-say MACRO global trends, waves of sales
(e.g. Tamaguchi), hits, flops,
market fluctuations, anomalous diffusion
demarketing
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Propagation effects - product propagation -
spread of ideas - epidemics - Internet
viruses - Social ills drugs, violence,
terror - Credit networks and bankruptcy
avalanches - production / trade practices -
real estate valuation - tax paying habits
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The Square Lattice is just for clarityThe
effects demonstrated are much more general
PotentialAdopters
Rejectors
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Density of potential adopters 26/48gt50
What Percent will actually
adopt?
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The Buyers are split in small clusters
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The epidemics, bankruptcy avalanche, idea,
product spread is limited to one cluster
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Density of potential adopters
26/48gt50 What Percent will actually adopt? 7/48
lt 15
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Density of potential adopters
26/48gt50 What Percent will actually adopt? 7/48
lt 15
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Only 15 will actually adopt! But what if add
one more potential adopter?
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If adds one more potential adopter 22 out of 27
potential adopters adopt 22/4846
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This is not just a fortuitous case for larger
systems the effect is even more dramatic
Adopters Density 55
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If lowering the price , or increasing quality,
or decreasing taxes or subsidizing adopters
(or affecting credit rate) etcone gains 5 more
potential adopters Thendensity of potential
adopters 60 How much will this increase the
actual adoption?
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60 potential adopters
55 potential adopters
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60 potential adopters
Theorem
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55 potential adopters
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59.3
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Fractal Sales Prediction Tool for product
success (15/17)
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55density
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fractal space distribution
Prediction of campaign success (15/17)
Goldenberg
Air-view of a sub-urban neighborhood crosses on
the roofs indicate air-conditioner purchase
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Market 'spikes' are seen by traders as freak
events.Physicists expect them
Small changes in product quality, price,
external conditions can produce large
effects(e.g. large market fluctuations) Small
deterioration in credit market can trigger large
waves of bankruptcies
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Market 'spikes' are seen by traders as freak
events.Physicists expect them
Lev Muchnik Phys. Scripta
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Levy, Solomon and Levy's Microscopic Simulation
of Financial Markets points us towards the
future of financial economics. If we restrict
ourselves to models which can be solved
analytically, we will be modeling for our mutual
entertainment, not to maximize explanatory or
predictive power."--HARRY M. MARKOWITZ, Nobel
Laureate in Economics
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Percolation transition
From non-sales at all to a lot of
sales Infinitely sharp at infinite size system
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• ALSO effects of
• Expectations Adaptation
• Self tunning to criticality
• Fractal fluctuations
• and correlations

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ALSO effects of Expectations Adaptation
Fractal space-time fluctuationsProduct Success
prediction (15/ 17)
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Resistance
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Resistance
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Resistance
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Resistance
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ANTI-Percolation Antivirus
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Figure 1 Comparing infection process evolution
with (bottom) and without (top) immunization
edges. On the top the network is being infected
fully by the virus. On the bottom the virus
cluster is reduced by more than half by
introducing immunization edges. The blue (dark
green) edges represent the original network
(further immunization) edges. During the spread,
an edge is coloured in red (turquoise) if it was
used to infect (immunize) a node. In both cases
we present four snapshots of each network in
different times. In addition, we present the time
(t ) varying graphs for the cluster development
over time.
The blue, red and green lines are used to present
the size of the susceptible, infected and
immunized clusters, respectively. Note that in
the bottom set, initially in snapshots 1 and 2,
the virus cluster develops uninterruptedly until
the immunization agent manages to escape the
border of the virus cluster, in snapshot 3, and
start immunizing the network therefore the agent
manages to immunize most of the network even
though the virus had a head start.
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Figure 2 Relative virus cluster size as a
function of immunization link density (loglog
scale). The dependence of the relative infected
cluster size on the relative edge addition q,
resulting from simulations over uncorrelated,
scale-free networks with power exponent -3, mean
degree 4 and network size 50,000200,000 nodes.
The ratio dependence shows a power-law form,
with an exponent close to -4/3. The error bars
present the 95 confidence interval.
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Figure 5 Comparison of virus cluster sizes for
the random-edge and the honey-pot architectures.
The different sets present different relative
edge additions, q. The clusters in the random
case are always larger than the clusters in the
honey-pot case as the network size grows, so
does the gap between the two architectures. The
reason behind this is that, whereas in the random
case the cluster size remains fairly constant as
we vary the network size, in the honey-pot case
as the network grows, so does the effectiveness
of the honey pots. This effect is mostly noted in
the middle range of the density values where the
immunization has an effect but the virus cluster
is not extremely small. The error bars present
the 95 confidence interval. show a power-law
ratio dependence
Figure 6 The dependence of the virus cluster on
the degree distribution power exponent. We ran a
sensitivity analysis where we varied the power
exponent of the Pareto degree distribution
characterizing the underlying topology between
1.8 and 3, which includes all degree
distributions found in real scale-free networks.
As can be seen, the effectiveness of the
immunization process grows with the
power exponent, owing to the fact that lower
exponents entail a higher density of edges, which
allows the virus to advance faster. However, this
variation is still minor compared with variations
in the relative edge addition, q, and in the
architecture type, which are illustrated by the
different data sets presented. The error
bars present the 95 confidence interval. HP
honey pot.
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Parallel Networks
Consumption home
Expectations work
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- Microscopic Investors and Macroscopic Crashes

/Power Laws         
MICRO - Investors, individual capital ,shares    
     INTER - sell/buy orders, gain/loss         
MACRO - social wealth distribution, market price
fluctuations (cycles, crushes,
booms, stabilization by noise)
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-Microscopic Concepts and Macroscopic Ideas MICRO
- concepts, connections between concepts INTER -
creating/deleting/activating connections between
concepts
- Microscopic Seers and Macroscopic Sight MICRO
- motion visual sensors for points and line
elements. INTER - time and space  local data
integration. MACRO - Perception of 3 Dimensional
global structure.
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- Microscopic Picassos and Macroscopic Drawings
MICRO - local line / motion features, mental
states, mental eventsINTER - line breaks and
mind events(changes) vs line/mind inertia.MACRO
- drawing shapes, emergence of representational
meaning
  - Microscopic Doctors and Macroscopic
Health MICRO  - Cells, Enzimes, Antigens,
Antibodies          INTER  - producing,
destroying, changing state of a
cell/enzime,          MACRO  - immunity, health,
infection, sickness, inflamation.

• Microscopic Drivers / police and Macroscopic Jams
• MICRO - cars
• INTER - go ahead/give way at intersections.
• MACRO - traffic flow, jamming self-organization
  useless police

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Microscopic Grimm Brothers and Macroscopic
Stories MICRO persons, relations INTER
change in relations acting MACRO plot, story,
meaning
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Internet study along the
same lines1. physical,2. information flow and
3. emergent / cognitive.
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• We exemplify this by studying two types of
  networks Genetic networks and the World Wide
  Web. In the first case we formulate a model
  including only random unbiased gene duplications
  and mutations. In the second case, the basic
  moves are website generation and rapid
  surf-induced link creation (/ destruction). In
  both cases we do reproduce the experimental
  observations at all scales.
• For the genetic network our model predicts a slow
  convergence toward a directed structure composed
  roughly of a core directing toward a periphery.
  By contrast, the WWW presents rapidly changing
  non-stationary bi-directionally linked clusters.
• In the genetic case the rough picture outside the
  core is of a tree-like structure with arrows
  preferentially directed towards the branches. In
  the WWW case, the hierarchy is rather in the form
  of strongly linked clusters-within clusters and
  the connections between clusters are generically
  pointing in both directions.

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Louzoun-Lev
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Gene network
Internet network
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Figure 1 - Mechanisms of individual node
evolution the 3 elementary processes defining
our genetic model. Their effect is demonstrated
on the configuration of the left upper corner
(only links and nodes relevant for the
explanation are explicitly shown). The effect of
a Node copying elementary event is shown in A) .
The blue node is duplicated by introducing the
new brown node that has the same targets for its
out-going links (and no incoming links at all).
The Node removal is illustrated in B). The
green node and all its links are deleted. The
drawing C) illustrates the elementary operation
of Link Mutation the pink link is copied. i.e.
a new link with the same origin but different
target is created . These 3 elementary
operations turn out to be sufficient for the
formation of a steady state directional
hierarchical scale free network, with the
experimentally observed sub-motif distribution.
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Microscopic Links, Macroscopic NetworksMICRO
Nodes, connections INTERACTIONS - Local changes
(node / link (dis-) appearance)MACRO- Global
connectivity, percolation, topology
New generation of network studiesInstead of
study generic properties that are not specific to
any particular system, Study specific macroscopic
collective properties implied by specific
elementary interactions..
Gene activation
WWW linking
site
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Figure 2 Node degree distribution in the genetic
model- Incoming (empty circles) and outgoing
(full squares) link distributions. The outgoing
link distribution is normal (as experimentally
observed). The incoming link distribution is
scale free over more than three orders of
magnitude (10-50,000). The straight line
corresponds on this double logarithmic graph to a
power law with exponent -2.2 (the value actually
observed in most genetic networks). Increasing
the network size has no effect on the exponent of
the power distribution it only increases its
validity range.
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Figure 3. Measures of the Small World character
of the genetic network. The main graph represents
the clustering coefficient (C) as a function of
the degree k. The clustering coefficient of the
node i, with a degree ki is defined as as Ci
2ni/ki(ki - 1), where ni denotes the number of
direct links connecting its ki nearest neighbors
among themselves. Ci is equal to 1 if the
neighbors of i are all connected one to the
other. A random (Erdos-Renyi) graph would produce
a flat very small clustering coefficient. One
sees from the graph that the actual distribution,
far from being a small constant is fitted by a
straight line that represents on the double
logarithmic scale a power law with exponent -1 as
observed in genetic networks (and in contrast
with the preferential attachment dynamics). The
fit is excellent with no free parameters. The
inset plots the distribution of distances between
arbitrary pairs of nodes in the network. A
regular one dimensional lattice would produce a
distance proportional to the network size
(50,000). The combination of a distance of the
order of the log of the network size (inset) and
the existence of high clustering coefficient are
the hallmark of a "small world network".
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Figure 6 Double logarithmic histogram of the
nodes rank distribution in the WWW model. Results
show a power law for both incoming (empty
circles exponent 2.1/-0.1) and outgoing links
(full squares exponent 3.1 /- 0.2). These
exponents are in perfect agreement with the
experimental data. The inset shows the average
node distance as predicted by the WWW model. The
distance grows as the log of the network size,
and thus the network is indeed a small world
network in agreement with the experiments.
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Executive Abstract

• Logistic dynamics has been recognized since 200
  years to govern a wide range of social, economic,
  biological and cognitive systems.
• In the past the predictions of the logistic
  equation have been invalidated almost
  systematically in many occasions.
• In particular they predicted often falsely the
  decay of the dynamics in adverse conditions.
• We show that the correct accounting for the
  discrete character of the elementary components
  of the system leads to dramatically different
  predictions
• In particular the emergence of adaptive
  collective objects that insure survival and
  development in conditions in which the naïve
  continuous/ global treatment would predict
  complete and uniform decay.
• The emergence of stable Pareto-Zipf power laws
  even in very non-stationary conditions.
• We review a series of applications, predictions
  and their validation.

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Objective Algorithm to Evaluate Interdisciplinary
researchers relevance
- map the interdisciplinary cooperation
network(- people are nodes - cooperations
andcommon papers, are links).
Discipline3
Discipline 1
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This was a Particular case of Logistics dynamics
(with Corrections!!) Other technological
change innovations diffusion (Rogers) new
product diffusion / market penetration
(Bass) social change diffusion

dX/dt X(N X )
X number of people that have already adopted
the change and N -X number of remaining
customers
Logarithmic scale
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Naïve logistic
10
1
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• Insert LSS book

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POSTEXT
Shalit A. Erez T. Deters A. Hershberg U. Shir E.
Solomon S.
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I am here
My papers
New (Dynamic, Distributed, Open, Free, Self-Org,
Ontology
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EMPTY SHELLS
New (Dynamic, Distributed, Open, Free, Self-Org,
Ontology
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-emergence of High-Tech communities-start-ups
connections to previous businesses-entrepreneurs
emerging from old businesses-partners having
previous common institutions
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-emergence of High-Tech communities-start-ups
connections to previous businesses-entrepreneurs
emerging from old businesses-partners having
previous common institutions
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Realistic macroscopic simulations require a new
causal framework discrete / delayed/ conditional
/ nested causality
instead of the usual Markov
infinitesimal one
New mathematical concept Markov Webs