The Science of Man-made systems

Gábor Vattay

Physics of Complex Systems

Eötvös University

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Advent of quantitative science

• 5 July 1686

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

In the last 300 years

• Reductionist strategy was very successful

• Elementary parts: electron, photon, atoms and molecules, proton, neutron, quarks, gluons …

• Almost complete understanding of how these interact (attract, repel, kick …) and affect each other in general

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Understanding the arrow of time

• Ludwig Boltzmann• Rudolf Clausius• Entropy• 2nd law of

thermodynamics

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

During the last 150 years

• Statistical mechanics/physics was very successful

• Laws of physics do not distinguish between past and future

• Yet, we see that past and future are different

• Things go from order to disorder

• Coffee cools, sugar dissolves …

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Wait a second!

• Formation of atoms from nucleons and electrons.• More and more complicated atoms…• Formation of molecules from atoms.• More and more complicated molecules …• Formation of condensed matter from molecules.• More and more complicated forms of condensed

matter …• …• Formation of cells, tissues …

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

The science of complexity

• Ilya Prigogine• 1977 Nobel Prize in

Chemistry• Entropy can decrease• Makes life possible• Order Out of Chaos

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

In the last 40 years

• I can increase my order if I can export my mess to you …

• Entropy inside can decrease if the system is open and can pump it out into the environment

• Understanding open dissipative structures

• Understanding the complexity of nonlinear dynamics, bifurcations, chaos.

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Evolution

• Ok! We understand that it is physically possible to increase the complexity of systems

• Ok! We understand how this happens technically

• But, why the hell is this happening? • Any law of evolution?• Darwinian selection is a good start, but not

enough

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Cooperation

• Robert Axelrod• Evolution of

cooperation 1981• Competition of agents• Fundamentally selfish

agents will spontaneously cooperate

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Post human aspects of evolution

• Humans form societies• Humans create, design, build man-made

systems • Start their own human assisted evolution

• Emergence of language• Evolution of communication starts • Communication is a special MMS

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Evolution via design

• John Doyle 1999• The human assisted

evolution of different man-made systems share some common features

• Robustness• Fragility• Highly Optimized

Tolerance

• Robustness is more important than– materials– energy– entropy– information– computation

• Extreme robustness: “robust yet fragile.”• Developing new theories of complexity that focus

on robustness• (slides borrowed from Doyle)

Power outages

104 105 106 10710-2

10-1

100

101

N= # of customers affected by outage

Frequency(per year) of outages > N

1984-1997

August 10, 1996

Square site percolation or simplified “forest fire” model.

The simplest possible toy model of cascading failure.

connected

notconnected

Connected clusters

A “spark” that hits a cluster causes loss of that cluster.

yield =

density- loss

Assume: one randomly located spark

(average)

yield =

density- loss

Think of (toy) forest fires.

(average)

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(avg.)yield

density

“critical point”

N=100

Critical point

criticality

This picture is very generic.

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Power laws Criticality

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Power laws: only at the critical point

low density

high density

Life, networks, the brain, the universe and everything are at “criticality” or the “edge of chaos.”

Does anyone really believe this?

Self-organized criticality:dynamics have critical point as global attractor

Simpler explanation: systems that reward yield will naturally evolve to critical point.

Would you design a

system this way?

Maybe random networks aren’t

so great

High yields

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isolated

critical

tolerant

Why power laws?Why power laws?

Almost any distribution

of sparks

OptimizeYield

Power law distribution

of events

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random

“optimized”

density

yield

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5

10

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30

Probability distribution (tail of normal)

High probability region

Optimal “evolved”

“Evolved” = add one site at a time to maximize incremental (local) yield

Very local and limited optimization, yet still gives very high yields.

Small events likely

large events are unlikely

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random

“optimized”

density

High yields.

Optimized gridSmall events likely

large events are unlikely

Optimized grid

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random

grid

High yields.

This source of power This source of power laws is quite universal.laws is quite universal.

Almost any distribution

of sparks

OptimizeYield

Power law distribution

of events

Tolerance is very different from criticality.

• Mechanism generating power laws.• Higher densities.• Higher yields, more robust to sparks. • Nongeneric, won’t arise due to random fluctuations. • Not fractal, not self-similar.• Extremely sensitive to small perturbations that were not designed for, “changes in the rules.”

Extreme robustness and extreme hypersensitivity.

Small flaws

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Evolution of Communication

humans and beyond …

Evolution beyond humans

• Communication networks are man-made systems: we think we evolve them

• Yet, they are special: • Structural changes happen the way we work• Changes our collaboration pattern• Restructures our time• Restructures human sexuality• We are part of the system: they strongly shape our

own evolution

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Evolution of communication

• More information further and faster:• Voice: short range~ 10 m• Courier (on horse)• Light and smoke signaling• Post service (horse based)• Steam engine, railroad, post (railroad based) • Electricity, copper wire, telegraph, telephone• For 100 years …

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Telephone exchange and network

Puskás Tivadar

1878

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Computer appears

ENIAC 1946

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Internet

Growth of the ARPANET (a) December 1969. (b) July 1970.• (c) March 1971. (d) April 1972. (e) September 1972.

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

The Beast

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Evergrow, ETOMIC, CNDA

• Understanding the future of the Internet

• Understanding the evolution of computer communication

• Understanding how computers compete and cooperate

• Power laws of Internet

roboust yet fragile

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Robust yet fragile topology

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Roboust yet fragile traffic

One day in Europe

Gábor Vattay Center for Network Data Analysis, Collegium Budapest

Thank you!