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

N= # of customers affected by outage Frequency (per year) of outages > N August 10, 1996

Square site percolation or simplified “forest fire” model. The simplest possible toy model of cascading failure.

connected not connected 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)

(avg.) yield density “critical point” N=100

Critical point

criticality This picture is very generic.

Power laws Criticality

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

isolated critical tolerant

Why power laws? Almost any distribution of sparks Optimize Yield Power law distribution of events

random “optimized” density yield

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

random “optimized” density High yields.

Optimized grid Small events likely large events are unlikely

Optimized grid random grid High yields.

This source of power laws is quite universal. Almost any distribution of sparks Optimize Yield 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

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 (b) July (c) March (d) April (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!