Complexity Theory in Biological and Social Systems

- George Kampis
- Basler Chair, ETSU
- 2007 Spring

Basler lectures, 2007

Complexity theory

- Historical remarks Math, Phys, (PhilSci)
- Modern theory ABM and Networks Soc/Biol
- (and then came the Hungarians)
- Generic properties of complex networks
- Problems
- Food webs as an example
- Future work (limited to our own)

(1) Complex systems, math

- Information theory statistical complexity of

messages (no content telephone eng.) C. Shannon,

W. Weaver 1948 - Kolmogorov (Chaitin) algorithmic complexity 1966

difficulty of description - Both reduce c. to a compression problem, so must

be (and are) equivalent - E.g. (uniform) random numbers, highest entropy,

highest complexity - Random not origin, but math properties, e.g.

unpredictability, cant win against - Kolmogorov version No shorter description (e.g.

choice sequence) - Most sequences are random (complex) in this

sense! - Study of complexity must be fundamental on purely

formal grounds - But does it matter? (randomness vs. true

complexity, most things are not random in any

intuitive sense) - Uses in theoretical computer science and

foundations of math

A.N. Kolmogorov

C. Shannon

W. Weaver

G. Chaitin

Complexity and simplicity

- Mandelbrot set a very complex object
- e.g. infinite zoom, infinite details
- But, a simple algorithm
- Then, simple or complex?
- Preservation of complexity from initial conditions

LOW-COMPLEXITY ART Jürgen Schmidhuber

www.idsia.ch/juergen

(2) Complex Systems, phys

- Nonlinear dynamics
- Feedback (activation, inhibition)
- Chaos, catastrophe theory, bifurcations,

fractals - Itinerancies, long lived transients, strange

attractors - adaptive dynamics (ie learning and other

restructuring processes) - emergent phenomena (e.g. dyamic structures)

E. Lorenz A.M. Turing

N. Packard

I. Tsuda K. Kaneko

Complexity and simplicity 2.

- Internet topology a very complex object
- Finite but excessive details, multilevel zoom

needed - No simple algorithm to generate
- Yet simple structural measures help (preferential

attachment, scale-free etc.)

Common features of complex systems

- Unpredictability (but lets be precise about

this!) - Counter-intuitive nature (possible limits of

understanding?) - Complicated behaviours, complex spatio-temporal

phenomena - Non-generalizability of behavior (details matter)
- Necessity of different approaches (complexity is

complex)

Three Classes of Complexity

- Warren Weaver 1968
- Organized simplicity (pendulum, oscillator)
- Disorganized complexity (statistical systems)
- Organized complexity
- Heterogeneity, many components

(3) Complex Systems, Biol/Soc

- Weaver class 3 systems
- Approaches
- Local simulation (no analitic model may exist),

ABM (upshot from 1.) - Global network theory (upshot from 2.)

Social Networks

e.g. Stanley Wasserman

Narrative theory

social psychology

Financial etc market flows

Networks. A Hungarian Phenomenon

Okay, who is this?

Easy, and completely unrelated.

Networks. A Hungarian Phenomenon

Okay, who is this?

Networks. A Hungarian Phenomenon

Frigyes Karinthy (1887 - 1938, author,

playwright, poet, translator)

Networks. A Hungarian Phenomenon

"A mathematician is a device for turning coffee

into theorems."

Erdos number project

- Erdos EN0, co-author EN1, co-author-of-coauthor

EN2 etc. - http//www.oakland.edu/enp/
- Kevin Bacon numbers http//oracleofbacon.org/
- In fact, according to the Oracle of Bacon site,

Paul Erdös himself has an official Bacon number

of 4, by virtue of the N is a Number (a

documentary about him), and lots of other

mathematicians have finite Bacon number through

this film. (CAVEAT bogus?) - Citation networks, friendship networks, sex,

(No Transcript)

High school friendship James Moody Race, school

integration, and friendship segregation in

America, American Journal of Sociology 107,

679-716 (2001).

http//www-personal.umich.edu/mejn/networks/

The science of links

- 1. Properties of random graphs (networks)
- 2. Six degrees of separation
- 3. Small worlds the strength of weak ties
- 4. Hubs and connectors
- 5. The 80/20 rule
- 6. Rich get richer preferential attachment
- 7. Einstein's legacy
- 8. Achilles' heel
- 9. Viruses and fads
- 10. The fragmented Web
- Albert-Laszlo Barabasi, Linked The New Science

of Networks (Perseus, 2002)

Random network theory

- P. Erdos and A. Renyi, (1959) "On Random Graphs

I, Publ. Math. Debrecen 6, p. 290297. - One is a threshold one acquaintance per person,

one link to at least one other neuron for each

neuron in the brain. - As the average number of links per node increases

beyond the critical one, the number of nodes left

out the giant cluster decreases exponentially. - If the network is large, despite the links'

completely random placement, almost all nodes

will have approximately the same number of links.

(Poisson distribution) - Mathematicians call this phenomenon the emergence

of a giant component, one that includes a large

fraction of all nodes. Physicists call it

percolation and we just witness a phase

transition, similar to the moment in which water

freezes.

Six degrees of separation

- S. Milgram experiment (1967) proof of small

world - ftp//cs.ucl.ac.uk/genetic/papers/Milgram1967Small

.pdf - D. Watts and S. Strogatz (1998)
- http//en.wikipedia.org/wiki/Watts_and_Strogatz_mo

del - http//en.wikipedia.org/wiki/Small-world_network
- http//en.wikipedia.org/wiki/Clustering_coefficien

t - (near-)cliques plus bridges formed by hubs
- Preferential attachment can generate similar

Weak ties

Granovetter, Mark.(1973). "The Strength of Weak

Ties" American Journal of Sociology, Vol. 78,

No. 6., May 1973, pp 1360-1380.

Of those who found jobs through personal contacts

(N54), 16.7 reported seeing their contact

often, 55.6 reported seeing their contact

occasionally, and 27.8 rarely. When asked

whether a friend had told them about their

current job, the most frequent answer was not a

friend, an acquaintance. The conclusion from

this study is that weak ties are an important

resource in occupational mobility. When seen from

a macro point of view, weak ties play a role in

effecting social cohesion.

Granovetter's basic argument is that your

relationship to family members and close friends

("strong ties") will not supply you with as much

diversity of knowledge as your relationship to

acquaintances, distant friends, and the like

("weak ties"). Hence, a person or an organization

may be able to enhance exposure or influence by

creating or maintaining contacts with "weak

ties". In marketing or politics, the weak ties

enable reaching populations and audience that are

not accessible via strong ties.

So this is a bad picture, eh? ?

Weak ties typically not transitive, unlike

strong ties

bridges

Erdos numbers, contd

- Perhaps the most famous contemporary

mathematician, Andrew Wiles, was too old to

receive a Fields Medal (but was given a Special

Tribute by the Committee at the 1998 ICM). He has

an Erdös number of at most 3, via Erdös to ANDREW

ODLYZKO to Chris M. Skinner. - And surely the most famous contemporary "computer

personality" with a small Erdös number is William

H. (Bill) Gates, who published with Christos H.

Papadimitriou in 1979, who published with Xiao

Tie Deng, who published with Erdös coauthor PAVOL

HELL, giving Gates Erdös number at most 4. - A prolific biologist has an Erdös number of 2,

through Laszlo A. Szekely, Eugene V. Koonin, at

the National Center for Biotechnology

Information. This gives many biologists small

finite Erdös numbers, as well. Indeed, it is

probably possible to connect almost everyone who

has published in the biological sciences to

Erdös. . - Here is a message from another biologist, Bruce

Kristal, who has Erdös number 2 and lots of

coauthors, which may provide useful hints for

other searchers in this area I recently

published with D Frank Hsu (Erdös number 1), and

I am writing to briefly point out some potential

implications of this that Frank and I found very

interesting. Specifically, I am a biologist who

works across several areas. Because of this, I

have published with, among others, major figures

in research on AIDS, aging, neurologic injury and

neurodegeneration, and nutritional epidemiology.

I believe that one of the neuroscientists I have

published with, M. F. Beal, is among the most

highly cited in this area. In the last area,

nutritional epidemiology, I am on one (position)

paper with many of the world leaders, including

Walter Willett. Walt has over 1000 publications

and was recently named as the most highly cited

biomedical researcher in the last decade.

Likewise, Frank is a computer scientist with ties

in both mathematics and information retrieval as

well as some biology citations. I mention these

because Frank and I have discussed, among other

issues, whether I may serve as a weak link of

sufficient breadth to impact the overall network

structure both within biology and between biology

and these other areas of math and computer

science. Koonin is clearly more prolific than I

am, but our fields may be sufficiently different

to complement. Interested people can contact him

directly.

Hubs are connectors

Scale free (i.e. power law)

Pareto 80-20 rule, e.g. 80 of profit is produced

by 20 of firms

wherever you are, the ratio is invariant e.g.

n times fewer people have k times more friends,

Pn/k is constant across x, the number of friends

considered

Simulation library of basics

e.g. in NetLogo

Erdos-Rényi Barabási

Watts-Strogatz

Topics in network theory

- Fault tolerance and resilience
- Topological transitions (e.g. scale free - star)
- Modularity versus globality
- Evolvability
- Network optimization (a combination of these)
- Self-healing etc.

Scale free universal

- Paretos Law
- Zipfs Law
- Levy flight http//en.wikipedia.org/wiki/Levy_flig

ht Earthquakes http//www.iop.org/EJ/article/0295-

5075/65/4/581/epl8017.html - Gutenberg-Richter Law
- Rain (Noe effect)
- Internet web, emails, site visits..
- .
- A compilation http//www.insna.org/INSNA/Hot/scal

e_free.htm

http//www.hpl.hp.com/research/idl/papers/ranking/

ranking.html

Power and weakness of scale free

- Scale-free networks are extremely tolerant of

random failures. In a random network, a small

number of random failures can collapse the

network. A scale-free network can absorb random

failures up to 80 of its nodes before it

collapses. The reason for this is the

inhomogeneity of the nodes on the network --

failures are much more likely to occur on

relatively small nodes. - Scale-free networks are extremely vulnerable to

attacks on their hubs. - Scale-free networks are extremely vulnerable to

epidemics. Same is true for purely random

networks (Erdos-Rényi networks)

Structure and tie strengths in mobile

communication networks J.-P. Onnela, J.

Saramäki, J. Hyvönen, G. Szabó, D. Lazer, K.

Kaski, J. Kertész, A.-L. Barabási (2006)

http//arxiv.org/abs/physics/0610104

Distribution of degrees and link strength

Giant component size vs removal, and percolation

(connectivity)

Strong and weak links in real and random case

Confirms Granovetter. Exercise question is this

result nevertheless trivial?

Scale free universal?

- (1) Subnetworks of scale free nets are not scale

free! - (2) Drosophila PIM is not...
- (3) Food webs are not

(No Transcript)

Drosophila PIM

- Originally published in Science Express on 6

November 2003 Science 5 December 2003 Vol. 302.

no. 5651, pp. 1727 - 1736 DOI 10.1126/science.109

0289 - RESEARCH ARTICLES
- A Protein Interaction Map of Drosophila

melanogaster - L. Giot,1 J. S. Bader,1 C. Brouwer,1 A.

Chaudhuri,1 B. Kuang,1 Y. Li,1 Y. L. Hao,1 C. E.

Ooi,1 B. Godwin,1 E. Vitols,1 G. Vijayadamodar,1

P. Pochart,1 H. Machineni,1 M. Welsh,1 Y. Kong,1

B. Zerhusen,1 R. Malcolm,1 Z. Varrone,1 A.

Collis,1 M. Minto,1 S. Burgess,1 L. McDaniel,1 E.

Stimpson,1 F. Spriggs,1 J. Williams,1 K.

Neurath,1 N. Ioime,1 M. Agee,1 E. Voss,1 K.

Furtak,1 R. Renzulli,1 N. Aanensen,1 S.

Carrolla,1 E. Bickelhaupt,1 Y. Lazovatsky,1 A.

DaSilva,1 J. Zhong,2 C. A. Stanyon,2 R. L.

Finley, Jr.,2 K. P. White,3 M. Braverman,1 T.

Jarvie,1 S. Gold,1 M. Leach,1 J. Knight,1 R. A.

Shimkets,1 M. P. McKenna,1 J. Chant,1 J. M.

Rothberg1 - Drosophila melanogaster is a proven model system

for many aspects of human biology. Here we

present a two-hybridbased protein-interaction

map of the fly proteome. A total of 10,623

predicted transcripts were isolated and screened

against standard and normalized complementary DNA

libraries to produce a draft map of 7048 proteins

and 20,405 interactions.

(No Transcript)

http//www.biocomp.unibo.it/school/html2004/ABSTRA

CT/Caldarelli.pdf

Food webs

D. Lavigne The North-Atlantic Food Web

Neo Martinez http//www.foodwebs.org/index.html

Food Webs as Networks

Williams et al 2002 Two degrees of separation in

complex food webs, PNAS 99, 12913-6. But then

A keystone species is a species that has a

disproportionate effect on its environment

relative to its abundance. Such an organism plays

a role in its ecosystem that is analogous to the

role of a keystone in an arch. While the keystone

feels the least pressure of any of the stones in

an arch, the arch still collapses without it.

Similarly, an ecosystem may experience a dramatic

shift if a keystone species is removed, even

though that species was a small part of the

ecosystem by measures of biomass or productivity.

It has become a very popular concept in

conservation biology.

Are keystone species weak links?

Sea stars eat mussels to make room for other

species, grizzlys import sea nutrients

R. Albert, H. Jeong, A.-L. Barabási Error and

attack tolerance of complex networks, Nature 406,

378-482 (2000).

Sometimes weak links are hubs (Barabasi),

sometimes they link up hubs (Csermely), sometimes

keystones are weak links, sometimes not

Unresolved the relation bw hubs, keystones,

weak links

Jordán, F., Liu, W.-C. and Davis, A.J. 2006,

Oikos, 112535-546, Topological keystone species

measures of positional importance in food webs.

Connectivity/stability

- Translates as a diversity/stability problem in

ecology - May-Wigner theorem (1971) low connectivity

stabilizes - McCann (2000) high diversity/generalist species

stabilize - A mixing of methodologies ABM study of the

evolution of foodwebs modeled as phenotype

interaction networks

(Work in progress)

with W. de Back at Collegium Budapest

Question are there generic emergent properties

in the toplogy of trophic interaction nets? How

do they depend on biological parameters (agent

properties, external perturbations

etc.) Obviously, a selective (self-simplifying)

process. Is it systematic or contingent? If the

former (or latter), how does this relate to real

ecosystems? The study of such questions has just

began (and not only for our team)

Summary

- Complexity not (just) Math and Phys
- ABM and networks provide two typical Biol/Soc

paradigms - Networks have universal properties
- which are not
- Study of real and real (i.e. ABM) networks
- A final word networks (and/or ABM) are fun!

THANK YOU