Fres 1010:Complex Adaptive Systems

Prof. Eileen Kraemer

Fall 2005

Lecture 1

Theme:

Simple agents following simple rules can generate amazingly complex structures.

What are complex adaptive systems?

Systems composed of many interacting parts that evolve and adapt over time.

Organized behavior emerges from the simultaneous interactions of parts without any global plan.

Properties of Complex Adaptive Systems

• Many interacting parts• Emergent phenomena• Adaptation• Specialization & modularity• Dynamic change• Competition and cooperation• Decentralization• Non-linearities

Many interacting parts

Businesses made of people, colonies made of ants, brains made of neurons, networks composed of hosts and routers, etc.Systems are more than mere collections because of interactions among the elementsSize matters

A critical number of amoeba needed to create clusters in slime molds

Massive parallelismOften, all agents do same, simple thingComplexity comes from interactions

Slime mold??

Slime mold does something interesting

Cool damp conditions: reddish-orange mass

It moves! (slowly, but it does)

Cooler, wetter: disappears!!

Dictyostelium discoideum

Slime mold

Spends much of its life as distinct single-celled units, each moving separatelyRight conditions: cells coalesce into single, larger organism that crawls across forest floor, eating rotting wood and leavesOscillates between single creature and swarm modes …

How is aggregation controlled?

Fact: slime molds emit acrasin (cyclic AMP)

Original (centralized control) theory:Swarms formed at the command of pacemaker cells that order the other cells to begin aggregating

Idea: pacemakers emit cyclic AMP, others follow suit, cells follow trails, cluster forms

Problem: no one could find the pacemakers

How is aggregation controlled?

Distributed control:Slime mold cells follow trails of cyclic AMP

Slime mold cells generate trails of cyclic AMP

If slime cells start to pump out enough cyclic AMP, cells begin following trails started by other cells, clusters form, which leave more cyclic AMP, which causes more cells to join … & so on: a positive feedback loop develops

Classic study in bottom-up behavior

Other example systems

Slime mold (Keller & Segel)

City neighborhoods (Jane Jacobs)

Human brain (Marvin Minsky)

Ants (E.O. Wilson)

Common elements:

Solve problems by drawing on masses of simple elements, rather than use of a centralized intelligent controller

Agents residing on one scale produce behavior that resides on a scale above them

Definitions of Emergence

Whole is more than sum of parts

Higher-level phenomena not easily predicted from lower-level behaviors

Higher-level descriptionsSpecial laws apply

High-level phenomena are not built in explicitlypredator-prey cycles

Fractal images

“gliders”

Emergence

“Active essay” on emergence at MIT:

http://llk.media.mit.edu/projects/emergence/

Adaptation

Improved performance over timeThree time courses of adaptation

Within a single event presented to an organismPerception of an organized formAdaptation of parts to each otherAdaptation of parts to external world

Within the lifetime of an organismLearning

Across lifetimesEvolution

Do interactions exist among these levels?

Specialization and Modularity

Originally homogenous agents become differentiated as a result of interactions with each other

Shift from renaissance thinkers to specialized scientistsIncreased dependency of partsThe more dependencies between parts, the more organism-like is the whole

Self-organization - systems become more structured than they were originally

Advantages of modularitySpeedEfficiencybenefit of information encapsulation: module does not need to know about what is going on in the rest of the system

Specialization and Cooperation: The Jack of all Trades

10 stages, 20 antsProb ant completes a stage = 0.4Prob ant finishes = 0.410 = 0.0001Prob ant fails = (1-0.0001) = 0.9999Prob all 20 ants fail = (0.9999)20 = 0.998Prob at least one completes = 1 – 0.998 = 0.002

Specialization and Cooperation: Specialization

10 stages, 20 antsProb ant completes a stage = 0.4Prob ant fails a stage = 1 – 0.4 = 0.6Prob both ants fail = 0.62 = 0.36Prob of stage completion = 0.64Prob at least one completed task = (0.64)10 = 0.012

Moral: by specializing, probability of completion is 6 times greater.

Dynamic Change

Complex adaptive systems viewed in terms of trajectories rather than fixed points

Complex systems often times never “settle down”

Competition and Cooperation

Simple interactions: facilitation and antagonismExcitation and inhibition in neuronsDiffusion and reaction

Oscillating chemical reactions

Predator-prey dynamicsPositive and negative feedback cycles

Decentralization

Self-organization without leaders Queen ants and head birds in a flock are not “in charge” Alternatives to centralized mind-sets (Resnick, 1994)

Peer-to-peer computing gridsThe World Wide WebGrass-roots movementsAdvantages of decentralization

AdaptabilitySystem can be “smarter” than smartest agent

Nonlinearities

Output is not proportional to inputCan’t predict how system will work by understanding parts separately,and combining them additively

The tipping point (Gladwell)Cascades of consequences from small eventsIdeas are “sticky”Hushpuppies and a couple of East Village kids

1994: 30,000 sold1995: 430,0001996: 2,000,000

Phase transitions: ice to water to steamSymmetry breaking: Systems that start out (nearly) symmetric develop qualitatively large asymmetries

Milk dropsDevelopment of a fetus from blastula to embryo

Symmetry Breaking in a droplet of milk

Symmetry breaking in a fetal development

Model aesthetics

High-level phenomenon is explained, not assumedMechanism-oriented accounts

Simplest system that produces phenomena is preferredComplex adaptive system models as caricatures

Want explanations, not clonesconcentrate on essence of a system

Do parameters of variation correspond to existing natural systems?

Can most naturally occurring systems be modeled with parametric variations? Do most parametric variations result in patterns that are found in nature?

Constraint is goodWant a system that could not have predicted anything

Raup’s Shell Generator

Shells grow as tubesCapture variations in shells with as few parameters as possible (explaining patterns that occur, and only those patterns)

Flare: expansion rate of spiral2 = for every turn, spiral opens out to twice its previous size (spiral, not tube)

Verm: How much tube fills area of spiral.7 = distance from center of spiral to the inner margin of tube is 70% of the distance from center to outer margin.

Spire: rate at which tube creeps up 3-D cone0 = all windings are in one plane

Raup's CubeCan explain many types of shells that are found Cube is larger than set of existing shells, but this will always be the case.

Raup’s Shell Generator

Raup’s Shell Generator

Raup’s Cube

Dawkin’s Blind Snailmaker

Dawkin’s Blind Snailmaker

D’arcy Thompson’s constrained transformations

Explain regularities in animal and plant forms by constrained transformations

Transformations explained by growth processes

Four standard transformationsStretch the dimensions

Taper

Shear

Radial coordinates from a fixed focus

D’arcy Thompson’s constrained transformations

D’arcy Thompson’s constrained transformations

D’arcy Thompson’s constrained transformations

D’arcy Thompson’s constrained transformations

Next week

More on slime mold

Ants too!