# 2015 Complexity and Modeling Program Word Wall

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 2015 Complexity and Modeling Program Navigation

Complex vs. Complicated

Complex: individual behaviors and local interactions, goal-specific emergent structure, scale-dependent predictability and unpredictability, high level of throughput.

Complicated: is deliberate, has specific goal driven behavior, predictable behavior at all scales, system throughout manages within specifications.

-Leaderless: individual behaviors and local interactions not directed by central organization or control.
-Emergent: unexpected structure that comes from a system that does not have a direct connection to the system.
-Nonlinear: inputs and outputs are related but not in a linear fashion. Highly sensitive initial and ambient conditions.
-Self-organizing: organization comes from within the system and is nonhierarchical

## Asymmetry

Asymmetry refers to items which display no bilateral or radial symmetry. In economics or game theory, it refers to scenarios in which one or more players have more or less information than one or more others.

## Chaos

A phenomenon seen in dynamical systems, in which the system's future behavior is highly sensitive to the initial conditions of the system. See also butterfly effect.

## Complexity

This term means different things in different disciplines, and is not rigorously defined outside of a specific context. In general, the complexity of a system emerges from the interactions of its interrelated elements as opposed to the characteristics of those elements in and of themselves. Complexity science is the study of such emergent system behavior, and seeks to understand how the complex behavior of a whole system arises from its interacting parts. Complex behavior generally cannot be reduced to, or derived from, the sum of the behavior of the system's components.

## Dynamical System

A system that is described by temporal change of a point in a state space (or phase space). At any given time, the system is in a particular state in its space, and it follows an evolution rule that describes how the system changes states over time. Generally, a continuous dynamical system will be described by differential equations, while a discrete dynamical system will be described by difference equations. Stochastic dynamical systems will have solutions related to a probability distribution, while deterministic dynamical systems will have exact solutions.

## Emergent Behavior

Emergent behaviors are global-level attributes of system that arise from the interactions of the components of the system, and that are not explainable by the behavior of individual components of the system or the sum of the components acting as individuals.

## Entropy

Entropy, in the thermodynamic sense, is the tendency of a system to move from a more ordered state to a less ordered state. In Boltzmann's statistical mechanics, the notion of "order" and "disorder", and thus the definition of entropy, corresponded to the number of possible microstates corresponding to a given macrostate. In information theory, Shannon entropy and Hartley entropy measure the distribution of discrete states in a system. A uniform distribution would have maximum entropy. Shannon entropy measures frequencies of states, while Hartley entropy ignores frequency and only examines the presence of states (out of all possible states).

## Feedback

is a process in which information about the past or the present influences the same phenomenon in the present or future. As part of a chain of cause-and-effect that forms a circuit or loop, the event is said to "feed back" into itself.

## Fitness

In evolutionary biology, fitness is the relative success in reproduction, or occasionally survival, among members of a group of organisms. In evolutionary computation (or genetic algorithms), fitness is typically an externally imposed measure of "goodness" of an individual in the population, where individuals represent candidate solutions to a problem. See also fitness function.

## Fractal

A geometric object or shape which exhibits self-similarity across scales. See also fractal dimension.

## Game Theory

The mathematical study of decision making in situations of cooperation or conflict with multiple actors, each trying to maximize their own gain or utility.

## Hierarchy

Abstractly, a hierarchy can be modelled mathematically as a rooted tree: the root of the tree forms the top level, and the children of a given vertex are at the same level, below their common parent.

## Network

A network (or graph) is a collection of elements, called vertices or nodes, connected by edges or links. Edges typically are either one-way or two-way connections. A network is often represented by an adjacency matrix.

## Occam's Razor

The one with the fewest assumptions should be selected==

## Pheromone

is a secreted or excreted chemical factor that triggers a social response in members of the same species. Pheromones are chemicals capable of acting outside the body of the secreting individual to impact the behavior of the receiving individual.

## Power Law

A power law is a functional relationship between two variables of the form f(x) = \alpha x^{k}. The degree distribution among nodes in growing scale free networks and other phenomena involving preferential attachment, such as continuously self-compounding acquisition proportionate to current assets, create power-law distributions.

## Prisoner’s Dilemma

is a canonical example of a game analyzed in game theory that shows why two purely "rational" individuals might not cooperate, even if it appears that it is in their best interests to do so.

## Resilience

Resilience describes the ability of a system to persist and maintain its core functions and/or purpose in the presence of disturbances, stresses or other changes in its environment.

## Robustness

Robustness describes the ability of a system to maintain a certain behavior, trait, or characteristic regardless of changing environmental conditions. Robustness is often contrasted with optimization, especially in human-constructed systems. This is because the quality of being robust usually requires that one or more components of a system operate at sub-optimal levels in some situations in order to maintain the ability to operate acceptably at any level under most conceivable scenarios. Conversely, a system that is highly optimized typically operates very well under certain conditions but then becomes less than operational if those conditions change.

## Sierpinski Triangle

is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.

## Stigmergy

Stigmergy is a form of self-organization. It produces complex, seemingly intelligent structures, without need for any planning, control, or even direct communication between the agents.

## Stochasticity

A system is whose state is non-deterministic (i.e., "random")

## Superfluid

Superfluidity is a state of matter in which the matter behaves like a fluid with zero viscosity; where it appears to exhibit the ability to self-propel and travel in a way that defies the forces of gravity and surface tension.

## Throughput

The rate of successful delivery in a channel

### CAMP Quotes

You have to play the game to get the results - JP