Complex systems in the context of "Herbert A. Simon"

Regulation is the management of complex systems according to a set of rules and trends. In systems theory, these types of rules exist in various fields of biology and society, but the term has slightly different meanings according to context. For example:

• in government, typically regulation (or its plural) refers to the delegated legislation which is adopted to enforce primary legislation; including land-use regulation
• in economy: regulatory economics
• in finance: financial regulation
• in business, industry self-regulation occurs through self-regulatory organizations and trade associations which allow industries to set and enforce rules with less government involvement; and,
• in biology, gene regulation and metabolic regulation allow living organisms to adapt to their environment and maintain homeostasis;
• in psychology, self-regulation theory is the study of how individuals regulate their thoughts and behaviors to reach goals.

Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.

Holism in science, holistic science, or methodological holism is an approach to research that emphasizes the study of complex systems. Systems are approached as coherent wholes whose component parts are best understood in context and in relation to both each other and to the whole. Holism typically stands in contrast with reductionism, which describes systems by dividing them into smaller components in order to understand them through their elemental properties.

The holism-individualism dichotomy is especially evident in conflicting interpretations of experimental findings across the social sciences, and reflects whether behavioural analysis begins at the systemic, macro-level (ie. derived from social relations) or the component micro-level (ie. derived from individual agents).

Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or are not caused deterministically.

It is the opposite of determinism and related to chance. It is highly relevant to the philosophical problem of free will, particularly in the form of metaphysical libertarianism. In science, most specifically quantum theory in physics, indeterminism is the belief that no event is certain and the entire outcome of anything is probabilistic. Heisenberg's uncertainty principle and the "Born rule", proposed by Max Born, are often starting points in support of the indeterministic nature of the universe. Indeterminism is also asserted by Sir Arthur Eddington, and Murray Gell-Mann. Indeterminism has been promoted by the French biologist Jacques Monod's essay "Chance and Necessity".The physicist-chemist Ilya Prigogine argued for indeterminism in complex systems.

Structural functionalism, or simply functionalism, is "a framework for building theory that sees society as a complex system whose parts work together to promote solidarity and stability".

This approach looks at society through a macro-level orientation, which is a broad focus on the social structures that shape society as a whole, and believes that society has evolved like organisms. This approach looks at both social structure and social functions. Functionalism addresses society as a whole in terms of the function of its constituent elements; namely norms, customs, traditions, and institutions.

Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanical force fields. MD simulations are widely applied in chemical physics, materials science, and biophysics.

Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such complex systems analytically; MD simulation circumvents this problem by using numerical methods. However, long MD simulations are mathematically ill-conditioned, generating cumulative errors in numerical integration that can be minimized with proper selection of algorithms and parameters, but not eliminated.

In cybernetics, the term variety denotes the total number of distinguishable elements of a set, most often the set of states, inputs, or outputs of a finite-state machine or transformation, or the binary logarithm of the same quantity. Variety is used in cybernetics as an information theory that is easily related to deterministic finite automata, and less formally as a conceptual tool for thinking about organization, regulation, and stability. It is an early theory of complexity in automata, complex systems, and operations research.