Complex systems in the context of Emergence

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.

Equifinality is the principle that in open systems a given end state can be reached by many potential means. The term and concept is due to the German Hans Driesch, the developmental biologist, later applied by the Austrian Ludwig von Bertalanffy, the founder of general systems theory, and by William T. Powers, the founder of perceptual control theory. Driesch and von Bertalanffy prefer this term, in contrast to "goal", in describing complex systems' similar or convergent behavior. Powers simply emphasised the flexibility of response, since it emphasizes that the same end state may be achieved via many different paths or trajectories.

In closed systems, a direct cause-and-effect relationship exists between the initial condition and the final state of the system: When a computer's 'on' switch is pushed, the system powers up. Open systems (such as biological and social systems), however, operate quite differently. The idea of equifinality suggests that similar results may be achieved with different initial conditions and in many different ways. This phenomenon has also been referred to as isotelesis (from Greek ἴσος isos "equal" and τέλεσις telesis: "the intelligent direction of effort toward the achievement of an end") when in games involving superrationality.

Regime shifts are large, abrupt, persistent changes in the structure and function of ecosystems, the climate, financial systems or other complex systems. A regime is a characteristic behaviour of a system which is maintained by mutually reinforced processes or feedbacks. Regimes are considered persistent relative to the time period over which the shift occurs. The change of regimes, or the shift, usually occurs when a smooth change in an internal process (feedback) or a single disturbance (external shocks) triggers a completely different system behavior. Although such non-linear changes have been widely studied in different disciplines ranging from atoms to climate dynamics, regime shifts have gained importance in ecology because they can substantially affect the flow of ecosystem services that societies rely upon, such as provision of food, clean water or climate regulation. Moreover, regime shift occurrence is expected to increase as human influence on the planet increases – the Anthropocene – including current trends on human induced climate change and biodiversity loss. When regime shifts are associated with a critical or bifurcation point, they may also be referred to as critical transitions.

Viscount Ilya Romanovich Prigogine (/prɪˈɡoʊʒiːn/; Russian: Илья́ Рома́нович Приго́жин; 25 January [O.S. 12 January] 1917 – 28 May 2003) was a Belgian physical chemist of Russian-Jewish origin, noted for his work on dissipative structures, complex systems, and irreversibility.

Prigogine's work most notably earned him the 1977 Nobel Prize in Chemistry “for his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures”, as well as the Francqui Prize in 1955, and the Rumford Medal in 1976.

Herbert Alexander Simon (June 15, 1916 – February 9, 2001) was an American scholar whose work influenced the fields of computer science, economics, and cognitive psychology. His primary research interest was decision-making within organizations and he is best known for the theories of "bounded rationality" and "satisficing". He received the Turing Award in 1975 and the Nobel Memorial Prize in Economic Sciences in 1978. His research was noted for its interdisciplinary nature, spanning the fields of cognitive science, computer science, public administration, management, and political science. He was at Carnegie Mellon University for most of his career, from 1949 to 2001, where he helped found the Carnegie Mellon School of Computer Science, one of the first such departments in the world.

Notably, Simon was among the pioneers of several modern-day scientific domains such as artificial intelligence, information processing, decision-making, problem-solving, organization theory, and complex systems. He was among the earliest to analyze the architecture of complexity and to propose a preferential attachment mechanism to explain power law distributions.