Stochastic, from the Greek "Στόχος" which means "aim, guess", means of, relating to, or characterized by conjecture and randomness. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly In Mathematics, a conjecture is a Mathematical statement which appears resourceful but has not been formally proven to be true under the rules of Randomness is a lack of order Purpose, cause, or predictability
A stochastic process is one whose behavior is non-deterministic in that a state does not fully determine its next state. A stochastic process, or sometimes random process, is the counterpart to a deterministic process (or Deterministic system) in Probability theory. Determinism is the philosophical Proposition that every event including human cognition and behaviour decision and action is causally determined Stochastic crafts are complex systems whose practitioners, even if complete experts, cannot guarantee success. Classical examples of this are medicine: a doctor can administer the same treatment to multiple patients suffering from the same symptoms, however, the patients may not all react to the treatment the same way. Medicine is the art and science of healing It encompasses a range of Health care practices evolved to maintain and restore Human Health by the This makes medicine a stochastic process. [1] Additional examples are warfare and rhetoric, where the successes and failures cannot be certainly predicted. Warfare refers to the conduct of conflict between opponents and usually involves escalation of aggression from the proverbial "war of words" between politicians Rhetoric has had many definitions no simple definition can do it justice
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Mathematical theory
In mathematics, specifically in probability theory, the field of stochastic processes has for some decades been a major area of research. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Probability theory is the branch of Mathematics concerned with analysis of random phenomena A stochastic process, or sometimes random process, is the counterpart to a deterministic process (or Deterministic system) in Probability theory. It is often assumed to be related to statistics; this is in fact a mistake, as stochastics are often used in physical systems. So studying stochastics is not the same as studying statistics.
A stochastic matrix is a matrix that has non-negative real entries that sum to 1 in each column. In Mathematics, a stochastic matrix, probability matrix, or transition matrix is used to describe the transitions of a Markov chain. In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally In Mathematics, the real numbers may be described informally in several different ways
Artificial intelligence
In artificial intelligence stochastic programs work by using probabilistic methods to solve problems, as in simulated annealing, stochastic neural networks, stochastic optimization, and genetic algorithms. Simulated annealing (SA is a generic probabilistic Meta-algorithm for the Global optimization problem namely locating a good approximation to the Stochastic neural networks are a type of Artificial neural networks, which is a tool of artificial intelligence. Stochastic optimization (SO methods are optimization Algorithms which incorporate probabilistic (random elements either in the problem data (the A genetic algorithm (GA is a Search technique used in Computing to find exact or Approximate solutions to optimization and Search A problem itself may be stochastic as well, as in planning under uncertainty. A deterministic environment is much simpler for an agent to deal with. Determinism is the philosophical Proposition that every event including human cognition and behaviour decision and action is causally determined
Natural science
An example of a stochastic process in the natural world is pressure in a gas as modeled by the Wiener process. A stochastic process, or sometimes random process, is the counterpart to a deterministic process (or Deterministic system) in Probability theory. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface This page is about the physical properties of gas as a state of matter In Mathematics, the Wiener process is a continuous-time Stochastic process named in honor of Norbert Wiener. Even though (classically speaking) each molecule is moving in a deterministic path, the motion of a collection of them is computationally and practically unpredictable. A large enough set of molecules will exhibit stochastic characteristics, such as filling the container, exerting equal pressure, diffusing along concentration gradients, etc. These are emergent properties of the system. For other uses see Emergence (disambiguation, Emergent, and Emergency.
Biology
In biological systems, introducing stochastic 'noise' has been found to help improve the signal strength of the internal feedback loops for balance and other vestibular communication. Stochastic resonance (also known as SR) is observed when noise added to a system improves the systems performance in some fashion It has been found to help diabetic and stroke patients with balance control. [2]
Geology
Music
In music, stochastic elements are randomly generated elements created by strict mathematical processes. Haematopoiesis (from Ancient Greek haima blood poiesis to make (or hematopoiesis in the United States sometimes also haemopoiesis or A meander in general is a bend in a sinuous watercourse also known as an oxbow loop or simply an Oxbow. Music is an Art form in which the medium is Sound organized in Time. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and
Stochastic processes can be used in music to compose a fixed piece or can be produced in performance. Stochastic music was pioneered by Iannis Xenakis, who used probability, game theory, group theory, set theory, and Boolean algebra, and frequently used computers to produce his scores. Iannis Xenakis (Ιάννης Ξενάκης (May 29 1922 - February 4 2001 was a Greek modernist composer musical theoretician and architect Probability is the likelihood or chance that something is the case or will happen Game theory is a branch of Applied mathematics that is used in the Social sciences (most notably Economics) Biology, Engineering, Group theory is a mathematical discipline the part of Abstract algebra that studies the Algebraic structures known as groups. Boolean algebra (or Boolean logic) is a logical calculus of truth values, developed by George Boole in the late 1830s A computer is a Machine that manipulates data according to a list of instructions. Earlier, John Cage and others had composed aleatoric or indeterminate music, which is created by chance processes but does not have the strict mathematical basis (Cage's Music of Changes, for example, uses a system of charts based on the I-Ching). WikipediaWikiProject Composers#Lead section --> John Milton Cage Jr Aleatoric music (also aleatory music or chance music; from the Latin word alea, meaning " Dice " is Music Indeterminacy in music which began early in the twentieth century in the music of Charles Ives, and was continued in the 1930s by Henry Cowell and carried on by his Ambient 3 Music Of Changes is a 1994 compilation album released on the Virgin Records label part of its ''Ambient'' series. The I Ching ( Wade-Giles) or “Yì Jīng” ( Pinyin) also called “Classic of Changes” or “Book of Changes” is one of the oldest of the
Color reproduction
When color reproductions are made, the image is separated into its component colors by taking multiple photographs filtered for each color. One resultant film or plate represents each of the cyan, magenta, yellow, and black data. Color printing is a binary system, where ink is either present or not present, so all color separations to be printed must be translated into dots at some stage of the workflow. Traditional linescreens which are amplitude modulated had problems with moiré but were used until stochastic screening became available. Halftone is the Reprographic technique that simulates Continuous tone imagery through the use of equally spaced dots of varying size Amplitude modulation ( AM) is a technique used in electronic communication most commonly for transmitting information via a Radio Carrier wave A stochastic (or frequency modulated) dot pattern creates a more photorealistic image.
Language and linguistics
Non-deterministic approaches in language studies are largely inspired by the work of Ferdinand de Saussure. Ferdinand de Saussure (fɛʁdinɑ̃ də soˈsyːʁ ( November 26, 1857 – February 22, 1913) was a Swiss linguist In usage-based linguistic theories, for example, where it is argued that competence, or langue, is based on performance, or parole, in the sense that linguistic knowledge is based on frequency of experience, grammar is often said to be probabilistic and variable rather than fixed and absolute. A performance, in Performing arts, generally comprises an event in which one group of people (the performer or performers behave in a particular way for another group of people Parole may have different meanings depending on the field and judiciary system Probability is the likelihood or chance that something is the case or will happen This is so, because one's competence changes in accordance with one's experience with linguistic units. This way, the frequency of usage-events determines one's knowledge of the language in question. For much later work in this area, see Julia Kristeva on her usage of the 'semiotic,' Luce Irigaray on reverse Heideggerian epistomology, and Pierre Bourdieu on polythetic space for examples of stochastic social science theory. Julia Kristeva (Юлия Кръстева (born 24 June 1941) is a Bulgarian - French Philosopher, Literary critic, Luce Irigaray (born 1932 Belgium) is a French feminist, Philosopher, Linguist, psychoanalytic and cultural theorist Pierre Bourdieu ( August 1, 1930 – January 23, 2002) was an acclaimed French Sociologist and writer known for his
Finance
The financial markets use stochastic models to value options on stock prices, bond prices, and on interest rates, see Markov models. In Mathematics, a Markov chain, named after Andrey Markov, is a Stochastic process with the Markov property. Moreover, it is at the heart of the insurance industry. Insurance, in Law and Economics, is a form of Risk management primarily used to hedge against the Risk of a contingent loss
Not to be confused with stochastic oscillators in Technical Analysis. The stochastic oscillator is a momentum indicator used in Technical analysis, introduced by George Lane in the 1950s to compare the closing price of a Technical analysis is a Financial markets technique that claims the ability to forecast the future direction of security prices through the study of past market
References
- ^ Brad Inwood. Goal and Target in Stoicism [1]. The Journal of Philosophy, Vol. 83, No. 10, Eighty-Third Annual Meeting American Philosophical Association, Eastern Division (Oct. , 1986), pp. 547-556 doi:10. 2307/2026429
- ^ Priplata A. et al. Noise-Enhanced Balance Control in Patients with Diabetes and Patients with Stroke. Ann Neurol 2006;59:4–12. PMID 16287079.
Further reading
- Formalized Music: Thought and Mathematics in Composition by Iannis Xenakis, ISBN 1-57647-079-2
- Frequency and the Emergence of Linguistic Structure by Joan Bybee and Paul Hopper (eds. Iannis Xenakis (Ιάννης Ξενάκης (May 29 1922 - February 4 2001 was a Greek modernist composer musical theoretician and architect ), ISBN 1-58811-028-1/ISBN 90-272-2948-1 (Eur. )
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