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Mathematical Principles Of Reinforcement
The mathematical principles of reinforcement (MPR) constitute of a set of mathematical equations set forth by Peter Killeen and his colleagues attempting to describe and predict the most fundamental aspects of behavior (Killeen & Sitomer, 2003). The three key principles of MPR, arousal, constraint, and coupling, describe how incentives motivate responding, how time constrains it, and how reinforcers become associated with specific responses, respectively. Mathematical models are provided for these basic principles in order to articulate the necessary detail of actual data. First principle: arousal The first basic principle of MPR is arousal. Arousal refers to the activation of behavior by the presentation of incentives. An increase in activity level following repeated presentations of incentives is a fundamental aspect of conditioning. Killeen, Hanson, and Osborne (1978) proposed that adjunctive (or schedule induced) behaviors are normally occurring parts of an organism's repert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematical Equation
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. The " =" symbol, which appears in every equatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Epoch
In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided by congruity, or by following conventions understood from the epoch in question. The epoch moment or date is usually defined from a specific, clear event of change, an ''epoch event''. In a more gradual change, a deciding moment is chosen when the ''epoch criterion'' was reached. Calendar eras Pre-modern eras * The Yoruba calendar (''Kọ́jọ́dá'') uses 8042 BC as the epoch, regarded as the year of the creation of Ile-Ife by the god Obatala, also regarded as the creation of the earth. * '' Anno Mundi'' it. "Year of the World"(years since the creation of the world) is used in ** the Byzantine calendar (5509 BC). ** the Hebrew calendar (3761 BC). * The Mesoamerican Long Count Calendar uses the creation of the fourth worl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Power Series
In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots where ''a_n'' represents the coefficient of the ''n''th term and ''c'' is a constant called the ''center'' of the series. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, the center ''c'' is equal to zero, for instance for Maclaurin series. In such cases, the power series takes the simpler form \sum_^\infty a_n x^n = a_0 + a_1 x + a_2 x^2 + \dots. The partial sums of a power series are polynomials, the partial sums of the Taylor series of an analytic function are a sequence of converging polynomial approximations to the function at the center, and a converging power series can be seen as a kind of generalized polynom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Probability
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."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . 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 formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fundamental Equation
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus. The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory. Some of these are classification theorems of objects which are mainly dealt with in the field. For instance, the fundamental theorem of curves describes classification of regular curves in space up to translation and rotation. Likewise, the mathematical literature sometimes refers to the fundamental lemma of a field. The term lemma is conventionally used to denote a proven proposition which is used as a stepping stone to a larger result, rather than as a useful statement in-and-of itself. Fundamental theorems of mathematical topics * Fundamental theorem of algebra * Fundamental theorem of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Coefficient
In mathematics, a coefficient is a Factor (arithmetic), multiplicative factor involved in some Summand, term of a polynomial, a series (mathematics), series, or any other type of expression (mathematics), expression. It may be a Dimensionless quantity, number without units, in which case it is known as a numerical factor. It may also be a constant (mathematics), constant with units of measurement, in which it is known as a constant multiplier. In general, coefficients may be any mathematical expression, expression (including Variable (mathematics), variables such as , and ). When the combination of variables and constants is not necessarily involved in a product (mathematics), product, it may be called a ''parameter''. For example, the polynomial 2x^2-x+3 has coefficients 2, −1, and 3, and the powers of the variable x in the polynomial ax^2+bx+c have coefficient parameters a, b, and c. A , also known as constant term or simply constant, is a quantity either implicitly attach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Reinforcement
In Behaviorism, behavioral psychology, reinforcement refers to consequences that increase the likelihood of an organism's future behavior, typically in the presence of a particular ''Antecedent (behavioral psychology), antecedent stimulus''. For example, a rat can be trained to push a lever to receive food whenever a light is turned on; in this example, the light is the antecedent stimulus, the lever pushing is the ''operant behavior'', and the food is the ''reinforcer''. Likewise, a student that receives attention and praise when answering a teacher's question will be more likely to answer future questions in class; the teacher's question is the antecedent, the student's response is the behavior, and the praise and attention are the reinforcements. Punishment (psychology), Punishment is the inverse to reinforcement, referring to any behavior that decreases the likelihood that a response will occur. In operant conditioning terms, punishment does not need to involve any type of p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Subinterval
In mathematics, a real interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive or negative infinity, indicating the interval extends without a bound. A real interval can contain neither endpoint, either endpoint, or both endpoints, excluding any endpoint which is infinite. For example, the set of real numbers consisting of , , and all numbers in between is an interval, denoted and called the unit interval; the set of all positive real numbers is an interval, denoted ; the set of all real numbers is an interval, denoted ; and any single real number is an interval, denoted . Intervals are ubiquitous in mathematical analysis. For example, they occur implicitly in the epsilon-delta definition of continuity; the intermediate value theorem asserts that the image of an interval by a continuous function is an interval; integrals of real functions are defined over an interval; etc. Interval arithmeti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Rate Of Reinforcement
In behaviorism, rate of reinforcement is number of reinforcements per time, usually per minute. Symbol of this rate is usually ''Rf''. Its first major exponent was B.F. Skinner (1939). It is used in the Matching Law. ''Rf'' = ''# of reinforcements/unit of time'' = ''SR+''/''t'' See also * Rate of response References * Herrnstein, R.J. (1961). Relative and absolute strength of responses as a function of frequency of reinforcement. ''Journal of the Experimental Analysis of Behaviour'', 4, 267–272. * Herrnstein, R.J. (1970). On the law of effect. ''Journal of the Experimental Analysis of Behavior'', 13, 243–266. * Skinner, B.F. (1938). The behavior of organisms: An experimental analysis. , . Behaviorism Quantitative analysis of behavior Reinforcement In Behaviorism, behavioral psychology, reinforcement refers to consequences that increase the likelihood of an organism's future behavior, typically in the presence of a particular ''Antecedent (behavioral psychology), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Incentive
In general, incentives are anything that persuade a person or organization to alter their behavior to produce the desired outcome. The laws of economists and of behavior state that higher incentives amount to greater levels of effort and therefore higher levels of performance. For comparison, a disincentive is something that discourages from certain actions. Divisions An incentive is a powerful tool to influence certain desired behaviors or action often adopted by governments and businesses. Incentives can be broadly broken down into two categories: intrinsic incentives and extrinsic incentives. Overall, both types of incentives can be powerful tools often employ to increase effort and higher performance according to the "law of behavior." Incentives are most studied in the area of personnel economics where economic analysts, such as those who take part in human resources management practices, focus on how firms make employees more motivated, through pay and career concerns, Fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Asymptote
In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity. The word asymptote is derived from the Greek ἀσύμπτωτος (''asumptōtos'') which means "not falling together", from ἀ priv. + σύν "together" + πτωτ-ός "fallen". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve. There are three kinds of asymptotes: ''horizontal'', ''vertical'' and ''oblique''. For curves given by the graph of a function , horizontal asymptotes are horizontal lines that the graph of the function approaches as ''x'' tends to Vertical asymptotes are vertical lines near which the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
