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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 r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Mathematical Equation
In mathematics, an equation is a 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. An equation is written as two expressions, connected b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 behavioral psychology, reinforcement is a consequence applied that will strengthen an organism's future behavior whenever that behavior is preceded by a specific antecedent stimulus. This strengthening effect may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Exponential Function
The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to opine that the exponential function is "the most important function in mathematics". The exponential function satisfies the exponentiation identity e^ = e^x e^y \text x,y\in\mathbb, which, along with the definition e = \exp(1), shows that e^n=\underbrace_ for posi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."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, . The higher the probability of an event, the more likely it is that the event will occur. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 describe classification of regular curves in space up to translation, 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 algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves variables, they may also be called parameters. 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. The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the number 3 and the parameter ''c'', respectively. The coefficient attached to the highest degree of the variable in a polynomial is referred to as the leading coefficient. For example, in the expressions above, the leading coefficients are 2 and ''a'', respectively. Terminology and definition In mathematics, a coefficient is a multiplicative factor in some ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Reinforcement
In behavioral psychology, reinforcement is a consequence applied that will strengthen an organism's future behavior whenever that behavior is preceded by a specific antecedent stimulus. This strengthening effect may be measured as a higher frequency of behavior (e.g., pulling a lever more frequently), longer duration (e.g., pulling a lever for longer periods of time), greater magnitude (e.g., pulling a lever with greater force), or shorter latency (e.g., pulling a lever more quickly following the antecedent stimulus). The model of self-regulation has three main aspects of human behavior, which are self-awareness, self-reflection, and self-regulation. Reinforcements traditionally align with self-regulation. The behavior can be influenced by the consequence but behavior also needs antecedents. There are four types of reinforcement: positive reinforcement, negative reinforcement, extinction, and punishment. Positive reinforcement is the application of a positive reinforcer. Nega ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Subinterval
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers satisfying is an interval which contains , , and all numbers in between. Other examples of intervals are the set of numbers such that , the set of all real numbers \R, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element). Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure. Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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'' (years since the creation of the world) is used in the Byzantine calendar (5509 BC). * ''Anno Mundi'' (years since the creation of the world) as used in the Hebrew calendar (3761 BC). * Olympiads, the ancient Greek era of four-yea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Incentive
In general, incentives are anything that persuade a person to alter their behaviour. It is emphasised that incentives matter by the basic law of economists and the laws of behaviour, which state that higher incentives amount to greater levels of effort and therefore, higher levels of performance. Divisions Incentives can be broken down into two categories; intrinsic incentives and extrinsic incentives. The motivation of people's behaviour comes from within. In activities, they are often motivated by the task itself or the internal reward rather than the external reward. There are many internal rewards, for example, participating in activities can satisfy people's sense of achievement and bring them positive emotions. An intrinsic incentive is when a person is motivated to act in a certain way for their own personal satisfaction. This means that when a person is intrinsically incentivised, they perform a certain task to please themselves and are not seeking any external reward, no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Theory
A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings. In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction (" falsify") of it. Scientific theories are the most reliable, rigorous, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |