Brouwer fixed-point theoremBrouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function mapping a nonempty compact convex set to itself there is a point such that . The simplest forms of Brouwer's theorem are for continuous functions from a closed interval in the real numbers to itself or from a closed disk to itself. A more general form than the latter is for continuous functions from a nonempty convex compact subset of Euclidean space to itself.
Extended real number lineIn mathematics, the affinely extended real number system is obtained from the real number system by adding two infinity elements: and where the infinities are treated as actual numbers. It is useful in describing the algebra on infinities and the various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration. The affinely extended real number system is denoted or or It is the Dedekind–MacNeille completion of the real numbers.
Arbitrary-precision arithmeticIn computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision.
Mean absolute errorIn statistics, mean absolute error (MAE) is a measure of errors between paired observations expressing the same phenomenon. Examples of Y versus X include comparisons of predicted versus observed, subsequent time versus initial time, and one technique of measurement versus an alternative technique of measurement. MAE is calculated as the sum of absolute errors divided by the sample size: It is thus an arithmetic average of the absolute errors , where is the prediction and the true value.
Real analysisIn mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability. Real analysis is distinguished from complex analysis, which deals with the study of complex numbers and their functions.
Interpersonal communicationInterpersonal communication is an exchange of information between two or more people. It is also an area of research that seeks to understand how humans use verbal and nonverbal cues to accomplish a number of personal and relational goals. Interpersonal communication research addresses at least six categories of inquiry: 1) how humans adjust and adapt their verbal communication and nonverbal communication during face-to-face communication; 2) how messages are produced; 3) how uncertainty influences behavior and information-management strategies; 4) deceptive communication; 5) relational dialectics; and 6) social interactions that are mediated by technology.
Round-off errorIn computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them. This is a form of quantization error.
Least absolute deviationsLeast absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical optimization technique based on minimizing the sum of absolute deviations (also sum of absolute residuals or sum of absolute errors) or the L1 norm of such values. It is analogous to the least squares technique, except that it is based on absolute values instead of squared values.
Accuracy and precisionAccuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements (observations or readings) are to their true value, while precision is how close the measurements are to each other. In other words, precision is a description of random errors, a measure of statistical variability. Accuracy has two definitions: More commonly, it is a description of only systematic errors, a measure of statistical bias of a given measure of central tendency; low accuracy causes a difference between a result and a true value; ISO calls this trueness.
Communication studiesCommunication studies or communication science is an academic discipline that deals with processes of human communication and behavior, patterns of communication in interpersonal relationships, social interactions and communication in different cultures. Communication is commonly defined as giving, receiving or exchanging ideas, information, signals or messages through appropriate media, enabling individuals or groups to persuade, to seek information, to give information or to express emotions effectively.
Nonverbal communicationNonverbal communication (NVC) is the transmission of messages or signals through a nonverbal platform such as eye contact, facial expressions, gestures, posture, use of objects and body language. It includes the use of social cues, kinesics, distance (proxemics) and physical environments/appearance, of voice (paralanguage) and of touch (haptics). A signal has three different parts to it, including the basic signal, what the signal is trying to convey, and how it is interpreted.
Mean percentage errorIn statistics, the mean percentage error (MPE) is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast. The formula for the mean percentage error is: where at is the actual value of the quantity being forecast, ft is the forecast, and n is the number of different times for which the variable is forecast. Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result the formula can be used as a measure of the bias in the forecasts.
