Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Discrete mathematicsDiscrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry.
Evidence (law)The law of evidence, also known as the rules of evidence, encompasses the rules and legal principles that govern the proof of facts in a legal proceeding. These rules determine what evidence must or must not be considered by the trier of fact in reaching its decision. The trier of fact is a judge in bench trials, or the jury in any cases involving a jury. The law of evidence is also concerned with the quantum (amount), quality, and type of proof needed to prevail in litigation.
Non-uniform discrete Fourier transformIn applied mathematics, the nonuniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both). It is a generalization of the shifted DFT. It has important applications in signal processing, magnetic resonance imaging, and the numerical solution of partial differential equations.
Circumstantial evidenceCircumstantial evidence is evidence that relies on an inference to connect it to a conclusion of fact—such as a fingerprint at the scene of a crime. By contrast, direct evidence supports the truth of an assertion directly—i.e., without need for any additional evidence or inference. On its own, circumstantial evidence allows for more than one explanation. Different pieces of circumstantial evidence may be required, so that each corroborates the conclusions drawn from the others.
AttentionAttention is the concentration of awareness on some phenomenon to the exclusion of other stimuli. It is a process of selectively concentrating on a discrete aspect of information, whether considered subjective or objective. William James (1890) wrote that "Attention is the taking possession by the mind, in clear and vivid form, of one out of what seem several simultaneously possible objects or trains of thought. Focalization, concentration, of consciousness are of its essence.
Computer visionComputer vision tasks include methods for , , and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical or symbolic information, e.g. in the forms of decisions. Understanding in this context means the transformation of visual images (the input to the retina in the human analog) into descriptions of the world that make sense to thought processes and can elicit appropriate action.
Randomized controlled trialA randomized controlled trial (or randomized control trial; RCT) is a form of scientific experiment used to control factors not under direct experimental control. Examples of RCTs are clinical trials that compare the effects of drugs, surgical techniques, medical devices, diagnostic procedures or other medical treatments. Participants who enroll in RCTs differ from one another in known and unknown ways that can influence study outcomes, and yet cannot be directly controlled.
Sampling (statistics)In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.
Continuous functionIn mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is .
