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Steven's Power Law
Stevens' power law is an empirical relationship in psychophysics between an increased intensity or strength in a physical stimulus and the perceived magnitude increase in the sensation created by the stimulus. It is often considered to supersede the Weber–Fechner law, which is based on a logarithmic relationship between stimulus and sensation, because the power law describes a wider range of sensory comparisons, down to zero intensity. The theory is named after psychophysicist Stanley Smith Stevens (1906–1973). Although the idea of a power law had been suggested by 19th-century researchers, Stevens is credited with reviving the law and publishing a body of psychophysical data to support it in 1957. The general form of the law is :\psi(I) = k I ^a, where ''I'' is the intensity or strength of the stimulus in physical units (energy, weight, pressure, mixture proportions, etc.), ψ(''I'') is the magnitude of the sensation evoked by the stimulus, ''a'' is an exponent that depend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Source
A point source is a single identifiable ''localized'' source of something. A point source has a negligible extent, distinguishing it from other source geometries. Sources are called point sources because, in mathematical modeling, these sources can usually be approximated as a mathematical point to simplify analysis. The actual source need not be physically small if its size is negligible relative to other length scales in the problem. For example, in astronomy, stars are routinely treated as point sources, even though they are in actuality much larger than the Earth. In three dimensions, the density of something leaving a point source decreases in proportion to the inverse square of the distance from the source, if the distribution is isotropic, and there is no absorption or other loss. Mathematics In mathematics, a point source is a singularity from which flux or flow is emanating. Although singularities such as this do not exist in the observable universe, mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale (ratio)
The scale ratio of a model represents the proportional ratio of a linear dimension of the model to the same feature of the original. Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. In such cases the scale is dimensionless and exact throughout the model or drawing. The scale can be expressed in four ways: in words (a lexical scale), as a ratio, as a fraction and as a graphical (bar) scale. Thus on an architect's drawing one might read 'one centimeter to one meter', 1:100, 1/100, or . A bar scale would also normally appear on the drawing. Colon may also be substituted with a specific, slightly raised ratio symbol , ie. . General representation Generally, a representation may involve more than one scale at the same time. For example, a drawing showing a new road in elevation might use different horizontal and vertical scales. An elevation of a bridge might be annotated with arrows with a length proportion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Psychology
Mathematical psychology is an approach to psychology, psychological research that is based on mathematical modeling of perceptual, thought, Cognition, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving Hypothesis, hypotheses that are more exact and thus yield stricter empirical validations. There are five major research areas in mathematical psychology: learning and memory, perception and psychophysics, choice and decision-making, language and Thought, thinking, and measurement and Feature scaling, scaling. Although psychology, as an independent subject of science, is a more recent discipline than physics, the application of mathematics to psychology has been done in the hope of emulating the success of this approach in the Physical Sciences, physical sciences, which dat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychophysics
Psychophysics is the field of psychology which quantitatively investigates the relationship between physical stimulus (physiology), stimuli and the sensation (psychology), sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and Sensation (psychology), sensation" or, more completely, as "the analysis of perceptual processes by studying the effect on a subject's experience or behaviour of systematically varying the properties of a stimulus along one or more physical dimensions". ''Psychophysics'' also refers to a general class of methods that can be applied to study a perceptual system. Modern applications rely heavily on threshold measurement, ideal observer analysis, and Detection theory, signal detection theory. Psychophysics has widespread and important practical applications. For instance, in the realm of digital signal processing, insights from psychophysics have guided the development of models a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Laws
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent: one quantity varies as a power of another. The change is independent of the initial size of those quantities. For instance, the area of a square has a power law relationship with the length of its side, since if the length is doubled, the area is multiplied by 2, while if the length is tripled, the area is multiplied by 3, and so on. Empirical examples The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, cloud sizes, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words in most languages, frequencies of family names, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Behavioral Concepts
Behavior (American English) or behaviour (British English) is the range of actions of individuals, organisms, systems or artificial entities in some environment. These systems can include other systems or organisms as well as the inanimate physical environment. It is the computed response of the system or organism to various stimuli or inputs, whether internal or external, conscious or subconscious, overt or covert, and voluntary or involuntary. While some behavior is produced in response to an organism's environment (extrinsic motivation), behavior can also be the product of intrinsic motivation, also referred to as "agency" or "free will". Taking a behavior informatics perspective, a behavior consists of actor, operation, interactions, and their properties. This can be represented as a behavior vector. Models Biology Definition Behavior may be defined as "the internally coordinated responses (actions or inactions) of whole living organisms (individuals or groups) to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neil Smelser
Neil Joseph Smelser (1930–2017) was an American sociologist who served as professor of sociology at the University of California, Berkeley. He was an active researcher from 1958 to 1994. His research was on collective behavior, sociological theory, economic sociology, sociology of education, social change, and comparative methods. Among many lifetime achievements, Smelser "laid the foundations for economic sociology." Biography Smelser was born in Kahoka, Missouri, on July 22, 1930. He received his undergraduate degree from Harvard University in 1952 in the Department of Social Relations. From 1952 to 1954, he was a Rhodes scholar at Magdalen College, Oxford, where he studied economics, philosophy, and politics and was awarded a Bachelor of Arts degree. During his first year of graduate school at the age of 24, he co-authored ''Economy and Society'' with Talcott Parsons, first published in 1956. He earned his Doctor of Philosophy degree in sociology from Harvard in 1958, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sone
The sone () is a unit of loudness, the subjective perception of sound pressure. The study of perceived loudness is included in the topic of psychoacoustics and employs methods of psychophysics. Doubling the perceived loudness doubles the sone value. Proposed by Stanley Smith Stevens in 1936, it is not an SI unit. Definition and conversions According to Stevens' definition, a loudness of 1 sone is equivalent to 40 phons (a 1 kHz tone at 40 dB SPL). The phons scale aligns with dB, not with loudness, so the sone and phon scales are not proportional. Rather, the loudness in sones is, at least very nearly, a power law function of the signal intensity, with an exponent of 0.3. With this exponent, each 10 phon increase (or 10 dB at 1 kHz) produces almost exactly a doubling of the loudness in sones. : At frequencies other than 1 kHz, the loudness level in phons is calibrated according to the frequency response of human hearing, via a set of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perception
Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous system, which in turn result from physical or chemical stimulation of the sensory system.Goldstein (2009) pp. 5–7 Vision involves light striking the retina of the eye; smell is mediated by odor molecules; and hearing involves pressure waves. Perception is not only the passive receipt of these signals, but it is also shaped by the recipient's learning, memory, expectation, and attention. Gregory, Richard. "Perception" in Gregory, Zangwill (1987) pp. 598–601. Sensory input is a process that transforms this low-level information to higher-level information (e.g., extracts shapes for object recognition). The following process connects a person's concepts and expectations (or knowledge) with restorative and selective mechanisms, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Detection Theory
Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called Stimulus (psychology), stimulus in living organisms, Signal (electronics), signal in machines) and random patterns that distract from the information (called Noise (electronics), noise, consisting of background stimuli and random activity of the detection machine and of the nervous system of the operator). In the field of electronics, signal recovery is the separation of such patterns from a disguising background. According to the theory, there are a number of determiners of how a detecting system will detect a signal, and where its threshold levels will be. The theory can explain how changing the threshold will affect the ability to discern, often exposing how adapted the system is to the task, purpose or goal at which it is aimed. When the detecting system is a human being, characteristics such as experience, expectations, physiological sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiomatic System
In mathematics and logic, an axiomatic system is a set of formal statements (i.e. axioms) used to logically derive other statements such as lemmas or theorems. A proof within an axiom system is a sequence of deductive steps that establishes a new statement as a consequence of the axioms. An axiom system is called complete with respect to a property if every formula with the property can be derived using the axioms. The more general term theory is at times used to refer to an axiomatic system and all its derived theorems. In its pure form, an axiom system is effectively a syntactic construct and does not by itself refer to (or depend on) a formal structure, although axioms are often defined for that purpose. The more modern field of model theory refers to mathematical structures. The relationship between an axiom systems and the models that correspond to it is often a major issue of interest. Properties Four typical properties of an axiom system are consistency, relativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportionality (mathematics)
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called ''coefficient of proportionality'' (or ''proportionality constant'') and its reciprocal is known as ''constant of normalization'' (or ''normalizing constant''). Two sequences are inversely proportional if corresponding elements have a constant product. Two functions f(x) and g(x) are ''proportional'' if their ratio \frac is a constant function. If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., (for details see Ratio). Proportionality is closely related to ''linearity''. Direct proportionality Given an independent variable ''x'' and a dependent variable ''y'', ''y'' is directly proportional to ''x'' if there is a positive constant ''k'' such that: : y = kx The relation is oft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
