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Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, 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).
In mathematics, computer science and network science, network theory is a part of graph theory.It defines networks as graphs where the vertices or edges possess attributes. . Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) compone
Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" [1] or, more completely, as "the analysis of perceptual processes by studying the effect on a subject's experience or behaviour of systematically varying the ...
The main difference between modular decomposition and power graph analysis is the emphasis of power graph analysis in decomposing graphs not only using modules of nodes but also modules of edges (cliques, bicliques). Indeed, power graph analysis can be seen as a loss-less simultaneous clustering of both nodes and edges.
A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are spatial elements associated with geometric objects, i.e., the nodes are located in a space equipped with a certain metric.
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, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...
Graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for an undirected simple graph) or is incident on (for an undirected multigraph) {,} = {} which is not in {{,},}. To allow loops, the definitions must be expanded.
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters.