Search results
Results from the WOW.Com Content Network
An example where convolutions of generating functions are useful allows us to solve for a specific closed-form function representing the ordinary generating function for the Catalan numbers, C n. In particular, this sequence has the combinatorial interpretation as being the number of ways to insert parentheses into the product x 0 · x 1 ·⋯ ...
Central pattern generators (CPGs) are self-organizing biological neural circuits [1] [2] that produce rhythmic outputs in the absence of rhythmic input. [3] [4] [5] They are the source of the tightly-coupled patterns of neural activity that drive rhythmic and stereotyped motor behaviors like walking, swimming, breathing, or chewing.
Other generating functions of random variables include the moment-generating function, the characteristic function and the cumulant generating function. The probability generating function is also equivalent to the factorial moment generating function , which as E [ z X ] {\displaystyle \operatorname {E} \left[z^{X}\right]} can also be ...
A receptor potential can also cause the release of neurotransmitters from one cell that will act on another cell, generating an action potential in the second cell. [4] The magnitude of the receptor potential determines the frequency with which action potentials are generated and is controlled by adaptation, stimulus strength, and temporal ...
In statistics and in empirical sciences, a data generating process is a process in the real world that "generates" the data one is interested in. [1] This process encompasses the underlying mechanisms, factors, and randomness that contribute to the production of observed data.
Consider the problem of distributing objects given by a generating function into a set of n slots, where a permutation group G of degree n acts on the slots to create an equivalence relation of filled slot configurations, and asking about the generating function of the configurations by weight of the configurations with respect to this equivalence relation, where the weight of a configuration ...
Pages for logged out editors learn more. Contributions; Talk; Examples of generating functions
Consistent with this, Luce (1990, p. 73) observed that "by introducing contexts such as background noise in loudness judgements, the shape of the magnitude estimation functions certainly deviates sharply from a power function". Indeed, nearly all sensory judgments can be changed by the context in which a stimulus is perceived.