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Summation, which includes both spatial summation and temporal summation, is the process that determines whether or not an action potential will be generated by the combined effects of excitatory and inhibitory signals, both from multiple simultaneous inputs (spatial summation), and from repeated inputs (temporal summation).
In 2004, the BrainGate pilot clinical trial was initiated to "test the safety and feasibility of a neural interface system based on an intracortical 100-electrode silicon recording array". This initiative has been successful in advancement of BCIs and in 2011, published data showing long term computer control in a patient with tetraplegia ...
This is when the likelihood of the neuron to reach its threshold potential for the signal to propagate to the next neuron decreases. This phenomenon is typically observed as the spectral intensity decreases from the summation of these neurons firing, which can be utilized to differentiate cognitive function or neural isolation.
Hence, the function of coincidence detection is to reduce the jitter caused by spontaneous neuronal activity, and while random sub-threshold stimulations from cells may not often fire coincidentally, coincident synaptic inputs derived from a unitary external stimulus ensure that a target neuron will fire as a result of the stimulus.
The sinc function for a non-Cartesian lattice (e.g., hexagonal lattice) is a function whose Fourier transform is the indicator function of the Brillouin zone of that lattice. For example, the sinc function for the hexagonal lattice is a function whose Fourier transform is the indicator function of the unit hexagon in the frequency space. For a ...
Summation by parts is frequently used to prove Abel's theorem and Dirichlet's test. One can also use this technique to prove Abel's test: If is a convergent series, and a bounded monotone sequence, then = = converges. Proof of Abel's test.
In mathematics, Dirichlet's test is a method of testing for the convergence of a series that is especially useful for proving conditional convergence. It is named after its author Peter Gustav Lejeune Dirichlet , and was published posthumously in the Journal de Mathématiques Pures et Appliquées in 1862.
Abel's uniform convergence test is a criterion for the uniform convergence of a series of functions or an improper integration of functions dependent on parameters. It is related to Abel's test for the convergence of an ordinary series of real numbers, and the proof relies on the same technique of summation by parts. The test is as follows.