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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).
The product of 1-D sinc functions readily provides a multivariate sinc function for the square Cartesian grid : sinc C (x, y) = sinc(x) sinc(y), whose Fourier transform is the indicator function of a square in the frequency space (i.e., the brick wall defined in 2-D space).
When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β. Ptolemy's theorem is important in the history of trigonometric identities, as it is how results equivalent to the sum and difference formulas ...
In classic brain theory the summation of electrical inputs to the dendrites and soma (cell body) of a neuron either inhibit the neuron or excite it and set off an action potential down the axon to where it synapses with the next neuron. However, this fails to account for different varieties of synapses beyond the traditional axodendritic (axon ...
According to temporal summation one would expect the inhibitory and excitatory currents to be summed linearly to describe the resulting current entering the cell. However, when inhibitory and excitatory currents are on the soma of the cell, the inhibitory current causes the cell resistance to change (making the cell "leakier"), thereby ...
In mathematics, the Fourier sine and cosine transforms are integral equations that decompose arbitrary functions into a sum of sine waves representing the odd component of the function plus cosine waves representing the even component of the function. The modern Fourier transform concisely contains both the sine and
Zero summation occurs when each cone photoreceptor cell contacts a single ganglion cell via a single bipolar cell. [1] High summation increases sensitivity to light at the expense of visual acuity. Low retinal summation results in high visual acuity, with individual photoreceptor cells sending their own signals.
A trigonometric polynomial can be considered a periodic function on the real line, with period some divisor of , or as a function on the unit circle.. Trigonometric polynomials are dense in the space of continuous functions on the unit circle, with the uniform norm; [4] this is a special case of the Stone–Weierstrass theorem.