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Basic ways that neurons can interact with each other when converting input to output. 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 ...
The two ways that synaptic potentials can add up to potentially form an action potential are spatial summation and temporal summation. [5] Spatial summation refers to several excitatory stimuli from different synapses converging on the same postsynaptic neuron at the same time to reach the threshold needed to reach an action potential.
Temporal summation means that the effects of impulses received at the same place can add up if the impulses are received in close temporal succession. Thus the neuron may fire when multiple impulses are received, even if each impulse on its own would not be sufficient to cause firing.
Bernard Katz pioneered the study of these mEPSPs at the neuromuscular junction (often called miniature end-plate potentials [6]) in 1951, revealing the quantal nature of synaptic transmission. Quantal size can then be defined as the synaptic response to the release of neurotransmitter from a single vesicle, while quantal content is the number ...
Since the Gibbs phenomenon comes from undershooting, it may be eliminated by using kernels that are never negative, such as the Fejér kernel. [12] [13]In practice, the difficulties associated with the Gibbs phenomenon can be ameliorated by using a smoother method of Fourier series summation, such as Fejér summation or Riesz summation, or by using sigma-approximation.
It is an interpolating function, i.e., sinc(0) = 1, and sinc(k) = 0 for nonzero integer k. The functions x k (t) = sinc(t − k) (k integer) form an orthonormal basis for bandlimited functions in the function space L 2 (R), with highest angular frequency ω H = π (that is, highest cycle frequency f H = 1 / 2 ). Other properties of the ...
Holonomic brain theory is a branch of neuroscience investigating the idea that consciousness is formed by quantum effects in or between brain cells. Holonomic refers to representations in a Hilbert phase space defined by both spectral and space-time coordinates. [1]
A closely related summation method, also called Mittag-Leffler summation, is given as follows (Sansone & Gerretsen 1960). Suppose that the Borel transform B 1 y ( z ) {\displaystyle {\mathcal {B}}_{1}y(z)} converges to an analytic function near 0 that can be analytically continued along the positive real axis to a function growing sufficiently ...