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Gamma waves. A gamma wave or gamma rhythm is a pattern of neural oscillation in humans with a frequency between 30 and 100 Hz, the 40 Hz point being of particular interest. [1] Gamma waves with frequencies between 30 and 70 hertz may be classified as low gamma, and those between 70 and 150 hertz as high gamma.
Thus computing the gamma function becomes a matter of evaluating only a small number of elementary functions and multiplying by stored constants. The Lanczos approximation was popularized by Numerical Recipes , according to which computing the gamma function becomes "not much more difficult than other built-in functions that we take for granted ...
Phase-of-firing code is a neural coding scheme that combines the spike count code with a time reference based on oscillations. This type of code takes into account a time label for each spike according to a time reference based on phase of local ongoing oscillations at low [39] or high frequencies. [40]
Stronger excitation from sharp waves results in ripple oscillations, whereas weaker stimulations generate fast gamma patterns. [15] Besides they are shown to be region dependent, ripples that are the fastest oscillations are present in the CA1 region pyramidal cells while gamma oscillations dominate in CA3 region and parahippocampal structures.
The sinc function, the impulse response for an ideal low-pass filter, illustrating ringing for an impulse. The Gibbs phenomenon, illustrating ringing for a step function.. By definition, ringing occurs when a non-oscillating input yields an oscillating output: formally, when an input signal which is monotonic on an interval has output response which is not monotonic.
Here is the autocovariance function of X t, is the standard deviation of the input noise process, and , is the Kronecker delta function. Because the last part of an individual equation is non-zero only if m = 0 , the set of equations can be solved by representing the equations for m > 0 in matrix form, thus getting the equation
The number of parameters in the Duffing equation can be reduced by two through scaling (in accord with the Buckingham π theorem), e.g. the excursion and time can be scaled as: [2] = and = /, assuming is positive (other scalings are possible for different ranges of the parameters, or for different emphasis in the problem studied).
The part of this equation involving ^ can be computed directly using the wave function at time , but to compute the exponential involving ^ we use the fact that in frequency space, the partial derivative operator can be converted into a number by substituting for , where is the frequency (or more properly, wave number, as we are dealing with a ...