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The peristimulus time histogram is sometimes called perievent time histogram, and post-stimulus and peri-stimulus are often hyphenated. The prefix peri, for through, is typically used in the case of periodic stimuli, in which case the PSTH show neuron firing times wrapped to one cycle of the stimulus.
A further division by the interval length Δt yields time-dependent firing rate r(t) of the neuron, which is equivalent to the spike density of PSTH (Chapter 1.5 in [14]). For sufficiently small Δt, r(t)Δt is the average number of spikes occurring between times t and t+Δt over multiple trials.
Integrate-and-fire models with output noise can be used to predict the peristimulus time histogram (PSTH) of real neurons under arbitrary time-dependent input. [22] For non-adaptive integrate-and-fire neurons, the interval distribution under constant stimulation can be calculated from stationary renewal theory. [27]
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The histogram approach uses the idea that the differential entropy of a probability distribution () for a continuous random variable , = ()can be approximated by first approximating () with a histogram of the observations, and then finding the discrete entropy of a quantization of
In theory both approaches give equally good ways of determining a suitable matrix A, but there are differences in computation time. Let z = (z 1, ..., z N) T be a vector whose components are N independent standard normal variates (which can be generated, for example, by using the Box–Muller transform). Let x be μ + Az. This has the desired ...
The top row is a series of plots using the escape time algorithm for 10000, 1000 and 100 maximum iterations per pixel respectively. The bottom row uses the same maximum iteration values but utilizes the histogram coloring method. Notice how little the coloring changes per different maximum iteration counts for the histogram coloring method plots.
At this time, the Lyapunov exponent λ is maximized, and the state is the most chaotic. The value of λ for the logistic map at r = 4 can be calculated precisely, and its value is λ = log 2. Although a strict mathematical definition of chaos has not yet been unified, it can be shown that the logistic map with r = 4 is chaotic on [0, 1 ...