Publications
Footnotes
[1] Incidentally, this is older than the universe is estimated to have existed (Jantsch 1980).
[2] The terms "element" and "compartment" are used interchangeably in this passage. "Element" is often used in fluid dynamics where PDEs are solved by Finite Element Methods. The term "compartment" is predominatley used by computational neuroscientists.
[3] For example: terminal endings have one neighbor, cable continuation regions have two neighbors, branch points have three neighbors, and the soma can have an arbitrary number of neighbors.
[4] The voltage-dependent rate constants are nonlinear
terms typically fit by experimental data to the form
, where A,B, C, D, and E are
constants. Calcium-dependent rate constants are not typically as standard in form, but are also
nonlinear and fit from experimental data.
[5] The time constant, tau, is the product of the
membrane capacitance and resistance in a passive membrane model.
. However, Traub's capacitive
value is considered unphysiologically high and may have the effect of excessively scaling the
voltage derivative. Likewise, the membrane resistance is low according to recent experimental
estimates (Spruston and Johnston 1992). Rm = 30,000
μcm2 and Cm = 1.0 μF/cm2 are more reasonable values. We did not
deviate from Traub's values in this study such that our final results could be more directly
compared to his.
[6] Unfortunately, it remains unclear what distinguishes the differences between function classes.
[7] Two identical points are randomly selected along the length of two parent strings, dividing each into three segments. The first and third segments from the first parent and the second segment from the second parent are recombined to produce the offspring strings. 2-point crossover can be generalized to n-point crossover, where n is the number of crossover points.
[8] A probability Po characterizes the degree of disruption. A random number is drawn for each parameter along the string. If the value of this random number is greater than Po, then the value from parent 1 is used to produce the offspring string. If the random number is less than Po, parent 2's value is used. The greatest disruption occurs when Po = 0.5.
[9] We experimented with other recombination operators, but they consistently yielded success rates less than 2.5%. These included: 1) inversion operators that reordered the 114 parameter from the left to right ordering [1 2 3 ... 112 113 114] to the right to left ordering [114 113 112 ... 3 2 1]; and 2) alignment operators that performed a self-crossover by reordering adjacent sections of a string, for example from [1 2 3 ... 56 57 58 ... 112 113 114] to [56 57 58 ... 112 113 114 ... 1 2 3 ...]. Two versions of each operator were developed to exploit both spatial ordering and channel ordering.
[10] Essentially, we increased the population size until no further gains were made in the rate of "best population member" improvement over the evolution of twenty generations.
[11] The data collected from neurons is far too noisy and neurons themselves are far to adaptively to become overly concerned with distinguishing between the other three classes of time series behavior at this point. However, a neuron that is alive would respond to the current injection by producing spikes or bursts.
[12] Speedup is calculated as the serial execution time divided by the parallel execution time. Linear speedup means that the ratio for a given algorithm is proportional to the number of processors. We have seen some applications where parallelization resulted in worse performance than the serial version. Such applications spend a large amount of time message passing relative to the computation time that is performed.
[13] See Eichler West (1996) for a detailed description of the channel manifolds and their interpretation.