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I show that the mean walk length is a constant:L̄ =e−1, where e≈2.72.
Asymptotic results for general distributions of the random fitness component are obtained using extreme value theory, and it is found that the walk length attains a non-trivial limit for L→∞, different from its values for c=0 and c="∞, if c is scaled with L in an appropriate combination.
When the random fitness component is chosen from the Gumbel distribution, explicit expressions for the distribution of the number of steps taken by the greedy walk are obtained, and it is shown that the walk length varies non-monotonically with the strength of the fitness gradient when the starting point is sufficiently close to the reference sequence.
To avoid excessively long computation time we cap the maximum walk length at 50 000 and stop extension if a particular k-mer is visited twice.
A random walk typically starts from the given gene, walks through several nodes, and terminates according to some pre-defined parameters, such as walk length and edge weights.
Bounding the walk length is not only convenient from a computational viewpoint, it also allows to control the level of locality (or, conversely, the level of diffusion through the network) while connecting seed nodes.
Similar(52)
You'd be told to put on two sweatshirts and walk lengths of the foam pit to sweat it off.
A single similarity measure based on the different walk lengths is necessary.
The walking length in total is about 105 m.
Similar methods can differ in walking length, and different populations weaken the comparisons.
Such differences could be related to feeding regimens including the type of diet, frequency of receiving titbits, frequency of scavenging, frequency and length of walks, length of time off leash, number and length of dog to dog interactions et cetera.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com