E. C. CASTRO, B. A. R. PELI CANO

Copyright © 2013 SciRes. OJAppS

to the transition probability, the trajectory of least action

for the motion can be described. The optimized path in

free space does not depend on the frequency of the par-

ticle to pass through a certain point, but depends on the

most probable point in space in relation to the particle’s

current position. Even though the transition probability is

independent of the history of the Brownian motion, the

path of least action is indirectly affected by the initial

positions.

Brownian motion in a neural network still has a clas-

sical characteristic, i.e. the trajectory most likely follows

a straight line fro m the starting position to the d esignated

point. Whereas, the installation of the cond ition of a final

point never appears in the transition probability calcula-

tion. It appears to be that it is inherent to the transition

probability itself that the Brownian motion is subject to

follow a horizontal of vertical displacement. The final

position can then be reached if the Brownian motion ap-

proaches the point, which can be done by orienting the

edges of t he directed graph.

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