Date of Award
12-16-2015
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Remus Osan
Second Advisor
Vladimir Bondarenko
Third Advisor
Yi Jiang
Abstract
Understanding the complex growth process of dendritic arbors is essential for the medical field and disciplines like Biology and Neurosciences. The establishment of the dendritic patterns has received increasing attention from experimental researchers that seek to determine the cellular mechanisms that play a role in the growth of neural trees. Our goal in this thesis was to prove the recurrence formula for the probability distribution of all possible neural trees, as well as the formulas of the expected number of active branches and their variances. We also derived formulas for the spatial locations of the optimal targeting region for a tree with branching probability. These formulas were necessary for the simplified stochastic computational model that Osan et al have developed in order to examine how changes in branching probability influence the success of targeting neurons located at different distances away from a starting point.
DOI
https://doi.org/10.57709/7899434
Recommended Citation
Nieto, Bernardo, "Accurate Approximation Series for Optimal Targeting Regions in a Neural Growth Model with a Low –branching Probability." Thesis, Georgia State University, 2015.
doi: https://doi.org/10.57709/7899434