Abstract
Network and complex system models are useful for studying a wide range of
phenomena, from disease spread to traffic flow. Because of the broad applicability
of the framework it is important to develop effective simulations and algorithms for
complex networks. This dissertation presents contributions to two applied problems
in this area
First, we study an electro-optical, nonlinear, and time-delayed feedback loop
commonly used in applications that require a broad range of chaotic behavior. For
this system we detail a discrete-time simulation model, exploring the model’s synchronization
behavior under specific coupling conditions. Expanding upon already
published results that investigated changes in feedback strength, we explore how
both time-delay and nonlinear sensitivity impact synchronization. We also relax
the requirement of strictly identical systems components to study how synchronization
regions are affected when coupled systems have non-identical components
(parameters). Last, we allow wider variance in coupling strengths, including unique
strengths to each system, to identify a rich synchronization region not previously
seen.
In our second application, we take a complex networks approach to improving
genome assembly algorithms. One key part of sequencing a genome is solving the
orientation problem. The orientation problem is finding the relative orientations
for each data fragment generated during sequencing. By viewing the genomic data
as a network we can apply standard analysis techniques for community finding
and utilize the significantly modular structure of the data. This structure informs
development and application of two new heuristics based on (A) genetic algorithms
and (B) hierarchical clustering for solving the orientation problem.
Genetic algorithms allow us to preserve some internal structure while quickly
exploring a large solution space. We present studies using a multi-scale genetic
algorithm to solve the orientation problem. We show that this approach can be
used in conjunction with currently used methods to identify a better solution to the
orientation problem.
Our hierarchical algorithm further utilizes the modular structure of the data.
By progressively solving and merging sub-problems together we pick optimal ‘local’
solutions while allowing more global corrections to occur later. Our results show
significant improvements over current techniques for both generated data and real
assembly data.