Network Algorithms for Complex Systems with Applications to Non-linear Oscillators and Genome Assembly

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.