We study EC3, a variant of Exact Cover which is equivalent to Positive 1-in-3 SAT. Random instances of EC3 were recently used as benchmarks for simulations of an adiabatic quantum algorithm. Empirical results suggest that EC3 has a phase transition from satisfiabil-ity to unsatisfiability when the ratio r of clauses to variables exceeds some threshold r * ≈… (More)
This thesis represents the first formal presentation of the algorithm for-machine reconstruction from spectral data called-machine spectral reconstruction theory or MSR. As might be expected from a work that introduces a novel approach—let alone one that is written by a student to satisfy the requirements of a degree—there is significant attention given to… (More)
Multiplex networks arise in many real-world systems when different kinds of relationship connect the elements of the network. As a result, studying methods to detect communities in such network becomes increasingly important. Common approaches to this problem try to generalize methods from monoplex networks or apply tensor decomposition, but this field… (More)
iii Dedication ...to that which inspires and fascinates, and to those who leverage inspiration and fascination not only lovingly but toward fostering love itself.