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Physical Models In Community Detection With Applications To Identifying Structure In Complex Amorphous Systems, Peter Ronhovde
Physical Models In Community Detection With Applications To Identifying Structure In Complex Amorphous Systems, Peter Ronhovde
All Theses and Dissertations (ETDs)
We present an exceptionally accurate spin-glass-type Potts model for the graph theoretic problem of community detection. With a simple algorithm, we find that our approach is exceptionally accurate, robust to the effects of noise, and competitive with the best currently available algorithms in terms of speed and the size of solvable systems. Being a "local" measure of community structure, our Potts model is free from a "resolution limit" that hinders community solutions for some popular community detection models. It further remains a local measure on weighted and directed graphs. We apply our community detection method to accurately and quantitatively evaluate …
Equivariant Deformations Of Horospherical Surfaces, Michael Deutsch
Equivariant Deformations Of Horospherical Surfaces, Michael Deutsch
All Theses and Dissertations (ETDs)
The classical Goursat transform for minimal surfaces is interpreted as conformal transformation of the Gauss map, allowing us to "bend" these surfaces for certain geometric purposes. A simple analogue of this deformation is defined for CMC1 surfaces which makes the Goursat transform equivariant with respect to the Lawson correspondence, thereby increasing the number of explicitly computable examples of minimal/CMC1 cousin pairs. We then indicate how the Goursat transformation law and integrability conditions for the "spin curve" of a horospherical surface are analogous to the Lorentz transformation law and equations of motion for the wavefunction of a massless fermion.
Modeling Aerial Refueling Operations, Allen Mccoy
Modeling Aerial Refueling Operations, Allen Mccoy
All Theses and Dissertations (ETDs)
Aerial Refueling: AR) is the act of offloading fuel from one aircraft: the tanker) to another aircraft: the receiver) in mid flight. Meetings between tanker and receiver aircraft are referred to as AR events and are scheduled to: escort one or more receivers across a large body of water; refuel one or more receivers; or train receiver pilots, tanker pilots, and boom operators. In order to efficiently execute the Aerial Refueling Mission, the Air Mobility Command: AMC) of the United States Air Force: USAF) depends on computer models to help it make tanker basing decisions, plan tanker sorties, schedule aircraft, …
Properties Of Truncated Toeplitz Operators, Nicholas Sedlock
Properties Of Truncated Toeplitz Operators, Nicholas Sedlock
All Theses and Dissertations (ETDs)
We discuss the multiplication of truncated Toeplitz operators: or TTOs) on backward shift invariant subspaces of the Hardy space of the unit disc. Specifically we discuss when the product of two TTOs is itself a TTO, finding an equivalent to a similar result of Brown and Halmos for ordinary Toeplitz operators. This leads us to investigate the commutants of certain rank-one perturbations of the compressed shift operator, deriving a symbol calculus for TTOs, as well as several other results.