The tithe: Public research university STEM faculty perspectives on sponsored research indirect costs

This study sought to understand the phenomenon of faculty involvement in indirect cost under-recovery. The focus of the study was on public research university STEM (science, technology, engineering and mathematics) faculty, and their perspectives on, and behavior towards, a higher education fiscal policy. The explanatory scheme was derived from anthropological theory, and incorporated organizational culture, faculty socialization, and political bargaining models in the conceptual framework. This study drew on two key assumptions. The first assumption was that faculty understanding of, and behavior toward, indirect cost recovery represents values, beliefs, and choices drawn from the distinct professional socialization and distinct culture of faculty. The second assumption was that when faculty and institutional administrators are in conflict over indirect cost recovery, the resultant formal administrative decision comes about through political bargaining over critical resources. The research design was a single site, qualitative case study with a focus on learning the meaning of the phenomenon as understood by the informants. In this study the informants were tenured and tenure track research university faculty in the STEM fields who were highly successful at obtaining Federal sponsored research funds, with individual sponsored research portfolios of at least one million dollars. The data consisted of 11 informant interviews, bolstered by documentary evidence. The findings indicated that faculty socialization and organizational culture were the most dominant themes, while political bargaining emerged as significantly less prominent. Public research university STEM faculty are most concerned about the survival of their research programs and the discovery facilitated by their research programs. They resort to conjecture when confronted by the issue of indirect cost recovery. The findings direct institutional administrators to consider less emphasis on compliance and hierarchy when working with expert professionals such as science faculty. Instead a more effective focus might be on communication and clarity in budget processes and organizational decision-making, and a concentration on critical administrative support that can relieve faculty administrative burdens. For higher education researchers, the findings suggest that we need to create more sophisticated models to help us understand organizations dependent on expert professionals.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.

Two-State Thermodynamics of Supercooled Water

Water has been called the “most studied and least understood” of all liquids, and upon supercooling its behavior becomes even more anomalous. One particularly fruitful hypothesis posits a liquid-liquid critical point terminating a line of liquid-liquid phase transitions that lies just beyond the reach of experiment. Underlying this hypothesis is the conjecture that there is a competition between two distinct hydrogen-bonding structures of liquid water, one associated with high density and entropy and the other with low density and entropy. The competition between these structures is hypothesized to lead at very low temperatures to a phase transition between a phase rich in the high-density structure and one rich in the low-density structure. Equations of state based on this conjecture have given an excellent account of the thermodynamic properties of supercooled water. In this thesis, I extend that line of research. I treat supercooled aqueous solutions and anomalous behavior of the thermal conductivity of supercooled water. I also address supercooled water at negative pressures, leading to a framework for a coherent understanding of the thermodynamics of water at low temperatures. I supplement analysis of experimental results with data from the TIP4P/2005 model of water, and include an extensive analysis of the thermodynamics of this model.