AN EMPIRICAL ANALYSIS OF FARM STRUCTURE AND OFF-FARM WORK DECISIONS

This study considers the extent to which farm structure may be endogenous to off-farm labor supply decisions. The empirical analysis utilizes structural models consisting of three equation systems describing labor supply, scale and scope in an effort to evaluate the extent to which farm and off-farm labor decisions are jointly made.Farm Management,

The Classical Limit of QuantumTheory

This essay treats of the relationship between quantum and classical mechanics. Both physicists and philosophers hold that quantum mechanics reduces to classical mechanics as h-\u3e0, or that classical mechanics is a special case of quantum mechanics in this limit. If one theory reduces to another, certain formal and nonformal conditions must be satisfied. These conditions are formulated and it is shown that the Wigner transformation can serve as a natural reduction function in a reduction which satisfies the formal and nonformal conditions. Finally, it is argued that this reduction does not aid in solving the problem of providing an adequate metaphysical interpretation of quantum theory

Recovering Structured Low-rank Operators Using Nuclear Norms

This work considers the problem of recovering matrices and operators from limited and/or noisy observations. Whereas matrices result from summing tensor products of vectors, operators result from summing tensor products of matrices. These constructions lead to viewing both matrices and operators as the sum of "simple" rank-1 factors. A popular line of work in this direction is low-rank matrix recovery, i.e., using linear measurements of a matrix to reconstruct it as the sum of few rank-1 factors. Rank minimization problems are hard in general, and a popular approach to avoid them is convex relaxation. Using the trace norm as a surrogate for rank, the low-rank matrix recovery problem becomes convex. While the trace norm has received much attention in the literature, other convexifications are possible. This thesis focuses on the class of nuclear norms—a class that includes the trace norm itself. Much as the trace norm is a convex surrogate for the matrix rank, other nuclear norms provide convex complexity measures for additional matrix structure. Namely, nuclear norms measure the structure of the factors used to construct the matrix. Transitioning to the operator framework allows for novel uses of nuclear norms in recovering these structured matrices. In particular, this thesis shows how to lift structured matrix factorization problems to rank-1 operator recovery problems. This new viewpoint allows nuclear norms to measure richer types of structures present in matrix factorizations. This work also includes a Python software package to model and solve structured operator recovery problems. Systematic numerical experiments in operator denoising demonstrate the effectiveness of nuclear norms in recovering structured operators. In particular, choosing a specific nuclear norm that corresponds to the underlying factor structure of the operator improves the performance of the recovery procedures when compared, for instance, to the trace norm. Applications in hyperspectral imaging and self-calibration demonstrate the additional flexibility gained by utilizing operator (as opposed to matrix) factorization models.</p

Determining Particle Size of Polymeric Micelles in Thermothickening Aqueous Solutions

Many active pharmaceutical ingredients (APIs) are poorly soluble and cause inadequate drug absorption. Soluplus®, a polyvinyl caprolactam-polyvinyl acetate-polyethylene glycol graft copolymer, is a commercial excipient (BASF Corp) that enhances the solubility and bioavailability of many APIs. The mechanism of enhancement is related to the ability to form polymeric micelles in solution. These micelles store insoluble APIs in their hydrophobic interior and transport them to targeted sites in the body. An important characteristic of solubility enhancers is the particle size exhibited in solution before and after loading with APIs. This is most commonly determined by dynamic light scattering (DLS) methods. However, DLS measurements involving thermothickening polymer solutions can be complicated by the temperature dependence of viscosity and refractive index, solution properties that directly impact the size analysis algorithms in DLS. In this project, the temperature dependence of viscosity for Soluplus® solutions were evaluated and used as a correction to particle size measurements by DLS. Solution concentrations ranging 1.0% to 30.0% (w/w) of Soluplus® were studied from 5.0 °C to 40.0 °C using a cone-and-plate rheometer. Refractive index of Soluplus® solutions were also studied and used in the correction of particle size. It was found that correcting viscosity and refractive index data drastically affected hydrodynamic effective diameter, where viscosity was more highly weighted. The corrected particle size of Soluplus® solutions was inversely proportional to concentration with the 0.1% and 10.0% solutions showing effective diameters of 63.13 ± 0.76 nm and 24.98 ± 0.30 nm at 25.0 °C, respectively. By properly accounting for these variables in DLS algorithms, particle size of thermoresponsive polymer solutions can be more accurately characterized