Hypothesis testing near singularities and boundaries

The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as highlighted by recent work of Drton. Indeed, poor behavior of a $\chi^2$ for testing near singularities and boundaries is apparent in simulations, and can lead to conservative or anti-conservative tests. Here we develop a new distribution designed for use in hypothesis testing near singularities and boundaries, which asymptotically agrees with that of the likelihood ratio statistic. For two example trinomial models, arising in the context of inference of evolutionary trees, we show the new distributions outperform a $\chi^2$.Comment: 32 pages, 12 figure

Flow and thermal effects in continuous flow electrophoresis

In continuous flow electrophoresis the axial flow structure changes from a fully developed rectilinear form to one characterized by meandering as power levels are increased. The origin of this meandering is postulated to lie in a hydrodynamic instability driven by axial (and possibly lateral) temperature gradients. Experiments done at MSFC show agreement with the theory

Underperforming policy networks : the biopesticides network in the United Kingdom

Loosely integrated and incomplete policy networks have been neglected in the literature. They are important to consider in terms of understanding network underperformance. The effective delivery and formulation of policy requires networks that are not incomplete or underperforming. The biopesticides policy network in the United Kingdom is considered and its components identified with an emphasis on the lack of integration of retailers and environmental groups. The nature of the network constrains the actions of its agents and frustrates the achievement of policy goals. A study of this relatively immature policy network also allows for a focus on network formation. The state, via an external central government department, has been a key factor in the development of the network. Therefore, it is important to incorporate such factors more systematically into understandings of network formation. Feedback efforts from policy have increased interactions between productionist actors but the sphere of consumption remains insufficiently articulated

Tensor Rank, Invariants, Inequalities, and Applications

Though algebraic geometry over $\mathbb C$ is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the $n\times n\times n$ tensors of rank $n$ over $\mathbb C$, which has as a dense subset the orbit of a single tensor under a natural group action. We construct polynomial invariants under this group action whose non-vanishing distinguishes this orbit from points only in its closure. Together with an explicit subset of the defining polynomials of the variety, this gives a semialgebraic description of the tensors of rank $n$ and multilinear rank $(n,n,n)$. The polynomials we construct coincide with Cayley's hyperdeterminant in the case $n=2$, and thus generalize it. Though our construction is direct and explicit, we also recast our functions in the language of representation theory for additional insights. We give three applications in different directions: First, we develop basic topological understanding of how the real tensors of complex rank $n$ and multilinear rank $(n,n,n)$ form a collection of path-connected subsets, one of which contains tensors of real rank $n$. Second, we use the invariants to develop a semialgebraic description of the set of probability distributions that can arise from a simple stochastic model with a hidden variable, a model that is important in phylogenetics and other fields. Third, we construct simple examples of tensors of rank $2n-1$ which lie in the closure of those of rank $n$.Comment: 31 pages, 1 figur

A smart end-effector for assembly of space truss structures

A unique facility, the Automated Structures Research Laboratory, is being used to investigate robotic assembly of truss structures. A special-purpose end-effector is used to assemble structural elements into an eight meter diameter structure. To expand the capabilities of the facility to include construction of structures with curved surfaces from straight structural elements of different lengths, a new end-effector has been designed and fabricated. This end-effector contains an integrated microprocessor to monitor actuator operations through sensor feedback. This paper provides an overview of the automated assembly tasks required by this end-effector and a description of the new end-effector's hardware and control software

The Effect of Information Literacy Exposure on the Transition to Early College Writing

FYW courses introduce most students to effective database research as essential to the writing process. However, the growing trend towards dual enrollment complicates the traditional exposure to information literacy. Information literacy competencies between dual-enrollment students and traditionally-enrolled freshmen can be ascertained to determine if differences should be addressed