The Development of Instruments for Assessment of Instructional Practices in Standards-Based Teaching

We provide a description and rationale for the development of two instruments: 1) a classroom observation protocol; and, 2) a teacher interview protocol—designed to document the impact of reform-based professional development with undergraduate mathematics and science faculty, and its impact on the resultant preparation of teachers. Constructed upon review of the research on teaching and standards documents in mathematics and science, these instruments form the basis for data collection in a three-year longitudinal study of teaching practice among early career teachers as well as undergraduate college faculty. In addition, we suggest further applications of the observation protocol beyond the original purpose of our research study

Adapting structuration theory to understand the role of reflexivity: Problematization, clinical audit and information systems

This paper is an exploratory account of the further development and application of a hybrid framework, StructurANTion, that is based on Structuration Theory and Actor Network Theory (ANT). The use of social theories in general and their use in information systems (IS) research in particular is explored leading to the use of the framework to examine the concept of what are termed humanchine networks in the context of clinical audit, within a healthcare Primary Care Trust (PCT). A particular focus is on the manner in which information systems-based reflexivity contributes to both entrenching a networks’ structurated order as well as contributing to its emancipatory change. The case study compares clinic-centric and patientcentric audit and seeks to further extend the understanding of the role of information and information systems within structurated humanchine activity systems. Conclusions indicate that the use of more socially informed IS methods and approaches can incorporate more emancipatory ideals and lead to greater adoption and usage of more relevant and useful clinical information systems and practices

Randomized Smoothing for Stochastic Optimization

We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic optimization procedures, both in expectation and with high probability, that have optimal dependence on the variance of the gradient estimates. To the best of our knowledge, these are the first variance-based rates for non-smooth optimization. We give several applications of our results to statistical estimation problems, and provide experimental results that demonstrate the effectiveness of the proposed algorithms. We also describe how a combination of our algorithm with recent work on decentralized optimization yields a distributed stochastic optimization algorithm that is order-optimal.Comment: 39 pages, 3 figure

The Effects of Spin-Orbit Coupling on Gravitational Wave Uncertainties

Paper discusses the expected uncertainty of orbital parameters of binary stars as measured by the space-based gravitational wave observatory LISA (Laser Interferometer Space Antenna) and how the inclusion of spin in the model of the binary stars affects the uncertainty. The uncertainties are found by calculating the received gravitational wave from a binary pair and then performing a linear least-squares parameter estimation. The case of a 1500 solar mass black hole that is 20 years from coalescing with a 1000 solar mass black hole--both of which are 50 x 10^6 light years away--is analyzed, and the results show that the inclusion of spin has a negligible effect upon the angular resolution of LISA but can increase the accuracy in mass and distance measurements by factors of 15 and 65, respectively

Asymptotic silence-breaking singularities

We discuss three complementary aspects of scalar curvature singularities: asymptotic causal properties, asymptotic Ricci and Weyl curvature, and asymptotic spatial properties. We divide scalar curvature singularities into two classes: so-called asymptotically silent singularities and non-generic singularities that break asymptotic silence. The emphasis in this paper is on the latter class which have not been previously discussed. We illustrate the above aspects and concepts by describing the singularities of a number of representative explicit perfect fluid solutions.Comment: 25 pages, 6 figure

A new proof of the Bianchi type IX attractor theorem

We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The `Bianchi type IX attractor theorem' states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively short and self-contained new proof of this theorem. The proof we give is interesting in itself, but more importantly it illustrates and emphasizes that type IX is special, and to some extent misleading when one considers the broader context of generic models without symmetries.Comment: 26 pages, 5 figure

Spherically symmetric relativistic stellar structures

We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space, thereby avoiding the non-regularity problems associated with the Tolman-Oppenheimer-Volkoff equation. The global picture of the solution space thus obtained is used to derive qualitative features and to prove theorems about mass-radius properties. The perfect fluids we discuss are described by barotropic equations of state that are asymptotically polytropic at low pressures and, for certain applications, asymptotically linear at high pressures. We employ dimensionless variables that are asymptotically homology invariant in the low pressure regime, and thus we generalize standard work on Newtonian polytropes to a relativistic setting and to a much larger class of equations of state. Our dynamical systems framework is particularly suited for numerical computations, as illustrated by several numerical examples, e.g., the ideal neutron gas and examples that involve phase transitions.Comment: 23 pages, 25 figures (compressed), LaTe

Self-similar Bianchi models: I. Class A models

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration constants. We apply the geometrical results for tilted perfect fluids sources and give the general Bianchi II self-similar solution and the form of the similarity vector field. In addition we show that self-similar perfect fluid Bianchi VII$_0$ models and irrotational Bianchi VI$_0$ models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit