Entropy and reduced distance for Ricci expanders

Perelman has discovered two integral quantities, the shrinker entropy \cW and the (backward) reduced volume, that are monotone under the Ricci flow \pa g_{ij}/\pa t=-2R_{ij} and constant on shrinking solitons. Tweaking some signs, we find similar formulae corresponding to the expanding case. The {\it expanding entropy} \ctW is monotone on any compact Ricci flow and constant precisely on expanders; as in Perelman, it follows from a differential inequality for a Harnack-like quantity for the conjugate heat equation, and leads to functionals $\mu_+$ and $\nu_+$. The {\it forward reduced volume} $\theta_+$ is monotone in general and constant exactly on expanders. A natural conjecture asserts that $g(t)/t$ converges as $t\to\infty$ to a negative Einstein manifold in some weak sense (in particular ignoring collapsing parts). If the limit is known a-priori to be smooth and compact, this statement follows easily from any monotone quantity that is constant on expanders; these include \Vol(g)/t^{n/2} (Hamilton) and $\bar\lambda$ (Perelman), as well as our new quantities. In general, we show that if \Vol(g) grows like $t^{n/2}$ (maximal volume growth) then \ctW, $\theta_+$ and $\bar\lambda$ remain bounded (in their appropriate ways) for all time. We attempt a sharp formulation of the conjecture

Analysis of IUE observations of hydrogen in comets

The large body of hydrogen Lyman-alpha observations of cometary comae obtained with the International Ultraviolet Explorer satellite has gone generally unanalyzed because of two main modeling complications. First, the inner comae of many bright (gas productive) comets are often optically thick to solar Lyman-alpha radiation. Second, even in the case of a small comet (low gas production) the large IUE aperture is quite small as compared with the immense size of the hydrogen coma, so an accurate model which properly accounts for the spatial distribution of the coma is required to invert the inferred brightnesses to column densities and finally to H atom production rates. Our Monte Carlo particle trajectory model (MPTM), which for the first time provides the realistic full phase space distribution of H atoms throughout the coma was used as the basis for the analysis of IUE observations of the inner coma. The MCPTM includes the effects of the vectorial ejection of the H atoms upon dissociation of their parent species (H2O and OH) and of their partial collisional thermalization. Both of these effects are crucial to characterize the velocity distribution of the H atoms. A new spherical radiative transfer calculation based on our MCPTM was developed to analyze IUE observations of optically thick H comae. The models were applied to observations of comets P/Giacobini-Zinner and P/Halley

Purposes, Uses, and Practices of Leadership Assessment in Education

Explores recent research literature dealing with personnel evaluations, professional learning, accountability, and the relation of leadership to learning, in order to clarify how leadership assessment practices impact student achievement

Re-Examination of Globally Flat Space-Time

In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of `dark energy', `dark matter', and `dark flow'. Instead of assuming the existence of these theoretical concepts, we take an alternative route and choose to redefine what we consider to be inertial motion as well as what constitutes an inertial frame of reference in flat space-time. We adopt none of the features of our current cosmological models except for the requirement that special and general relativity be local approximations within our revised definition of inertial systems. Implicit in our ideas is the assumption that at "large enough" scales one can treat objects within these inertial systems as point-particles having an insignificant effect on the curvature of space-time. We then proceed under the assumption that time and space are fundamentally intertwined such that time- and spatial-translational invariance are not inherent symmetries of flat space-time (i.e. observable clock rates depend upon both relative velocity and spatial position within these inertial systems) and take the geodesics of this theory in the radial Rindler chart as the proper characterization of inertial motion. With this commitment, we are able to model solely with inertial motion the observed effects expected to be the result of `dark energy', `dark matter', and `dark flow'. In addition, we examine the potential observable implications of our theory in a gravitational system located within a confined region of an inertial reference frame, subsequently interpreting the Pioneer anomaly as support for our redefinition of inertial motion. As well, we extend our analysis into quantum mechanics by quantizing for a real scalar field and find a possible explanation for the asymmetry between matter and antimatter within the framework of these redefined inertial systems.Comment: 55 pages, 3 figures, 2 tables, 6 appendices; added two unpublished sections with supplementary material (see Comments section of PLoS ONE publication link). None of the physical content of the original article has change

Spectral Properties of Elementwise-Transformed Spiked Matrices

This work concerns elementwise-transformations of spiked matrices: $Y_n = n^{-1/2} f( \sqrt{n} X_n + Z_n)$. Here, $f$ is a function applied elementwise, $X_n$ is a low-rank signal matrix, and $Z_n$ is white noise. We find that principal component analysis is powerful for recovering signal under highly nonlinear or discontinuous transformations. Specifically, in the high-dimensional setting where $Y_n$ is of size $n \times p$ with $n,p \rightarrow \infty$ and $p/n \rightarrow \gamma > 0$, we uncover a phase transition: for signal-to-noise ratios above a sharp threshold -- depending on $f$, the distribution of elements of $Z_n$, and the limiting aspect ratio $\gamma$ -- the principal components of $Y_n$ (partially) recover those of $X_n$. Below this threshold, the principal components of $Y_n$ are asymptotically orthogonal to the signal. In contrast, in the standard setting where $X_n + n^{-1/2}Z_n$ is observed directly, the analogous phase transition depends only on $\gamma$. A similar phenomenon occurs with $X_n$ square and symmetric and $Z_n$ a generalized Wigner matrix

The gas production rate of periodic comet d'Arrest

Comet P/d'Arrest is a potential target for a rendezvous mission to a short period comet. Its light curve is rather peculiar, the comet being active only after perihelion passage. One apparition out of two is easy to observe from the ground. The 1995 apparition of the comet will offer a unique opportunity to characterize the outgassing properties of its nucleus

Collaborative Caring: Stories and Reflections on Teamwork in Health Care

[Excerpt] There are many theoretical and conceptual books and countless articles that have explored issues of teamwork in general and teamwork in health care in particular. The editors, and many of the authors in this book, have read most, and have even written some of them. To tackle the issue of teamwork, we have, however, taken a different approach. Rather than write a theoretical book about what teamwork is, what it is not, where it exists in health care, what barriers prevent its implementation and how they can be removed, we have chosen instead to address these questions through narratives and reflections that vividly describe good teamwork as well as problems in creating, leading, and working on genuine teams. What we believe is too often lacking in the literature is a clear and compelling picture of what teamwork looks like on the ground, in the institutions where health care work is delivered and where teams play well, or don\u27t play well, on a daily basis. The question we ask here is thus: What is the state of play in most health care institutions? To describe the state of play, we have asked clinicians to write what we think of as where the rubber hits the road stories or reflections about the nature of teamwork in their own particular work setting. To gather these stories, we talked to many people in different health care disciplines. In the invitation for submissions we wrote the following: We are seeking short, concise narratives that describe a concrete example in which you personally have been involved. The idea here is not to focus so much on the individual doctor-patient, nurse-patient, therapist-patient communication but the teamwork that was involved in ensuring that the standard of care was met or exceeded. If the patient or family was involved, so much the better. Stories can deal with interprofessional or intraprofessional teamwork. On balance, we would prefer to have more stories about interprofessional or occupational teamwork. Nonetheless, we recognize that interprofessional work depends on the ability to create teamwork within an occupation or profession. Stories involving support staff, such as housekeepers who spoke up about a patient safety issue, are definitely within the purview of this book. We would also welcome personal reflections that would enhance our understanding of either how to produce genuine teamwork or the obstacles that stand in its way

Outlaw Murals

9 p