An NP-Complete Problem in Grid Coloring

A c-coloring of G(n,m)=n x m is a mapping of G(n,m) into {1,...,c} such that no four corners forming a rectangle have the same color. In 2009 a challenge was proposed via the internet to find a 4-coloring of G(17,17). This attracted considerable attention from the popular mathematics community. A coloring was produced; however, finding it proved to be difficult. The question arises: is the problem of grid coloring is difficult in general? We present three results that support this conjecture, (1) an NP completeness result, (2) a lower bound on Tree-resolution, (3) a lower bound on Tree-CP proofs. Note that items (2) and (3) yield statements from Ramsey Theory which are of size polynomial in their parameters and require exponential size in various proof systems.Comment: 25 page

An examination of teacher evaluation in Iowa

Teacher evaluation is one of the most challenging tasks facing school administrators today. Effective July 1, 1990, an individual employed as an administrator or supervisor in an Iowa public school, who conducts teacher evaluation, must possess an evaluator approval certificate. This study utilized the Teacher Evaluation Profile (TEP) to examine teachers\u27 perceptions of the quality and impact of teacher evaluation in Iowa. The instrument was modified to allow teachers to reflect on their most recent evaluation and their evaluation three years previous to their most recent evaluation;The data were gathered from 1040 Iowa teachers from 208 randomly selected schools. Five teachers, from each of the 104 elementary schools, 52 middle school/junior high schools and 52 high schools, were randomly selected to participate in the study;Teachers responses on the instrument were used to assess their perceptions of quality and impact of their teacher evaluation experiences. Teachers were also asked to rate the following attributes identified by the TEP as contributing factors to the quality and impact of teacher evaluation; (1) attributes of the teacher (2) attributes of the feedback (3) attributes of the evaluator and (4) attributes of the procedures;Statistical treatment of the data was completed using the the Statistical package SPSSX. Descriptive statistics were computed to study the relative value of the study variables. Frequencies, t-tests, and correlations were used to assess the differences;The analysis revealed that evaluator approval training had significant effects on the overall quality of evaluation. In other words, evaluator training greatly enhanced evaluation planning, lesson observations, and evaluator feedback. There were also significant effects on evaluation attributes, including attributes of the teacher, attributes of the feedback, attributes of the evaluator, and attributes of the procedures. The study, however, revealed no significant effect on the impact of teacher evaluation. Specifically, the training did not significantly alter teaching practices, attitudes about teaching, and understanding about teaching. In addition, nearly sixty percent of the teachers rated teacher evaluation as moderately good to super good . Only six percent of the teachers rated evaluation as poor to super poor

Photorefractive Materials for Optical Signal Processing

The optical response of the photorefractive crystals KNbO3:Ta, KNbO3:Fe, LiNbO3:Fe, and nominally pure BaTiO3 is investigated. In the experiment, a holographic grating is built in the crystal under investigation via a two-wave mixing scheme that utilizes the signal-processing capacities of two acousto-optic Bragg cells. The dynamic interaction of the Bragg cells with the photorefractive grating causes a heterodyned RF signal to appear on the output laser beam, enabling the real-time, direct measurement of the amplitude and phase of the space-charge fields in the crystal. Experimental results are presented for the amplitude and phase of the space-charge fields, the diffraction efficiency, and the grating time constant as a function of spatial frequency. Quantitative understanding of some of the fundamental processes and material properties responsible for the optical response is gained through comparison of the measured data to theoretical models. In this analysis, the diffusion and photovoltaic transport lengths, Debye screening length, net trap concentration, and net conductivity factor are determined

Ultrastructure of Lymphocystis in the Heart of the Silver Perch, Bairdiella chrysura (Lacépède), Including Observations on Normal Heart Structure

The fine structure of normal heart muscle from the silver perch, Bairdiella chrysura (Lacépède), is similar to that previously reported for marine and freshwater teleosts. Cardiac lymphocystis is a viral disease manifested by single, giant-cell lesions variously located in the epicardium, trabecular spaces, and subendocardium – in direct apposition to myocardial cells. Occasionally, the hyaline capsule of lymphocystis cells partially surround myocardial cells but cause no pathological changes or inflammatory reaction. The lymphocystis cells contain typical cellular organelles, including the viroplasmic net unique to these cells. Annulate lamellae, often continuous with the rough endoplasmic reticulum, are present, usually along the periphery of the cell. Some elements of the rough endoplasmic reticulum are dilated and contain a finely granular material, but others contain cross-banded fibrils, each having a periodicity of 30 nm. Similar fibrils are present in the perinuclear cisternae

Thrombospondin-1: An Islet Endothelial Cell Signal of Importance for β-Cell Function

OBJECTIVE: Loss of thrombospondin (TSP)-1 in pancreatic islets has been shown to cause islet hyperplasia. This study tested the hypothesis that endothelial-derived TSP-1 is important for β-cell function. RESEARCH DESIGN AND METHODS: Islet function was evaluated both in vivo and in vitro. Messenger RNA and protein expression were measured by real-time PCR and Western blot, respectively. The role of endothelial-derived TSP-1 for β-cell function was determined using a transplantation design in which recipient blood vessels either were allowed to grow or not into the transplanted islets. RESULTS: TSP-1–deficient mice were glucose intolerant, despite having an increased β-cell mass. Moreover, their islets had decreased glucose-stimulated insulin release, (pro)insulin biosynthesis, and glucose oxidation rate, as well as increased expression of uncoupling protein-2 and lactate dehydrogenase-A when compared with control islets. Almost all TSP-1 in normal islets were found to be derived from the endothelium. Transplantation of free and encapsulated neonatal wild-type and TSP-1–deficient islets was performed in order to selectively reconstitute with TSP-1–positive or –negative blood vessels in the islets and supported that the β-cell defects occurring in TSP-1–deficient islets reflected postnatal loss of the glycoprotein in the islet endothelial cells. Treatment of neonatal TSP-1–deficient mice with the transforming growth factor (TGF)β-1–activating sequence of TSP-1 showed that reconstitution of TGFβ-1 activation prevented the development of decreased glucose tolerance in these mice. Thus, endothelial-derived TSP-1 activates islet TGFβ-1 of importance for β-cells. CONCLUSIONS: Our study indicates a novel role for endothelial cells as functional paracrine support for pancreatic β-cells

The Light Curve of the Weakly-Accreting T Tauri Binary KH 15D from 2005-10: Insights into the Nature of its Protoplanetary Disk

Photometry of the unique pre-main sequence binary system KH 15D is presented, spanning the years 2005-2010. This system has exhibited photometric variations and eclipses over the last 50 years caused by a precessing circumbinary disk. Advancement of the occulting edge across the binary orbit has continued and the photospheres of both stars are now completely obscured at all times. The system is now visible only by scattered light, and yet it continues to show a periodic variation on the orbital cycle with an amplitude exceeding two magnitudes. This variation, which depends only on the binary phase, has likely been present in the data since at least 1995. It can, by itself, account for shoulders on the light curve prior to ingress and following egress, obviating the need for components of extant models such as a scattering halo around star A or forward scattering from a fuzzy disk edge. A plausible source for the variable scattering component is reflected light from the far side of a warped occulting disk. We have detected color changes in V-I of several tenths of a magnitude to both the blue and red that occur during times of minima. These may indicate the presence of a third source of light (faint star) within the system, or a change in the reflectance properties of the disk as the portion being illuminated varies with the orbital motion of the stars. The data support a picture of the circumbinary disk as a geometrically thin, optically thick layer of perhaps mm or cm-sized particles that has been sculpted by the binary stars and possibly other components into a decidedly nonplanar configuration. A simple (infinitely sharp) knife-edge model does a good job of accounting for all of the recent (2005-2010) occultation data.Comment: To appear in The Astronomical Journa

A Systems Thinking Approach to Redesigning the Patient Experience to Reduce 30 Day Hospital Readmission

INTRODUCTION The cost of medical care is spiraling out of control, and one of the many reasons is lack of preventative care, poor communication to the patient and primary caregiver(s) both in an inpatient and outpatient setting. There are potentially many reasons for this cost escalation, one of the drivers of this cost is 30 day readmission after a hospitalization and this is what was examined in this analysis. The purpose of this paper in particular is to share what has been learned using a systems thinking approach to hospital readmissions and the patient experience. It is critical to understand the problems that occurred in the past. In addition, we will explain the methodology utilized and bring awareness to the iterative process. We will also demonstrate a suggested redesigned model

An efficient basis set representation for calculating electrons in molecules

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N)) multiplication operations, not O(N^4), where N is the number of basis functions; N = n^3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one- (He^+, H_2^+ ), two- (H_2, He), ten- (CH_4) and 56-electron (C_8H_8) systems.Comment: Submitted to JC