Differential Forms and Wave Equations for General Relativity

Recently, Choquet-Bruhat and York and Abrahams, Anderson, Choquet-Bruhat, and York (AACY) have cast the 3+1 evolution equations of general relativity in gauge-covariant and causal ``first-order symmetric hyperbolic form,'' thereby cleanly separating physical from gauge degrees of freedom in the Cauchy problem for general relativity. A key ingredient in their construction is a certain wave equation which governs the light-speed propagation of the extrinsic curvature tensor. Along a similar line, we construct a related wave equation which, as the key equation in a system, describes vacuum general relativity. Whereas the approach of AACY is based on tensor-index methods, the present formulation is written solely in the language of differential forms. Our approach starts with Sparling's tetrad-dependent differential forms, and our wave equation governs the propagation of Sparling's 2-form, which in the ``time-gauge'' is built linearly from the ``extrinsic curvature 1-form.'' The tensor-index version of our wave equation describes the propagation of (what is essentially) the Arnowitt-Deser-Misner gravitational momentum.Comment: REVTeX, 26 pages, no figures, 1 macr

MULTIVARIATE STATISTICAL ANALYSIS OF COLEOPTERA SPECTRAL REFLECTANCE

The insect order Coleoptera, commonly known as beetles, comprises 40% of all insects which in turn account for half of all identified animal species alive today. Coleopterans frequently have large elytra (the hardened front wings) that can have a wide range of colors. Spectral reflectance readings from these elytra may be used to uniquely identify coleopteran taxonomic groups. Multiple samples of eleven species of wood boring beetles were selected from the University of Idaho William Barr Entomology Museum. Spectrometer readings for each specimen were then fit to normal distribution mixture models to identify multiple peak reflectance wavelengths. Eighteen prominent peaks were identified across all taxonomic groups and genders creating a multivariate response structure. Multivariate statistical procedures including principal component and discriminant analyses were employed to assess the differentiation of taxonomic groups and genders based on spectral reflectance. The first three axes of the principal component analysis accounted for 96% of the variation and provided a clear clustering of genus and gender for a subset of taxonomic groups. The linear discriminant analysis under an assumption of multivariate normality provided a distinct classification of taxonomic groups resulting in an overall 4% misclassification rate; while the nearest neighbor discriminant analysis with a proportional prior gave an overall error rate of 5.2%. Internal bootstrap validation of the latter discriminant model yielded an average error rate of 3.5%. An external cross validation of the same model, conducted on independent samples of the same species with new individuals resulted in an average misclassification error rate of only 6.5%. Given the low error rates of misclassification, such multivariate statistical approaches are recommended for analysis of spectral reflectance in Coleoptera and other similar insect groups

Natural personalised ventilation for hospital wards: experimental validation

Personalised ventilation (PV) systems are useful in protecting vulnerable hospitalised patients from airborne infection due to localised delivery of clean air. A natural personalised ventilation (NPV) system has previously been shown to be a feasible, natural and low-energy alternative to mechanised PV systems. The original NPV system was investigated using three conceptual designs which used dynamic thermal modelling and steady-state computational fluid dynamics to simulate a single-bed hospital ward. Findings from these designs led to optimisation of the NPV system components (stack and ducts) which also serve as the basis for this experimental validation. The objective of this research is to validate the flow characteristics of the optimised NPV system using scaled model experiments in addition to computational fluid dynamics (CFD) studies. Water-bath modelling (WBM) was carried out in a large Perspex tank and a scaled version of the single-bed ward was also constructed in Perspex. Results improve our understanding of the proposed NPV strategy, in particular showing that different locations of heat sources within the model leads to considerably different internal temperatures at steady state. Close similarities between CFD and WBM simulations were also observed

Understanding supply chain security strategy

In the post-9/11 environment, organizations are acutely aware of the need to secure their supply chains from risks of being a target of, or an unwilling participant in, a terror attack. However, supply chain security (SCS) comes at a cost and increasing levels of protection have increasing levels of costs to the firm. So some firms engage in strategic initiatives to secure the supply chain (SC) while others do not; and each firm engages in varying degrees of activities to ensure SCS. Therefore, in this study, the researchers sought to explore what types of SCS strategies exist. The researchers analyze 162 responses to a SCS survey completed by executives from a broad range of firms and industries and identify three general SCS strategies: Advanced, Laggards, and Compliant. Implications for researchers and practitioners are presented

Implications of the problem orientated medical record (POMR) for research using electronic GP databases: a comparison of the Doctors Independent Network Database (DIN) and the General Practice Research Database (GPRD).

Background The General Practice Research Database (GPRD) and Doctor's Independent Network Database (DIN), are large electronic primary care databases compiled in the UK during the 1990s. They provide a valuable resource for epidemiological and health services research. GPRD (based on VAMP) presents notes as a series of discrete episodes, whereas DIN is based on a system (MEDITEL) that used a Problem Orientated Medical Record (POMR) which links prescriptions to diagnostic problems. We have examined the implications for research of these different underlying philosophies. Methods Records of 40,183 children from 141 practices in DIN and 76,310 from 464 practices in GRPD who were followed to age 5 were used to compare the volume of recording of prescribing and diagnostic codes in the two databases. To assess the importance and additional value of the POMR within DIN, the appropriateness of diagnostic linking to skin emollient prescriptions was investigated. Results Variation between practices for both the number of days on which prescriptions were issued and diagnoses were recorded was marked in both databases. Mean number of "prescription days" during the first 5 years of life was similar in DIN (19.5) and in GPRD (19.8), but the average number of "diagnostic days" was lower in DIN (15.8) than in GPRD (22.9). Adjustment for linkage increased the average "diagnostic days" to 23.1 in DIN. 32.7% of emollient prescriptions in GPRD appeared with an eczema diagnosis on the same day compared to only 19.4% in DIN; however, 86.4% of prescriptions in DIN were linked to an earlier eczema diagnosis. More specifically 83% of emollient prescriptions appeared under a problem heading of eczema in the 121 practices that were using problem headings satisfactorily. Conclusion Prescribing records in DIN and GPRD are very similar, but the usage of diagnostic codes is more parsimonious in DIN because of its POMR structure. Period prevalence rates will be underestimated in DIN unless this structure is taken into account. The advantage of the POMR is that in 121 of 141 practices using problem headings as intended, most prescriptions can be linked to a problem heading providing a specific reason for their issue

Membranous Glomerulonephritis With Crescents.

INTRODUCTION: Membranous glomerulonephritis (MGN) is rarely associated with necrotizing and crescentic glomerulonephritis (NCGN). METHODS: We report the clinical and pathologic findings in 15 patients with MGN and NCGN associated with anti-neutrophil cytoplasm antibodies (ANCAs), anti-glomerular basement membrane (GBM), or anti-phospholipase A2 receptor (PLA2R) antibodies. RESULTS: The cohort consisted of 15 patients: 7 males and 8 females with a median age of 63 years (range: 18-79). In 12 of 15 patients, MGN and NCGN were diagnosed at the time of the biopsy, and in 3 cases, MGN predated the NCGN. ANCA was positive in 7 cases (6 MPO myeloperoxidase (MPO)-ANCA and 1 PR3-ANCA), anti-GBM antibodies were detected in 5 cases, and anti-PLA2R antibodies were found in 2 cases. One case was negative for all antibodies. Microscopic hematuria was present in all but one patient who was anuric, and median urinary protein-to-creatinine ratio was 819.5 mg/mmol (range: 88-5600). Pathologic evaluation revealed MGN and NCGN with crescents involving 28% of glomeruli (median; range: 5%-100%). Follow-up was available for all 15 patients; all were treated with steroids; 10 with cyclophosphamide, and 6 also received rituximab. At a median follow-up of 72 months, 9 had stabilization or improvement of renal function, 6 had progressed to end-stage renal disease, and 4 died during the follow-up period. CONCLUSION: MGN with crescents associated with ANCAs or anti-GBM antibodies is a rare dual glomerulopathy. Patients present with heavy proteinuria, microscopic hematuria, and acute kidney injury and should be treated for a rapidly progressive glomerulonephritis. Prognosis is variable, and 40% of patients progress to end-stage renal disease