Hochster's theta invariant and the Hodge-Riemann bilinear relations

Let R be an isolated hypersurface singularity, and let M and N be finitely generated R-modules. As R is a hypersurface, the torsion modules of M against N are eventually periodic of period two (i.e., Tor_i^R(M,N) is isomorphic to Tor_{i+2}^R(M,N) for i sufficiently large). Since R has only an isolated singularity, these torsion modules are of finite length for i sufficiently large. The theta invariant of the pair (M,N) is defined by Hochster to be length(Tor_{2i}^R(M,N)) - length(Tor_{2i+1}^R(M,N)) for i sufficiently large. H. Dao has conjectured that the theta invariant is zero for all pairs (M,N) when R has even dimension and contains a field. This paper proves this conjecture under the additional assumption that R is graded with its irrelevant maximal ideal giving the isolated singularity. We also give a careful analysis of the theta pairing when the dimension of R is odd, and relate it to a classical pairing on the smooth variety Proj(R).Comment: 20 page

The effect of diabetes and insulin on the turnover of hexokinase II in the skeletal muscle

Studies were undertaken to determine the nature of the cause(s) for the reported decrease in the measurable hexokinase II activity in the skeletal muscle of the streptozotocin-diabetic rat. An ELISA procedure was developed to determine the amount of hexokinase II protein in the skeletal muscle extracts, and immunoprecipitation was utilized to determine the hexokinase II activity. Both hexokinase II activity and the amount of hexokinase II protein decreased in the diabetic rat. Both increased toward normal treatment with insulin. The specific activity of the hexokinase II was found to be the same in the skeletal muscle extracts from normal, diabetic, and diabetic insulin-treated rats;The rate of synthesis of hexokinase II in the skeletal muscle was determined the rate of incorporation of (\u273)H leucine into hexokinase II. This rate was compared to that of the total cytosolic proteins to determine if the rate of hexokinase II synthesis was specifically affected by insulin. This relative rate of synthesis of hexokinase II was found to be approximately two times greater in the normal as compared to the diabetic rat. The administration of insulin to the diabetic animal was found to increase the relative rate of hexokinase synthesis to approximately normal levels;The apparent rate constants of degradation were determined using a double-isotope technique and from these constants it was possible to calculate the apparent half-lives. The apparent half-life of hexokinase II obtained for the normal, diabetic, and diabetic insulin-treated animals was compared to the half-lives of the average of the total cytosolic proteins for each respective state. This was done to determine if the degradation of hexokinase II was specifically affected by insulin or the diabetic state. This corrected apparent half-life was found to be approximately 2.3 times greater in the normal as compared to the diabetic rat and approximately 2 times greater in the insulin-treated as compared to the diabetic;This study suggests that the decrease in measurable hexokinase II activity in the diabetic skeletal muscle is due to a decrease in the synthesis and an increase in the degradation of the enzyme. The results also suggest that insulin may play a role in increasing the synthesis of the enzyme, but does not alter the specific activity of the enzyme

INDOT DNR Maintenance Memorandum

On March 13, 1997, INDOT and the Department of Natural Resources signed a memorandum of understanding that exempted specified main-tenance activities from the Flood Control and Navigable Waterways Act. There has been much confusion and many interpretation variances in the interim. INDOT has been working with the DNR to update the MOU to provide clarity to areas of conflicting interpretation. Join us for a discussion

JMC’s Interdisciplinary Smoking Cessation Program

No abstract availabl

Cell Cycle: The Art of Multi-Tasking

SummarySeparase is the protease that cleaves the cohesive link between sister chromatids to trigger chromosome segregation in mitosis and meiosis. This enzyme is known to orchestrate additional mitotic events and we now gain new insight into how it promotes cytokinesis in the nematode Caenorhabditis elegans

Product assurance policies and procedures for flight dynamics software development

The product assurance policies and procedures necessary to support flight dynamics software development projects for Goddard Space Flight Center are presented. The quality assurance and configuration management methods and tools for each phase of the software development life cycles are described, from requirements analysis through acceptance testing; maintenance and operation are not addressed

Keep it Simple? Predicting Primary Health Care Costs with Measures of Morbidity and Multimorbidity

In this paper we investigate the relationship between patients’ primary care costs (consultations, tests, drugs) and their age, gender, deprivation and alternative measures of their morbidity and multimorbidity. Such information is required in order to set capitation fees or budgets for general practices to cover their expenditure on providing primary care services. It is also useful to examine whether practices’ expenditure decisions vary equitably with patient characteristics. Electronic practice record keeping systems mean that there is very rich information on patient diagnoses. But the diagnostic information (with over 9000 possible diagnoses) is too detailed to be practicable for setting capitation fees or practice budgets. Some method of summarizing such information into more manageable measures of morbidity is required. We therefore compared the ability of eight measures of patient morbidity and multimorbidity to predict future primary care costs using data on 86,100 individuals in 174 English practices. The measures were derived from four morbidity descriptive systems (17 chronic diseases in the Quality and Outcomes Framework (QOF), 17 chronic diseases in the Charlson scheme, 114 Expanded Diagnosis Clusters (EDCs), and 68 Adjusted Clinical Groups (ACGs)). We found that, in general, for a given disease description system, counts of diseases and sets of disease dummy variables had similar explanatory power and that measures with more categories did better than those with fewer. The EDC measures performed best, followed by the QOF and ACG measures. The Charlson measures had the worst performance but still improved markedly on models containing only age, gender, deprivation and practice effects. Allowing for individual patient morbidity greatly reduced the association of age and cost. There was a pro-deprived bias in expenditure: after allowing for morbidity, patients in areas in the highest deprivation decile had costs which were 22% higher than those in the lowest deprivation decile. The predictive ability of the best performing morbidity and multimorbidity measures was very good for this type of individual level cross section data, with R2 ranging from 0.31 to 0.46. The statistical method of estimating the relationship between patient characteristics and costs was less important than the type of morbidity measure. Rankings of the morbidity and multimorbidity measures were broadly similar for generalised linear models with log link and Poisson errors and for OLS estimation. It would be currently feasible to combine the results from our study with the data on the number of patients with each QOF disease, which is available on all practices in England, to calculate budgets for general practices to cover their primary care costs.multimorbidity; primary care; utilisation; costs; deprivation; budgets