Automatic generation of simplified weakest preconditions for integrity constraint verification

Given a constraint $c$ assumed to hold on a database $B$ and an update $u$ to be performed on $B$, we address the following question: will $c$ still hold after $u$ is performed? When $B$ is a relational database, we define a confluent terminating rewriting system which, starting from $c$ and $u$, automatically derives a simplified weakest precondition $wp(c,u)$ such that, whenever $B$ satisfies $wp(c,u)$, then the updated database $u(B)$ will satisfy $c$, and moreover $wp(c,u)$ is simplified in the sense that its computation depends only upon the instances of $c$ that may be modified by the update. We then extend the definition of a simplified $wp(c,u)$ to the case of deductive databases; we prove it using fixpoint induction

On the variational interpretation of the discrete KP equation

We study the variational structure of the discrete Kadomtsev-Petviashvili (dKP) equation by means of its pluri-Lagrangian formulation. We consider the dKP equation and its variational formulation on the cubic lattice ${\mathbb Z}^{N}$ as well as on the root lattice $Q(A_{N})$. We prove that, on a lattice of dimension at least four, the corresponding Euler-Lagrange equations are equivalent to the dKP equation.Comment: 24 page

Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Soil Conditioner Formula Enriched by Humic Substance to Enhance Productivity of Ultisols Taman Bogo, Lampung

The objectives of this research are : (1) to find enrichment substance from various organic material to increase the effectiveness of the soil conditioner, (2) to study the effect of humic substance contained in organic matter on soil properties and crop productivity. Research preceded by humic substance extraction from various organic matter. Reseach was conducted at green house using Ultisols from Taman Bogo, Center of Lampung. The experimental design used a factorial with four replications, treatment that tested were factor I: some organic material: municipal waste compost, manure compost, coal and peat, whereas factor II: enrichment types: extracted (HLS) and no extracted. The results of the research showed that HLS (humic like substances) from peat contained the highest humic substances (humat and fulvic acid), whereas HLS from manure contained the lowest humic substance. Manure was better applied in the form of compost than HLS. Organic materials with a high C/N ratio and low nutrient content (i.e. coal, peat, municipal wastes), that was applied in HSL form did not effect plant growth and biomass production significantly

Female Sterilization: Comparative Study of Hysteroscopic versus Laparoscopic Sterilization

Overview and Aims: Female sterilization is increasingly requested as a contraceptive method. Hysteroscopic sterilization by transcervical placing of Essure® micro-inserts in the initial portion of the tubes is a recent alternative to laparoscopic sterilization. The objective of this study is to evaluate the safety and effectiveness of hysteroscopic versus laparoscopic sterilization. Study Design: Retrospective cohort study. Population: A total of 98 women undergoing sterilization in an outpatient clinic between July 2005 and July 2009. Methods: Patients’ age, associated diseases, anesthesic risk, procedure time, discomfort, adverse events and success rate were evaluated. Results: Mean age at surgery was 37.8 years (19-49), and there were no statistically significant differences between the groups regarding this parameter. Women in the hysteroscopic group had a significant number of associated diseases (98% versus 47%), obesity (31% versus 6%), and anesthesic risk (ASA III- 31% versus 0%). The mean duration of the procedure was the same for both techniques (laparoscopy 28 minutes and hysteroscopy 26 minutes). All laparoscopic sterilizations were successfully completed. In the hysteroscopic group 4% failed to complete the technique. There were no cases of severe pain. Women in the hysteroscopy group reported pain less frequently (40% versus 57%, χ2 p<0.05). Long term success rate was similar in both groups (96% for hysteroscopy and 98% for laparoscopy). Conclusions: In spite of a higher incidence of associated diseases, obesity and anesthetic risks in the hysteroscopy group, there were no significant differences in the duration of the procedure, adverse events and success rate. The hysteroscopic approach can therefore be considered an alternative to laparoscopy, eliminating the need for incisional surgery and for general anaesthesia. If women with high surgical risk and several associated diseases can safely undergo this procedure, it could well become the preferred method for women who want a permanent and irreversible contraceptive method

Gold(I)-Catalysed Direct Thioetherifications Using Allylic Alcohols: an Experimental and Computational Study

A gold(I)-catalysed direct thioetherification reaction between allylic alcohols and thiols is presented. The reaction is generally highly regioselective (S(N)2′). This dehydrative allylation procedure is very mild and atom economical, producing only water as the by-product and avoiding any unnecessary waste/steps associated with installing a leaving or activating group on the substrate. Computational studies are presented to gain insight into the mechanism of the reaction. Calculations indicate that the regioselectivity is under equilibrium control and is ultimately dictated by the thermodynamic stability of the products

Ribosomal S6K1 in POMC and AgRP Neurons Regulates Glucose Homeostasis but Not Feeding Behavior in Mice.

SummaryHypothalamic ribosomal S6K1 has been suggested as a point of convergence for hormonal and nutrient signals in the regulation of feeding behavior, bodyweight, and glucose metabolism. However, the long-term effects of manipulating hypothalamic S6K1 signaling on energy homeostasis and the cellular mechanisms underlying these roles are unclear. We therefore inactivated S6K1 in pro-opiomelanocortin (POMC) and agouti-related protein (AgRP) neurons, key regulators of energy homeostasis, but in contrast to the current view, we found no evidence that S6K1 regulates food intake and bodyweight. In contrast, S6K1 signaling in POMC neurons regulated hepatic glucose production and peripheral lipid metabolism and modulated neuronal excitability. S6K1 signaling in AgRP neurons regulated skeletal muscle insulin sensitivity and was required for glucose sensing by these neurons. Our findings suggest that S6K1 signaling is not a general integrator of energy homeostasis in the mediobasal hypothalamus but has distinct roles in the regulation of glucose homeostasis by POMC and AgRP neurons