Heat kernel asymptotics with mixed boundary conditions

We calculate the coefficient $a_5$ of the heat kernel asymptotics for an operator of Laplace type with mixed boundary conditions on a general compact manifold.Comment: 26 pages, LaTe

Collecting Critical Data to Assess the Sustainability of Rural Infrastructure in Low-Income Countries

Rural water systems in low-income countries often fail to deliver potable water sustainably.Reasons include socio-economic, financial, and technical challenges that are specific to the community. Improved assessment methods are critical if decision makers want to provide sustainable solutions; however, to be useful, such methods require substantial data about the complex interaction between people, water, and infrastructure. Such interaction is affected by, and in turn, affects the behavior of community members regarding water usage, resources for infrastructure maintenance, and choice of assets. Unfortunately, much of these data are not readily available, in a large part because of the site-specific context associated with each rural community. Because of the difficulty and expense in obtaining site-specific data, it is important to identify the most critical needs for field studies versus the data that can be obtained from sources such as non-governmental organizations and the general literature.We examine this issue by first using an extensive data set from Malawi to identify the critical data needs. We then present several examples of field studies in Honduras and Uganda where we collected some of that critical data. Throughout, we discuss best practices for conducting and using focused field studies versus the general literature

Heat-kernel coefficients of the Laplace operator on the D-dimensional ball

We present a very quick and powerful method for the calculation of heat-kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non-trivial commutation of series and integrals and skilful analytic continuation of zeta functions on the complex plane. We apply our method to the case of the heat-kernel expansion of the Laplace operator on a $D$-dimensional ball with either Dirichlet, Neumann or, in general, Robin boundary conditions. The final formulas are quite simple. Using this case as an example, we illustrate in detail our scheme ---which serves for the calculation of an (in principle) arbitrary number of heat-kernel coefficients in any situation when the basis functions are known. We provide a complete list of new results for the coefficients $B_3,...,B_{10}$, corresponding to the $D$-dimensional ball with all the mentioned boundary conditions and $D=3,4,5$.Comment: 29 pages, LaTex, lines had been cut in the previous version by transmission, no further change

Asymptotics of the heat equation with `exotic' boundary conditions or with time dependent coefficients

The heat trace asymptotics are discussed for operators of Laplace type with Dirichlet, Robin, spectral, D/N, and transmittal boundary conditions. The heat content asymptotics are discussed for operators with time dependent coefficients and Dirichlet or Robin boundary conditions.Comment: A talk of P.B. Gilkey at "Quantum Gravity and Spectral Geometry", Naples, July 2001, to appear in the proceedings v2: a misprint in eq. (3) correcte

Xanthine oxidase inhibition for the improvement of long-term outcomes following ischaemic stroke and transient ischaemic attack (XILO-FIST) - Protocol for a randomised double blind placebo-controlled clinical trial

Background: Allopurinol, a xanthine oxidase inhibitor, reduced progression of carotid-intima media thickness and lowered blood pressure in a small clinical trial in people with ischaemic stroke. Xanthine oxidase inhibition for improvement of long-term outcomes following ischaemic stroke and transient ischaemic attack (XILO-FIST) aims to assess the effect of allopurinol treatment on white matter hyperintensity progression and blood pressure after stroke. This paper describes the XILO-FIST protocol. Methods: XILO-FIST is a multicentre randomised double-blind, placebo-controlled, parallel group clinical trial funded by the British Heart Foundation and the Stroke Association. The trial has been adopted by the Scottish Stroke Research Network and the UK Clinical Research Network. The trial is registered in clinicaltrials.gov (registration number NCT02122718). XILO-FIST will randomise 464 participants, aged greater than 50 years, with ischaemic stroke within the past month, on a 1:1 basis, to two years treatment with allopurinol 300 mg twice daily or placebo. Participants will undergo brain magnetic resonance imaging, cognitive assessment, ambulatory blood pressure monitoring and blood sampling at baseline and after two years treatment. The primary outcome will be white matter hyperintensity progression, measured using the Rotterdam progression scale. Secondary outcomes will include change in white matter hyperintensity volume, mean day-time systolic blood pressure and measures of cognitive function. Up to 100 will undergo additional cardiac magnetic resonance imaging in a sub-study of left ventricular mass. Discussion: If white matter hyperintensity progression is reduced, allopurinol could be an effective preventative treatment for patients with ischaemic stroke and clinical endpoint studies would be needed. If allopurinol reduces blood pressure after stroke, then it could be used to help patients reach blood pressure targets

Heat-kernels and functional determinants on the generalized cone

We consider zeta functions and heat-kernel expansions on the bounded, generalized cone in arbitrary dimensions using an improved calculational technique. The specific case of a global monopole is analysed in detail and some restrictions thereby placed on the $A_{5/2}$ coefficient. The computation of functional determinants is also addressed. General formulas are given and known results are incidentally, and rapidly, reproduced.Comment: 26p,LaTeX.(Cosmetic changes and eqns (9.8),(11.2) corrected.

Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario

We study the spectral geometry of an operator of Laplace type on a manifold with a singular surface. We calculate several first coefficients of the heat kernel expansion. These coefficients are responsible for divergences and conformal anomaly in quantum brane-world scenario.Comment: latex, 25 p

5‑Substituted Pyridine-2,4-dicarboxylate Derivatives Have Potential for Selective Inhibition of Human Jumonji‑C Domain-Containing Protein 5

Jumonji-C domain-containing protein 5 (JMJD5) is a 2-oxoglutarate (2OG)-dependent oxygenase that plays important roles in development, circadian rhythm, and cancer through unclear mechanisms. JMJD5 has been reported to have activity as a histone protease, as an Nε-methyl lysine demethylase, and as an arginine residue hydroxylase. Small-molecule JMJD5-selective inhibitors will be useful for investigating its (patho)physiological roles. Following the observation that the broad-spectrum 2OG oxygenase inhibitor pyridine-2,4-dicarboxylic acid (2,4-PDCA) is a 2OG-competing JMJD5 inhibitor, we report that 5-aminoalkyl-substituted 2,4-PDCA derivatives are potent JMJD5 inhibitors manifesting selectivity for JMJD5 over other human 2OG oxygenases. Crystallographic analyses with five inhibitors imply induced fit binding and reveal that the 2,4-PDCA C5 substituent orients into the JMJD5 substrate-binding pocket. Cellular studies indicate that the lead compounds display similar phenotypes as reported for clinically observed JMJD5 variants, which have a reduced catalytic activity compared to wild-type JMJD5