A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

Arterial inflammation in mice lacking the interleukin 1 receptor antagonist gene

Branch points and flexures in the high pressure arterial system have long been recognized as sites of unusually high turbulence and consequent stress in humans are foci for atherosclerotic lesions. We show that mice that are homozygous for a null mutation in the gene encoding an endogenous antiinflammatory cytokine, interleukin 1 receptor antagonist (IL-1ra), develop lethal arterial inflammation involving branch points and flexures of the aorta and its primary and secondary branches. We observe massive transmural infiltration of neutrophils, macrophages, and CD4(+) T cells. Animals appear to die from vessel wall collapse, stenosis, and organ infarction or from hemorrhage from ruptured aneurysms. Heterozygotes do not die from arteritis within a year of birth but do develop small lesions, which suggests that a reduced level of IL-1ra is insufficient to fully control inflammation in arteries. Our results demonstrate a surprisingly specific role for IL-1ra in the control of spontaneous inflammation in constitutively stressed artery walls, suggesting that expression of IL-1 is likely to have a significant role in signaling artery wall damage

Analysis of LIGO data for gravitational waves from binary neutron stars

We report on a search for gravitational waves from coalescing compact binary systems in the Milky Way and the Magellanic Clouds. The analysis uses data taken by two of the three LIGO interferometers during the first LIGO science run and illustrates a method of setting upper limits on inspiral event rates using interferometer data. The analysis pipeline is described with particular attention to data selection and coincidence between the two interferometers. We establish an observational upper limit of $\mathcal{R}<$1.7 \times 10^{2}$per year per Milky Way Equivalent Galaxy (MWEG), with 90coalescence rate of binary systems in which each component has a mass in the range 1--3$M_\odot$.Comment: 17 pages, 9 figure

Plasma protein binding of diphenylhydantoin effects of sex hormones, renal and hepatic disease

The in vitro binding of diphenylhydantoin (DPH) to the protein in plasma from 97 volunteers has been studied using ultrafiltration at 37° C. The capacity of plasma protein to bind DPH did not differ significantly between pregnant women (11.6 ± 1.7% of total drug unbound), women taking oral contraceptives (9.9 ± 1.7% unbound), healthy males (10.6 ± 1.3% unbound), and healthy females (11.0 ± 3.2% unbound). However, in plasma from patients with renal disease (15.8 ± 3.9% unbound), hepatic disease (15.9 ∥ 6.0%) or hepatorenal disease (15.6 ± 5.4%), the protein binding of DPH was significantly decreased. These changes in protein binding were found to correlate better with changes in albumin and bilirubin levels in plasma than with any o f 13 other biochemical parameters examined

The renal handling of diphenylhydantoin and 5-(p-hydroxyphenyl)-5-phenylhydantoin

The renal clearances of diphenylhydantoin (DPH) and its major metabolite, 5-(p-hydroxyphenyl)-5-phenylhydantoin (HPPH) have been measured in groups of 16 and 14 ambulant epileptic patients, respectively. All patients had normal renal function (creatinine clearances, 83 to 148 ml per minute), and were taking oral diphenylhydantoin sodium in doses of 300 to 500 mg per day. DPH clearance (3 to 23 ml per minute, depending on urine flow rate) was considerably less than that expected for inulin, and it seems probable that DPH undergoes net resorption in its passage through the kidney. HPPH clearance (76 to 420 ml per minute depending on urine flow rate) exceeded expected inulin clearance if urine flow rates were sufficiently high, allowing the suggestion that net secretion of HPPH occurs during its passage through the nephron. Although the clearances of both compounds increase with urine flow rate, it is concluded that neither oliguria nor polyuria would be likely to greatly influence plasma DPH concentration in the short term, making dosage adjustment in these two circumstances unnecessary, at least as a matter of urgency

The effect of certain drugs on the plasma protein binding of phenytoin

Summary: Most of the phenytoin in plasma is protein bound. Anti‐convulsants are often prescribed in combination and it is important to know if other anticonvulsants displace phenytoin from its plasma‐protein binding sites. If this happened, the biological effect of phenytoin could be altered without much change in its total concentration in plasma. The binding of phenytoin to serum albumin and plasma protein in vitro has been studied by ultrafiltration techniques and equilibrium dialysis at a variety of temperatures and in the presence of “therapeutic” concentrations of other anticonvulsants and aspirin. Equilibrium dialysis and ultrafiltration yielded comparable results. Phenytoin binding de‐creased with increasing temperature (92% bound at 3 °C, 80% bound at 37 °C). With the possible exception of sulthiame, the other anticonvulsants tested (phenobarbitone, ethosuximide, diazepam and carbamazepine), and also aspirin, did not displace phenytoin from its plasma protein binding sites. These findings may be helpful in interpreting plasma phenytoin concentrations when other anticonvulsants are prescribed simultaneously

Electron-capture gas chromatographic assay for metoclopramide in plasma

An original electron-capture gas chromatographic assay has been developed for the quantitation of metoclopramide in human plasma. The method involves derivatization with heptafluorobutyryl imidazole after alkaline extraction, acid backwash, and a further alkaline extraction. Plasma levels of metoclopramide as low as 5 μg/l can be measured using 1 ml of plasma, and no interference from related substances or commonly prescribed drugs has been found. The percentage recovery of drug from plasma ranges from 88% to virtually 100%, and the between-run variation in the assay is 4.3%. The assay has been used for the study of metoclopramide pharmacokinetics in man following intravenous single-dose administration. The resultant plasma concentration vs. time curve was biexponential, with a terminal half-life of 5.0 h, and a distribution half-time of 0.3 h