Accuracy of one-dimensional collision integral in the rigid spheres approximation

The accuracy of calculation of spectral line shapes in one-dimensional approximation is studied analytically in several limiting cases for arbitrary collision kernel and numerically in the rigid spheres model. It is shown that the deviation of the line profile is maximal in the center of the line in case of large perturber mass and intermediate values of collision frequency. For moderate masses of buffer molecules the error of one-dimensional approximation is found not to exceed 5%.Comment: LaTeX, 24 pages, 8 figure

An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci

A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutation-selection balance. Other results include the nonexistence of 'viability analogous, Hardy-Weinberg' modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded introductory and discussion sections, added corollaries, new results on modifier polymorphisms, minor corrections. 49 pages, 64 reference

Iterative approximation of k-limited polling systems

The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient

Boundary-layer turbulence as a kangaroo process

A nonlocal mixing-length theory of turbulence transport by finite size eddies is developed by means of a novel evaluation of the Reynolds stress. The analysis involves the contruct of a sample path space and a stochastic closure hypothesis. The simplifying property of exhange (strong eddies) is satisfied by an analytical sampling rate model. A nonlinear scaling relation maps the path space onto the semi-infinite boundary layer. The underlying near-wall behavior of fluctuating velocities perfectly agrees with recent direct numerical simulations. The resulting integro-differential equation for the mixing of scalar densities represents fully developed boundary-layer turbulence as a nondiffusive (Kubo-Anderson or kangaroo) type of stochastic process. The model involves a scaling exponent (with → in the diffusion limit). For the (partly analytical) solution for the mean velocity profile, excellent agreement with the experimental data yields 0.58. © 1995 The American Physical Society

Potential of essential fatty acid deficiency with extremely low fat diet in lipoprotein lipase deficiency during pregnancy: A case report

BACKGROUND: Pregnancy in patients with lipoprotein lipase deficiency is associated with high risk of maternal pancreatitis and fetal death. A very low fat diet (< 10% of calories) is the primary treatment modality for the prevention of acute pancreatitis, a rare but potentially serious complication of severe hypertriglyceridemia. Since pregnancy can exacerbate hypertriglyceridemia in the genetic absence of lipoprotein lipase, a further reduction of dietary fat intake to < 1–2% of total caloric intake may be required during the pregnancy, along with the administration of a fibrate. It is uncertain if essential fatty acid deficiency will develop in the mother and fetus with this extremely low fat diet, or whether fibrates will cross the placenta and concentrate in the fetus. CASE PRESENTATION: A 23 year-old gravida 1 woman with primary lipoprotein lipase deficiency was seen at 7 weeks of gestation in the Lipid Clinic for management of severe hypertriglyceridemia that had worsened with pregnancy. While on her habitual fat intake of 10% of total calories, her pregnancy resulted in an exacerbation of the hypertriglyceridemia, which prompted further restriction of fat intake to < 2% of total calories, as well as administration of gemfibrozil at a lower than average dose. The level of gemfibrozil, as the active metabolite, in the venous and arterial fetal cord blood was within the expected therapeutic range for adults. The clinical signs and a biomarker of essential fatty acid deficiency, namely the ratio of 20:3 [n-9] to 20:4 [n-6] fatty acids, were closely monitored throughout her pregnancy. Despite her extremely low fat diet, the levels of essential fatty acids measured in the mother and in the fetal blood immediately postpartum were normal. Normal essential fatty acid levels may have been achieved by the topical application of sunflower oil. CONCLUSIONS: An extremely low fat diet in combination with topical sunflower oil and gemfibrozil administration was safely implemented in pregnancy associated with the severe hypertriglyceridemia of lipoprotein lipase deficiency