Wright-Fisher diffusion with negative mutation rates

We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the classical Wright-Fisher diffusions, except that the "mutation rates" are now nonpositive. This model, suggested by Aldous, appears in the study of a conjectured diffusion limit for a Markov chain on Cladograms. The striking feature of these models is that the boundary is not reflecting, and we kill the process once it hits the boundary. We derive the explicit exit distribution from the simplex and probabilistic bounds on the exit time. We also prove that these processes can be viewed as a "stochastic time-reversal" of a Wright-Fisher process of increasing dimensions and conditioned at a random time. A key idea in our proofs is a skew-product construction using certain one-dimensional diffusions called Bessel-square processes of negative dimensions, which have been recently introduced by Going-Jaeschke and Yor.Comment: Published in at http://dx.doi.org/10.1214/11-AOP704 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Three-dimensional inviscid analysis of radial turbine flow and a limited comparison with experimental data

The three-dimensional inviscid DENTON code is used to analyze flow through a radial-inflow turbine rotor. Experimental data from the rotor are compared with analytical results obtained by using the code. The experimental data available for comparison are the radial distributions of circumferentially averaged values of absolute flow angle and total pressure downstream of the rotor exit. The computed rotor-exit flow angles are generally underturned relative to the experimental values, which reflect the boundary-layer separation at the trailing edge and the development of wakes downstream of the rotor. The experimental rotor is designed for a higher-than-optimum work factor of 1.126 resulting in a nonoptimum positive incidence and causing a region of rapid flow adjustment and large velocity gradients. For this experimental rotor, the computed radial distribution of rotor-exit to turbine-inlet total pressure ratios are underpredicted due to the errors in the finite-difference approximations in the regions of rapid flow adjustment, and due to using the relatively coarser grids in the middle of the blade region where the flow passage is highly three-dimensional. Additional results obtained from the three-dimensional inviscid computation are also presented, but without comparison due to the lack of experimental data. These include quasi-secondary velocity vectors on cross-channel surfaces, velocity components on the meridional and blade-to-blade surfaces, and blade surface loading diagrams. Computed results show the evolution of a passage vortex and large streamline deviations from the computational streamwise grid lines. Experience gained from applying the code to a radial turbine geometry is also discussed

Comparative Field Evaluation of Combinations of Long-Lasting Insecticide Treated Nets and Indoor Residual Spraying, Relative to Either Method Alone, for Malaria Prevention in an Area where the main Vector is Anopheles Arabiensis.

Long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS) are commonly used together in the same households to improve malaria control despite inconsistent evidence on whether such combinations actually offer better protection than nets alone or IRS alone. Comparative tests were conducted using experimental huts fitted with LLINs, untreated nets, IRS plus untreated nets, or combinations of LLINs and IRS, in an area where Anopheles arabiensis is the predominant malaria vector species. Three LLIN types, Olyset®, PermaNet 2.0® and Icon Life® nets and three IRS treatments, pirimiphos-methyl, DDT, and lambda cyhalothrin, were used singly or in combinations. We compared, number of mosquitoes entering huts, proportion and number killed, proportions prevented from blood-feeding, time when mosquitoes exited the huts, and proportions caught exiting. The tests were done for four months in dry season and another six months in wet season, each time using new intact nets. All the net types, used with or without IRS, prevented >99% of indoor mosquito bites. Adding PermaNet 2.0® and Icon Life®, but not Olyset® nets into huts with any IRS increased mortality of malaria vectors relative to IRS alone. However, of all IRS treatments, only pirimiphos-methyl significantly increased vector mortality relative to LLINs alone, though this increase was modest. Overall, median mortality of An. arabiensis caught in huts with any of the treatments did not exceed 29%. No treatment reduced entry of the vectors into huts, except for marginal reductions due to PermaNet 2.0® nets and DDT. More than 95% of all mosquitoes were caught in exit traps rather than inside huts. Where the main malaria vector is An. arabiensis, adding IRS into houses with intact pyrethroid LLINs does not enhance house-hold level protection except where the IRS employs non-pyrethroid insecticides such as pirimiphos-methyl, which can confer modest enhancements. In contrast, adding intact bednets onto IRS enhances protection by preventing mosquito blood-feeding (even if the nets are non-insecticidal) and by slightly increasing mosquito mortality (in case of LLINs). The primary mode of action of intact LLINs against An. arabiensis is clearly bite prevention rather than insecticidal activity. Therefore, where resources are limited, priority should be to ensure that everyone at risk consistently uses LLINs and that the nets are regularly replaced before being excessively torn. Measures that maximize bite prevention (e.g. proper net sizes to effectively cover sleeping spaces, stronger net fibres that resist tears and burns and net use practices that preserve net longevity), should be emphasized

Fast algorithms for computing defects and their derivatives in the Regge calculus

Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson like scheme. In such cases it is essential that efficient algorithms be used when computing the defect angles and their derivatives with respect to the leg-lengths. The purpose of this paper is to present details of such an algorithm.Comment: 38 pages, 10 figure

Computational study of hole shape effect on film cooling performance

Film cooling effectiveness has been studied by using a computational approach based on solving the Reynolds-averaged Navier–Stokes equations. A wind tunnel test configuration is considered with a total of four cooling hole geometries as a cylindrical hole, a cylindrical hole with an upstream wedge (called ‘ramp’ thereafter), a shaped diffuser, and a double console slot. In all cases, the hole centreline has an inclination angle of 35° against the mainstream airflow and the blowing ratio is unity. Choosing the cylindrical model as a baseline, simulations have been carried out for grid convergence and turbulence model influence studies. Results are compared with available experimental data and other numerical predictions and good agreement has been achieved. Further computations continue with three remaining geometries, using the baseline flow conditions and configuration. Comparing to the results from the baseline model, it was found that the centreline adiabatic cooling effectiveness has shown incremental increases for the ‘ramp’ model, while results from the console slot model and the shape diffuser model have exhibited significant improvements by a factor of 1.5 and 2, respectively. The reason for such a step change in cooling effectiveness is mainly due to the weakening of the vortex structures in the vicinity of the hole exit, thus significantly reducing the entrainment of surrounding ‘hot’ fluids

Insecticide resistance and the future of malaria control in Zambia.

BACKGROUND: In line with the Global trend to improve malaria control efforts a major campaign of insecticide treated net distribution was initiated in 1999 and indoor residual spraying with DDT or pyrethroids was reintroduced in 2000 in Zambia. In 2006, these efforts were strengthened by the President's Malaria Initiative. This manuscript reports on the monitoring and evaluation of these activities and the potential impact of emerging insecticide resistance on disease transmission. METHODS: Mosquitoes were captured daily through a series of 108 window exit traps located at 18 sentinel sites. Specimens were identified to species and analyzed for sporozoites. Adult Anopheles mosquitoes were collected resting indoors and larva collected in breeding sites were reared to F1 and F0 generations in the lab and tested for insecticide resistance following the standard WHO susceptibility assay protocol. Annual cross sectional household parasite surveys were carried out to monitor the impact of the control programme on prevalence of Plasmodium falciparum in children aged 1 to 14 years. RESULTS: A total of 619 Anopheles gambiae s.l. and 228 Anopheles funestus s.l. were captured from window exit traps throughout the period, of which 203 were An. gambiae malaria vectors and 14 An. funestus s.s.. In 2010 resistance to DDT and the pyrethroids deltamethrin, lambda-cyhalothrin and permethrin was detected in both An. gambiae s.s. and An. funestus s.s.. No sporozoites were detected in either species. Prevalence of P. falciparum in the sentinel sites remained below 10% throughout the study period. CONCLUSION: Both An. gambiae s.s. and An. funestus s.s. were controlled effectively with the ITN and IRS programme in Zambia, maintaining a reduced disease transmission and burden. However, the discovery of DDT and pyrethroid resistance in the country threatens the sustainability of the vector control programme