Possible Solution of the long-standing discrepancy in the Microlensing Optical Depth Toward the Galactic Bulge by correcting the stellar number count

We find that significant incompleteness in stellar number counts results in a significant overestimate of the microlensing optical depth $\tau$ and event rate per star per year $\Gamma$ toward the Galactic bulge from the first two years of the MOA-II survey. We find that the completeness in Red Clump Giant (RCG) counts $f_{\rm RC}$ decreases proportional to the galactic latitude $b$, as $f_{\rm RC}=(0.63\pm0.11)-(0.052\pm0.028)\times b$, ranging between 1 and 0.7 at $b=-6^\circ\sim-1.5^\circ$. The previous measurements using all sources by Difference Image Analysis (DIA) by MACHO and MOA-I suffer the same bias. On the other hand, the measurements using a RCG sample by OGLE-II, MACHO and EROS were free from this bias because they selected only the events associated with the resolved stars. Thus, the incompleteness both in the number of events and stellar number count cancel out. We estimate $\tau$ and $\Gamma$ by correcting this incompleteness. In the central fields with $|l|<5^\circ$, we find $\Gamma=[18.74\pm0.91]\times10^{-6}\exp[(0.53\pm0.05)(3-|b|)]$ star$^{-1}$ yr$^{-1}$ and $\tau_{200}=[1.84\pm0.14]\times10^{-6}\exp[(0.44\pm0.07)(3-|b|)]$ for the 427 events with $t_{\rm E}\leq200\,$days using all sources brighter than $I_s\leq20$ mag. Our revised all-source $\tau$ measurements are about 2-$\sigma$ smaller than the other all-source measurements and are consistent with the RCG measurements within 1-$\sigma$. We conclude that the long-standing problem on discrepancy between the high $\tau$ with all-source samples by DIA and low $\tau$ with RCG samples can probably be explained by the incompleteness of the stellar number count. A model fit to these measurements predicts $\Gamma=4.60\pm0.25\times10^{-5}$ star$^{-1}$ yr$^{-1}$ at $|b|\sim-1^\circ.4$ and $-2^\circ.25<l<3^\circ.75$ for sources with $I<20$, where the future space mission WFIRST will observe.Comment: 39 pages, 15 figures, 5 tables, accepted for publication in ApJ. arXiv admin note: substantial text overlap with arXiv:1305.018

Influence of design parameters on occurence of oil whirl

Oil whirl instability is a serious problem in oil lubricated journal bearings. The phenomenon is characterized by a subsynchronous vibration of the journal within the bush and is particularly apparent in turbogenerators, aeroengines and electric motors. A review is presented of previous papers on the subject of oil whirl, and a simple theory is described which was used to aid the design of an oil whirl test rig. Predictions of the onset of oil whirl made by the theory presented were found to agree with those of previous researchers. They showed that increasing the shaft flexibility, or the lubricant viscosity, and decreasing the bearing radial clearance tended to reduce the oil whirl onset speed thus making the system more unstable

Study of high altitude plume impingement

Computer program has been developed as analytical tool to predict severity of effects of exhaust of rocket engines on adjacent spacecraft surfaces. Program computes forces, moments, pressures, and heating rates on surfaces immersed in or subjected to exhaust plume environments. Predictions will be useful in design of systems where such problems are anticipated

Patient variability in the blood-stage dynamics of Plasmodium falciparum captured by clustering historical data

BACKGROUND: Mathematical models provide an understanding of the dynamics of a Plasmodium falciparum blood-stage infection (within-host models), and can predict the impact of control strategies that affect the blood-stage of malaria. However, the dynamics of P. falciparum blood-stage infections are highly variable between individuals. Within-host models use different techniques to capture this inter-individual variation. This struggle may be unnecessary because patients can be clustered according to similar key within-host dynamics. This study aimed to identify clusters of patients with similar parasitaemia profiles so that future mathematical models can include an improved understanding of within-host variation. METHODS: Patients' parasitaemia data were analyzed to identify (i) clusters of patients (from 35 patients) that have a similar overall parasitaemia profile and (ii) clusters of patients (from 100 patients) that have a similar first wave of parasitaemia. For each cluster analysis, patients were clustered based on key features which previous models used to summarize parasitaemia dynamics. The clustering analyses were performed using a finite mixture model. The centroid values of the clusters were used to parameterize two established within-host models to generate parasitaemia profiles. These profiles (that used the novel centroid parameterization) were compared with profiles that used individual-specific parameterization (as in the original models), as well as profiles that ignored individual variation (using overall means for parameterization). RESULTS: To capture the variation of within-host dynamics, when studying the overall parasitaemia profile, two clusters efficiently grouped patients based on their infection length and the height of the first parasitaemia peak. When studying the first wave of parasitaemia, five clusters efficiently grouped patients based on the height of the peak and the speed of the clearance following the peak of parasitaemia. The clusters were based on features that summarize the strength of patient innate and adaptive immune responses. Parameterizing previous within host-models based on cluster centroid values accurately predict individual patient parasitaemia profiles. CONCLUSION: This study confirms that patients have personalized immune responses, which explains the variation of parasitaemia dynamics. Clustering can guide the optimal inclusion of within-host variation in future studies, and inform the design and parameterization of population-based models

Insights from modelling malaria vaccines for policy decisions: the focus on RTS,S

Mathematical models are increasingly used to inform decisions throughout product development pathways from pre-clinical studies to country implementation of novel health interventions. This review illustrates the utility of simulation approaches by reviewing the literature on malaria vaccine modelling, with a focus on its link to the development of policy guidance for the first licensed product, RTS,S/AS01. The main contributions of modelling studies have been in inferring the mechanism of action and efficacy profile of RTS,S; to predicting the public health impact; and economic modelling mainly comprising cost-effectiveness analysis. The value of both product-specific and generic modelling of vaccines is highlighted

The competition dynamics of resistant and sensitive infections

Antimicrobial resistance is a major health problem with complex dynamics. Resistance may occur in an area because treated infections mutated and developed resistance, and the proportion of infections in a population may then increase. We developed a novel and flexible model that captures several features of resistance dynamics and competition. The model is able to account for many antimicrobials and thus can generally explore competition dynamics and their impact on pathogens and bacteria. Unlike simpler models, our nested model allows the population of resistant pathogen to smoothly increase or decrease. Time dependent dynamics are incorporated into difference equations which examines the effects of 12 parameters. This enables us to explicitly include three key competition dynamics: the transmission cost of resistance that occurs between hosts, the fitness cost of resistance that occurs within untreated hosts, and the release of this competition (from the fitness cost) that occurs once a host is treated. For malaria, our results suggest that without competitive release, drug resistance does not emerge. However, once emerged, competitive release has little effect, and the best way to mitigate the spread is to ensure that treatment is very effective

Comparing families of dynamic causal models

Mathematical models of scientific data can be formally compared using Bayesian model evidence. Previous applications in the biological sciences have mainly focussed on model selection in which one first selects the model with the highest evidence and then makes inferences based on the parameters of that model. This “best model” approach is very useful but can become brittle if there are a large number of models to compare, and if different subjects use different models. To overcome this shortcoming we propose the combination of two further approaches: (i) family level inference and (ii) Bayesian model averaging within families. Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest. For example: What are the inputs to the system? Is processing serial or parallel? Is it linear or nonlinear? Is it mediated by a single, crucial connection? We apply Bayesian model averaging within families to provide inferences about parameters that are independent of further assumptions about model structure. We illustrate the methods using Dynamic Causal Models of brain imaging data

Model-informed target product profiles of long-acting-injectables for use as seasonal malaria prevention

Seasonal malaria chemoprevention (SMC) has proven highly efficacious in reducing malaria incidence. However, the continued success of SMC is threatened by the spread of resistance against one of its main preventive ingredients, Sulfadoxine-Pyrimethamine (SP), operational challenges in delivery, and incomplete adherence to the regimens. Via a simulation study with an individual-based model of malaria dynamics, we provide quantitative evidence to assess long-acting injectables (LAIs) as potential alternatives to SMC. We explored the predicted impact of a range of novel preventive LAIs as a seasonal prevention tool in children aged three months to five years old during late-stage clinical trials and at implementation. LAIs were co-administered with a blood-stage clearing drug once at the beginning of the transmission season. We found the establishment of non-inferiority of LAIs to standard 3 or 4 rounds of SMC with SP-amodiaquine was challenging in clinical trial stages due to high intervention deployment coverage. However, our analysis of implementation settings where the achievable SMC coverage was much lower, show LAIs with fewer visits per season are potential suitable replacements to SMC. Suitability as a replacement with higher impact is possible if the duration of protection of LAIs covered the duration of the transmission season. Furthermore, optimising LAIs coverage and protective efficacy half-life via simulation analysis in settings with an SMC coverage of 60% revealed important trade-offs between protective efficacy decay and deployment coverage. Our analysis additionally highlights that for seasonal deployment for LAIs, it will be necessary to investigate the protective efficacy decay as early as possible during clinical development to ensure a well-informed candidate selection process