Flow structure in a model of aircraft trailing vortices

We consider a model of incompressible trailing vortices consisting of an array of counter-rotating structures in a doubly periodic domain, infinite in the vertical direction. The two-dimensional vortex array of Mallier and Maslowe is combined with an axial velocity profile chosen proportional to the initial axial vorticity to provide an initial condition for the vortex wake. This base flow is a weak solution of the steady Euler equations with three velocity components that are functions of two spatial coordinates, thus allowing its linear stability properties to be investigated. These are used to interpret several stages in the development of vortex structure observed in fully three-dimensional direct numerical simulation (DNS) at Reynolds numbers Gamma/(2pinu)=[script O](1000). For sufficiently high axial velocity, its effect can be seen, in that each vortex in the linear array first develops helical structures before undergoing a period of relaminarization. At later times the more slowly growing cooperative elliptical instabilities become apparent, but the helical structure persists and the observed vortical structures remain coherent for longer periods than in the absence of axial velocity. Using the stretched-vortex subgrid model, large-eddy simulation runs are performed at large Reynolds numbers and a mixing transition identified at about Re=1–2×10^4. Similar phenomena are observed in these simulations as are seen in the DNS

Bivariate stochastic modeling of functional response with natural mortality

A correction due to Abbott (1925) is the standard method of dealing with control mortality in insect bioassay to estimate the mortality of an insect conditional on control mortality not having occurred. In this article a bivariate stochastic process for overall mortality is developed in which natural mortality and predation are jointly modeled to take account of the competing-risks associated with prey loss. The total mortality estimate from this model is essentially identical with that from more classical modeling. However, when predation loss is estimated in the absence of control mortality the results are somewhat different, with the estimate from the bivariate model being lower than that from using Abbott’s formula in conjunction with the classical model. It is argued that overdispersion in observed mortality data corresponds to correlated outcomes (death or survival) for the prey initially present, while Abbott’s correction relies implicitly on independence

Mean and Variance Modeling of Under-Dispersed and Over-Dispersed Grouped Binary Data

This article describes the R package BinaryEPPM and its use in determining maximum likelihood estimates of the parameters of extended Poisson process models for grouped binary data. These provide a Poisson process family of flexible models that can handle unlimited under-dispersion but limited over-dispersion in such data, with the binomial distribution being a special case. Within BinaryEPPM, models with the mean and variance related to covariates are constructed to match a generalized linear model formulation. Combining such under-dispersed models with standard over-dispersed models such as the beta binomial distribution provides a very general form of residual distribution for modeling grouped binary data. Use of the package is illustrated by application to several data-sets

Accuracy of at-sea commercial size grading of tiger prawns (Penaeus esculentus and P-semisulcatus) in the Australian northern prawn fishery

The size-frequency distribution of the commercial catch is often used as the basis of fisheries stock assessments (Paul and Morgan, 1987; Gulland and Rosenberg, 1992) because most dynamic processes of populations (growth, survival, recruitment) are reflected in changes in this distribution. The data are generally collected, often at great expense, by sampling the catch at landing sites and markets, or onboard fishing vessels. Size-frequency distributions of prawns (Penaeus esculentus and P. semisulcatus) can also be obtained from fish processors, who grade landings by size. These data are easier and cheaper to obtain than research samples, but unfortunately they are also considered less accurate and lack spatial information. However, they have been used in stock assessment of prawns in Kuwait (Jones and van Zalinge, 1981) and Malaysia (Simpson and Kong, 1978). It is often difficult to relate size data obtained from a processor to time and place of capture of the prawns, but this is not the case when the product is packed onboard, as in Australia's northern prawn fishery (NPF). Trawler operators in the NPF have voluntarily recorded size composition since 1985, when provision for this was made in operators' daily logbooks (between 30% and 45% of the tiger prawn catch reported in the logbooks contain size information). These books are therefore the most comprehensive source of information on the spatial and temporal size distribution of the commercial catch of the NPF. Present assessments of the fishery are based on deterministic growth and deterministic seasonal recruitment patterns (Wang and Die, 1996) and do not use size-structured data. If available, these data would help relax the recruitment and improve current stock assessments of the NPF. Before the size data recorded in the logbooks can be used, however, the accuracy of size grading at sea needs to the assessed. This paper examines the accuracy of grading tiger prawns, by using data collected from a private firm, A. Raptis and Sons, that operates a large modern processing factory that regularly assesses the onboard grading of product purchased from NPF trawler operators. Although the work presented here relates specifically to the NPF, the practice of onboard size grading is widespread in other fisheries around the world. Therefore our methods have potential application to other fisheries

Prediction of age at menopause from assessment of ovarian reserve may be improved by using body mass index and smoking status.

OBJECTIVE: Menopause is the consequence of exhaustion of the ovarian follicular pool. AMH, an indirect hormonal marker of ovarian reserve, has been recently proposed as a predictor for age at menopause. Since BMI and smoking status are relevant independent factors associated with age at menopause we evaluated whether a model including all three of these variables could improve AMH-based prediction of age at menopause. METHODS: In the present cohort study, participants were 375 eumenorrheic women aged 19-44 years and a sample of 2,635 Italian menopausal women. AMH values were obtained from the eumenorrheic women. RESULTS: Regression analysis of the AMH data showed that a quadratic function of age provided a good description of these data plotted on a logarithmic scale, with a distribution of residual deviates that was not normal but showed significant left-skewness. Under the hypothesis that menopause can be predicted by AMH dropping below a critical threshold, a model predicting menopausal age was constructed from the AMH regression model and applied to the data on menopause. With the AMH threshold dependent on the covariates BMI and smoking status, the effects of these covariates were shown to be highly significant. CONCLUSIONS: In the present study we confirmed the good level of conformity between the distributions of observed and AMH-predicted ages at menopause, and showed that using BMI and smoking status as additional variables improves AMH-based prediction of age at menopause

The relationship between anti-mullerian hormone in women receiving fertility assessments and age at menopause in subfertile women: evidence from large population studies

<p>Context: Anti-Müllerian hormone (AMH) concentration reflects ovarian aging and is argued to be a useful predictor of age at menopause (AMP). It is hypothesized that AMH falling below a critical threshold corresponds to follicle depletion, which results in menopause. With this threshold, theoretical predictions of AMP can be made. Comparisons of such predictions with observed AMP from population studies support the role for AMH as a forecaster of menopause.</p> <p>Objective: The objective of the study was to investigate whether previous relationships between AMH and AMP are valid using a much larger data set.</p> <p>Setting: AMH was measured in 27 563 women attending fertility clinics.</p> <p>Study Design: From these data a model of age-related AMH change was constructed using a robust regression analysis. Data on AMP from subfertile women were obtained from the population-based Prospect-European Prospective Investigation into Cancer and Nutrition (Prospect-EPIC) cohort (n = 2249). By constructing a probability distribution of age at which AMH falls below a critical threshold and fitting this to Prospect-EPIC menopausal age data using maximum likelihood, such a threshold was estimated.</p> <p>Main Outcome: The main outcome was conformity between observed and predicted AMP.</p> <p>Results: To get a distribution of AMH-predicted AMP that fit the Prospect-EPIC data, we found the critical AMH threshold should vary among women in such a way that women with low age-specific AMH would have lower thresholds, whereas women with high age-specific AMH would have higher thresholds (mean 0.075 ng/mL; interquartile range 0.038–0.15 ng/mL). Such a varying AMH threshold for menopause is a novel and biologically plausible finding. AMH became undetectable (<0.2 ng/mL) approximately 5 years before the occurrence of menopause, in line with a previous report.</p> <p>Conclusions: The conformity of the observed and predicted distributions of AMP supports the hypothesis that declining population averages of AMH are associated with menopause, making AMH an excellent candidate biomarker for AMP prediction. Further research will help establish the accuracy of AMH levels to predict AMP within individuals.</p&gt

Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable Switch

Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.Comment: 14 pages, 4 figure

A Validated Model of Serum Anti-Müllerian Hormone from Conception to Menopause

Background Anti-Müllerian hormone (AMH) is a product of growing ovarian follicles. The concentration of AMH in blood may also reflect the non-growing follicle (NGF) population, i.e. the ovarian reserve, and be of value in predicting reproductive lifespan. A full description of AMH production up to the menopause has not been previously reported. Methodology/Principal Findings By searching the published literature for AMH concentrations in healthy pre-menopausal females, and using our own data (combined ) we have generated and robustly validated the first model of AMH concentration from conception to menopause. This model shows that 34% of the variation in AMH is due to age alone. We have shown that AMH peaks at age 24.5 years, followed by a decline to the menopause. We have also shown that there is a neonatal peak and a potential pre-pubertal peak. Our model allows us to generate normative data at all ages. Conclusions/Significance These data highlight key inflection points in ovarian follicle dynamics. This first validated model of circulating AMH in healthy females describes a transition period in early adulthood, after which AMH reflects the progressive loss of the NGF pool. The existence of a neonatal increase in gonadal activity is confirmed for females. An improved understanding of the relationship between circulating AMH and age will lead to more accurate assessment of ovarian reserve for the individual woman.Publisher PDFPeer reviewe