Derivatives of the Incomplete Beta Function

The incomplete beta function is defined as where Beta(p, q) is the beta function. Dutka (1981) gave a history of the development and numerical evaluation of this function. In this article, an algorithm for computing first and second derivatives of Ix,p,q with respect to p and q is described. The algorithm is useful, for example, when fitting parameters to a censored beta, truncated beta, or a truncated beta-binomial model.

Some effects of fast neutron irradiation upon M̲e̲ḻo̲i̲ḏo̲g̲y̲ṉe̲ I̲ṉc̲o̲g̲ṉi̲ṯa̲ (Kofoid and White, 1919) Chitwood, 1949

Two groups of Meloidogyne incognita (Kofoid and White, 1919) Chitwood, 1949 eggs (Stage I = 50% of total number of eggs at a stage of embryological development exceeding the four-cell stage; Stage II = 50% of total number of eggs at a stage of embryological development equal to or less than the four-cell stage) were irradiated at 7, 22, and 32°C with 0, 1, 2, 3, or 4 Kilorads (Krads) of fast neutrons. Radiation treatment had an effect on the hatch of both Stage I and Stage II eggs. The hatch of Stage I eggs was inversely proportional to the radiation levels and was independent of irradiation temperature. However, the hatch of Stage II eggs was not proportional and was associated with irradiation temperature. More Stage II eggs hatched at 2 Krads, 7°C treatment than at any of the other treatments at the same temperature. Significantly fewer eggs hatched at the 1 Krad treatment. The 0, 3, and 4 Krad, 7°C hatches were intermediate between and differed from the hatches at 1 and 2 Krads. At 22°C, all radiation treatments at Stage II showed significant increases over the hatch at 0 Krads with peaks at 1 and 3 Krads. The Stage I eggs followed a pattern similar to that noted at 7°C. At 32°C, the greatest number of eggs hatched at Stage I, Host differential studies showed that eggs produced by females developing from Stage II eggs receiving 1, 2, and 3 Krads at 7°C and by females developing from both Stage I and Stage II eggs receiving 1, 2, 3, and 4 Krads at 32°C developed into larvae capable of parasitizing and reproducing on a resistant variety of cowpea, Vigna sinensis \u27Breeding Line M57-13N\u27. A change in the ability of Stage I, 7°C and Stage I, 32°C 3 Krad larvae to parasitize a normally susceptible water-melon, Citrulus vulgaris \u27Charleston Grey\u27, was noted. It was also observed that larvae developing from eggs laid by females developing from Stage I eggs exposed to 2 Krads at 7°C and from Stage II eggs exposed to 1 and 3 Krads at the same temperature were able to parasitize and reproduce on Nicotiana tabacum \u27NC-95\u27, a normally resistant variety of tobacco. Similar changes were noted in larvae developing from eggs laid by females developing from Stage II eggs exposed to 1 Krad at 32°C

Stability of a twisted Plateau border with line tension and bending stiffness

The stability of a Plateau border between three soap films is considered, taking into account the effects of line tension and bending stiffness in the border. A simple geometry is considered, in which the border initially lies in equilibrium along the axis of a circular cylinder, with three equally-spaced films radiating outwards to meet the inside wall of the cylinder. The films are pinned at the two ends of the cylinder with a fixed relative twist, so the initial film surfaces are helicoids. The stability of this system to small perturbations, involving both the films and the border, is investigated as a function of the cylinder aspect ratio, twist angle, film surface tension, border line tension, and border bending stiffness. Analytically, the stability problem is reduced to finding the first occurrence of a zero eigenvalue of an infinite matrix, which is then estimated numerically. The results from this calculation are in good agreement with full numerical simulations

Stability of a helicoidal surface inside a cylinder with pinned diameters

A mathematical analysis is presented of the stability of a soap film with uniform surface tension when stretched between two diameters on the inside of a circular cylinder. The stability boundary is found as a critical twist angle θ between the two diameters, as a function of the aspect ratio l of the cylinder. Numerical and asymptotic results agree well with previous numerical simulations and experiments by Cox & Jones (J.\ Engr Math, 2014, 86, 1-7). Their hypothesis that the stability boundary for the multiple-vane case is identical to the single film case is confirmed. It is also shown that two distinct instability mechanisms operate. For moderate and small θ/l, the instability is driven by the decrease in area caused by the film moving to an off-diameter position. But for larger θ/l (more twisted films), the decrease in area is dominated by an internal rearrangement of the surface. The latter mechanism is more relevant to Plateau borders in foams, and our results indicate that straight Plateau borders should be stable at any length provided the total twist is less than π/√2

Strange Cepheids and RR Lyrae

Strange modes can occur in radiative classical Cepheids and RR Lyrae models. These are vibrational modes that are trapped near the surface as a result of a 'potential barrier' caused by the sharp hydrogen partial ionization region. Typically the modal number of the strange mode falls between the 7th and 12th overtone, depending on the astrophysical parameters of the equilibrium stellar models (L, M, \Teff, X, Z). Interestingly these modes can be linearly unstable outside the usual instability strip, in which case they should be observable as new kinds of variable stars, 'strange Cepheids' or 'strange RR Lyrae' stars. The present paper reexamines the linear stability properties of the strange modes by taking into account the effects of an isothermal atmosphere, and of turbulent convection. It is found that the linear vibrational instability of the strange modes is resistant to both of these effects. Nonlinear hydrodynamic calculations indicate that the pulsation amplitude of these modes is likely to saturate at the millimagnitude level. These modes should therefore be detectable albeit not without effort.Comment: 6 pages, 7 figures, submitted to Ap

“It’s just not something we do at school”. Adolescent boys’ understanding, perceptions and experiences of muscular fitness activity

Background: English youth typically do not sufficiently engage in the types and intensities of physical activity that develop muscular fitness. The aim of this study was to use a combination of qualitative techniques to explore adolescent boys’ understanding, perceptions, and experiences of physical activity and the role muscular fitness plays within boys’ physically active lifestyles. Methods: Focus group interviews with a write, draw, show, and tell activity were conducted with 32 adolescent boys aged 14–16 years from 3 secondary schools. Three separate sources of data (frequency counts, verbatim transcripts, and visual data) were generated and were pooled together and triangulated. Data were analysed deductively, first using the Youth Physical Activity Promotion model as a thematic framework, and then inductively. Results: Physical activity was frequently associated with organised sport, and most boys were unaware of current UK physical activity guidelines. Co-participation was frequently reported as a reinforcing factor to physical activity. Conclusions: There was a perceived lack of opportunity to participate in muscular fitness activities, particularly in school, and knowledge of how to conduct muscular fitness activities was limited. The contribution of physical education was highlighted as being key to facilitating exposure to muscular fitness activities

Derivatives of the Incomplete Beta Function

The incomplete beta function is defined as where Beta(p, q) is the beta function. Dutka (1981) gave a history of the development and numerical evaluation of this function. In this article, an algorithm for computing first and second derivatives of Ix,p,q with respect to p and q is described. The algorithm is useful, for example, when fitting parameters to a censored beta, truncated beta, or a truncated beta-binomial model

Regulatory activity revealed by dynamic correlations in gene expression noise

Gene regulatory interactions are context dependent, active in some cellular states but not in others. Stochastic fluctuations, or 'noise', in gene expression propagate through active, but not inactive, regulatory links^(1,2). Thus, correlations in gene expression noise could provide a noninvasive means to probe the activity states of regulatory links. However, global, 'extrinsic', noise sources generate correlations even without direct regulatory links. Here we show that single-cell time-lapse microscopy, by revealing time lags due to regulation, can discriminate between active regulatory connections and extrinsic noise. We demonstrate this principle mathematically, using stochastic modeling, and experimentally, using simple synthetic gene circuits. We then use this approach to analyze dynamic noise correlations in the galactose metabolism genes of Escherichia coli. We find that the CRP-GalS-GalE feed-forward loop is inactive in standard conditions but can become active in a GalR mutant. These results show how noise can help analyze the context dependence of regulatory interactions in endogenous gene circuits