Approximate factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

Fast approximate calculation of multiply scattered lidar returns

An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance, of photon direction and position. The result is that for an N-point profile the calculation is O(N-2) efficient and implicitly includes up to N-order scattering, making it ideal for use in iterative retrieval algorithms for which speed is crucial. In contrast, models that explicitly consider each scattering order separately are at best O(N-m/m!) efficient for m-order scattering and often cannot be performed to more than the third or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view, the new algorithm is as accurate as an explicit calculation truncated at the fifth or sixth order but faster by several orders of magnitude. (C) 2006 Optical Society of America.

Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic

We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical geopotential and shallow atmosphere approximations in addition to the hydrostatic approximation. As is well known, a consistent application of the shallow atmosphere approximation requires omission of those Coriolis terms that vary as the cosine of latitude and of certain other terms in the components of the momentum equation. An approximate model is here regarded as consistent if it formally preserves conservation principles for axial angular momentum, energy and potential vorticity, and (following R. Müller) if its momentum component equations have Lagrange's form. Within these criteria, four consistent approximate global models, including the HPEs themselves, are identified in a height-coordinate framework. The four models, each of which includes the spherical geopotential approximation, correspond to whether the shallow atmosphere and hydrostatic (or quasi-hydrostatic) approximations are individually made or not made. Restrictions on representing the spatial variation of apparent gravity occur. Solution methods and the situation in a pressure-coordinate framework are discussed. © Crown copyright 2005.

Using a runway paradigm to assess the relative strength of rats' motivations for enrichment objects

Laboratory animals should be provided with enrichment objects in their cages; however, it is first necessary to test whether the proposed enrichment objects provide benefits that increase the animals’ welfare. The two main paradigms currently used to assess proposed enrichment objects are the choice test, which is limited to determining relative frequency of choice, and consumer demand studies, which can indicate the strength of a preference but are complex to design. Here, we propose a third methodology: a runway paradigm, which can be used to assess the strength of an animal’s motivation for enrichment objects, is simpler to use than consumer demand studies, and is faster to complete than typical choice tests. Time spent with objects in a standard choice test was used to rank several enrichment objects in order to compare with the ranking found in our runway paradigm. The rats ran significantly more times, ran faster, and interacted longer with objects with which they had previously spent the most time. It was concluded that this simple methodology is suitable for measuring rats’ motivation to reach enrichment objects. This can be used to assess the preference for different types of enrichment objects or to measure reward system processes.

Developmental changes in the germinability, desiccation tolerance, hardseededness, and longevity of individual seeds of Trifolium ambiguum

Background and Aims: Using two parental clones of outcrossing Trifolium ambiguum as a potential model system, we examined how during seed development the maternal parent, number of seeds per pod, seed position within the pod, and pod position within the inflorescence influenced individual seed fresh weight, dry weight, water content, germinability, desiccation tolerance, hardseededness, and subsequent longevity of individual seeds. Methods: Near simultaneous, manual reciprocal crosses were carried out between clonal lines for two experiments. Infructescences were harvested at intervals during seed development. Each individual seed was weighed and then used to determine dry weight or one of the physiological behaviour traits. Key Results: Whilst population mass maturity was reached at 33–36 days after pollination (DAP), seed-to-seed variation in maximum seed dry weight, when it was achieved, and when maturation drying commenced, was considerable. Individual seeds acquired germinability between 14 and 44 DAP, desiccation tolerance between 30 and 40 DAP, and the capability to become hardseeded between 30 and 47 DAP. The time for viability to fall to 50 % (p50) at 60 % relative humidity and 45 °C increased between 36 and 56 DAP, when the seed coats of most individuals had become dark orange, but declined thereafter. Individual seed f. wt at harvest did not correlate with air-dry storage survival period. Analysing survival data for cohorts of seeds reduced the standard deviation of the normal distribution of seed deaths in time, but no sub-population showed complete uniformity of survival period. Conclusions: Variation in individual seed behaviours within a developing population is inherent and inevitable. In this outbreeder, there is significant variation in seed longevity which appears dependent on embryo genotype with little effect of maternal genotype or architectural factors.

Hydrolyzable tannin structures influence relative globular and random coil protein binding strengths

Binding parameters for the interactions of pentagalloyl glucose (PGG) and four hydrolyzable tannins (representing gallotannins and ellagitannins) with gelatin and bovine serum albumin (BSA) have been determined from isothermal titration calorimetry data. Equilibrium binding constants determined for the interaction of PGG and isolated mixtures of tara gallotannins and of sumac gallotannins with gelatin and BSA were of the same order of magnitude for each tannin (in the range of 10(4)-10(5) M-1 for stronger binding sites when using a binding model consisting of two sets of multiple binding sites). In contrast, isolated mixtures of chestnut ellagitannins and of myrabolan ellagitannins exhibited 3-4 orders of magnitude greater equilibrium binding constants for the interaction with gelatin (similar to 2 x 10(6) M-1) than for that with BSA (similar to 8 x 10(2) M-1). Binding stoichiometries revealed that the stronger binding sites on gelatin outnumbered those on BSA by a ratio of at least similar to 2:1 for all of the hydrolyzable tannins studied. Overall, the data revealed that relative binding constants for the interactions with gelatin and BSA are dependent on the structural flexibility of the tannin molecule.

Mutant alleles at the rugosus loci in pea affect seed moisture sorption isotherms and the relations between seed longevity and moisture content

Pea (Pisum sativum L.) mutant near-isogenic lines (RRrbrb, rrRbRb, rrrbrb) with lower starch but higher lipid contents, brought about by lesions in the starch biosynthetic pathway, had seed moisture sorption isotherms displaced below that of the wild type (RRRbRb). The negative logarithmic relationship between seed longevity and seed storage moisture content (%, f.wt basis), determined in hermetic storage at 65 degreesC, also differed: longevity in the mutant near-isogenic lines was poorer and less sensitive to moisture content than in the wild type (i.e. C-w was lower). The low-moisture-content limit (m(c)) to this relation also differed, being lower in the mutant near-isogenic lines (5.4-5.9%) than in the wild type (6.1%). In contrast, all four near-isogenic lines showed no difference (P >0.25) in the negative semilogarithmic relationship between equilibrium relative humidity (ERH) and seed longevity. It is concluded that the effect of these alleles at the r and rb loci on seed longevity. was largely indirect; a consequence of their effect on seed composition and hence on moisture sorption isotherms. However, this explanation could not be invoked at moisture contents below mc where differences in longevity remained substantial (RRRbRb double that of rrrbrb). Hence, these mutant alleles affected seed longevity directly at very low moisture contents.

Examination of the persistency of milk fatty acid composition responses to fish oil and sunflower oil in the diet of dairy cows

Based on the potential benefits of cis-9, trans-11 conjugated linoleic acid (CLA) for human health, there is a need to develop effective strategies for enhancing milk fat CLA concentrations. Levels of cis-9, trans-11 CLA in milk can be increased by supplements of fish oil (FO) and sunflower oil (SO), but there is considerable variation in the response. Part of this variance may reflect time-dependent ruminal adaptations to high levels of lipid in the diet, which lead to alterations in the formation of specific biohydrogenation intermediates. To test this hypothesis, 16 late lactation Holstein-British Friesian cows were used in a repeated measures randomized block design to examine milk fatty acid composition responses to FO and SO in the diet over a 28-d period. Cows were allocated at random to corn silage-based rations (8 per treatment) containing 0 (control) or 45 g of oil supplement/ kg of dry matter consisting (1:2; wt/wt) of FO and SO (FSO), and milk composition was determined on alternate days from d 1. Compared with the control, the FSO diet decreased mean dry matter intake (21.1 vs. 17.9 kg/d), milk fat (47.7 vs. 32.6 g/kg), and protein content (36.1 vs. 33.3 g/kg), but had no effect on milk yield (27.1 vs. 26.4 kg/d). Reductions in milk fat content relative to the FSO diet were associated with increases in milk trans-10 18: 1, trans-10, cis-12 CLA, and trans-9, cis-11 CLA concentrations (r(2) = 0.74, 0.57, and 0.80, respectively). Compared with the control, the FSO diet reduced milk 4: 0 to 18: 0 and cis 18:1 content and increased trans 18:1, trans 18:2, cis-9, trans-11 CLA, 20: 5 n-3, and 22: 6 n-3 concentrations. The FSO diet caused a rapid elevation in milk cis-9, trans-11 CLA content, reaching a maximum of 5.37 g/100 g of fatty acids on d 5, but these increases were transient, declining to 2.35 g/100 g of fatty acids by d 15. They remained relatively constant thereafter. Even though concentrations of trans-11 18: 1 followed the same pattern of temporal changes as cis-9, trans-11 CLA, the total trans 18:1 content of FSO milk was unchanged because of the concomitant increases in the concentration of other isomers (Delta(4-10) and Delta(12-15)), predominantely trans-10 18:1. In conclusion, supplementing diets with FSO enhances milk fat cis-9, trans-11 CLA content, but the high level of enrichment declines because of changes in ruminal biohydrogenation that result in trans-10 replacing trans-11 as the major 18:1 biohydrogenation intermediate formed in the rumen.

Adaptive approximate Bayesian computation

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappe et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC.

An approximate Bayesian computation approach to overcome biases that arise when using amplified fragment length polymorphism markers to study population structure

There is great interest in using amplified fragment length polymorphism (AFLP) markers because they are inexpensive and easy to produce. It is, therefore, possible to generate a large number of markers that have a wide coverage of species genotnes. Several statistical methods have been proposed to study the genetic structure using AFLP's but they assume Hardy-Weinberg equilibrium and do not estimate the inbreeding coefficient, F-IS. A Bayesian method has been proposed by Holsinger and colleagues that relaxes these simplifying assumptions but we have identified two sources of bias that can influence estimates based on these markers: (i) the use of a uniform prior on ancestral allele frequencies and (ii) the ascertainment bias of AFLP markers. We present a new Bayesian method that avoids these biases by using an implementation based on the approximate Bayesian computation (ABC) algorithm. This new method estimates population-specific F-IS and F-ST values and offers users the possibility of taking into account the criteria for selecting the markers that are used in the analyses. The software is available at our web site (http://www-leca.uif-grenoble.fi-/logiciels.htm). Finally, we provide advice on how to avoid the effects of ascertainment bias.