Nilpotent normal form for divergence-free vector fields and volume-preserving maps

We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in $\mathbb{R}^3$ has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. The analogue for volume-preserving diffeomorphisms gives an optimal normal form in which the truncation of the normal form at any degree gives an exactly volume-preserving map whose inverse is also polynomial inverse with the same degree.Comment: laTeX, 20 pages, 1 figur

Cold gas accretion in galaxies

Evidence for the accretion of cold gas in galaxies has been rapidly accumulating in the past years. HI observations of galaxies and their environment have brought to light new facts and phenomena which are evidence of ongoing or recent accretion: 1) A large number of galaxies are accompanied by gas-rich dwarfs or are surrounded by HI cloud complexes, tails and filaments. It may be regarded as direct evidence of cold gas accretion in the local universe. It is probably the same kind of phenomenon of material infall as the stellar streams observed in the halos of our galaxy and M31. 2) Considerable amounts of extra-planar HI have been found in nearby spiral galaxies. While a large fraction of this gas is produced by galactic fountains, it is likely that a part of it is of extragalactic origin. 3) Spirals are known to have extended and warped outer layers of HI. It is not clear how these have formed, and how and for how long the warps can be sustained. Gas infall has been proposed as the origin. 4) The majority of galactic disks are lopsided in their morphology as well as in their kinematics. Also here recent accretion has been advocated as a possible cause. In our view, accretion takes place both through the arrival and merging of gas-rich satellites and through gas infall from the intergalactic medium (IGM). The infall may have observable effects on the disk such as bursts of star formation and lopsidedness. We infer a mean ``visible'' accretion rate of cold gas in galaxies of at least 0.2 Msol/yr. In order to reach the accretion rates needed to sustain the observed star formation (~1 Msol/yr), additional infall of large amounts of gas from the IGM seems to be required.Comment: To appear in Astronomy & Astrophysics Reviews. 34 pages. Full-resolution version available at http://www.astron.nl/~oosterlo/accretionRevie

Impact of female age and male infertility on ovarian reserve markers to predict outcome of assisted reproduction technology cycles

<p>Abstract</p> <p>Background</p> <p>This study was designed to assess the capability of ovarian reserve markers, including baseline FSH levels, baseline anti-Müllerian hormone (AMH) levels, and antral follicle count (AFC), as predictors of live births during IVF cycles, especially for infertile couples with advanced maternal age and/or male factors.</p> <p>Methods</p> <p>A prospective cohort of 336 first IVF/ICSI cycles undergoing a long protocol with GnRH agonist was investigated. Patients with endocrine disorders or unilateral ovaries were excluded.</p> <p>Results</p> <p>Among the ovarian reserve tests, AMH and age had a greater area under the receiving operating characteristic curve than FSH in predicting live births. Furthermore, AMH and age were the sole predictive factors of live births for women greater than or equal to 35 years of age; while AMH was the major determinant of live births for infertile couples with absence of male factors by multivariate logistic regression analysis. However, all the studied ovarain reserve tests were not preditive of live births for women < 35 years of age or infertile couples with male factors.</p> <p>Conclusion</p> <p>The serum AMH levels were prognostic for pregnancy outcome for infertile couples with advanced female age or absence of male factors. The predictive capability of ovarian reserve tests is clearly influenced by the etiology of infertility.</p

Indirect Genetic Effects and Housing Conditions in Relation to Aggressive Behaviour in Pigs

Indirect Genetic Effects (IGEs), also known as associative effects, are the heritable effects that an individual has on the phenotype of its social partners. Selection for IGEs has been proposed as a method to reduce harmful behaviours, in particular aggression, in livestock and aquaculture. The mechanisms behind IGEs, however, have rarely been studied. The objective was therefore to assess aggression in pigs which were divergently selected for IGEs on growth (IGEg). In a one generation selection experiment, we studied 480 offspring of pigs (Sus scrofa) that were selected for relatively high or low IGEg and housed in homogeneous IGEg groups in either barren or enriched environments. Skin lesion scores, a proxy measure of aggression, and aggressive behaviours were recorded. The two distinct IGEg groups did not differ in number of skin lesions, or in amount of reciprocal fighting, both under stable social conditions and in confrontation with unfamiliar pigs in a 24 h regrouping test. Pigs selected for a positive effect on the growth of their group members, however, performed less non-reciprocal biting and showed considerably less aggression at reunion with familiar group members after they had been separated during a 24 h regrouping test. The enriched environment was associated with more skin lesions but less non-reciprocal biting under stable social conditions. Changes in aggression between pigs selected for IGEg were not influenced by G×E interactions with regard to the level of environmental enrichment. It is likely that selection on IGEg targets a behavioural strategy, rather than a single behavioural trait such as aggressiveness