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

The growth hormone receptor gene deleted for exon three (GHRd3) polymorphism is associated with birth and placental weight.

Human growth hormone receptor (GHR) transcripts have two isoforms, full-length (GHRfl) or exon 3 deleted (GHRd3). An association of these isoforms has been found with small for gestational age (SGA) infants but does not influence adult height. The role of this polymorphism in the birth size spectrum in the general population is unclear

Elevated arousal at time of decision-making is not the arbiter of risk avoidance in chickens

The somatic marker hypothesis proposes that humans recall previously experienced physiological responses to aid decision-making under uncertainty. However, little is known about the mechanisms used by non-human animals to integrate risk perception with predicted gains and losses. We monitored the behaviour and physiology of chickens when the choice between a high-gain (large food quantity), high-risk (1 in 4 probability of receiving an air-puff) option (HGRAP) or a low-gain (small food quantity), no-risk (of an air-puff) (LGNAP) option. We assessed when arousal increased by considering different stages of the decision-making process (baseline, viewing, anticipation, reward periods) and investigated whether autonomic responses influenced choice outcome both immediately and in the subsequent trial. Chickens were faster to choose and their heart-rate significantly increased between the viewing and anticipation (post-decision, pre-outcome) periods when selecting the HGRAP option. This suggests that they responded physiologically to the impending risk. Additionally, arousal was greater following a HGRAP choice that resulted in an air-puff, but this did not deter chickens from subsequently choosing HGRAP. In contrast to human studies, we did not find evidence that somatic markers were activated during the viewing period, suggesting that arousal is not a good measure of avoidance in non-human animals

A Case Study of Eukaryogenesis: The Evolution of Photoreception by Photolyase/Cryptochrome Proteins

Eukaryogenesis, the origin of the eukaryotes, is still poorly understood. Herein, we show how a detailed all-kingdom phylogenetic analysis overlaid with a map of key biochemical features can provide valuable clues. The photolyase/cryptochrome family of proteins are well known to repair DNA in response to potentially harmful effects of sunlight and to entrain circadian rhythms. Phylogenetic analysis of photolyase/cryptochrome protein sequences from a wide range of prokaryotes and eukaryotes points to a number of horizontal gene transfer events between ancestral bacteria and ancestral eukaryotes. Previous experimental research has characterised patterns of tryptophan residues in these proteins that are important for photoreception, specifically a tryptophan dyad, a canonical tryptophan triad, an alternative tryptophan triad, a tryptophan tetrad and an alternative tetrad. Our results suggest that the spread of the different triad and tetrad motifs across the kingdoms of life accompanied the putative horizontal gene transfers and is consistent with multiple bacterial contributions to eukaryogenesis

Phenotypic and molecular assessment of seven patients with 6p25 deletion syndrome: Relevance to ocular dysgenesis and hearing impairment

BACKGROUND: Thirty-nine patients have been described with deletions involving chromosome 6p25. However, relatively few of these deletions have had molecular characterization. Common phenotypes of 6p25 deletion syndrome patients include hydrocephalus, hearing loss, and ocular, craniofacial, skeletal, cardiac, and renal malformations. Molecular characterization of deletions can identify genes that are responsible for these phenotypes. METHODS: We report the clinical phenotype of seven patients with terminal deletions of chromosome 6p25 and compare them to previously reported patients. Molecular characterization of the deletions was performed using polymorphic marker analysis to determine the extents of the deletions in these seven 6p25 deletion syndrome patients. RESULTS: Our results, and previous data, show that ocular dysgenesis and hearing impairment are the two most highly penetrant phenotypes of the 6p25 deletion syndrome. While deletion of the forkhead box C1 gene (FOXC1) probably underlies the ocular dysgenesis, no gene in this region is known to be involved in hearing impairment. CONCLUSIONS: Ocular dysgenesis and hearing impairment are the two most common phenotypes of 6p25 deletion syndrome. We conclude that a locus for dominant hearing loss is present at 6p25 and that this locus is restricted to a region distal to D6S1617. Molecular characterization of more 6p25 deletion patients will aid in refinement of this locus and the identification of a gene involved in dominant hearing loss

Influence of topography on tide propagation and amplification in semi-enclosed basins

An idealized model for tide propagation and amplification in semi-enclosed rectangular basins is presented, accounting for depth differences by a combination of longitudinal and lateral topographic steps. The basin geometry is formed by several adjacent compartments of identical width, each having either a uniform depth or two depths separated by a transverse topographic step. The problem is forced by an incoming Kelvin wave at the open end, while allowing waves to radiate outward. The solution in each compartment is written as the superposition of (semi)-analytical wave solutions in an infinite channel, individually satisfying the depth-averaged linear shallow water equations on the f plane, including bottom friction. A collocation technique is employed to satisfy continuity of elevation and flux across the longitudinal topographic steps between the compartments. The model results show that the tidal wave in shallow parts displays slower propagation, enhanced dissipation and amplified amplitudes. This reveals a resonance mechanism, occurring when\ud the length of the shallow end is roughly an odd multiple of the quarter Kelvin wavelength. Alternatively, for sufficiently wide basins, also Poincaré waves may become resonant. A transverse step implies different wavelengths of the incoming and reflected Kelvin wave, leading to increased amplitudes in shallow regions and a shift of amphidromic points in the direction of the deeper part. Including the shallow parts near the basin’s closed end (thus capturing the Kelvin resonance mechanism) is essential to reproduce semi-diurnal and diurnal\ud tide observations in the Gulf of California, the Adriatic Sea and the Persian Gulf

Using magnetoencephalography to investigate brain activity during high frequency deep brain stimulation in a cluster headache patient

PURPOSE: Treatment-resistant cluster headache can be successfully alleviated with deep brain stimulation (DBS) of the posterior hypothalamus [1]. Magnetoencephalography (MEG) is a non-invasive functional imaging technique with both high temporal and high spatial resolution. However, it is not known whether the inherent electromagnetic (EM) noise produced by high frequency DBS is compatible with MEG. MATERIALS AND METHODS: We used MEG to record brain activity in an asymptomatic cluster headache patient with a DBS implanted in the right posterior hypothalamus while he made small movements during periods of no stimulation, 7 Hz stimulation and 180 Hz stimulation. RESULTS: We were able to measure brain activity successfully both during low and high frequency stimulation. Analysis of the MEG recordings showed similar activation in motor areas in during the patient's movements as expected. We also observed similar activations in cortical and subcortical areas that have previously been reported to be associated with pain when the patient's stimulator was turned on or off [2,3]. CONCLUSION: These results show that MEG can be used to measure brain activity regardless of the presence of high frequency deep brain stimulation

Chiral Polymerization in Open Systems From Chiral-Selective Reaction Rates

We investigate the possibility that prebiotic homochirality can be achieved exclusively through chiral-selective reaction rate parameters without any other explicit mechanism for chiral bias. Specifically, we examine an open network of polymerization reactions, where the reaction rates can have chiral-selective values. The reactions are neither autocatalytic nor do they contain explicit enantiomeric cross-inhibition terms. We are thus investigating how rare a set of chiral-selective reaction rates needs to be in order to generate a reasonable amount of chiral bias. We quantify our results adopting a statistical approach: varying both the mean value and the rms dispersion of the relevant reaction rates, we show that moderate to high levels of chiral excess can be achieved with fairly small chiral bias, below 10%. Considering the various unknowns related to prebiotic chemical networks in early Earth and the dependence of reaction rates to environmental properties such as temperature and pressure variations, we argue that homochirality could have been achieved from moderate amounts of chiral selectivity in the reaction rates.Comment: 15 pages, 6 figures, accepted for publication in Origins of Life and Evolution of Biosphere