Asymptotic Stability for a Class of Metriplectic Systems

Using the framework of metriplectic systems on $\R^n$ we will describe a constructive geometric method to add a dissipation term to a Hamilton-Poisson system such that any solution starting in a neighborhood of a nonlinear stable equilibrium converges towards a certain invariant set. The dissipation term depends only on the Hamiltonian function and the Casimir functions

Slicing Sets and Measures, and the Dimension of Exceptional Parameters

We consider the problem of slicing a compact metric space \Omega with sets of the form \pi_{\lambda}^{-1}\{t\}, where the mappings \pi_{\lambda} \colon \Omega \to \R, \lambda \in \R, are \emph{generalized projections}, introduced by Yuval Peres and Wilhelm Schlag in 2000. The basic question is: assuming that \Omega has Hausdorff dimension strictly greater than one, what is the dimension of the 'typical' slice \pi_{\lambda}^{-1}{t}, as the parameters \lambda and t vary. In the special case of the mappings \pi_{\lambda} being orthogonal projections restricted to a compact set \Omega \subset \R^{2}, the problem dates back to a 1954 paper by Marstrand: he proved that for almost every \lambda there exist positively many $t \in \R$ such that \dim \pi_{\lambda}^{-1}{t} = \dim \Omega - 1. For generalized projections, the same result was obtained 50 years later by J\"arvenp\"a\"a, J\"arvenp\"a\"a and Niemel\"a. In this paper, we improve the previously existing estimates by replacing the phrase 'almost all \lambda' with a sharp bound for the dimension of the exceptional parameters.Comment: 31 pages, three figures; several typos corrected and large parts of the third section rewritten in v3; to appear in J. Geom. Ana

Ray helicity: a geometric invariant for multi-dimensional resonant wave conversion

For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning it must be invariant under two groups of transformations: congruence transformations (which shuffle components of the multi-component wave field) and canonical transformations (which act on the ray phase space). It is shown that for conversion between two waves there is a new invariant not previously discussed: the intrinsic helicity of the ray

Mid-J CO Shock Tracing Observations of Infrared Dark Clouds I

Infrared dark clouds (IRDCs) are dense, molecular structures in the interstellar medium that can harbour sites of high-mass star formation. IRDCs contain supersonic turbulence, which is expected to generate shocks that locally heat pockets of gas within the clouds. We present observations of the CO J = 8-7, 9-8, and 10-9 transitions, taken with the Herschel Space Observatory, towards four dense, starless clumps within IRDCs (C1 in G028.37+00.07, F1 and F2 in G034.43+0007, and G2 in G034.77-0.55). We detect the CO J = 8-7 and 9-8 transitions towards three of the clumps (C1, F1, and F2) at intensity levels greater than expected from photodissociation region (PDR) models. The average ratio of the 8-7 to 9-8 lines is also found to be between 1.6 and 2.6 in the three clumps with detections, significantly smaller than expected from PDR models. These low line ratios and large line intensities strongly suggest that the C1, F1, and F2 clumps contain a hot gas component not accounted for by standard PDR models. Such a hot gas component could be generated by turbulence dissipating in low velocity shocks.Comment: 14 pages, 8 figures, 5 tables, accepted by A&A, minor updates to match the final published versio

HIV-1 envelope protein gp41: An NMR study of dodecyl phosphocholine embedded gp41 reveals a dynamic prefusion intermediate conformation.

Human immunodeficiency viral (HIV-1) fusion is mediated by the viral envelope gp120/gp41 complex (ENVelope glycoprotein). After gp120 shedding, gp41 is exposed and elicits membrane fusion via a cascade of conformational changes. In contrast to prefusion and postfusion conformation, little is known about any intermediate conformation. We report on a solution NMR investigation of homotrimeric HIV-1 gp4127–194, comprising the transmembrane region and reconstituted in dodecyl phosphocholine (DPC) micelles. The protein is mainly α-helical, but experiences internal dynamics on the nanosecond and micro to millisecond time scale and transient α-helical behavior for certain residues in the N-terminal heptad repeat (NHR). Strong lipid interactions are observed, in particular for C-terminal residues of the NHR and imunodominant loop region connecting NHR and C-terminal heptad repeat (CHR). Our data indicate an extended conformation with features anticipated for a prefusion intermediate, presumably in exchange with a lowly populated postfusion six-helical bundle conformation

Seasonal Variation in Carcinops pumilio (Coleoptera: Histeridae) Dispersal and Potential for Suppression of Dispersal Behavior

Seasonal dispersal of Carcinops pumilio (Erichson) was evaluated using two trapping methods-a black-light pitfall trap and a mesh-bottomed trap placed on poultry manure. The black-light trap collected larger numbers than the mesh-bottomed trap from March through June. The mesh-bottomed trap gathered larger numbers of beetles from June through August and numbers were less variable throughout the year. Often, when very low numbers of beetles were recovered from manure cores, large numbers of beetles could be collected with the black-light trap suggesting that beetle density may not be an important factor in dispersal behavior. The greatest dispersal in the dispersal arenas (≈90%) occurred using beetles collected by both trap types in June 2000. Beginning in March and ending in August, a cyclic rise and then fall pattern in both laboratory dispersal and beetle collections was observed. Trap collection patterns were similar in both years of the study. In January and March, we were unable to prevent dispersal behavior of beetles captured in black-light traps. However, in May, after beetles had been in a dispersal phase for several months, we were able to suppress dispersal. In contrast, dispersal behavior among beetles captured with the mesh-bottomed trap did not change following the photoperiod-altered exposur

Poor attention rather than hyperactivity/impulsivity predicts academic achievement in very preterm and full-term adolescents

Background: Very preterm (VP) children are at particular risk for attention deficit/hyperactivity disorder (ADHD) of the inattentive subtype. It is unknown whether the neurodevelopmental pathways to academic underachievement are the same as in the general population. This study investigated whether middle childhood attention or hyperactivity/impulsivity problems are better predictors of VP adolescents' academic achievement. Method: In a geographically defined prospective whole-population sample of VP (<32 weeks gestation) and/or very low birth weight (<1500 g birth weight) (VLBW/VP; n = 281) and full-term control children (n = 286) in South Germany, ADHD subtypes were assessed at 6 years 3 months and 8 years 5 months using multiple data sources. Academic achievement was assessed at 13 years of age. Results: Compared with full-term controls, VLBW/VP children were at higher risk for ADHD inattentive subtype [6 years 3 months: odds ratio (OR) 2.8, p < 0.001; 8 years 5 months: OR 1.7, p = 0.020] but not for ADHD hyperactive-impulsive subtype (6 years 3 months: OR 1.4, p = 0.396; 8 years 5 months: OR 0.9, p = 0.820). Childhood attention measures predicted academic achievement in VLBW/VP and also full-term adolescents, whereas hyperactive/impulsive behaviour did not. Conclusions: Attention is an important prerequisite for learning and predicts long-term academic underachievement. As ADHD inattentive subtype and cognitive impairments are frequent in VLBW/VP children, their study may help to identify the neurofunctional pathways from early brain development and dysfunction to attention problems and academic underachievement