On the Invariant Theory of Weingarten Surfaces in Euclidean Space

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal surfaces, surfaces of constant mean curvature and surfaces of constant Gauss curvature.Comment: 16 page

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

The Hamiltonian theory of Earth rotation, known as the Kinoshita-Souchay theory, operates with nonosculating Andoyer elements. This situation parallels a similar phenomenon that often happens (but seldom gets noticed) in orbital dynamics, when the standard Lagrange-type or Delaunay-type planetary equations unexpectedly render nonosculating orbital elements. In orbital mechanics, osculation loss happens when a velocity-dependent perturbation is plugged into the standard planetary equations. In attitude mechanics, osculation is lost when an angular-velocity-dependent disturbance is plugged in the standard dynamical equations for the Andoyer elements. We encounter exactly this situation in the theory of Earth rotation, because this theory contains an angular-velocity-dependent perturbation (the switch from an inertial frame to that associated with the precessing ecliptic of date). While the osculation loss does not influence the predictions for the figure axis of the planet, it considerably alters the predictions for the instantaneous spin-axis' orientation. We explore this issue in great detail

Satellite estimates of net community production indicate predominance of net autotrophy in the Atlantic Ocean

There is ongoing debate as to whether the oligotrophic ocean is predominantly net autotrophic and acts as a CO2 sink, or net heterotrophic and therefore acts as a CO2 source to the atmosphere. This quantification is challenging, both spatially and temporally, due to the sparseness of measurements. There has been a concerted effort to derive accurate estimates of phytoplankton photosynthesis and primary production from satellite data to fill these gaps; however there have been few satellite estimates of net community production (NCP). In this paper, we compare a number of empirical approaches to estimate NCP from satellite data with in vitro measurements of changes in dissolved O2 concentration at 295 stations in the N and S Atlantic Ocean (including the Antarctic), Greenland and Mediterranean Seas. Algorithms based on power laws between NCP and particulate organic carbon production (POC) derived from 14C uptake tend to overestimate NCP at negative values and underestimate at positive values. An algorithm that includes sea surface temperature (SST) in the power function of NCP and 14C POC has the lowest bias and root-mean square error compared with in vitro measured NCP and is the most accurate algorithm for the Atlantic Ocean. Nearly a 13 year time series of NCP was generated using this algorithm with SeaWiFS data to assess changes over time in different regions and in relation to climate variability. The North Atlantic subtropical and tropical Gyres (NATL) were predominantly net autotrophic from 1998 to 2010 except for boreal autumn/winter, suggesting that the northern hemisphere has remained a net sink for CO2 during this period. The South Atlantic sub-tropical Gyre (SATL) fluctuated from being net autotrophic in austral spring-summer, to net heterotrophic in austral autumn–winter. Recent decadal trends suggest that the SATL is becoming more of a CO2 source. Over the Atlantic basin, the percentage of satellite pixels with negative NCP was 27%, with the largest contributions from the NATL and SATL during boreal and austral autumn–winter, respectively. Variations in NCP in the northern and southern hemispheres were correlated with climate indices. Negative correlations between NCP and the multivariate ENSO index (MEI) occurred in the SATL, which explained up to 60% of the variability in NCP. Similarly there was a negative correlation between NCP and the North Atlantic Oscillation (NAO) in the Southern Sub-Tropical Convergence Zone (SSTC), which explained 90% of the variability. There were also positive correlations with NAO in the Canary Current Coastal Upwelling (CNRY) and Western Tropical Atlantic (WTRA) which explained 80% and 60% of the variability in each province, respectively. MEI and NAO seem to play a role in modifying phases of net autotrophy and heterotrophy in the Atlantic Ocean.Chinese State Scholarship Fund | Ref. 201206310058Ministerio de Ciencia e Innovación | Ref. CTM2011-2961

Projective dynamics and classical gravitation

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is a 2-plane containing the ray. Throwing the particle with a given initial impulsion defines a projective trajectory. It is a curve in the space of rays S(V), together with an impulsion attached to each ray. In the simplest example where the force is identically zero, the curve is a straight line and the impulsion a constant bivector. A striking feature of projective dynamics appears: the trajectories are not parameterized. Among the projective force fields corresponding to a central force, the one defining the Kepler problem is simpler than those corresponding to other homogeneities. Here the thrown ray describes a quadratic cone whose section by a hyperplane corresponds to a Keplerian conic. An original point of view on the hidden symmetries of the Kepler problem emerges, and clarifies some remarks due to Halphen and Appell. We also get the unexpected conclusion that there exists a notion of divergence-free field of projective forces if and only if dim V=4. No metric is involved in the axioms of projective dynamics.Comment: 20 pages, 4 figure

The Serret-Andoyer Formalism in Rigid-Body Dynamics: I. Symmetries and Perturbations

This paper reviews the Serret-Andoyer (SA) canonical formalism in rigid-body dynamics and presents some new results. As is well known, the problem of unsupported and unperturbed rigid rotator can be reduced. The availability of this reduction is offered by the underlying symmetry, which stems from conservation of the angular momentum and rotational kinetic energy. When a perturbation is turned on, these quantities are no longer preserved. Nonetheless, the language of reduced description remains extremely instrumental even in the perturbed case. We describe the canonical reduction performed by the Serret-Andoyer (SA) method, and discuss its applications to attitude dynamics and to the theory of planetary rotation. Specifically, we consider the case of angular-velocity-dependent torques, and discuss the variation-of-parameters-inherent antinomy between canonicity and osculation. Finally, we address the transformation of the Andoyer variables into the action-angle ones, using the method of Sadov

Case report: an unexpected link between partial deletion of the SHANK3 gene and Heller’s dementia infantilis, a rare subtype of autism spectrum disorder

International audienceAbstractBackgroundDeletions and mutations involving the SHANK3 gene lead to a nonspecific clinical presentation with moderate to profound intellectual disability, severely delayed or absent speech, and autism spectrum disorders (ASD).Better knowledge of the clinical spectrum of SHANK3 haploinsufficiency is useful to facilitate clinical care monitoring and to guide molecular diagnosis, essential for genetic counselling.Case presentationHere, we report a detailed clinical description of a 10-year-old girl carrying a pathogenic interstitial 22q13.3 deletion encompassing only the first 17 exons of SHANK3.The clinical features displayed by the girl strongly suggested the diagnosis of dementia infantilis, described by Heller in 1908, also known as childhood disintegrative disorder.ConclusionOur present case confirms several observations according to which regression may be part of the clinical phenotype of SHANK3 haploinsufficiency. Therefore, we think it is crucial to look for mutations in the gene SHANK3 in patients diagnosed for childhood disintegrative disorder or any developmental disorder with a regressive pattern involving social and communicative skills as well as cognitive and instinctual functions, with onset around 3 years

Pro-apoptotic and antiproliferative activity of human KCNRG, a putative tumor suppressor in 13q14 region

Deletion of 13q14.3 and a candidate gene KCNRG (potassium channel regulating gene) is the most frequent chromosomal abnormality in B-cell chronic lymphocytic leukemia and is a common finding in multiple myeloma (MM). KCNRG protein may interfere with the normal assembly of the K+ channel proteins causing the suppression of Kv currents. We aimed to examine possible role of KCNRG haploinsufficiency in chronic lymphocytic leukemia (CLL) and MM cells. We performed detailed genomic analysis of the KCNRG locus; studied effects of the stable overexpression of KCNRG isoforms in RPMI-8226, HL-60, and LnCaP cells; and evaluated relative expression of its transcripts in various human lymphomas. Three MM cell lines and 35 CLL PBL samples were screened for KCNRG mutations. KCNRG exerts growth suppressive and pro-apoptotic effects in HL-60, LnCaP, and RPMI-8226 cells. Direct sequencing of KCNRG exons revealed point mutation delT in RPMI-8226 cell line. Levels of major isoform of KCNRG mRNA are lower in DLBL lymphomas compared to normal PBL samples, while levels of its minor mRNA are decreased across the broad range of the lymphoma types. The haploinsufficiency of KCNRG might be relevant to the progression of CLL and MM at least in a subset of patients

Is There a Seamount Effect on Microbial Community Structure and Biomass? The Case Study of Seine and Sedlo Seamounts (Northeast Atlantic)

Seamounts are considered to be “hotspots” of marine life but, their role in oceans primary productivity is still under discussion. We have studied the microbial community structure and biomass of the epipelagic zone (0–150 m) at two northeast Atlantic seamounts (Seine and Sedlo) and compared those with the surrounding ocean. Results from two cruises to Sedlo and three to Seine are presented. Main results show large temporal and spatial microbial community variability on both seamounts. Both Seine and Sedlo heterotrophic community (abundance and biomass) dominate during winter and summer months, representing 75% (Sedlo, July) to 86% (Seine, November) of the total plankton biomass. In Seine, during springtime the contribution to total plankton biomass is similar (47% autotrophic and 53% heterotrophic). Both seamounts present an autotrophic community structure dominated by small cells (nano and picophytoplankton). It is also during spring that a relatively important contribution (26%) of large cells to total autotrophic biomass is found. In some cases, a “seamount effect” is observed on Seine and Sedlo microbial community structure and biomass. In Seine this is only observed during spring through enhancement of large autotrophic cells at the summit and seamount stations. In Sedlo, and despite the observed low biomasses, some clear peaks of picoplankton at the summit or at stations within the seamount area are also observed during summer. Our results suggest that the dominance of heterotrophs is presumably related to the trapping effect of organic matter by seamounts. Nevertheless, the complex circulation around both seamounts with the presence of different sources of mesoscale variability (e.g. presence of meddies, intrusion of African upwelling water) may have contributed to the different patterns of distribution, abundances and also changes observed in the microbial community

Stable Isotope Biogeochemistry of Seabird Guano Fertilization: Results from Growth Chamber Studies with Maize (Zea Mays)

Stable isotope analysis is being utilized with increasing regularity to examine a wide range of issues (diet, habitat use, migration) in ecology, geology, archaeology, and related disciplines. A crucial component to these studies is a thorough understanding of the range and causes of baseline isotopic variation, which is relatively poorly understood for nitrogen (δ(15)N). Animal excrement is known to impact plant δ(15)N values, but the effects of seabird guano have not been systematically studied from an agricultural or horticultural standpoint.This paper presents isotopic (δ(13)C and δ(15)N) and vital data for maize (Zea mays) fertilized with Peruvian seabird guano under controlled conditions. The level of (15)N enrichment in fertilized plants is very large, with δ(15)N values ranging between 25.5 and 44.7‰ depending on the tissue and amount of fertilizer applied; comparatively, control plant δ(15)N values ranged between -0.3 and 5.7‰. Intraplant and temporal variability in δ(15)N values were large, particularly for the guano-fertilized plants, which can be attributed to changes in the availability of guano-derived N over time, and the reliance of stored vs. absorbed N. Plant δ(13)C values were not significantly impacted by guano fertilization. High concentrations of seabird guano inhibited maize germination and maize growth. Moreover, high levels of seabird guano greatly impacted the N metabolism of the plants, resulting in significantly higher tissue N content, particularly in the stalk.The results presented in this study demonstrate the very large impact of seabird guano on maize δ(15)N values. The use of seabird guano as a fertilizer can thus be traced using stable isotope analysis in food chemistry applications (certification of organic inputs). Furthermore, the fertilization of maize with seabird guano creates an isotopic signature very similar to a high-trophic level marine resource, which must be considered when interpreting isotopic data from archaeological material

Persistence of butterfly populations in fragmented habitats along urban density gradients: motility helps

In a simulation study of genotypes conducted over 100 generations for more than 1600 butterfly’s individuals, we evaluate how the increase of anthropogenic fragmentation and reduction of habitat size along urbanisation gradients (from 7% to 59% of impervious land cover) influences genetic diversity and population persistence in butterfly species. We show that in areas characterised by a high urbanisation rate (> 56% impervious land cover), a large decrease of both genetic diversity (loss of 60-80% of initial observed heterozygosity) and population size (loss of 70-90% of individuals) is observed over time. This is confirmed by empirical data available for the mobile butterfly species Pieris rapae in a sub-part of the study area. Comparing simulated data for P. rapae with its normal dispersal ability and with a reduced dispersal ability, we also show that a higher dispersal ability can be an advantage to survive in an urban or highly fragmented environment. The results obtained here suggest that it is of high importance to account for population persistence, and confirm that it is crucial to maintain habitat size and connectivity in the context of land-use planning