Compact convex sets of the plane and probability theory

The Gauss-Minkowski correspondence in $\mathbb{R}^2$ states the existence of a homeomorphism between the probability measures $\mu$ on $[0,2\pi]$ such that $\int_0^{2\pi} e^{ix}d\mu(x)=0$ and the compact convex sets (CCS) of the plane with perimeter~1. In this article, we bring out explicit formulas relating the border of a CCS to its probability measure. As a consequence, we show that some natural operations on CCS -- for example, the Minkowski sum -- have natural translations in terms of probability measure operations, and reciprocally, the convolution of measures translates into a new notion of convolution of CCS. Additionally, we give a proof that a polygonal curve associated with a sample of $n$ random variables (satisfying $\int_0^{2\pi} e^{ix}d\mu(x)=0$) converges to a CCS associated with $\mu$ at speed $\sqrt{n}$, a result much similar to the convergence of the empirical process in statistics. Finally, we employ this correspondence to present models of smooth random CCS and simulations

Magnitude bias of microlensed sources towards the Large Magellanic Cloud

There are lines of evidence suggesting that some of the observed microlensing events in the direction of the Large Magellanic Cloud (LMC) are caused by ordinary star lenses as opposed to dark Machos in the Galactic halo. Efficient lensing by ordinary stars generally requires the presence of one or more additional concentrations of stars along the line of sight to the LMC disk. If such a population behind the LMC disk exists, then the source stars (for lensing by LMC disk objects) will be drawn preferentially from the background population and will show systematic differences from LMC field stars. One such difference is that the (lensed) source stars will be farther away than the average LMC field stars, and this should be reflected in their apparent baseline magnitudes. We focus on red clump stars: these should appear in the color-magnitude diagram at a few tenths of a magnitude fainter than the field red clump. Suggestively, one of the two near-clump confirmed events, MACHO-LMC-1, is a few tenths of magnitude fainter than the clump.Comment: To appear in ApJ Letters. Shortened to match the accepted version, 8 pages plus 1 ps figur

The Arabidopsis pop2-1 mutant reveals the involvement of GABA transaminase in salt stress tolerance

<p>Abstract</p> <p>Background</p> <p>GABA (γ-aminobutyric acid) is a non protein amino acid that has been reported to accumulate in a number of plant species when subjected to high salinity and many other environmental constraints. However, no experimental data are to date available on the molecular function of GABA and the involvement of its metabolism in salt stress tolerance in higher plants. Here, we investigated the regulation of GABA metabolism in <it>Arabidopsis thaliana </it>at the metabolite, enzymatic activity and gene transcription levels upon NaCl stress.</p> <p>Results</p> <p>We identified the GABA transaminase (GABA-T), the first step of GABA catabolism, as the most responsive to NaCl. We further performed a functional analysis of the corresponding gene <it>POP2 </it>and demonstrated that the previously isolated loss-of-function <it>pop2-1 </it>mutant was oversensitive to ionic stress but not to osmotic stress suggesting a specific role in salt tolerance. NaCl oversensitivity was not associated with overaccumulation of Na⁺and Cl^-but mutant showed a slight decrease in K⁺. To bring insights into <it>POP2 </it>function, a promoter-reporter gene strategy was used and showed that <it>POP2 </it>was mainly expressed in roots under control conditions and was induced in primary root apex and aerial parts of plants in response to NaCl. Additionally, GC-MS- and UPLC-based metabolite profiling revealed major changes in roots of <it>pop2-1 </it>mutant upon NaCl stress including accumulation of amino acids and decrease in carbohydrates content.</p> <p>Conclusions</p> <p>GABA metabolism was overall up-regulated in response to NaCl in <it>Arabidopsis</it>. Particularly, GABA-T was found to play a pivotal function and impairment of this step was responsible for a decrease in salt tolerance indicating that GABA catabolism was a determinant of <it>Arabidopsis </it>salt tolerance. GABA-T would act in salt responses in linking N and C metabolisms in roots.</p

Cold Acclimation Favors Metabolic Stability in Drosophila suzukii

The invasive fruit fly pest, Drosophila suzukii, is a chill susceptible species, yet it is capable of overwintering in rather cold climates, such as North America and North Europe, probably thanks to a high cold tolerance plasticity. Little is known about the mechanisms underlying cold tolerance acquisition in D. suzukii. In this study, we compared the effect of different forms of cold acclimation (at juvenile or at adult stage) on subsequent cold tolerance. Combining developmental and adult cold acclimation resulted in a particularly high expression of cold tolerance. As found in other species, we expected that cold-acclimated flies would accumulate cryoprotectants and would be able to maintain metabolic homeostasis following cold stress. We used quantitative target GC-MS profiling to explore metabolic changes in four different phenotypes: control, cold acclimated during development or at adult stage or during both phases. We also performed a time-series GC-MS analysis to monitor metabolic homeostasis status during stress and recovery. The different thermal treatments resulted in highly distinct metabolic phenotypes. Flies submitted to both developmental and adult acclimation were characterized by accumulation of cryoprotectants (carbohydrates and amino acids), although concentrations changes remained of low magnitude. After cold shock, non-acclimated chill-susceptible phenotype displayed a symptomatic loss of metabolic homeostasis, correlated with erratic changes in the amino acids pool. On the other hand, the most cold-tolerant phenotype was able to maintain metabolic homeostasis after cold stress. These results indicate that cold tolerance acquisition of D. suzukii depends on physiological strategies similar to other drosophilids: moderate changes in cryoprotective substances and metabolic robustness. In addition, the results add to the body of evidence supporting that mechanisms underlying the different forms of acclimation are distinct

Metabolic and Proteomic Profiling of Diapause in the Aphid Parasitoid Praon volucre

Background: Diapause, a condition of developmental arrest and metabolic depression exhibited by a wide range of animals is accompanied by complex physiological and biochemical changes that generally enhance environmental stress tolerance and synchronize reproduction. Even though some aspects of diapause have been well characterized, very little is known about the full range of molecular and biochemical modifications underlying diapause in non-model organisms. Methodology/Principal Findings: In this study we focused on the parasitic wasp, Praon volucre that exhibits a pupal diapause in response to environmental signals. System-wide metabolic changes occurring during diapause were investigated using GC-MS metabolic fingerprinting. Moreover, proteomic changes were studied in diapausing versus nondiapausing phenotypes using a combination of two-dimensional differential gel electrophoresis (2D-DIGE) and mass spectrometry. We found a reduction of Krebs cycle intermediates which most likely resulted from the metabolic depression. Glycolysis was galvanized, probably to favor polyols biosynthesis. Diapausing parasitoids accumulated high levels of cryoprotective polyols, especially sorbitol. A large set of proteins were modulated during diapause and these were involved in various functions such as remodeling of cytoskeleton and cuticle, stress tolerance, protein turnover, lipid metabolism and various metabolic enzymes. Conclusions/Significance: The results presented here provide some first clues about the molecular and biochemical events that characterize the diapause syndrome in aphid parasitoids. These data are useful for probing potential commonality of parasitoids diapause with other taxa and they will help creating a general understanding of diapause underpinnings and a background for future interpretations

Adaptations of a native Subantarctic flightless fly to dehydration stress: more plastic than we thought? ( Short Communication)

Water conservation is a critical aspect affecting the survival, distribution and abundance of terrestrial arthropods. In this study we investigate mechanisms of dehydration tolerance of the native, flightless fly, Calycopteryx moseleyi, inhabiting contrasting environments at two localities in the Kerguelen Islands. We compare the survival abilities and management of body water content of adult flies from two different ecophenotypes when exposed to conditions of low relative humidity. Our results suggest a broad plasticity in the responses of C. moseleyi to desiccation, showing distinct local adaptations to environmental conditions

Direct syntheses of stereoisomers of 3-fluoro GABA and β-fluoroamine analogues of the calcium receptor (CaR) agonists, cinacalcet, tecalcet, fendilines and NPS R-467

Synthetic routes following a sequential MacMillan organocatalytic asymmetric α-fluorination protocol for aldehydes and then reductive amination, have allowed ready access to bioactive β-fluoroamines. The approach is demonstrated with a short synthesis of (S)-3-fluoro-γ-aminobutyric acid (3F-GABA) and was extended to β-fluoroamine stereoisomers of cinacalcet, tecalcet, fendiline and NPS R-467, all allosteric modulators of the calcium receptor (CaR). Stereoisomers of the fluorinated calcimimetic analogues were then assayed in a CaR receptor assay and a comparison of β-fluoroamine matched pair stereoisomers revealed a binding mode preference to the receptor as deduced from conformations which will be favoured as a consequence of the electrostatic gauche effect.Publisher PDFPeer reviewe