372 research outputs found
Extremal -invariant eigenvalues of the Laplacian of -invariant metrics
The study of extremal properties of the spectrum often involves restricting
the metrics under consideration. Motivated by the work of Abreu and Freitas in
the case of the sphere endowed with -invariant metrics, we consider
the subsequence of the spectrum of a Riemannian manifold
which corresponds to metrics and functions invariant under the action of a
compact Lie group . If has dimension at least 1, we show that the
functional admits no extremal metric under volume-preserving
-invariant deformations. If, moreover, has dimension at least three,
then the functional is unbounded when restricted to any conformal
class of -invariant metrics of fixed volume. As a special case of this, we
can consider the standard O(n)-action on ; however, if we also require the
metric to be induced by an embedding of in , we get an
optimal upper bound on .Comment: To appear in Mathematische Zeitschrif
Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds
We give upper bounds for the eigenvalues of the La-place-Beltrami operator of
a compact -dimensional submanifold of . Besides the dimension
and the volume of the submanifold and the order of the eigenvalue, these bounds
depend on either the maximal number of intersection points of with a
-plane in a generic position (transverse to ), or an invariant which
measures the concentration of the volume of in . These bounds are
asymptotically optimal in the sense of the Weyl law. On the other hand, we show
that even for hypersurfaces (i.e., when ), the first positive eigenvalue
cannot be controlled only in terms of the volume, the dimension and (for ) the differential structure.Comment: To appear, London Math Societ
Proteome-wide measurement of non-canonical bacterial mistranslation by quantitative mass spectrometry of protein modifications.
The genetic code is virtually universal in biology and was likely established before the advent of cellular life. The extent to which mistranslation occurs is poorly understood and presents a fundamental question in basic research and production of recombinant proteins. Here we used shotgun proteomics combined with unbiased protein modification analysis to quantitatively analyze in vivo mistranslation in an E. coli strain with a defect in the editing mechanism of leucyl-tRNA synthetase. We detected the misincorporation of a non-proteinogenic amino acid norvaline on 10% of all measured leucine residues under microaerobic conditions and revealed preferential deployment of a tRNA(Leu)(CAG) isoacceptor during norvaline misincorporation. The strain with the norvalylated proteome demonstrated a substantial reduction in cell fitness under both prolonged aerobic and microaerobic cultivation. Unlike norvaline, isoleucine did not substitute for leucine even under harsh error-prone conditions. Our study introduces shotgun proteomics as a powerful tool in quantitative analysis of mistranslation
Premi\`ere valeur propre du laplacien, volume conforme et chirurgies
We define a new differential invariant a compact manifold by , where is the conformal volume of for
the conformal class , and prove that it is uniformly bounded above. The
main motivation is that this bound provides a upper bound of the
Friedlander-Nadirashvili invariant defined by \inf_g\sup_{\tilde
g\in[g]}\lambda_1(M,\tilde g)\Vol(M,\tilde g)^{\frac 2n}.
The proof relies on the study of the behaviour of when
one performs surgeries on .Comment: 11 pages, 5 figures, in Frenc
Pulsation modes in rapidly rotating stellar models based on the Self-Consistent Field method
Context: New observational means such as the space missions CoRoT and Kepler
and ground-based networks are and will be collecting stellar pulsation data
with unprecedented accuracy. A significant fraction of the stars in which
pulsations are observed are rotating rapidly.
Aims: Our aim is to characterise pulsation modes in rapidly rotating stellar
models so as to be able to interpret asteroseismic data from such stars.
Methods: The pulsation code developed in Ligni\`eres et al. (2006) and Reese
et al. (2006) is applied to stellar models based on the self-consistent field
(SCF) method (Jackson et al. 2004, 2005, MacGregor et al. 2007).
Results: Pulsation modes in SCF models follow a similar behaviour to those in
uniformly rotating polytropic models, provided that the rotation profile is not
too differential. Pulsation modes fall into different categories, the three
main ones being island, chaotic, and whispering gallery modes, which are
rotating counterparts to modes with low, medium, and high l-|m| values,
respectively. The frequencies of the island modes follow an asymptotic pattern
quite similar to what was found for polytropic models. Extending this
asymptotic formula to higher azimuthal orders reveals more subtle behaviour as
a function of m and provides a first estimate of the average advection of
pulsation modes by rotation. Further calculations based on a variational
principle confirm this estimate and provide rotation kernels that could be used
in inversion methods. When the rotation profile becomes highly differential, it
becomes more and more difficult to find island and whispering gallery modes at
low azimuthal orders. At high azimuthal orders, whispering gallery modes, and
in some cases island modes, reappear.Comment: 16 pages, 11 figures, accepted for publication in A&
Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars
We develop the formalism required to study the nonlinear interaction of modes
in rotating Newtonian stars in the weakly nonlinear regime. The formalism
simplifies and extends previous treatments. At linear order, we elucidate and
extend slightly a formalism due to Schutz, show how to decompose a general
motion of a rotating star into a sum over modes, and obtain uncoupled equations
of motion for the mode amplitudes under the influence of an external force.
Nonlinear effects are added perturbatively via three-mode couplings. We
describe a new, efficient way to compute the coupling coefficients, to zeroth
order in the stellar rotation rate, using spin-weighted spherical harmonics.
We apply this formalism to derive some properties of the coupling
coefficients relevant to the nonlinear interactions of unstable r-modes in
neutron stars, postponing numerical integrations of the coupled equations of
motion to a later paper. From an astrophysical viewpoint, the most interesting
result of this paper is that many couplings of r-modes to other rotational
modes (modes with zero frequencies in the non-rotating limit) are small: either
they vanish altogether because of various selection rules, or they vanish to
lowest order in the angular velocity. In zero-buoyancy stars, the coupling of
three r-modes is forbidden entirely and the coupling of two r-modes to one
hybrid rotational mode vanishes to zeroth order in rotation frequency. In
incompressible stars, the coupling of any three rotational modes vanishes to
zeroth order in rotation frequency.Comment: 62 pages, no figures. Corrected error in computation of coupling
coefficients, added new selection rule and an appendix on energy and angular
momentum of mode
The planetary system host HR\,8799: On its Bootis nature
HR\,8799 is a Bootis, Doradus star hosting a planetary
system and a debris disk with two rings. This makes this system a very
interesting target for asteroseismic studies. This work is devoted to the
determination of the internal metallicity of this star, linked with its
Bootis nature (i.e., solar surface abundances of light elements, and
subsolar surface abundances of heavy elements), taking advantage of its
Doradus pulsations. This is the most accurate way to obtain this
information, and this is the first time such a study is performed for a
planetary-system-host star. We have used the equilibrium code CESAM and the
non-adiabatic pulsational code GraCo. We have applied the Frequency Ratio
Method (FRM) and the Time Dependent Convection theory (TDC) to estimate the
mode identification, the Brunt-Va\"is\"al\"a frequency integral and the mode
instability, making the selection of the possible models. When the
non-seismological constraints (i.e its position in the HR diagram) are used,
the solar abundance models are discarded. This result contradicts one of the
main hypothesis for explaining the Bootis nature, namely the
accretion/diffusion of gas by a star with solar abundance. Therefore, according
to these results, a revision of this hypothesis is needed. The inclusion of
accurate internal chemical mixing processes seems to be necessary to explain
the peculiar abundances observed in the surface of stars with internal subsolar
metallicities. The use of the asteroseismological constraints, like those
provided by the FRM or the instability analysis, provides a very accurate
determination of the physical characteristics of HR 8799. However, a dependence
of the results on the inclination angle still remains. The determination of
this angle, more accurate multicolour photometric observations, and high
resolution spectroscopy can definitively fix the mass and metallicity of this
star.Comment: 11 pages, 10 figures. Accepted for publication in MNRA
Photometric mode identification methods of nonradial pulsations in eclipsing binaries I. -- Dynamic Eclipse Mapping
We present the Dynamic Eclipse Mapping (DEM) method designed specifically to
reconstruct the surface intensity patterns of non-radial stellar oscillations
in eclipsing binaries. The method needs a geometric model of the binary,
accepts the light curve and the detected pulsation frequencies on input, and on
output yields estimates of the pulsation patterns, in form of images -- thus
allowing a direct identification of the surface mode numbers.
Since it has minimal modelling requirements and can operate on photometric
observations in arbitrary wavelength bands, DEM is well suited to analyze the
wide-band time series collected by space observatories.
The method was extensively tested on simulated data, in which almost all
photometrically detectable modes with a latitudinal complexity
were properly restored. Multimode pulsations can be also reconstructed in a
natural manner, as well as pulsations on components with tilted rotation axis
of known direction. It can also be used in principle to isolate the
contribution of hidden modes from the light curve.
Sensitivity tests show that moderate errors in the geometric parameters and
the assumed limb darkening can be partially tolerated by the inversion, in the
sense that the lower degree modes are still recoverable. Tidally induced or
mutually resonant pulsations, however, are an obstacle that neither the eclipse
mapping, nor any other inversion technique can ever surpass.
We conclude that, with reasonable assumptions, Dynamic Eclipse Mapping could
be a powerful tool for mode identification, especially in moderately close
eclipsing binary systems, where the pulsating component is not seriously
affected by tidal interactions so that the pulsations are intrinsic to them,
and not a consequence of the binarity.Comment: Accepted for publication in MNRAS. 16 pages, 11 figures and 5 table
The images of psychiatry scale: development, factor structure, and reliability.
BACKGROUND: This analysis is based on a survey questionnaire designed to describe medical educators' views of psychiatry and psychiatrists. Our goals in this paper were to assess the psychometric properties of the survey questions by (a) using exploratory factor analysis to identify the basic factor structure underlying 37 survey items; (b) testing the resulting factor structure using confirmatory factor analysis; and (c) assessing the internal reliability of each identified factor. To our knowledge, this is the first attempt to use these techniques to psychometrically assess a scale measuring the strength of stigma that medical educators attached to psychiatry. METHODS: Survey data were collected from a random sample of 1,059 teaching faculty in 23 academic teaching sites in 15 countries. We conducted exploratory and confirmatory factor analysis to identify the scale structure and Cronbach's alpha to assess internal consistency of the resulting scales. RESULTS: Results showed that a two-factor solution was the best fit for the data. Following exploratory factor analysis, we conducted confirmatory factor analysis on a split half of the sample. Results highlighted several items with low loadings. Excluding factors with low correlations and allowing for several correlated variances resulted in a good fitting model explaining 95% of the variance in the data. CONCLUSIONS: We identified two unidimensional scales. The Images Scale contained 11 items measuring stereotypic content concerning psychiatry and psychiatrists. The Efficacy of Psychiatry Scale contained 5 items addressing perceptions of the challenges and effectiveness of psychiatry as a discipline
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