Spatiospectral concentration on a sphere

We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere, or, alternatively, of strictly spacelimited functions that are optimally concentrated within the spherical harmonic domain. Such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications, as well as in medical imaging, computer science, cosmology and numerical analysis. The spherical Slepian functions can be found either by solving an algebraic eigenvalue problem in the spectral domain or by solving a Fredholm integral equation in the spatial domain. The associated eigenvalues are a measure of the spatiospectral concentration. When the concentration region is an axisymmetric polar cap the spatiospectral projection operator commutes with a Sturm-Liouville operator; this enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large. In the asymptotic limit of a small concentration region and a large spherical harmonic bandwidth the spherical concentration problem approaches its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant.Comment: 48 pages, 17 figures. Submitted to SIAM Review, August 24th, 200

Nonuniform cratering of the Moon and a revised crater chronology of the inner solar system

International audience► We model the cratering of the Moon and terrestrial planets. ► We account for cratering asymmetries and megaregolith. ► We revise the crater chronology method. ► We give new age estimates of key planetary surface

Pre-mRNA splicing in higher plants.

P re-mRNA splicing is one of the fundamental processes in constitutive and regulated gene expression in eukaryotes. During splicing, introns present in primary gene transcripts are removed and exons are ligated to produce translationally competent mRNAs. The basic mechanism of intron excision is similar in all eukaryotes. The reaction is mediated by the spliceosome, a large ribonucleoprotein (RNP) complex, which is assembled anew at each intron from small nuclear RNP particles (U-snRNPs) and numerous protein factors. Spliceosome assembly is a highly ordered and dynamic reaction, involving hydrolysis of several ATP molecules and many structural rearrangements Properties of plant introns The intron and exon organization of higher plant genes is similar to that of vertebrates In spite of these similarities, the requirements for intron recognition in plants differ from those in other eukaryotes, and plant cells generally fail to splice heterologous pre-mRNAs. The most important difference is a strong compositional bias for UA-or U-rich sequences in plant introns compared with those from yeast and vertebrates U12-type introns A minor class of nuclear pre-mRNA introns, referred to as U12-type or AT-AC introns (because they frequently start with AT and terminate with AC) have recently been described 3,13 . These introns contain different splice site and branch point sequences, and are excised by an alternative U12-type spliceosom

Asymmetric Distribution of Lunar Impact Basins Caused by Variations in Target Properties

Maps of crustal thickness derived from NASA's Gravity Recovery and Interior Laboratory (GRAIL) mission revealed more large impact basins on the nearside hemisphere of the Moon than on its farside. The enrichment in heat-producing elements and prolonged volcanic activity on the lunar nearside hemisphere indicate that the temperature of the nearside crust and upper mantle was hotter than that of the farside at the time of basin formation. Using the iSALE-2D hydrocode to model impact basin formation, we found that impacts on the hotter nearside would have formed basins up to two times larger than similar impacts on the cooler farside hemisphere. The size distribution of lunar impact basins is thus not representative of the earliest inner Solar system impact bombardment

Supplemental Information For: Asymmetric Distribution of Lunar Impact Basins Caused by Variations in Target Properties

Maps of crustal thickness derived from NASA's Gravity Recovery and Interior Laboratory (GRAIL) mission revealed more large impact basins on the nearside hemisphere of the Moon than on its farside. The enrichment in heat-producing elements and prolonged volcanic activity on the lunar nearside hemisphere indicate that the temperature of the nearside crust and uppermantle was hotter than that of the farside at the time of basin formation. Using the iSALE-2D hydrocode to model impact basin formation, we found that impacts on the hotter nearside would have formed basins up to two times larger than similar impacts on the cooler farside hemisphere. The size distribution of lunar impact basins is thus not representative of the earliest inner Solar system impact bombardmen

Gravity Recovery and Interior Laboratory (GRAIL) Mission: Status at the Initiation of the Science Mapping Phase

The Gravity Recovery And Interior Laboratory (GRAIL) mission, a component of NASA's Discovery Program, launched successfully from Cape Canaveral Air Force Station on September 10, 2011. The dual spacecraft traversed independent, low-energy trajectories to the Moon via the EL-1 Lagrange point and inserted into elliptical, 11.5-hour polar orbits around the Moon on December 31, 2011, and January 1, 2012. The spacecraft are currently executing a series of maneuvers to circularize their orbits at 55-km mean altitude. Once the mapping orbit is achieved, the spacecraft will undergo additional maneuvers to align them into mapping configuration. The mission is on track to initiate the Science Phase on March 8, 2012

Lunar Seismology: An Update on Interior Structure Models

An international team of researchers gathered, with the support of the Interna- tional Space Science Institute (ISSI), (1) to review seismological investigations of the lunar interior from the Apollo-era and up until the present and (2) to re-assess our level of knowl- edge and uncertainty on the interior structure of the Moon. A companion paper (Nunn et al. in Space Sci. Rev., submitted) reviews and discusses the Apollo lunar seismic data with the aim of creating a new reference seismic data set for future use by the community. In this study, we first review information pertinent to the interior of the Moon that has become available since the Apollo lunar landings, particularly in the past ten years, from orbiting spacecraft, continuing measurements, modeling studies, and laboratory experiments. Fol- lowing this, we discuss and compare a set of recent published models of the lunar interior, including a detailed review of attenuation and scattering properties of the Moon. Common features and discrepancies between models and moonquake locations provide a first esti- mate of the error bars on the various seismic parameters. Eventually, to assess the influence of model parameterisation and error propagation on inverted seismic velocity models, an inversion test is presented where three different parameterisations are considered. For this purpose, we employ the travel time data set gathered in our companion paper (Nunn et al. in Space Sci. Rev., submitted). The error bars of the inverted seismic velocity models demon- strate that the Apollo lunar seismic data mainly constrain the upper- and mid-mantle struc- ture to a depth of ∼1200 km. While variable, there is some indication for an upper mantle low-velocity zone (depth range 100–250 km), which is compatible with a temperature gradi- ◦ent around 1.7 C/km. This upper mantle thermal gradient could be related to the presence of the thermally anomalous region known as the Procellarum Kreep Terrane, which contains a large amount of heat producing elements

Localized gravity/topography admittance and correlation spectra on Mars: Implications for regional and global evolution

From gravity and topography data collected by the Mars Global Surveyor spacecraft we calculate gravity/topography admittances and correlations in the spectral domain and compare them to those predicted from models of lithospheric flexure. On the basis of these comparisons we estimate the thickness of the Martian elastic lithosphere (T_e) required to support the observed topographic load since the time of loading. We convert T_e to estimates of heat flux and thermal gradient in the lithosphere through a consideration of the response of an elastic/plastic shell. In regions of high topography on Mars (e.g., the Tharsis rise and associated shield volcanoes), the mass-sheet (small-amplitude) approximation for the calculation of gravity from topography is inadequate. A correction that accounts for finite-amplitude topography tends to increase the amplitude of the predicted gravity signal at spacecraft altitudes. Proper implementation of this correction requires the use of radii from the center of mass (collectively known as the planetary “shape”) in lieu of “topography” referenced to a gravitational equipotential. Anomalously dense surface layers or buried excess masses are not required to explain the observed admittances for the Tharsis Montes or Olympus Mons volcanoes when this correction is applied. Derived T_e values generally decrease with increasing age of the lithospheric load, in a manner consistent with a rapid decline of mantle heat flux during the Noachian and more modest rates of decline during subsequent epochs