Adler-Kostant-Symes systems as Lagrangian gauge theories

It is well known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.Comment: 10 pages, LaTeX2

Inverse problem for wave equation with sources and observations on disjoint sets

We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted Dirichlet-to-Neumann operator $\Lambda_{\Gamma_1,\Gamma_2}$. This operator corresponds the boundary measurements when we have smooth sources supported on $\Gamma_1$ and the fields produced by these sources are observed on $\Gamma_2$. We show that when $\Gamma_1$ and $\Gamma_2$ are disjoint but their closures intersect at least at one point, then the restricted Dirichlet-to-Neumann operator $\Lambda_{\Gamma_1,\Gamma_2}$ determines the Riemannian manifold and the metric on it up to an isometry. In the Euclidian space, the result yields that an anisotropic wave speed inside a compact body is determined, up to a natural coordinate transformations, by measurements on the boundary of the body even when wave sources are kept away from receivers. Moreover, we show that if we have three arbitrary non-empty open subsets $\Gamma_1,\Gamma_2$, and $\Gamma_3$ of the boundary, then the restricted Dirichlet-to-Neumann operators $\Lambda_{\Gamma_j,\Gamma_k}$ for $1\leq j<k\leq 3$ determine the Riemannian manifold to an isometry. Similar result is proven also for the finite-time boundary measurements when the hyperbolic equation satisfies an exact controllability condition

Diversification under sexual selection: the relative roles of mate preference strength and the degree of divergence in mate preferences

The contribution of sexual selection to diversification remains poorly understood after decades of research. This may be in part because studies have focused predominantly on the strength of sexual selection, which offers an incomplete view of selection regimes. By contrast, students of natural selection focus on environmental differences that help compare selection regimes across populations. To ask how this disparity in focus may affect the conclusions of evolutionary research, we relate the amount of diversification in mating displays to quantitative descriptions of the strength and the amount of divergence in mate preferences across a diverse set of case studies of mate choice. We find that display diversification is better explained by preference divergence rather than preference strength; the effect of the latter is more subtle, and is best revealed as an interaction with the former. Our findings cast the action of sexual selection (and selection in general) in a novel light: the strength of selection influences the rate of evolution, and how divergent selection is determines how much diversification can occur. Adopting this view will enhance tests of the relative role of natural and sexual selection in processes such as speciation

Diversification under sexual selection: the relative roles of mate preference strength and the degree of divergence in mate preferences

The contribution of sexual selection to diversification remains poorly understood after decades of research. This may be in part because studies have focused predominantly on the strength of sexual selection, which offers an incomplete view of selection regimes. By contrast, students of natural selection focus on environmental differences that help compare selection regimes across populations. To ask how this disparity in focus may affect the conclusions of evolutionary research, we relate the amount of diversification in mating displays to quantitative descriptions of the strength and the amount of divergence in mate preferences across a diverse set of case studies of mate choice. We find that display diversification is better explained by preference divergence rather than preference strength; the effect of the latter is more subtle, and is best revealed as an interaction with the former. Our findings cast the action of sexual selection (and selection in general) in a novel light: the strength of selection influences the rate of evolution, and how divergent selection is determines how much diversification can occur. Adopting this view will enhance tests of the relative role of natural and sexual selection in processes such as speciation

The age of the martian meteorite Northwest Africa 1195 and the differentiation history of the shergottites

Samarium-neodymium isotopic analyses of unleached and acid-leached mineral fractions from the recently identified olivine-bearing shergottite Northwest Africa 1195 yield a crystallization age of 348 {+-} 19 Ma and an {var_epsilon}{sub Nd}{sup 143} value of +40.1 {+-} 1.3. Maskelynite fractions do not lie on the Sm-Nd isochron and appear to contain a martian surface component with low {sup 147}Sm/{sup 144}Nd and {sup 143}Nd/{sup 144}Nd ratios that was added during shock. The Rb-Sr system is disturbed and does not yield an isochron. Terrestrial Sr appears to have affected all of the mineral fractions, although a maximum initial {sup 87}Sr/{sup 86}Sr ratio of 0.701614 {+-} 16 is estimated by passing a 348 Ma reference isochron through the maskelynite fraction that is least affected by contamination. The high initial {var_epsilon}{sub Nd}{sup 143} value and the low initial {sup 87}Sr/{sup 86}Sr ratio, combined with the geologically young crystallization age, indicate that Northwest Africa 1195 is derived from a source region characterized by a long-term incompatible element depletion. The age and initial Sr and Nd isotopic compositions of Northwest Africa 1195 are very similar to those of Queen Alexandra Range 94201, indicating these samples were derived from source regions with nearly identical Sr-Nd isotopic systematics. These similarities suggest that these two meteorites share a close petrogenetic relationship and might have been erupted from a common volcano. The meteorites Yamato 980459, Dar al Gani 476, Sayh al Uhaymir 005/008, and Dhofar 019 also have relatively old ages between 474-575 Ma and trace element and/or isotopic systematics that are indicative of derivation from incompatible-element-depleted sources. This suggests that the oldest group of meteorites is more closely related to one another than they are to the younger meteorites that are derived from less incompatible-element-depleted sources. Closed-system fractional crystallization of this suite of meteorites is modeled with the MELTS algorithm using the bulk composition of Yamato 980459 as a parent. These models reproduce many of the major element and mineralogical variations observed in the suite. In addition, the rare-earth element systematics of these meteorites are reproduced by fractional crystallization using the proportions of phases and extents of crystallization that are calculated by MELTS. The combined effects of source composition and fractional crystallization are therefore likely to account for the major element, trace element, and isotopic diversity of all shergottites. Thus, assimilation of a martian crustal component is not required to explain the geochemical diversity of the shergottites

Polarization Dependence of Bulk Ion Acceleration from Ultrathin Foils Irradiated by High-Intensity Ultrashort Laser Pulses

The acceleration of ions from ultrathin (10-100 nm) carbon foils has been investigated using intense (∼ 6 x1020 Wcm-2), ultrashort (45 fs) laser pulses, highlighting a strong dependence of the ion beam parameters on the laser polarization, with circularly polarized (CP) pulses producing the highest energies for both protons and carbons (25-30 MeV/nucleon); carbon ion energies obtained employing CP pulses were signicantly higher (∼2.5 times) than for irradiations employing linearly polarized (LP) pulses. Particle-in-cell simulations indicate that Radiation Pressure Acceleration becomes the dominant mechanism for the thinnest targets and CP pulses

In vitro culture with gemcitabine augments death receptor and NKG2D ligand expression on tumour cells

Much effort has been made to try to understand the relationship between chemotherapeutic treatment of cancer and the immune system. Whereas much of that focus has been on the direct effect of chemotherapy drugs on immune cells and the release of antigens and danger signals by malignant cells killed by chemotherapy, the effect of chemotherapy on cells surviving treatment has often been overlooked. In the present study, tumour cell lines: A549 (lung), HCT116 (colon) and MCF-7 (breast), were treated with various concentrations of the chemotherapeutic drugs cyclophosphamide, gemcitabine (GEM) and oxaliplatin (OXP) for 24 hours in vitro. In line with other reports, GEM and OXP upregulated expression of the death receptor CD95 (fas) on live cells even at sub-cytotoxic concentrations. Further investigation revealed that the increase in CD95 in response to GEM sensitised the cells to fas ligand treatment, was associated with increased phosphorylation of stress activated protein kinase/c-Jun N-terminal kinase and that other death receptors and activatory immune receptors were co-ordinately upregulated with CD95 in certain cell lines. The upregulation of death receptors and NKG2D ligands together on cells after chemotherapy suggest that although the cells have survived preliminary treatment with chemotherapy they may now be more susceptible to immune cell-mediated challenge. This re-enforces the idea that chemotherapy-immunotherapy combinations may be useful clinically and has implications for the make-up and scheduling of such treatments

Seismic tomography is locally ill-posed

We develop a general convergence analysis for a class of inexact Newton-type regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including Landweber and steepest decent iterations, iterated Tikhonov method, and method of conjugate gradients

Hot Electron and X-ray Production from Intense Laser Irradiation of Wavelength-Scale Polystyrene Spheres

Hot electron and x-ray production from solid targets coated with polystyrene-spheres which are irradiated with high-contrast, 100 fs, 400 nm light pulses at intensity up to 2×1017 W/cm2 have been studied. The peak hard x-ray signal from uncoated fused silica targets is an order of magnitude smaller than the signal from targets coated with submicron sized spheres. The temperature of the x-rays in the case of sphere-coated targets is twice as hot as that of uncoated glass. A sphere-size scan of the x-ray yield and observation of a peak in both the x-ray production and temperature at a sphere diameter of 0.26 μm, indicate that these results are consistent with Mie enhancements of the laser field at the sphere surface and multipass stochastic heating of the hot electrons in the oscillating laser field. These results also match well with particle-in-cell simulations of the interaction