On existence of canonical GG-bases

We describe a general method for expanding a truncated G-iterative Hasse-Schmidt derivation, where G is an algebraic group. We give examples of algebraic groups for which our method works

Cross-Country Evidence on the Link between the Level of Infrastructure and Capital Inflows

This paper empirically investigates the relationship between public infrastructrue and international capital flows. Out of a sample of thirty countries a cross-sectional econometric model is constructed to estimate the effects. Different components of infrastructure variables are tested in relation to their impact on different kinds of external capital liabilities. The resuts suggest a positive relationship between the level of infrastructure and capital inflows. However, statistical significance cannot be established for all variables in question.

Analyticity of the density of electronic wavefunctions

We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in ${\mathbb R}^3$ away from the nuclei.Comment: 19 page

A small population of hypothalamic neurons govern fertility: the critical role of VAX1 in GnRH neuron development and fertility maintenance.

Fertility depends on the correct maturation and function of approximately 800 gonadotropin-releasing hormone (GnRH) neurons in the brain. GnRH neurons are at the apex of the hypothalamic-pituitary-gonadal axis that regulates fertility. In adulthood, GnRH neurons are scattered throughout the anterior hypothalamic area and project to the median eminence, where GnRH is released into the portal vasculature to stimulate release of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) from the pituitary. LH and FSH then regulate gonadal steroidogenesis and gametogenesis. Absence of GnRH neurons or inappropriate GnRH release leads to infertility. Despite the critical role of GnRH neurons in fertility, we still have a limited understanding of the genes responsible for proper GnRH neuron development and function in adulthood. GnRH neurons originate in the olfactory placode then migrate into the brain. Homeodomain transcription factors expressed within GnRH neurons or along their migratory path are candidate genes for inherited infertility. Using a combined in vitro and in vivo approach, we have identified Ventral Anterior Homeobox 1 (Vax1) as a novel homeodomain transcription factor responsible for GnRH neuron maturation and fertility. GnRH neuron counts in Vax1 knock-out embryos revealed Vax1 to be required for the presence of GnRH-expressing cells at embryonic day 17.5 (E17.5), but not at E13.5. To localize the effects of Vax1 on fertility, we generated Vax1flox mice and crossed them with Gnrhcre mice to specifically delete Vax1 within GnRH neurons. GnRH staining in Vax1flox/flox:GnRHcre mice show a total absence of GnRH expression in the adult. We performed lineage tracing in Vax1flox/flox:GnRHcre:RosaLacZ mice which proved GnRH neurons to be alive, but incapable of expressing GnRH. The absence of GnRH leads to delayed puberty, hypogonadism and complete infertility in both sexes. Finally, using the immortalized model GnRH neuron cell lines, GN11 and GT1-7, we show that VAX1 is a direct regulator of Gnrh1 transcription by binding key ATTA sites within the Gnrh1 promoter. This study identifies VAX1 as a key transcription factor regulating GnRH expression and establishes VAX1 as a novel candidate gene implicated in heritable infertility

Spatiotemporal buildup of the Kondo screening cloud

We investigate how the Kondo screening cloud builds up as a function of space and time. Starting from an impurity spin decoupled from the conduction band, the Kondo coupling is switched on at time t=0. We work at the Toulouse point where one can obtain exact analytical results for the ensuing spin dynamics at both zero and nonzero temperature T. For t>0 the Kondo screening cloud starts building up in the wake of the impurity spin being transported to infinity. In this buildup process the impurity spin--conduction band spin susceptibility shows a sharp light cone due to causality, while the corresponding correlation function has a tail outside the light cone. At T=0 this tail has a power law decay as a function of distance from the impurity, which we interpret as due to initial entanglement in the Fermi sea.Comment: 10 pages, 9 figure

Inelastic relaxation and noise temperature in S/N/S junctions

We studied electronic relaxation in long diffusive superconductor / normal metal / superconductor (S/N/S) junctions by means of current noise and transport measurements down to very low temperature (100mK). Samples with normal metal lengths of 4, 10 and 60 micrometer have been investigated. In all samples the shot noise increases very rapidly with the voltage. This is interpreted in terms of enhanced heating of the electron gas confined between the two S/N interfaces. Experimental results are analyzed quantitatively taking into account electron-phonon interaction and heat transfer through the S/N interfaces. Transport measurements reveal that in all samples the two S/N interfaces are connected incoherently, as shown by the reentrance of the resistance at low temperature. The complementarity of noise and transport measurements allows us to show that the energy dependence of the reentrance at low voltage is essentially due to the increasing effective temperature of the quasiparticles in the normal metal.Comment: 5 pages, 4 figures, to be published in EPJ

Spiral and Taylor vortex fronts and pulses in axial through-flow

The influence of an axial through-flow on the spatiotemporal growth behavior of different vortex structures in the Taylor-Couette system with radius ratio eta=0.5 is determined. The Navier Stokes equations (NSE) linearized around the basic Couette-Poiseuille flow are solved numerically with a shooting method in a wide range of through-flow strengths Re and different rates of co- and counterrotating cylinders for toroidally closed vortices with azimuthal wave number m=0 and for spiral vortex flow with m=+1 and m=-1. For each of these three different vortex varieties we have investigated (i) axially extended vortex structures, (ii) axially localized vortex pulses, and (iii) vortex fronts. The complex dispersion relations of the linearized NSE for vortex modes with the three different m are evaluated for real axial wave numbers for (i) and over the plane of complex axial wave numbers for (ii,iii). We have also determined the Ginzburg-Landau amplitude equation (GLE) approximation in order to analyze its predictions for the vortex stuctures (ii,iii). Critical bifurcation thresholds for extended vortex structures are evaluated. The boundaries between absolute and convective instability of the basic state for vortex pulses are determined with a saddle-point analysis of the dispersion relations. Finally, the linearly selected front behavior of growing vortex structures is investigated. For the two front intensity profiles (increasing in positive or negative axial direction) we have determined front velocities, axial growth rates, and the wave numbers and frequencies of the unfolding vortex patterns with azimuthal wave numbers m=0, +1, -1, respectively.Comment: 15 pages, 9 figure