Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space

We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T(u) = - \int_{\rr^d} K(x,y) (u(y)-u(x)) \, dy. Here we consider a kernel $K(x,y)=\psi (y-a(x))+\psi(x-a(y))$ where $\psi$ is a bounded, nonnegative function supported in the unit ball and $a$ means a diffeomorphism on \rr^d. A simple example being a linear function $a(x)= Ax$. The upper and lower bounds that we obtain are given in terms of the Jacobian of $a$ and the integral of $\psi$. Indeed, in the linear case $a(x) = Ax$ we obtain an explicit expression for the first eigenvalue in the whole \rr^d and it is positive when the the determinant of the matrix $A$ is different from one. As an application of our results, we observe that, when the first eigenvalue is positive, there is an exponential decay for the solutions to the associated evolution problem. As a tool to obtain the result, we also study the behaviour of the principal eigenvalue of the nonlocal Dirichlet problem in the ball $B_R$ and prove that it converges to the first eigenvalue in the whole space as $R\to \infty$

LOFT as a discovery machine for jetted Tidal Disruption Events

This is a White Paper in support of the mission concept of the Large Observatory for X-ray Timing (LOFT), proposed as a medium-sized ESA mission. We discuss the potential of LOFT for the study of jetted tidal disruption events. For a summary, we refer to the paper.Comment: White Paper in Support of the Mission Concept of the Large Observatory for X-ray Timin

The spectrum of phenotypes associated with mutations in steroidogenic factor 1 (SF-1, NR5A1, Ad4BP) includes severe penoscrotal hypospadias in 46,XY males without adrenal insufficiency

OBJECTIVE. Hypospadias is a frequent congenital anomaly but in most cases an underlying cause is not found. Steroidogenic factor 1 (SF-1, NR5A1, Ad4BP) is a key regulator of human sex development and an increasing number of SF-1 (NR5A1) mutations are reported in 46,XY disorders of sex development (DSD). We hypothesized that NR5A1 mutations could be identified in boys with hypospadias. DESIGN AND METHODS. Mutational analysis of NR5A1 in 60 individuals with varying degrees of hypospadias from the German DSD network. RESULTS. Heterozygous NR5A1 mutations were found in three out of 60 cases. These three individuals represented the most severe end of the spectrum studied as they presented with penoscrotal hypospadias, variable androgenization of the phallus and undescended testes (three out of 20 cases (15%) with this phenotype). Testosterone was low in all three patients and inhibin B/anti-Müllerian hormone (AMH) were low in two patients. Two patients had a clear male gender assignment. Gender re-assignment to male occurred in the third case. Two patients harbored heterozygous nonsense mutations (p.Q107X/WT, p.E11X/WT). One patient had a heterozygous splice site mutation in intron 2 (c.103-3A/WT) predicted to disrupt the main DNA-binding motif. Functional studies of the nonsense mutants showed impaired transcriptional activation of an SF-1-responsive promoter (Cyp11a). To date, adrenal insufficiency has not occurred in any of the patients. CONCLUSIONS. SF-1 (NR5A1) mutations should be considered in 46,XY individuals with severe (penoscrotal) hypospadias, especially if undescended testes, low testosterone, or low inhibin B/AMH levels are present. SF-1 mutations in milder forms of idiopathic hypospadias are unlikely to be common

Intrinsic electric field effects on few-particle interactions in coupled GaN quantum dots

We study the multi-exciton optical spectrum of vertically coupled GaN/AlN quantum dots with a realistic three-dimensional direct-diagonalization approach for the description of few-particle Coulomb-correlated states. We present a detailed analysis of the fundamental properties of few-particle/exciton interactions peculiar of nitride materials. The giant intrinsic electric fields and the high electron/hole effective masses give rise to different effects compared to GaAs-based quantum dots: intrinsic exciton-exciton coupling, non-molecular character of coupled dot exciton wavefunction, strong dependence of the oscillator strength on the dot height, large ground state energy shift for dots separated by different barriers. Some of these effects make GaN/AlN quantum dots interesting candidates in quantum information processing.Comment: 23 pages, 8 figures, 1 tabl

Spin-based optical quantum gates via Pauli blocking in semiconductor quantum dots

We present a solid-state implementation of ultrafast conditional quantum gates. Our proposal for a quantum-computing device is based on the spin degrees of freedom of electrons confined in semiconductor quantum dots, thus benefiting from relatively long decoherence times. More specifically, combining Pauli blocking effects with properly tailored ultrafast laser pulses, we are able to obtain sub-picosecond spin-dependent switching of the Coulomb interaction, which is the essence of our conditional phase-gate proposal. This allows us to realize {\it a fast two qubit gate which does not translate into fast decoherence times} and paves the road for an all-optical spin-based quantum computer.Comment: 14 Pages RevTeX, 3 eps figures include

Biochemical mechanism of oxidative damage by redox-cycling drugs.

Biochemical mechanisms of production of redox intermediates of redox-cycling drugs include: photochemical events, either photoionization process or electron transfer from photoexcited states; electron exchange of reduced form of a drug with the oxy state of oxygen-binding hemoproteins; oxidation by catalytic metal centers (oxidases, peroxidases, oxygenases) of the reduced forms of drugs; or electron transfer to the oxidized form of a drug from activated intracellular electron transfer chain (mitochondria, microsomes, etc.). Further reaction of these drug free radicals can lead to oxidative damage by either direct attack of biological macromolecules or via oxygen reduction, giving O2-, H2O2, and OH. The reaction pathway depends on the presence of metal ions, natural scavengers, enzymes that control relative concentrations of reactive species, and availability of oxygen in the environment