A numerical study of two-photon ionization of helium using the Pyprop framework

Few-photon induced breakup of helium is studied using a newly developed ab initio numerical framework for solving the six-dimensional time-dependent Schroedinger equation. We present details of the method and calculate (generalized) cross sections for the process of two-photon nonsequential (direct) double ionization at photon energies ranging from 39.4 to 54.4 eV, a process that has been very much debated in recent years and is not yet fully understood. In particular, we have studied the convergence property of the total cross section in the vicinity of the upper threshold (54.4 eV), versus the pulse duration of the applied laser field. We find that the cross section exhibits an increasing trend near the threshold, as has also been observed by others, and show that this rise cannot solely be attributed to an unintended inclusion of the sequential two-photon double ionization process, caused by the bandwidth of the applied field.Comment: 7 pages, 3 figure

Functions preserving nonnegativity of matrices

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every entrywise nonnegative matrix $A$ of size $n\times n$. Towards this goal, we present a complete characterization of functions preserving nonnegativity of (block) upper-triangular matrices and those preserving nonnegativity of circulant matrices. We also derive necessary conditions and sufficient conditions for entire functions that preserve nonnegativity of symmetric matrices. We also show that some of these latter conditions characterize the even or odd functions that preserve nonnegativity of symmetric matrices.Comment: 20 pages; expanded and corrected to reflect referees' remarks; to appear in SIAM J. Matrix Anal. App

A combined R-matrix eigenstate basis set and finite-differences propagation method for the time-dependent Schr\"{od}dinger equation: the one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schr\"{o}dinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron's coordinates separated over two regions, that is regions $I$ and $II$. In region $I$ the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wavefunction. In region $II$ a grid representation of the wavefunction is considered and propagation in space and time is obtained through the finite-differences method. It appears this is the first time a combination of basis set and grid methods has been put forward for tackling multi-region time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multi-electron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely that beyond a certain distance (encompassing region $I$) a single ejected electron is distinguishable from the other electrons of the multi-electron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.Comment: 13 pages, 6 figures, submitte

Patients with IgA nephropathy exhibit high systemic PDGF-DD levels

Background. Platelet-derived growth factor (PDGF) is a central mediator of mesangioproliferative glomerulonephritis (GN). In experimental mesangioproliferative GN, PDGF-DD serum levels, unlike PDGF-BB, increased up to 1000-fold. Methods. We assessed disease activity in 72 patients with GN, established a novel PDGF-D ELISA and then determined their PDGF-DD levels. In parallel, we studied renal PDGF-DD mRNA expression by RT-PCR. Results. PDGF-DD serum levels in patients with IgA nephropathy (IgAN) were significantly higher (1.67 ± 0.45 ng/ml) and in patients with lupus nephritis significantly lower (0.66 ± 0.86 ng/ml) compared to healthy controls (1.17 ± 0.46 ng/ml), while patients with focal segmental glomerulosclerosis, membranous GN and ANCA-positive vasculitis did not differ from controls. The subgroup of IgAN patients with elevated PDGF-DD levels (27% of samples) did not differ in their clinical features from those with normal PDGF-DD levels. In IgAN patients with repetitive PDGF-DD determinations, most exhibited only minor fluctuations of serum levels over time. Intrarenal PDGF-DD mRNA expression did not differ between controls and patients, suggesting an extrarenal source of the elevated PDGF-DD in IgAN. Conclusions. Serum PDGF-DD levels were specifically elevated in patients with IgAN, in particular in those with early disease, i.e. preserved renal function. Our data support the rationale for anti-PDGF-DD therapy in mesangioproliferative G

Kernel Approximation on Manifolds II: The L∞L_{\infty}-norm of the L2L_2-projector

This article addresses two topics of significant mathematical and practical interest in the theory of kernel approximation: the existence of local and stable bases and the L_p--boundedness of the least squares operator. The latter is an analogue of the classical problem in univariate spline theory, known there as the "de Boor conjecture". A corollary of this work is that for appropriate kernels the least squares projector provides universal near-best approximations for functions f\in L_p, 1\le p\le \infty.Comment: 25 pages; minor revision; new proof of Lemma 3.9; accepted for publication in SIAM J. on Math. Ana

Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

Global Antifungal Profile Optimization of Chlorophenyl Derivatives against Botrytis cinerea and Colletotrichum gloeosporioides

Twenty-two aromatic derivatives bearing a chlorine atom and a different chain in the para or meta position were prepared and evaluated for their in vitro antifungal activity against the phytopathogenic fungi Botrytis cinerea and Colletotrichum gloeosporioides. The results showed that maximum inhibition of the growth of these fungi was exhibited for enantiomers S and R of 1-(40-chlorophenyl)- 2-phenylethanol (3 and 4). Furthermore, their antifungal activity showed a clear structure-activity relationship (SAR) trend confirming the importance of the benzyl hydroxyl group in the inhibitory mechanism of the compounds studied. Additionally, a multiobjective optimization study of the global antifungal profile of chlorophenyl derivatives was conducted in order to establish a rational strategy for the filtering of new fungicide candidates from combinatorial libraries. The MOOPDESIRE methodology was used for this purpose providing reliable ranking models that can be used later

One-way multigrid method in electronic structure calculations

We propose a simple and efficient one-way multigrid method for self-consistent electronic structure calculations based on iterative diagonalization. Total energy calculations are performed on several different levels of grids starting from the coarsest grid, with wave functions transferred to each finer level. The only changes compared to a single grid calculation are interpolation and orthonormalization steps outside the original total energy calculation and required only for transferring between grids. This feature results in a minimal amount of code change, and enables us to employ a sophisticated interpolation method and noninteger ratio of grid spacings. Calculations employing a preconditioned conjugate gradient method are presented for two examples, a quantum dot and a charged molecular system. Use of three grid levels with grid spacings 2h, 1.5h, and h decreases the computer time by about a factor of 5 compared to single level calculations.Comment: 10 pages, 2 figures, to appear in Phys. Rev. B, Rapid Communication

Many-body theory of positron-atom interactions

A many-body theory approach is developed for the problem of positron-atom scattering and annihilation. Strong electron-positron correlations are included non-perturbatively through the calculation of the electron-positron vertex function. It corresponds to the sum of an infinite series of ladder diagrams, and describes the physical effect of virtual positronium formation. The vertex function is used to calculate the positron-atom correlation potential and nonlocal corrections to the electron-positron annihilation vertex. Numerically, we make use of B-spline basis sets, which ensures rapid convergence of the sums over intermediate states. We have also devised an extrapolation procedure that allows one to achieve convergence with respect to the number of intermediate-state orbital angular momenta included in the calculations. As a test, the present formalism is applied to positron scattering and annihilation on hydrogen, where it is exact. Our results agree with those of accurate variational calculations. We also examine in detail the properties of the large correlation corrections to the annihilation vertex.Comment: 25 pages, 16 figure