Kernel density estimation via diffusion

We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.Comment: Published in at http://dx.doi.org/10.1214/10-AOS799 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Existence and regularity for higher dimensional H-systems

this paper we are concerned with the existence and regularity of solutions of the degenerate nonlinear elliptic systems known as H-systems. For a given real valued function H defined on (a subset of)

Partial regularity for almost minimizers of quasi-convex integrals

We consider almost minimizers of variational integrals whose integrands are quasiconvex. Under suitable growth conditions on the integrand and on the function determining the almost minimality, we establish almost everywhere regularity for almost minimizers and obtain results on the regularity of the gradient away from the singular set. We give examples of problems from the calculus of variations whose solutions can be viewed as such almost minimizers

Asymptotic behavior of, small eigenvalues, short geodesics and period matrices on degenerating hyperbolic Riemann surfaces

Consider {M-t} a semi-stable family of compact, connected algebraic curves which degenerate to a stable, noded curve M-0. The uniformization theorem allows us to endow each curve M-t in the family, as well as the limit curve M-0 (after its nodes have been removed), with its natural complete hyperbolic metric (i.e. constant negative curvature equal to -1), so that we are considering a degenerating family of compact hyperbolic Riemann surfaces. Assume that M-0 has k components and n nodes, so there are n families of geodesics whose lengths approach zero under degeneration and k - 1 families of eigenvalues of the Laplacian which approach zero under degeneration. A problem which has received considerable attention is to compare the rate at which the eigenvalues and the lengths of geodesics approach zero. In this paper, we will use results from complex algebraic geometry and from heat kernel analysis to obtain a precise relation involving the small eigenvalues, the short geodesics, and the period matrix of the underlying complex curve M-t. Our method leads naturally to a general conjecture in the setting of an arbitrary degenerating family of hyperbolic Riemann surfaces of finite volume

Dissipative orbiting in ^{136}Xe+^{209}Bi reactions at 28 and 62 AMeV

Correlations between the energy, charge and the deflection angle of the projectile-like fragments were studied for the ^{136}Xe + ^{209}Bi reaction at E∕A = 28 and 62 MeV. These correlations are seen to exhibit features characteristic of dissipative orbiting, commonly found at bombarding energies of a few MeV/nucleon above the interaction barrier, but also reported in the Fermi-energy domain. It was found, that in the studied bombarding energy range, the reaction cross section is still dominated by the dissipative binary reactions of well defined projectile- and target-like fragments

Optimizing the growth conditions of Al mirrors for superconducting nanowire single-photon detectors

We investigate the growth conditions for thin (less than 200 nm) sputtered aluminum (Al) films. These coatings are needed for various applications, e.g. for advanced manufacturing processes in the aerospace industry or for nanostructures for quantum devices. Obtaining high-quality films, with low roughness, requires precise optimization of the deposition process. To this end, we tune various sputtering parameters such as the deposition rate, temperature, and power, which enables 50 nm thin films with a root mean square (RMS) roughness of less than 1 nm and high reflectivity. Finally, we confirm the high quality of the deposited films by realizing superconducting single-photon detectors integrated into multi-layer heterostructures consisting of an aluminum mirror and a silicon dioxide dielectric spacer. We achieve an improvement in detection efficiency at 780 nm from 40 % to 70 % by this integration approach.Comment: 11 pages, 6 figure