Multiple Imputation von fehlenden Werten mit Daten über Unterernährung und Kindersterblichkeit

In dieser Arbeit werden die Auswirkungen einer Ersetzung von fehlenden Werten auf das Ergebnis einer Regressionsanalyse untersucht. Grundlage ist eine Untersuchung von Klasen (2000) über die Unterschiede im Zusammenhang zwischen Unterernährung und Kindersterblichkeit in Afrika und Südasien. In dem Makro-Datensatz, welcher 101 Entwicklungsländer umfasst, fällt etwa ein Drittel der 273 Beobachtungen weg, da für verschiedene verwendete Variablen die Werte fehlen. Die so verloren gegangenen Informationen sollen in dieser Untersuchung genutzt werden um die Schätzergebnisse zu verbessern. Hierzu wird ein Verfahren zur multiplen Imputation verwandt, in welchem mit einem Data-Augmentation-Verfahren mehrere vervollständigte Datensätze generiert werden, mit welchen dann getrennt Schätzungen durchgeführt werden. Die Ergebnisse der Schätzungen werden dann miteinander kombiniert. Durch die Auswertung mehrerer vervollständigter Datensätze wird eine höhere Effizienz der Schätzer erreicht. Ein Vergleich von Regressionsanalysen, die mit dem vervollständigten Daten durchgeführt wurden, mit einer Complete-case-Analyse hat gezeigt, dass sich bestimmte Koeffizienten in ihrer Größenordnung geändert haben. Bei manchen Koeffizienten sind unplausible Vorzeichen aus der Complete-case Analyse verschwunden. Es ist also vorteilhaft, bei Problemen mit fehlenden Werten moderne Imputationsverfahren zu verwenden. Die wesentlichen Ergebnisse aus der Untersuchung von Klasen (2000) konnten dennoch bestätigt werden. Durch die Ersetzung der fehlenden Werte konnten noch eine Reihe von Variablen zugänglich gemacht werden, die in den bisherigen Untersuchungen nicht verwendet wurden, da dadurch auf noch mehr Beobachtungen hätte verzichtet werden müssen

Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture

We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an irreducible characteristic polynomial that has a given Fibonacci index. For dimensions of the form 2^(2^k) we present a solution that shows an analogy to an open conjecture of Wiedemann in finite field theory. Finally, we discuss the equivalence of mutually unbiased bases.Comment: 11 pages, added chapter on equivalenc

Autonomous frequency domain identification: Theory and experiment

The analysis, design, and on-orbit tuning of robust controllers require more information about the plant than simply a nominal estimate of the plant transfer function. Information is also required concerning the uncertainty in the nominal estimate, or more generally, the identification of a model set within which the true plant is known to lie. The identification methodology that was developed and experimentally demonstrated makes use of a simple but useful characterization of the model uncertainty based on the output error. This is a characterization of the additive uncertainty in the plant model, which has found considerable use in many robust control analysis and synthesis techniques. The identification process is initiated by a stochastic input u which is applied to the plant p giving rise to the output. Spectral estimation (h = P sub uy/P sub uu) is used as an estimate of p and the model order is estimated using the produce moment matrix (PMM) method. A parametric model unit direction vector p is then determined by curve fitting the spectral estimate to a rational transfer function. The additive uncertainty delta sub m = p - unit direction vector p is then estimated by the cross spectral estimate delta = P sub ue/P sub uu where e = y - unit direction vectory y is the output error, and unit direction vector y = unit direction vector pu is the computed output of the parametric model subjected to the actual input u. The experimental results demonstrate the curve fitting algorithm produces the reduced-order plant model which minimizes the additive uncertainty. The nominal transfer function estimate unit direction vector p and the estimate delta of the additive uncertainty delta sub m are subsequently available to be used for optimization of robust controller performance and stability

Global attractors for Cahn-Hilliard equations with non constant mobility

We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one cannot expect uniqueness of the solution to the related initial and boundary value problems. Nevertheless, referring to J. Ball's theory of generalized semiflows, we are able to prove existence of compact quasi-invariant global attractors for the associated dynamical processes settled in the natural "finite energy" space. A key point in the proof is a careful use of the energy equality, combined with the derivation of a "local compactness" estimate for systems with supercritical nonlinearities, which may have an independent interest. Under growth restrictions on the configuration potential, we also show existence of a compact global attractor for the semiflow generated by the (weaker) solutions to the nonviscous equation characterized by a "finite entropy" condition

The Origin of Transverse Flow at the SPS

We study the transverse expansion in central Pb+Pb collisions at the CERN SPS. Strong collective motion of hadrons can be created. This flow is mainly due to meson baryon rescattering. It allows to study the angular distribution of intermediate mass meson baryon interactions.Comment: submitted to Phys. Lett.

Resonant tunneling-based spin ratchets

We outline a generic ratchet mechanism for creating directed spin-polarized currents in ac-driven double well or double dot structures by employing resonant spin transfer through the system engineered by local external magnetic fields. We show its applicability to semiconductor nanostructures by considering coherent transport through two coupled lateral quantum dots, where the energy levels of the two dots exhibit opposite Zeeman spin splitting. We perform numerical quantum mechanical calculations for the I-V characteristics of this system in the nonlinear regime, which requires a self-consistent treatment of the charge redistribution due to the applied finite bias. We show that this setting enables nonzero averaged net spin currents in the absence of net charge transport.Comment: 5 pages, 4 figure

Particle transfer and fusion cross-section for Super-heavy nuclei in dinuclear system

Within the dinuclear system (DNS) conception, instead of solving Fokker-Planck Equation (FPE) analytically, the Master equation is solved numerically to calculate the fusion probability of super-heavy nuclei, so that the harmonic oscillator approximation to the potential energy of the DNS is avoided. The relative motion concerning the energy, the angular momentum, and the fragment deformation relaxations is explicitly treated to couple with the diffusion process, so that the nucleon transition probabilities, which are derived microscopically, are time-dependent. Comparing with the analytical solution of FPE, our results preserve more dynamical effects. The calculated evaporation residue cross sections for one-neutron emission channel of Pb-based reactions are basically in agreement with the known experimental data within one order of magnitude.Comment: 19 pages, plus 6 figures, submitted to Phys. Rev.

Formation of ions by high energy photons

We calculate the electron energy spectrum of ionization by a high energy photon, accompanied by creation of electron-positron pair. The total cross section of the process is also obtained. The asymptotics of the cross section does not depend on the photon energies. At the photon energies exceeding a certain value $\omega_0$ this appeares to to be the dominant mechanism of formation of the ions. The dependence of $\omega_0$ on the value of nuclear charge is obtained. Our results are consistent with experimental data.Comment: 16 pages, 6 figure

Baryon stopping and strange baryon/antibaryon production at SPS energies

The amount of proton stopping in central Pb+Pb collisions from 20-160 AGeV as well as hyperon and antihyperon rapidity distributions are calculated within the UrQMD model in comparison to experimental data at 40, 80 and 160 AGeV taken recently from the NA49 collaboration. Furthermore, the amount of baryon stopping at 160 AGeV for Pb+Pb collisions is studied as a function of centrality in comparison to the NA49 data. We find that the strange baryon yield is reasonably described for central collisions, however, the rapidity distributions are somewhat more narrow than the data. Moreover, the experimental antihyperon rapidity distributions at 40, 80 and 160 AGeV are underestimated by up to factors of 3 - depending on the annihilation cross section employed - which might be addressed to missing multi-meson fusion channels in the UrQMD model.Comment: 18 pages, including 7 eps figures, to be published in Phys. Rev.