Connections and Metrics Respecting Standard Purification

Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one-to-one. Our methods are borrowed from elementary *-representation and fibre space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and ``add noise'' to a curve of pure states.Comment: Latex, 27 page

The Stanley Foundation Bipolar Network: Results of the naturalistic follow-up study after 2.5 years of follow-up in the German centres

The Stanley Foundation Bipolar Network (SFBN) is an international, multisite network investigating the characteristics and course of bipolar disorder. Methods (history, ratings and longitudinal follow-up) are standardized and equally applied in all 7 centres. This article describes demographics and illness characteristics of the first 152 German patients enrolled in them SFBN as well as the results of 2.5 years of follow-up. Patients in Germany were usually enrolled after hospitalisation. More than 72% of the study population suffered from bipolar I disorder and 25% from bipolar 11 disorder. The mean +/- SD age of the study participants was 42.08 +/- 13.5 years, and the mean SD age of onset 24.44 +/- 10.9 years. More than 40% of the sample reported a rapid-cycling course in history, and even more a cycle acceleration overtime. 37% attempted suicide at least once. 36% had an additional Axis I disorder, with alcohol abuse being the most common one, followed by anxiety disorders. During the follow-up period, only 27% remained stable, 56% had a recurrence, 12.8% perceived subsyndromal symptoms despite treatment and regular visits. 27% suffered from a rapid-cycling course during the follow-up period. Recurrences were significantly associated with bipolar I disorder, an additional comorbid Axis I disorder, rapid cycling in history, a higher number of mood stabilizers and the long-term use of typical antipsychotics. Rapid cycling during follow-up was only associated with a rapidcycling course in history, a higher number of mood stabilizers and at least one suicide attempt in history. Copyright (c) 2003 S. Karger AG, Basel

Improving Earthquake Monitoring and Early Warning Using GNSS Velocities and Machine Learning

Earthquake ground motions intersecting a population and seismically-triggered tsunamis have cost over 800,000 lives globally in the last 20 years. Distributed measurements of earthquake ground motions: 1) diagnose shaking intensity for rapid disaster response, 2) can alert to minimize damage ahead of the most destructive shaking and 3) are fundamental to understanding past events to inform future preparedness. Nearfield, conventional inertial seismic instruments saturate during the largest, most destructive earthquakes and may have limited regional availability. High-rate GNSS ground-station networks offer an alternative source of unsaturated ground motion measurements of medium to larger earthquakes. However, elevated noise levels of relative motion from space borne signals and minimal high-rate, larger magnitude event catalogs have limited the contribution of GNSS for current operational seismic monitoring, alerting and research. This thesis builds upon previous GNSS seismology research to address this gap between sensitivity and current functional range through a data-driven approach. A hemispheric network noise comparison determined time differenced carrier phase velocities is the geodetic processing method most sensitive to seismic signals. This method does not require external corrections and is more computationally efficient for our signal of interest at the highest rates and potentially on the network edge. This thesis then presents a supervised random forest classifier that outperformed existing detection methods when trained and tested on a catalog of high-rate GNSS velocity seismic waveforms to discriminate between signal and noise. This classifier can be run with minimal latency at high rates for robust stand-alone seismic-event detection. Lastly, zero-baseline inertial waveforms were augmented with stochastic GNSS noise time series to expand the GNSS seismic catalog. An expanded catalog improved generalization and will enable deeper learning. The analysis and models presented in this thesis lay a foundation for components of the next generation geodetic network.</p

Polarized Line Formation in Multi-Dimensional Media.III. Hanle Effect with Partial Frequency Redistribution

In the previous two papers, namely, \citet{anuknn11} and \citet{anuetal11} we solved the polarized radiative transfer (RT) equation in multi-dimensional (multi-D) geometries, with partial frequency redistribution (PRD) as the scattering mechanism. We assumed Rayleigh scattering as the only source of linear polarization ($Q/I, U/I$) in both these papers. In this paper we extend these previous works to include the effect of weak oriented magnetic fields (Hanle effect) on line scattering. We generalize the technique of Stokes vector decomposition in terms of the irreducible spherical tensors $\mathcal{T}^K_Q$, developed in \citet{anuknn11}, to the case of RT with Hanle effect. A fast iterative method of solution (based on the Stabilized Preconditioned Bi-Conjugate-Gradient technique), developed in \citet{anuetal11}, is now generalized to the case of RT in magnetized three-dimensional media. We use the efficient short-characteristics formal solution method for multi-D media, generalized appropriately to the present context. The main results of this paper are the following: (1) A comparison of emergent $(I, Q/I, U/I)$ profiles formed in one-dimensional (1D) media, with the corresponding emergent, spatially averaged profiles formed in multi-D media, shows that in the spatially resolved structures, the assumption of 1D may lead to large errors in linear polarization, especially in the line wings. (2) The multi-D RT in semi-infinite non-magnetic media causes a strong spatial variation of the emergent $(Q/I, U/I)$ profiles, which is more pronounced in the line wings. (3) The presence of a weak magnetic field modifies the spatial variation of the emergent $(Q/I, U/I)$ profiles in the line core, by producing significant changes in their magnitudes.Comment: 31 pages, 14 figures, Submitted to ApJ, Under revie

Covariance and Fisher information in quantum mechanics

Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show that there is a kind of dual one-to-one correspondence between the candidates of the two concepts. We emphasis that Fisher informations are obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.Comment: LATE

Transport limits in defect-engineered LaAlO3/SrTiO3 bilayers

The electrical properties of the metallic interface in LaAlO3/SrTiO3 (LAO/STO) bilayers are investigated with focus on the role of cationic defects in thin film STO. Systematic growth-control of the STO thin film cation stoichiometry (defect-engineering) yields a relation between cationic defects in the STO layer and electronic properties of the bilayer-interface. Hall measurements reveal a stoichiometry-effect primarily on the electron mobility. The results indicate an enhancement of scattering processes in as-grown non-stoichiometric samples indicating an increased density of defects. Furthermore, we discuss the thermodynamic processes and defect-exchange reactions at the LAO/STO-bilayer interface determined in high temperature equilibrium. By quenching defined defect states from high temperature equilibrium, we finally connect equilibrium thermodynamics with room temperature transport. The results are consistent with the defect-chemistry model suggested for LAO/STO interfaces. Moreover, they reveal an additional healing process of extended defects in thin film STO

Bures volume of the set of mixed quantum states

We compute the volume of the N^2-1 dimensional set M_N of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume of the Uhlmann 3-D hemisphere, embedded in R^4. We find also the area of the boundary of the set M_N and obtain analogous results for the smaller set of all real density matrices. An explicit formula for the Bures-Hall normalization constants is derived for an arbitrary N.Comment: 15 revtex pages, 2 figures in .eps; ver. 3, Eq. (4.19) correcte