Bayesian Generalized Probability Calculus for Density Matrices

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal. We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including analogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar "conventional" probability calculus and always retains the latter as a special case when all matrices are diagonal. We motivate both the conventional and the generalized Bayes rule with a minimum relative entropy principle, where the Kullbach-Leibler version gives the conventional Bayes rule and Umegaki's quantum relative entropy the new Bayes rule for density matrices. Whereas the conventional Bayesian methods maintain uncertainty about which model has the highest data likelihood, the generalization maintains uncertainty about which unit direction has the largest variance. Surprisingly the bounds also generalize: as in the conventional setting we upper bound the negative log likelihood of the data by the negative log likelihood of the MAP estimator

Large-scale Bright Fronts in the Solar Corona: A Review of "EIT waves"

``EIT waves" are large-scale coronal bright fronts (CBFs) that were first observed in 195 \AA\ images obtained using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the \emph{Solar and Heliospheric Observatory (SOHO)}. Commonly called ``EIT waves", CBFs typically appear as diffuse fronts that propagate pseudo-radially across the solar disk at velocities of 100--700 km s$^{-1}$ with front widths of 50-100 Mm. As their speed is greater than the quiet coronal sound speed ($c_s\leq$200 km s$^{-1}$) and comparable to the local Alfv\'{e}n speed ($v_A\leq$1000 km s$^{-1}$), they were initially interpreted as fast-mode magnetoacoustic waves ($v_{f}=(c_s^2 + v_A^2)^{1/2}$). Their propagation is now known to be modified by regions where the magnetosonic sound speed varies, such as active regions and coronal holes, but there is also evidence for stationary CBFs at coronal hole boundaries. The latter has led to the suggestion that they may be a manifestation of a processes such as Joule heating or magnetic reconnection, rather than a wave-related phenomena. While the general morphological and kinematic properties of CBFs and their association with coronal mass ejections have now been well described, there are many questions regarding their excitation and propagation. In particular, the theoretical interpretation of these enigmatic events as magnetohydrodynamic waves or due to changes in magnetic topology remains the topic of much debate.Comment: 34 pages, 19 figure

Catalytic co oxidation and H2_{2}O2_{2} direct synthesis over pd and pt-impregnated titania nanotubes

Titania nanotubes (TNTs) impregnated with Pd and Pt nanoparticles are evaluated as heterogeneous catalysts in different conditions in two reactions: catalytic CO oxidation (gas phase, up to 500 °C) and H$_{2}$O$_{2}$ direct synthesis (liquid phase, 30 °C). The TNTs are obtained via oxidation of titanium metal and the intermediate layer-type sodium titanate Na$_{2}$Ti$_{3}$O$_{7}$. Thereafter, the titanate layers are exfoliated and show self-rolling to TNTs, which, finally, are impregnated with Pd or Pt nanoparticles at room temperature by using Pd(ac)$_{2}$ and Pt(ac)$_{2}$. The resulting crystalline Pd/TNTs and Pt/TNTs are realized with different lengths (long TNTs: 2.0–2.5 µm, short TNTs: 0.23–0.27 µm) and a specific surface area up to 390 m$^{2}$/g. The deposited Pd and Pt particles are 2–5 nm in diameter. The TNT-derived catalysts show good thermal (up to 500 °C) and chemical stability (in liquid-phase and gas-phase reactions). The catalytic evaluation results in a low CO oxidation light-out temperature of 150 °C for Pt/TNTs (1 wt-%) and promising H$_{2}$O$_{2}$ generation with a productivity of 3240 mol$_{H2O2}$ kg$_{Pd}$$^{-1}$h$^{-1}$ (Pd/TNTs, 5 wt-%, 30 °C). Despite their smaller surface area, long TNTs outperform short TNTs with regard to both CO oxidation and H$_{2}$O$_{2}$ formation

On the Nature and Genesis of EUV Waves: A Synthesis of Observations from SOHO, STEREO, SDO, and Hinode

A major, albeit serendipitous, discovery of the SOlar and Heliospheric Observatory mission was the observation by the Extreme Ultraviolet Telescope (EIT) of large-scale Extreme Ultraviolet (EUV) intensity fronts propagating over a significant fraction of the Sun's surface. These so-called EIT or EUV waves are associated with eruptive phenomena and have been studied intensely. However, their wave nature has been challenged by non-wave (or pseudo-wave) interpretations and the subject remains under debate. A string of recent solar missions has provided a wealth of detailed EUV observations of these waves bringing us closer to resolving their nature. With this review, we gather the current state-of-art knowledge in the field and synthesize it into a picture of an EUV wave driven by the lateral expansion of the CME. This picture can account for both wave and pseudo-wave interpretations of the observations, thus resolving the controversy over the nature of EUV waves to a large degree but not completely. We close with a discussion of several remaining open questions in the field of EUV waves research.Comment: Solar Physics, Special Issue "The Sun in 360",2012, accepted for publicatio

Validation of Global EUV Wave MHD Simulations and Observational Techniques

Global EUV waves remain a controversial phenomenon more than 20 yr after their discovery by SOHO/EIT. Although consensus is growing in the community that they are most likely large-amplitude waves or shocks, the wide variety of observations and techniques used to identify and analyze them have led to disagreements regarding their physical properties and interpretation. Here, we use a 3D magnetohydrodynamic (MHD) model of the solar corona to simulate an EUV wave event on 2009 February 13 to enable a detailed validation of the various commonly used detection and analysis techniques of global EUV waves. The simulated event exhibits comparable behavior to that of a real EUV wave event, with similar kinematic behavior and plasma parameter evolution. The kinematics of the wave are estimated via visual identification and profile analysis, with both approaches providing comparable results. We find that projection effects can affect the derived kinematics of the wave, due to the variation in fast-mode wave speed with height in the corona. Coronal seismology techniques typically used for estimates of the coronal magnetic field are also tested and found to estimate fast-mode speeds comparable to those of the model. Plasma density and temperature variations of the wave front are also derived using a regularized inversion approach and found to be consistent with observed wave events. These results indicate that global waves are best interpreted as large-amplitude waves and that they can be used to probe the coronal medium using well-defined analysis techniques

Coronal Shock Waves, EUV waves, and Their Relation to CMEs. I. Reconciliation of "EIT waves", Type II Radio Bursts, and Leading Edges of CMEs

We show examples of excitation of coronal waves by flare-related abrupt eruptions of magnetic rope structures. The waves presumably rapidly steepened into shocks and freely propagated afterwards like decelerating blast waves that showed up as Moreton waves and EUV waves. We propose a simple quantitative description for such shock waves to reconcile their observed propagation with drift rates of metric type II bursts and kinematics of leading edges of coronal mass ejections (CMEs). Taking account of different plasma density falloffs for propagation of a wave up and along the solar surface, we demonstrate a close correspondence between drift rates of type II bursts and speeds of EUV waves, Moreton waves, and CMEs observed in a few known events.Comment: 30 pages, 15 figures. Solar Physics, published online. The final publication is available at http://www.springerlink.co

Coronal Shock Waves, EUV Waves, and Their Relation to CMEs. III. Shock-Associated CME/EUV Wave in an Event with a Two-Component EUV Transient

On 17 January 2010, STEREO-B observed in extreme ultraviolet (EUV) and white light a large-scale dome-shaped expanding coronal transient with perfectly connected off-limb and on-disk signatures. Veronig et al. (2010, ApJL 716, 57) concluded that the dome was formed by a weak shock wave. We have revealed two EUV components, one of which corresponded to this transient. All of its properties found from EUV, white light, and a metric type II burst match expectations for a freely expanding coronal shock wave including correspondence to the fast-mode speed distribution, while the transient sweeping over the solar surface had a speed typical of EUV waves. The shock wave was presumably excited by an abrupt filament eruption. Both a weak shock approximation and a power-law fit match kinematics of the transient near the Sun. Moreover, the power-law fit matches expansion of the CME leading edge up to 24 solar radii. The second, quasi-stationary EUV component near the dimming was presumably associated with a stretched CME structure; no indications of opening magnetic fields have been detected far from the eruption region.Comment: 18 pages, 10 figures. Solar Physics, published online. The final publication is available at http://www.springerlink.co

Looking at Vector Space and Language Models for IR using Density Matrices

In this work, we conduct a joint analysis of both Vector Space and Language Models for IR using the mathematical framework of Quantum Theory. We shed light on how both models allocate the space of density matrices. A density matrix is shown to be a general representational tool capable of leveraging capabilities of both VSM and LM representations thus paving the way for a new generation of retrieval models. We analyze the possible implications suggested by our findings.Comment: In Proceedings of Quantum Interaction 201

The dependence of the EIT wave velocity on the magnetic field strength

"EIT waves" are a wavelike phenomenon propagating in the corona, which were initially observed in the extreme ultraviolet (EUV) wavelength by the EUV Imaging Telescope (EIT). Their nature is still elusive, with the debate between fast-mode wave model and non-wave model. In order to distinguish between these models, we investigate the relation between the EIT wave velocity and the local magnetic field in the corona. It is found that the two parameters show significant negative correlation in most of the EIT wave fronts, {\it i.e.}, EIT wave propagates more slowly in the regions of stronger magnetic field. Such a result poses a big challenge to the fast-mode wave model, which would predict a strong positive correlation between the two parameters. However, it is demonstrated that such a result can be explained by the fieldline stretching model, \emph{i.e.,} that "EIT waves" are apparently-propagating brightenings, which are generated by successive stretching of closed magnetic field lines pushed by the erupting flux rope during coronal mass ejections (CMEs).Comment: 11 pages, 8 figures, accepted for publication in Solar Phy