Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models

Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models [arXiv:0802.0743]Comment: Published in at http://dx.doi.org/10.1214/07-STS235REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stability Analysis of a Bose-Einstein Condensate Trapped in a Generic Potential

We investigate the dynamical behavior of the Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in a spherical power law potential restricted to the repulsive case, from the dynamical system formalism point of view. A five-dimensional dynamical system is found (due the symmetry of the Gross-Pitaevskii equation interacting with a potential), where the Thomas-Fermi approximation constrains the parameter space of solutions. We show that for values of the power law exponent equal or smaller than 2 the system seems to be stable. However, when the corresponding exponent is bigger than 2, the instability of the system grows when the power law exponent grows, indicating that large values of the aforementioned parameter can be related to a loss in the number of particles from the condensed state. This fact can be used also to show that the stability conditions of the condensate are highly sensitive to the exponent associated with the external potential.Comment: 9 pages, 2 figure

A Statistical Study of Photospheric Magnetic Field Changes During 75 Solar Flares

Abrupt and permanent changes of photospheric magnetic fields have been observed during solar flares. The changes seem to be linked to the reconfiguration of magnetic fields, but their origin is still unclear. We carried out a statistical analysis of permanent line-of-sight magnetic field ($B_{\rm LOS}$) changes during 18 X-, 37 M-, 19 C- and 1 B-class flares using data from Solar Dynamics Observatory/Helioseismic and Magnetic Imager. We investigated the properties of permanent changes, such as frequency, areas, and locations. We detected changes of $B_{\rm LOS}$ in 59/75 flares. We find that strong flares are more likely to show changes, with all flares $\ge$ M1.6 exhibiting them. For weaker flares, permanent changes are observed in 6/17 C-flares. 34.3\% of the permanent changes occurred in the penumbra and 18.9\% in the umbra. Parts of the penumbra appeared or disappeared in 23/75 flares. The area where permanent changes occur is larger for stronger flares. Strong flares also show a larger change of flux, but there is no dependence of the magnetic flux change on the heliocentric angle. The mean rate of change of flare-related magnetic field changes is 20.7 Mx cm$^{-2}$ min$^{-1}$. The number of permanent changes decays exponentially with distance from the polarity inversion line. The frequency of the strength of permanent changes decreases exponentially, and permanent changes up to 750 Mx cm$^{-2}$ were observed. We conclude that permanent magnetic field changes are a common phenomenon during flares, and future studies will clarify their relation to accelerated electrons, white light emission, and sunquakes to further investigate their origin.Comment: Piblished in Ap

Carbon-fiber tips for scanning probe microscopes and molecular electronics experiments

We fabricate and characterize carbon-fiber tips for their use in combined scanning tunneling and force microscopy based on piezoelectric quartz tuning fork force sensors. An electrochemical fabrication procedure to etch the tips is used to yield reproducible sub-100-nm apex. We also study electron transport through single-molecule junctions formed by a single octanethiol molecule bonded by the thiol anchoring group to a gold electrode and linked to a carbon tip by the methyl group. We observe the presence of conductance plateaus during the stretching of the molecular bridge, which is the signature of the formation of a molecular junction.Comment: Conference Proceeding (Trends in NanoTechnology 2011, Tenerife SPAIN); Nanoscale Research Letters, (2012) 7:25

Computational approaches for the multimodal imaging of nanomaterials and their biochemical effects

Nanomaterial delivery systems constitute a group of drug delivery vehicles that have been used extensively in biodelivery. The proper characterization of the therapeutic function of these nanomaterials requires analytical methods to track the presence of the cargo and its biochemical effects. In some cases, the detection of the cargo and biochemical changes are not attainable in the same experiment, and more than one technique might be needed for the proper analysis of the drug delivery system. In this case, separate analysis of adjacent tissue sections is performed by techniques that offer complementary information such as MALDI-MS and LA-ICP-MS. However, the approaches to combine the information from these techniques to obtain insights into the mechanism of action of the nanomaterials have been limited to visual inspection and image overlay, which can only provide qualitative information. To advance towards a more quantitative analysis, in this dissertation we have developed computational techniques for image reconstruction, segmentation, and registration of MALDI-MS and LA-ICP-MS images to monitor the biodistribution, excretion and biochemical effects of nanomaterial delivery systems. First, we developed an open-source computational approach for LA-ICP-MS image reconstruction and segmentation using Python, which revealed that nanomaterials distribute in different sub-organ regions based on their chemical and physical properties. For instance, in the analysis of gold nanoparticles and bismuth nanorods, we find that the nanomaterials distribute in different regions of the spleen, suggesting differences in their biochemical interactions within the same organ. Next, we developed a computational workflow in Python to register LA-ICP-MS and MALDI-MS images using image registration approaches, obtaining a method with errors below 50 µm. Finally, we used the developed approaches for registration of LA-ICP-MS and MALDI-MS images to evaluate the delivery vehicles and cargo, obtaining quantitative information about the correlation of the signals obtained in the two image modalities. The use of image registration for the analysis of siRNA delivery via nanoparticle stabilized capsules (NPSC) reveals that expected changes in lipid levels occur at different locations than the NPSC accumulate, thus providing deeper insight into how siRNA delivery by NPSCs influences lipid biochemistry in vivo