Non-degenerate solutions of boundary-value problems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23291/1/0000228.pd

Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics

We consider geometries on the space of Riemannian metrics conformally equivalent to the widely studied Ebin L^2 metric. Among these we characterize a distinguished metric that can be regarded as a generalization of Calabi's metric on the space of K\"ahler metrics to the space of Riemannian metrics, and we study its geometry in detail. Unlike the Ebin metric, the geodesic equation involves non-local terms, and we solve it explicitly by using a constant of the motion. We then determine its completion, which gives the first example of a metric on the space of Riemannian metrics whose completion is strictly smaller than that of the Ebin metric.Comment: 28 page

Insights from in\ua0vivo micro-CT analysis: testing the hydraulic vulnerability segmentation in Acer pseudoplatanus and Fagus sylvatica seedlings

The seedling stage is the most susceptible one during a tree\u2032s life. Water relations may be crucial for seedlings due to their small roots, limited water buffers and the effects of drought on water transport. Despite obvious relevance, studies on seedling xylem hydraulics are scarce as respective methodical approaches are limited. Micro\u2010CT scans of intact Acer pseudoplatanus and Fagus sylvatica seedlings dehydrated to different water potentials (\u3a8) allowed the simultaneous observation of gas\u2010filled versus water\u2010filled conduits and the calculation of percentage loss of conductivity (PLC) in stems, roots and leaves (petioles or main veins). Additionally, anatomical analyses were performed and stem PLC measured with hydraulic techniques. In A. pseudoplatanus, petioles showed a higher \u3a8 at 50% PLC (\u3a850 121.13MPa) than stems ( 122.51 MPa) and roots ( 121.78 MPa). The main leaf veins of F. sylvatica had similar \u3a850 values ( 122.26 MPa) to stems ( 122.74 MPa) and roots ( 122.75 MPa). In both species, no difference between root and stems was observed. Hydraulic measurements on stems closely matched the micro\u2010CT based PLC calculations. Micro\u2010CT analyses indicated a species\u2010specific hydraulic architecture. Vulnerability segmentation, enabling a disconnection of the hydraulic pathway upon drought, was observed in A. pseudoplatanus but not in the especially shade\u2010tolerant F. sylvatica. Hydraulic patterns could partly be related to xylem anatomical traits

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

Assessment of the effects of different sample perfusion procedures on phase-contrast tomographic images of mouse spinal cord

Synchrotron X-ray Phase Contrast micro-Tomography (SXrPC\u3bcT) is a powerful tool in the investigation of biological tissues, including the central nervous system (CNS), and it allows to simultaneously detect the vascular and neuronal network avoiding contrast agents or destructive sample preparations. However, specific sample preparation procedures aimed to optimize the achievable contrast- and signal-to-noise ratio (CNR and SNR, respectively) are required. Here we report and discuss the effects of perfusion with two different fixative agents (ethanol and paraformaldehyde) and with a widely used contrast medium (MICROFIL\uae) on mouse spinal cord. As a main result, we found that ethanol enhances contrast at the grey/white matter interface and increases the contrast in correspondence of vascular features and fibres, thus providing an adequate spatial resolution to visualise the vascular network at the microscale. On the other hand, ethanol is known to induce tissue dehydration, likely reducing cell dimensions below the spatial resolution limit imposed by the experimental technique. Nonetheless, neurons remain well visible using either perfused paraformaldehyde or MICROFIL\uae compound, as these latter media do not affect tissues with dehydration effects. Paraformaldehyde appears as the best compromise: it is not a contrast agent, like MICROFIL\uae, but it is less invasive than ethanol and permits to visualise well both cells and blood vessels. However, a quantitative estimation of the relative grey matter volume of each sample has led us to conclude that no significant alterations in the grey matter extension compared to the white matter occur as a consequence of the perfusion procedures tested in this study

Experimental optimization of the energy for breast-CT with synchrotron radiation

Breast Computed Tomography (bCT) is a three-dimensional imaging technique that is raising interest among radiologists as a viable alternative to mammographic planar imaging. In X-rays imaging it would be desirable to maximize the capability of discriminating different tissues, described by the Contrast to Noise Ratio (CNR), while minimizing the dose (i.e. the radiological risk). Both dose and CNR are functions of the X-ray energy. This work aims at experimentally investigating the optimal energy that, at fixed dose, maximizes the CNR between glandular and adipose tissues. Acquisitions of both tissue-equivalent phantoms and actual breast specimens have been performed with the bCT system implemented within the Syrma-3D collaboration at the Syrmep beamline of the Elettra synchrotron (Trieste). The experimental data have been also compared with analytical simulations and the results are in agreement. The CNR is maximized at energies around 26–28 keV. These results are in line with the outcomes of a previously presented simulation study which determined an optimal energy of 28 keV for a large set of breast phantoms with different diameters and glandular fractions. Finally, a study on photon starvation has been carried out to investigate how far the dose can be reduced still having suitable images for diagnostics