The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

A systematic review opens the black box of “usual care” in stroke rehabilitation control groups and finds a black hole

INTRODUCTION: In experimental trials, new methods are tested against the “best” or “usual” care. To appraise control group (CG) interventions provided as “usual care,” we focused on stroke as a leading cause of disability demanding rehabilitation as a complex intervention. EVIDENCE ACQUISITION: For this methodological appraisal, we conducted a systematic review of RCTs without timespan limitation. The PICO included stroke survivors, rehabilitation, control group intervention, lower limb function. To assess the risk of bias, we used the Cochrane risk of bias tool (RoB). we identified the terminology describing the CG Program (CGP), performed a knowledge synthesis and conducted a frequency analysis of provided interventions. EVIDENCE SYNTHESIS: we included 155 publications. 13.6% of the articles did not describe the CG, and 11.6% indicated only the professionals involved. In the remaining 116 studies, three studies provided an intervention according to specific guidelines, 106 different “usual care” CGPs were detected, with nine proposed twice and two between four and five times. The most adopted terminology to state “usual care” was “conventional physiotherapy.” CONCLUSIONS: This study shows that usual care in CG does not actually exist, as both specific terminology and consistency within CGP contents are missing. Reporting guidelines should give better assistance on this issue. These results should be verified in other fields

Generalized Killing equations and Taub-NUT spinning space

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Simple solutions of the homogeneous part of these equations are expressed in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional euclidean Taub-NUT manifold.Comment: 10 pages, late

Density and P‐wave velocity structure beneath the Paraná Magmatic Province: Refertilization of an ancient lithospheric mantle

We estimate density and P‐wave velocity perturbations in the mantle beneath the southeastern South America plate from geoid anomalies and P‐wave traveltime residuals to constrain the structure of the lithosphere underneath the Paraná Magmatic Province (PMP) and conterminous geological provinces. Our analysis shows a consistent correlation between density and velocity anomalies. The P‐wave speed and density are 1% and 15 kg/m3 lower, respectively, in the upper mantle under the Late Cretaceous to Cenozoic alkaline provinces, except beneath the Goiás Alkaline Province (GAP), where density (+20 kg/m3) and velocity (+0.5%) are relatively high. Underneath the PMP, the density is higher by about 50 kg/m3 in the north and 25 kg/m3 in the south, to a depth of 250 − 300 km. These values correlate with high‐velocity perturbations of +0.5% and +0.3%, respectively. Profiles of density perturbation versus depth in the upper mantle are different for the PMP and the adjacent Archean São Francisco (SFC) and Amazonian (AC) cratons. The Paleoproterozoic PMP basement has a high‐density root. The density is relatively low in the SFC and AC lithospheres. A reduction of density is a typical characteristic of chemically depleted Archean cratons. A more fertile Proterozoic and Phanerozoic subcontinental lithospheric mantle has a higher density, as deduced from density estimates of mantle xenoliths of different ages and composition. In conjunction with Re‐Os isotopic studies of the PMP basalts, chemical and isotopic analyses of peridodite xenoliths from the GAP in the northern PMP, and electromagnetic induction experiments of the PMP lithosphere, our density and P‐wave speed models suggest that the densification of the PMP lithosphere and flood basalt generation are related to mantle refertilization. Metasomatic refertilization resulted from the introduction of asthenospheric components from the mantle wedge above Proterozoic subduction zones, which surrounded the Paraná lithosphere. The high‐density PMP lithosphere is presently gravitationally unstable and prone to delamination.Key Points:Density and P‐wave velocity in the lithospheric mantle beneath the Paraná Magmatic Province are highHigh density precludes a depleted cratonic lithosphere and indicates refertilized lithospheric mantleBasalt magmatism suggests refertilized mantle with asthenospheric components from mantle wedgePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134193/1/ggge21079-sup-0003-2016GC006369-fs02.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134193/2/ggge21079-sup-0004-2016GC006369-fs03.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134193/3/ggge21079-sup-0002-2016GC006369-fs01.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134193/4/ggge21079_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134193/5/ggge21079.pd

Autophagy and the lysosomal system in cancer

Autophagy and the lysosomal system, together referred to as the autophagolysosomal system, is a cellular quality control network which maintains cellular health and homeostasis by removing cellular waste including protein aggregates, damaged organelles, and invading pathogens. As such, the autophagolysosomal system has roles in a variety of pathophysiological disorders, including cancer, neurological disorders, immune- and inflammation-related diseases, and metabolic alterations, among others. The autophagolysosomal system is controlled by TFEB, a master transcriptional regulator driving the expression of multiple genes, including autophagoly sosomal components. Importantly, Reactive Oxygen Species (ROS) production and control are key aspects of the physiopathological roles of the autophagolysosomal system, and may hold a key for synergistic therapeutic interventions. In this study, we reviewed our current knowledge on the biology and physiopathology of the autophagolysosomal system, and its potential for therapeutic intervention in cancer

Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry

It is shown that the N=4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the spin-like operators constructed with the help of the same covariantly constant Killing-Yano tensors which generate Dirac-type operators. A parity operator is defined and some explicit transformations which connect the Dirac-type operators among themselves are given. These transformations form a discrete group which is a realization of the quaternion discrete group. The fifth Dirac operator constructed using the non-covariant Killing-Yano tensor of the Taub-NUT space is quite special. This non-standard Dirac operator is connected with the hidden symmetry and is not equivalent to the Dirac-type operators of the standard N=4 supersymmetry.Comment: 14 pages, latex, no figure