Gravitational singularities via acceleration: the case of the Schwarzschild solution and Bach's gamma metric

The so called gamma metric corresponds to a two-parameter family of axially symmetric, static solutions of Einstein's equations found by Bach. It contains the Schwarzschild solution for a particular value of one of the parameters, that rules a deviation from spherical symmetry. It is shown that there is invariantly definable singular behaviour beyond the one displayed by the Kretschmann scalar when a unique, hypersurface orthogonal, timelike Killing vector exists. In this case, a particle can be defined to be at rest when its world-line is a corresponding Killing orbit. The norm of the acceleration on such an orbit proves to be singular not only for metrics that deviate from Schwarzschild's metric, but also on approaching the horizon of Schwarzschild metric itself, in contrast to the discontinuous behaviour of the curvature scalar.Comment: 8 pages; text accepted for publication by Astronomische Nachrichte

Electrostatics and confinement in Einstein's unified field theory

A way for appending sources at the right-hand sides of the field equations of Einstein's unified field theory is recalled. Two exact solutions endowed with point sources in equilibrium are shown, and their physical meaning is discussed.Comment: 4 pages, talk given at MG11, Berlin, July 200

Cortical circuit alterations precede motor impairments in Huntington's disease mice

Huntington's disease (HD) is a devastating hereditary movement disorder, characterized by degeneration of neurons in the striatum and cortex. Studies in human patients and mouse HD models suggest that disturbances of neuronal function in the neocortex play an important role in disease onset and progression. However, the precise nature and time course of cortical alterations in HD have remained elusive. Here, we use chronic in vivo two-photon calcium imaging to longitudinally monitor the activity of identified single neurons in layer 2/3 of the primary motor cortex in awake, behaving R6/2 transgenic HD mice and wildtype littermates. R6/2 mice show age-dependent changes in cortical network function, with an increase in activity that affects a large fraction of cells and occurs rather abruptly within one week, preceeding the onset of motor defects. Furthermore, quantitative proteomics demonstrate a pronounced downregulation of synaptic proteins in the cortex, and histological analyses in R6/2 mice and human HD autopsy cases reveal a reduction in perisomatic inhibitory synaptic contacts on layer 2/3 pyramidal cells. Taken together, our study provides a time-resolved description of cortical network dysfunction in behaving HD mice and points to disturbed excitation/inhibition balance as an important pathomechanism in HD

Segmentation of Static and Dynamic Atomic-Resolution Microscopy Data Sets with Unsupervised Machine Learning Using Local Symmetry Descriptors

We present an unsupervised machine learning approach for segmentation of static and dynamic atomic-resolution microscopy data sets in the form of images and video sequences. In our approach, we first extract local features via symmetry operations. Subsequent dimension reduction and clustering analysis are performed in feature space to assign pattern labels to each pixel. Furthermore, we propose the stride and upsampling scheme as well as separability analysis to speed up the segmentation process of image sequences. We apply our approach to static atomic-resolution scanning transmission electron microscopy images and video sequences. Our code is released as a python module that can be used as a standalone program or as a plugin to other microscopy packages. Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of the Microscopy Society of America

The Electrostatics of Einstein's Unified Field Theory

When sources are added at their right-hand sides, and g_{(ik)} is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_{(ik)} in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_{(ik)}, however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by H\'ely. In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when H\'ely's physically correct metric is adopted.Comment: 15 pages. Misprints corrected. To appear in General Relativity and Gravitatio

Modified-release prednisone for polymyalgia rheumatica: a multicentre, randomised, active-controlled, double-blind, parallel-group study.

Objective: To assess the efficacy and safety of modified-release (MR) versus immediate-release (IR) prednisone in newly diagnosed glucocorticoid (GC)-na\uefve patients with polymyalgia rheumatica (PMR). Methods: Patients were randomised to double-blind MR prednisone (taken at approximately 22:00) or IR prednisone (taken in the morning), 15 mg/day for 4 weeks. The primary end point was complete response rate ( 6570% reduction in PMR visual analogue scale, duration of morning stiffness and C reactive protein (CRP) (or CRP < 2 7 upper limit of normal (ULN))) at week 4. Non-inferiority was decided if the lower 95% confidence limit (MR vs IR prednisone) was above -15%. 400 patients were planned but only 62 were enrolled due to difficulties in recruiting GC-na\uefve patients with PMR with CRP 652 7ULN. Results: The percentage of complete responders at week 4 was numerically greater for MR prednisone (53.8%) than for IR prednisone (40.9%). Non-inferiority of MR versus IR prednisone was not proven in the primary analysis on the per protocol population (N=48; treatment difference: 12.22%; 95% CI -15.82% to 40.25%). However, sensitivity analysis on the full analysis population showed an evident trend favouring MR prednisone (N=62; treatment difference: 15.56%; 95% CI -9.16% to 40.28%). Adverse events were generally mild and transient with no unexpected safety observations. Conclusions: The study showed a clear trend for favourable short-term efficacy of MR prednisone versus IR prednisone in early treatment of PMR. Further studies are warranted