Some remarks on the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians

We consider the problem of minimising the $k$th eigenvalue, $k \geq 2$, of the ($p$-)Laplacian with Robin boundary conditions with respect to all domains in $\mathbb{R}^N$ of given volume $M$. When $k=2$, we prove that the second eigenvalue of the $p$-Laplacian is minimised by the domain consisting of the disjoint union of two balls of equal volume, and that this is the unique domain with this property. For $p=2$ and $k \geq 3$, we prove that in many cases a minimiser cannot be independent of the value of the constant $\alpha$ in the boundary condition, or equivalently of the volume $M$. We obtain similar results for the Laplacian with generalised Wentzell boundary conditions $\Delta u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$.Comment: 16 page

Ictal quantitative surface electromyography correlates with postictal EEG suppression.

To test the hypothesis that neurophysiologic biomarkers of muscle activation during convulsive seizures reveal seizure severity and to determine whether automatically computed surface EMG parameters during seizures can predict postictal generalized EEG suppression (PGES), indicating increased risk for sudden unexpected death in epilepsy. Wearable EMG devices have been clinically validated for automated detection of generalized tonic-clonic seizures. Our goal was to use quantitative EMG measurements for seizure characterization and risk assessment. Quantitative parameters were computed from surface EMGs recorded during convulsive seizures from deltoid and brachial biceps muscles in patients admitted to long-term video-EEG monitoring. Parameters evaluated were the durations of the seizure phases (tonic, clonic), durations of the clonic bursts and silent periods, and the dynamics of their evolution (slope). We compared them with the duration of the PGES. We found significant correlations between quantitative surface EMG parameters and the duration of PGES (p < 0.001). Stepwise multiple regression analysis identified as independent predictors in deltoid muscle the duration of the clonic phase and in biceps muscle the duration of the tonic-clonic phases, the average silent period, and the slopes of the silent period and clonic bursts. The surface EMG-based algorithm identified seizures at increased risk (PGES ≥20 seconds) with an accuracy of 85%. Ictal quantitative surface EMG parameters correlate with PGES and may identify seizures at high risk. This study provides Class II evidence that during convulsive seizures, surface EMG parameters are associated with prolonged postictal generalized EEG suppression

Raman study of thin films of amorphous-to-microcrystalline silicon prepared by hot-wire chemical vapor deposition

A study was conducted on thin films of amorphous-to-microcrystalline silicon prepared by hot-wire chemical vapor deposition. The Raman scattering was used to study the structural change of the thin films in terms of the deposition parameters. The results showed that the change in the structure of the films depended on the SiH4 flow rate and total gas pressure

A mechanism for randomness

We investigate explicit functions that can produce truly random numbers. We use the analytical properties of the explicit functions to show that certain class of autonomous dynamical systems can generate random dynamics. This dynamics presents fundamental differences with the known chaotic systems. We present realphysical systems that can produce this kind of random time-series. We report theresults of real experiments with nonlinear circuits containing direct evidence for this new phenomenon. In particular, we show that a Josephson junction coupled to a chaotic circuit can generate unpredictable dynamics. Some applications are discussed.Comment: Accepted in Physics Letters A (2002). 11 figures (.eps

Intersecting 6-branes from new 7-manifolds with G_2 holonomy

We discuss a new family of metrics of 7-manifolds with G_2 holonomy, which are R^3 bundles over a quaternionic space. The metrics depend on five parameters and have two Abelian isometries. Certain singularities of the G_2 manifolds are related to fixed points of these isometries; there are two combinations of Killing vectors that possess co-dimension four fixed points which yield upon compactification only intersecting D6-branes if one also identifies two parameters. Two of the remaining parameters are quantized and we argue that they are related to the number of D6-branes, which appear in three stacks. We perform explicitly the reduction to the type IIA model.Comment: 25 pages, 1 figure, Latex, small changes and add refs, version appeared in JHE

Anisotropic transport in the two-dimensional electron gas in the presence of spin-orbit coupling

In a two-dimensional electron gas as realized by a semiconductor quantum well, the presence of spin-orbit coupling of both the Rashba and Dresselhaus type leads to anisotropic dispersion relations and Fermi contours. We study the effect of this anisotropy on the electrical conductivity in the presence of fixed impurity scatterers. The conductivity also shows in general an anisotropy which can be tuned by varying the Rashba coefficient. This effect provides a method of detecting and investigating spin-orbit coupling by measuring spin-unpolarized electrical currents in the diffusive regime. Our approach is based on an exact solution of the two-dimensional Boltzmann equation and provides also a natural framework for investigating other transport effects including the anomalous Hall effect.Comment: 10 pages, 1 figure included. Discussion of experimental impact enlarged; error in calculation of conductivity contribution corrected (cf. Eq. (A14)), no changes in qualitative results and physical consequence

European dermatology forum - updated guidelines on the use of extracorporeal photopheresis 2020 - part 1.

Following the first investigational study on the use of extracorporeal photopheresis for the treatment of cutaneous T-cell lymphoma published in 1983, this technology has received continued use and further recognition for additional earlier as well as refractory forms. After the publication of the first guidelines for this technology in the JEADV in 2014, this technology has maintained additional promise in the treatment of other severe and refractory conditions in a multi-disciplinary setting. It has confirmed recognition in well-known documented conditions such as graft-versus-host disease after allogeneic bone marrow transplantation, systemic sclerosis, solid organ transplant rejection including lung, heart and liver and to a lesser extent inflammatory bowel disease. In order to further provide recognized expert practical guidelines for the use of this technology for all indications, the European Dermatology Forum (EDF) again proceeded to address these questions in the hands of the recognized experts within and outside the field of dermatology. This was done using the recognized and approved guidelines of EDF for this task. All authors had the opportunity to review each contribution as it was added. These updated 2020 guidelines provide at present the most comprehensive available expert recommendations for the use of extracorporeal photopheresis based on the available published literature and expert consensus opinion. The guidelines are divided in two parts: PART I covers cutaneous T-cell lymphoma, chronic graft-versus-host disease and acute graft-versus-host disease while PART II will cover scleroderma, solid organ transplantation, Crohn's disease, use of ECP in paediatrics practice, atopic dermatitis, type 1 diabetes, pemphigus, epidermolysis bullosa acquisita and erosive oral lichen planus

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc