Upper bounds for the eigenvalues of Hessian equations

We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equationsComment: 15 pages, 1 figur

Nematic Films and Radially Anisotropic Delaunay Surfaces

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure

On "many black hole" space-times

We analyze the horizon structure of families of space times obtained by evolving initial data sets containing apparent horizons with several connected components. We show that under certain smallness conditions the outermost apparent horizons will also have several connected components. We further show that, again under a smallness condition, the maximal globally hyperbolic development of the many black hole initial data constructed by Chrusciel and Delay, or of hyperboloidal data of Isenberg, Mazzeo and Pollack, will have an event horizon, the intersection of which with the initial data hypersurface is not connected. This justifies the "many black hole" character of those space-times.Comment: several graphic file

Continuous time random walk for open systems: Fluctuation theorems and counting statistics

We consider continuous time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter a, which is set to a=1 if it decays at least as fast as t^{-2} at long times and therefore has a finite first moment. A WTD with a<1 decays as t^{-a-1}. A fluctuation theorem for the trajectory quantity R, defined as the logarithm of the ratio of the probability of a trajectory and the probability of the time reversed trajectory, holds for any CTRW. However, R can be identified as a trajectory entropy change only if the WTDs have a=1 and satisfy separability (also called "direction time independence"). For nonseparable WTDs with a=1, R can only be identified as a trajectory entropy change at long times, and a fluctuation theorem for the entropy change then only holds at long times. For WTDs with 0<a<1 no meaningful fluctuation theorem can be derived. We also show that the (experimentally accessible) n'th moments of the energy and matter transfers between the system and a given reservoir grow as t^{n a} at long times.Comment: 1 figure ; v2: version accepted in Phys.Rev.

Closed geodesics in Alexandrov spaces of curvature bounded from above

In this paper, we show a local energy convexity of $W^{1,2}$ maps into $CAT(K)$ spaces. This energy convexity allows us to extend Colding and Minicozzi's width-sweepout construction to produce closed geodesics in any closed Alexandrov space of curvature bounded from above, which also provides a generalized version of the Birkhoff-Lyusternik theorem on the existence of non-trivial closed geodesics in the Alexandrov setting.Comment: Final version, 22 pages, 2 figures, to appear in the Journal of Geometric Analysi

Screening Instrument for Dysphagia in People with an Intellectual Disability (SD-ID):Quick and Reliable Screening by Caregivers

Background and Aim: Timely diagnosis of dysphagia is important for people with an intellectual disability. Periodic screening of each individual by speech-language therapists is barely feasible with respect to limited resources. Therefore, preselection of individuals with an increased dysphagia risk through screening by caregivers is crucial.Objective: This study aimed to develop the novel Screening instrument for Dysphagia for people with an Intellectual Disability (SD-ID).Methods: The SD-ID was developed, validated and optimised in two rounds. Version 3, consisting of nine risk factors and 20 items concerning eating/drinking behaviour, was thoroughly studied for feasibility, concurrent validity and reliability, and then optimised.Outcomes and Results: The SD-ID (version 3) was filled out in an average of four minutes (feasibility). A strong positive association was found between scores on SD-ID and Dysphagia Disorder Survey (concurrent validity). Test-retest and interrater reliability were very good. Two additional risk factors were added and two items removed to yield the final version 4. The most optimal cut-off score appeared to be either 4 or 5.Conclusions and Implications: The SD-ID is a reliable instrument to screen for an increased risk of dysphagia in people with an intellectual disability. Ideally it is part of a cyclic work process: Screening with SD-ID (step 1), diagnostic work-up if necessary (step 2), recommendations (step 3), and evaluation (step 4).</p

STARD for Abstracts: Essential items for reporting diagnostic accuracy studies in journal or conference abstracts

Many abstracts of diagnostic accuracy studies are currently insufficiently informative. We extended the STARD (Standards for Reporting Diagnostic Accuracy) statement by developing a list of essential items that authors should consider when reporting diagnostic accuracy studies in journal or conference abstracts. After a literature review of published guidance for reporting biomedical studies, we identified 39 items potentially relevant to report in an abstract. We then selected essential items through a two round web based survey among the 85 members of the STARD Group, followed by discussions within an executive committee. Seventy three STARD Group members responded (86%), with 100% completion rate. STARD for Abstracts is a list of 11 quintessential items, to be reported in every abstract of a diagnostic accuracy study. We provide examples of complete reporting, and developed template text for writing informative abstract

Practical robustness evaluation in radiotherapy - A photon and proton-proof alternative to PTV-based plan evaluation

Background and purpose: A planning target volume (PTV) in photon treatments aims to ensure that the clinical target volume (CTV) receives adequate dose despite treatment uncertainties. The underlying static dose cloud approximation (the assumption that the dose distribution is invariant to errors) is problematic in intensity modulated proton treatments where range errors should be taken into account as well. The purpose of this work is to introduce a robustness evaluation method that is applicable to photon and proton treatments and is consistent with (historic) PTV-base