On the volume functional of compact manifolds with boundary with constant scalar curvature

We study the volume functional on the space of constant scalar curvature metrics with a prescribed boundary metric. We derive a sufficient and necessary condition for a metric to be a critical point, and show that the only domains in space forms, on which the standard metrics are critical points, are geodesic balls. In the zero scalar curvature case, assuming the boundary can be isometrically embedded in the Euclidean space as a compact strictly convex hypersurface, we show that the volume of a critical point is always no less than the Euclidean volume bounded by the isometric embedding of the boundary, and the two volumes are equal if and only if the critical point is isometric to a standard Euclidean ball. We also derive a second variation formula and apply it to show that, on Euclidean balls and ''small'' hyperbolic and spherical balls in dimensions 3 to 5, the standard space form metrics are indeed saddle points for the volume functional

Electronic structure study by means of X-ray spectroscopy and theoretical calculations of the "ferric star" single molecule magnet

The electronic structure of the single molecule magnet system M[Fe(L)2]3*4CHCl3 (M=Fe,Cr; L=CH3N(CH2CH2O)2) has been studied using X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, soft X-ray emission spectroscopy, and density functional calculations. There is good agreement between theoretical calculations and experimental data. The valence band mainly consists of three bands between 2 eV and 30 eV. Both theory and experiments show that the top of the valence band is dominated by the hybridization between Fe 3d and O 2p bands. From the shape of the Fe 2p spectra it is argued that Fe in the molecule is most likely in the 2+ charge state. Its neighboring atoms (O,N) exhibit a magnetic polarisation yielding effective spin S=5/2 per iron atom, giving a high spin state molecule with a total S=5 effective spin for the case of M = Fe.Comment: Fig.2 replaced as it will appear in J. Chem. Phy

Monitoring physical and psychosocial symptom trajectories in ovarian cancer patients receiving chemotherapy

<p>Abstract</p> <p>Background</p> <p>Diagnosis and treatment of ovarian cancer (OC) entail severe symptom burden and a significant loss of quality of life (QOL). Somatic and psychological impairments may persist well beyond active therapy. Although essential for optimal symptom management as well as for the interpretation of treatment outcomes, knowledge on the course of QOL-related issues is scarce. This study aimed at assessing the course of depressive symptoms, anxiety, fatigue and QOL in patients with OC over the course of chemotherapy until early after-care.</p> <p>Methods</p> <p>23 patients were assessed longitudinally (eight time points) with regard to symptom burden (depression, anxiety, fatigue, and QOL) by means of patient-reported outcome instruments (HADS, MFI-20, EORTC QLQ-C30/-OV28) and clinician ratings (HAMA/D) at each chemotherapy cycle and at the first two aftercare visits.</p> <p>Results</p> <p>Statistically significant decrease over time was found for depressive symptoms and anxiety as well as for all fatigue scales. With regard to QOL, results indicated significant increase for 11 of 15 QOL scales, best for Social (effect size = 1.95; <it>p </it>< 0.001), Emotional (e.s. = 1.62; <it>p </it>< 0.001) and Physical Functioning (e.s. = 1.47; <it>p </it>< 0.001). Abdominal Symptoms (e.s. = 1.01; <it>p </it>= 0.009) decreased, Attitudes towards Disease and Treatment (e.s. = 1.80; <it>p </it>< 0.001) improved significantly over time. Analysis of Sexual Functioning was not possible due to a high percentage of missing responses (61.9%).</p> <p>Conclusions</p> <p>The present study underlines the importance of longitudinal assessment of QOL in order to facilitate the identification of symptom burden in OC patients. We found that patients show high levels of fatigue, anxiety and depressive symptoms and severely impaired QOL post-surgery (i.e. at start of chemotherapy) but condition improves considerably throughout chemotherapy reaching nearly general population symptoms levels until aftercare.</p

Coracoid impingement syndrome: a literature review

Coracoid impingement syndrome is a less common cause of shoulder pain. Symptoms are presumed to occur when the subscapularis tendon impinges between the coracoid and lesser tuberosity of the humerus. Coracoid impingement should be included in the differential diagnosis when evaluating a patient with activity-related anterior shoulder pain. It is not thought to be as common as subacromial impingement, and the possibility of the coexistence of the two conditions must be taken into consideration before treatment of either as an isolated process. If nonoperative treatment fails to relieve symptoms, surgical decompression can be offered as an option

Efficient binary fuzzy measure representation and Choquet integral learning

The Choquet integral (ChI), a parametric function for information aggregation, is parameterized by the fuzzy measure (FM), which has 2N real-valued variables for N inputs. However, the ChI incurs huge storage and computational burden due to its exponential complexity relative to N and, as a result, its calculation, storage, and learning becomes intractable for even modest sizes (e.g., N = 15). Inspired by empirical observations in multi-sensor fusion and the more general need to mitigate the storage, computational, and learning limitations, we previously explored the binary ChI (BChI) relative to the binary fuzzy measure (BFM). The BChI is a natural _t for many applications and can be used to approximate others. Previously, we investigated different properties of the BChI and we provided an initial representation. In this article, we propose a new efficient learning algorithm for the BChI, called EBChI, by utilizing the BFM properties that add at most one variable per training instance. Furthermore, we provide an efficient representation of the BFM (EBFM) scheme that further reduces the number of variables required for storage and computation, thus enabling the use of the BChI for \big N". Finally, we conduct experiments on synthetic data that demonstrate the efficiency of our proposed techniques