The subgroup growth spectrum of virtually free groups

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. Moreover, we describe an algorithm to compute $\mu$

Spontaneous visual exploration during locomotion in patients with phobic postural vertigo

BACKGROUND Earlier studies on stance and gait with posturographic and EMG-recordings and automatic gait analysis in patients with phobic postural vertigo (PPV) or visual height intolerance (vHI) revealed similar patterns of body stiffening with muscle co-contraction and a slow, cautious gait. Visual exploration in vHI patients was characterized by a freezing of gaze-in-space when standing and reduced horizontal eye and head movements during locomotion. OBJECTIVE Based on the findings in vHI patients, the current study was performed with a focus on visual control of locomotion in patients with PPV while walking along a crowded hospital hallway. METHODS Twelve patients with PPV and eleven controls were recruited. Participants wore a mobile infrared video eye-tracking system that continuously measured eye-in-head movements in the horizontal and vertical planes and head orientation and motion in the yaw, pitch, and roll planes. Visual exploration behavior of participants was recorded at the individually preferred speed for a total walking distance of 200 m. Gaze-in-space directions were determined by combining eye-in-head and head-in-space orientation. Walking speeds were calculated based on the trial duration and the total distance traversed. Participants were asked to rate their feelings of discomfort during the walk on a 4-point numeric rating scale. The examiners rated the crowdedness of the hospital hallway on a 4-point numeric rating scale. RESULTS The major results of visual exploration behavior in patients with PPV in comparison to healthy controls were: eye and head positions were directed more downward in the vertical plane towards the ground ahead with increased frequency of large amplitude vertical orientation movements towards the destination, the end of the ground straight ahead. The self-adjusted speed of locomotion was significantly lower in PPV. Particularly those patients that reported high levels of discomfort exhibited a specific visual exploration of their horizontal surroundings. The durations of fixating targets in the visual surroundings were significantly shorter as compared to controls. CONCLUSION Gaze control of locomotion in patients with PPV is characterized by a preferred deviation of gaze more downward and by horizontal explorations for suitable auxiliary means for potential postural support in order to prevent impending falls. These eye movements have shorter durations of fixation as compared to healthy controls and patients with vHI. Finally, the pathological alterations in eye-head coordination during locomotion correlate with a higher level of discomfort and anxiety about falling

On the p-length of some finite p-soluble groups

The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose p-length is greater than 1, p a prime number. Alternative proofs and improvements of recent results about the influence of minimal p-subgroups on the p-nilpotence and p-length of a finite group arise as consequences of our study

Lava channel formation during the 2001 eruption on Mount Etna: evidence for mechanical erosion

We report the direct observation of a peculiar lava channel that was formed near the base of a parasitic cone during the 2001 eruption on Mount Etna. Erosive processes by flowing lava are commonly attributed to thermal erosion. However, field evidence strongly suggests that models of thermal erosion cannot explain the formation of this channel. Here, we put forward the idea that the essential erosion mechanism was abrasive wear. By applying a simple model from tribology we demonstrate that the available data agree favorably with our hypothesis. Consequently, we propose that erosional processes resembling the wear phenomena in glacial erosion are possible in a volcanic environment.Comment: accepted for publication in Physical Review Letter

On the representation ring of the polynomial algebra over a perfect field

We consider the tensor product of modules over the polynomial algebra corresponding to the usual tensor product of linear operators. We present a general description of the representation ring in case the ground field k is perfect. It is made explicit in the special cases when k is real closed respectively algebraically closed. Furthermore, we discuss the generalisation of this problem to representations of quivers. In particular the representation ring of quivers of extended Dynkin type A is provided.Comment: 17 page

A CMOS 130nm Evaluation digitzer chip for silicon strips readout

A CMOS 130nm evaluation chip intended to read Silicon strip detectors at the ILC has been designed and successfully tested. Optimized for a detector capacitance of 10 pF, it includes four channels of charge integration, pulse shaping, a 16-deep analogue sampler triggered on input analogue sums, and parallel analogue to digital conversion. Tests results of the full chain are reported, demonstrating the behaviour and performance of the full sampling process and analogue to digital conversion. Each channel dissipates less than one milli-Watt static power

Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids : slender rivulets and dry patches

Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t, the rivulet and dry patch widen or narrow according to |x|3/2, and the film thickens or thins according to |x|, where x denotes distance down the plane, and that at any station x, the rivulet and dry patch widen or narrow like |t|−1, and the film thickens or thins like |t|−1, independent of N

The camera of the fifth H.E.S.S. telescope. Part I: System description

In July 2012, as the four ground-based gamma-ray telescopes of the H.E.S.S. (High Energy Stereoscopic System) array reached their tenth year of operation in Khomas Highlands, Namibia, a fifth telescope took its first data as part of the system. This new Cherenkov detector, comprising a 614.5 m^2 reflector with a highly pixelized camera in its focal plane, improves the sensitivity of the current array by a factor two and extends its energy domain down to a few tens of GeV. The present part I of the paper gives a detailed description of the fifth H.E.S.S. telescope's camera, presenting the details of both the hardware and the software, emphasizing the main improvements as compared to previous H.E.S.S. camera technology.Comment: 16 pages, 13 figures, accepted for publication in NIM

Paediatric obsessive-compulsive disorder and depressive symptoms: clinical correlates and CBT treatment outcomes.

Depression frequently co-occurs with paediatric obsessive-compulsive disorder (OCD), yet the clinical correlates and impact of depression on CBT outcomes remain unclear. The prevalence and clinical correlates of depression were examined in a paediatric specialist OCD-clinic sample (N = 295; Mean = 15 [7 - 18] years, 42 % female), using both dimensional (Beck Depression Inventory-youth; n = 261) and diagnostic (Development and Wellbeing Assessment; n = 127) measures of depression. The impact of depressive symptoms and suspected disorders on post-treatment OCD severity was examined in a sub-sample who received CBT, with or without SSRI medication (N = 100). Fifty-one per-cent of patients reported moderately or extremely elevated depressive symptoms and 26 % (95 % CI: 18 - 34) met criteria for a suspected depressive disorder. Depressive symptoms and depressive disorders were associated with worse OCD symptom severity and global functioning prior to CBT. Individuals with depression were more likely to be female, have had a psychiatric inpatient admission and less likely to be attending school (ps < 0.01). OCD and depressive symptom severity significantly decreased after CBT. Depressive symptoms and depressive disorders predicted worse post-treatment OCD severity (βs = 0.19 and 0.26, ps < 0.05) but became non-significant when controlling for pre-treatment OCD severity (βs = 0.05 and 0.13, ns). Depression is common in paediatric OCD and is associated with more severe OCD and poorer functioning. However, depression severity decreases over the course of CBT for OCD and is not independently associated with worse outcomes, supporting the recommendation for treatment as usual in the presence of depressive symptoms

Meta-analysis in metastatic uveal melanoma to determine progression free and overall survival benchmarks : an international rare cancers initiative (IRCI) ocular melanoma study

Background: Despite the completion of numerous phase II studies, a standard of care treatment has yet to be defined for metastatic uveal melanoma (mUM). To determine benchmarks of progression free survival (PFS) and overall survival (OS), we carried out a meta-analysis using individual patient level trial data. Methods: Individual patient variables and survival outcomes were requested from 29 trials published from 2000 to 2016. Univariable and multivariable analysis were carried out for prognostic factors. The variability between trial arms and between therapeutic agents on PFS and OS was investigated. Results: OS data were available for 912 patients. The median PFS was 3.3 months (95% CI 2.9-3.6) and 6-month PFS rate was 27% (95% CI 24-30). Univariable analysis showed male sex, elevated (i.e. > versus = 3 cm versus Conclusion: Benchmarks of 6-month PFS and 1-year OS rates were determined accounting for prognostic factors. These may be used to facilitate future trial design and stratification in mUM.Peer reviewe