Some remarks on modified power entropy

The aim of this note is to point out some observations concerning modified power entropy of $\Z$- and $\N$-actions. First, we provide an elementary example showing that this quantity is sensitive to transient dynamics, and therefore does not satisfy a variational principle. Further, we show that modified power entropy is not suitable to detect the break of equicontinuity which takes place during the transition from almost periodic to almost automorphic minimal systems. In this respect, it differs from power entropy and amorphic complexity, which are two further topological invariants for zero entropy systems (`slow entropies'). Finally, we construct an example of an irregular Toeplitz flow with zero modified power entropy.Comment: 17 pages, to appear in AMS Contemporary Mathematics serie

Next-to-leading order QCD corrections to Higgs production at a future lepton-proton collider

Crucial information on the coupling of the Higgs boson to bottom quarks is expected from Higgs production in association with a forward tagging jet at a future high-energy lepton-proton collider. In order to control the theoretical uncertainties of the signal process, the impact of radiative corrections has to be quantified. We present the full next-to-leading order QCD corrections to e- p -> e- j H and e- p -> nu_e j H in the form of a flexible Monte-Carlo program allowing for the calculation of cross sections and kinematic distributions within experimentally feasible selection cuts. QCD corrections are found to be very small for cross sections, while the shape distortion of distributions can be as large as 20%. Residual scale uncertainties at next-to-leading order are at the permille level.Comment: 15 pages, 14 figure

The uniqueness of the solution of the Schrodinger equation with discontinuous coefficients

Consider the Schroeodinger equation: - Du(x) - l(x)u + s(x)u = 0, where D is the Laplacian, l(x) > 0 and s(x) is dominated by l(x). We shall extend the celebrated Kato's result on the asymptotic behavior of the solution to the case where l(x) has unbounded discontinuity. The result will be used to establish the limiting absorption principle for a class of reduced wave operators with discontinuous coefficients.Comment: 29 (twenty-nine) pages; no figures; to appear in Reviews of Mathematical Physic

On torus homeomorphisms semiconjugate to irrational rotations

In the context of the Franks–Misiurewicz conjecture, we study homeomorphisms of the two-torus semiconjugate to an irrational rotation of the circle. As a special case, this conjecture asserts uniqueness of the rotation vector in this class of systems. We first characterize these maps by the existence of an invariant ‘foliation’ by essential annular continua (essential subcontinua of the torus whose complement is an open annulus) which are permuted with irrational combinatorics. This result places the considered class close to skew products over irrational rotations. Generalizing a well-known result of Herman on forced circle homeomorphisms, we provide a criterion, in terms of topological properties of the annular continua, for the uniqueness of the rotation vector. As a byproduct, we obtain a simple proof for the uniqueness of the rotation vector on decomposable invariant annular continua with empty interior. In addition, we collect a number of observations on the topology and rotation intervals of invariant annular continua with empty interior

Influence of a six month endurance exercise program on the immune function of prostate cancer patients undergoing Antiandrogen or Chemotherapy: design and rationale of the ProImmun study

Background: Exercise seems to minimize prostate cancer specific mortality risk and treatment related side effects like fatigue and incontinence. However the influence of physical activity on the immunological level remains uncertain. Even prostate cancer patients undergoing palliative treatment often have a relatively long life span compared to other cancer entities. To optimize exercise programs and their outcomes it is essential to investigate the underlying mechanisms. Further, it is important to discriminate between different exercise protocols and therapy regimes. Methods/Design: The ProImmun study is a prospective multicenter patient preference randomized controlled trial investigating the influence of a 24 week endurance exercise program in 80–100 prostate cancer patients by comparing patients undergoing Antiandrogen therapy combined with exercise (AE), Antiandrogen therapy without exercise (A), Chemotherapy with exercise(CE) or Chemotherapy without exercise (C). The primary outcome of the study is a change in prostate cancer relevant cytokines and hormones (IL-6, MIF, IGF-1, Testosterone). Secondary endpoints are immune cell ratios, oxidative stress and antioxidative capacity levels, VO2 peak, fatigue and quality of life. Patients of the intervention group exercise five times per week, while two sessions are supervised. During the supervised sessions patients (AE and CE) exercise for 33 minutes on a bicycle ergometer at 70-75% of their VO2 peak. To assess long term effects and sustainability of the intervention two follow-up assessments are arranged 12 and 18 month after the intervention. Discussion: The ProImmun study is the first trial which primarily investigates immunological effects of a six month endurance exercise program in prostate cancer patients during palliative care. Separating patients treated with Antiandrogen therapy from those who are additionally treated with Chemotherapy might allow a more specific view on the influence of endurance training interventions and the impact of different therapy protocols on the immune function. Trial registration: German Clinical Trials Register: DRKS0000473

Street crossing behavior in younger and older pedestrians: an eye- and head-tracking study

Background Crossing a street can be a very difficult task for older pedestrians. With increased age and potential cognitive decline, older people take the decision to cross a street primarily based on vehicles’ distance, and not on their speed. Furthermore, older pedestrians tend to overestimate their own walking speed, and could not adapt it according to the traffic conditions. Pedestrians’ behavior is often tested using virtual reality. Virtual reality presents the advantage of being safe, cost-effective, and allows using standardized test conditions. Methods This paper describes an observational study with older and younger adults. Street crossing behavior was investigated in 18 healthy, younger and 18 older subjects by using a virtual reality setting. The aim of the study was to measure behavioral data (such as eye and head movements) and to assess how the two age groups differ in terms of number of safe street crossings, virtual crashes, and missed street crossing opportunities. Street crossing behavior, eye and head movements, in older and younger subjects, were compared with non-parametric tests. Results The results showed that younger pedestrians behaved in a more secure manner while crossing a street, as compared to older people. The eye and head movements analysis revealed that older people looked more at the ground and less at the other side of the street to cross. Conclusions The less secure behavior in street crossing found in older pedestrians could be explained by their reduced cognitive and visual abilities, which, in turn, resulted in difficulties in the decision-making process, especially under time pressure. Decisions to cross a street are based on the distance of the oncoming cars, rather than their speed, for both groups. Older pedestrians look more at their feet, probably because of their need of more time to plan precise stepping movement and, in turn, pay less attention to the traffic. This might help to set up guidelines for improving senior pedestrians’ safety, in terms of speed limits, road design, and mixed physical-cognitive trainings