Polynomial–exponential equations and Zilber's conjecture

Assuming Schanuel's conjecture, we prove that any polynomial–exponential equation in one variable must have a solution that is transcendental over a given finitely generated field. With the help of some recent results in Diophantine geometry, we obtain the result by proving (unconditionally) that certain polynomial–exponential equations have only finitely many rational solutions. This answers affirmatively a question of David Marker, who asked, and proved in the case of algebraic coefficients, whether at least the one variable case of Zilber's strong exponential-algebraic closedness conjecture can be reduced to Schanuel's conjecture

Validation of seat-off and seat-on in repeated sit-to-stand movements using a single body fixed sensor

The identification of chair rise phases is a prerequisite for quantifying sit-to-stand movements. The aim of this study is to validate seat-off and seat-on detection using a single-body-fixed sensor against detection based on chair switches. A single sensor system with three accelerometers and three gyroscopes was fixed around the waist. Synchronized on-off switches were placed under the chair. Thirteen older adults were recruited from a residential care home and fifteen young adults were recruited among college students. Subjects were asked to complete two sets of five trials each. Six features of the trunk movement during seat-off and seat-on were calculated automatically, and a model was developed to predict the moment of seat-off and seat-on transitions. The predictions were validated with leave-one-out cross-validation. Feature extraction failed in two trials (0.7%). For the optimal combination of seat-off predictors, cross-validation yielded a mean error of 0ms and a mean absolute error of 51ms. For the best seat-on predictor, cross-validation yielded a mean error of -3ms and a mean absolute error of 127ms. The results of this study demonstrate that seat-off and seat-on in repeated sit-to-stand movements can be detected semi-automatically in young and older adults using a one-body-fixed sensor system with an accuracy of 51 and 127ms, respectively. The use of the ambulatory instrumentation is feasible for non-technically trained personnel. This is an important step in the development of an automated method for the quantification of sit-to-stand movements in clinical practice. © 2012 Institute of Physics and Engineering in Medicine

Fragility and compressibility at the glass transition

Isothermal compressibilities and Brillouin sound velocities from the literature allow to separate the compressibility at the glass transition into a high-frequency vibrational and a low-frequency relaxational part. Their ratio shows the linear fragility relation discovered by x-ray Brillouin scattering [1], though the data bend away from the line at higher fragilities. Using the concept of constrained degrees of freedom, one can show that the vibrational part follows the fragility-independent Lindemann criterion; the fragility dependence seems to stem from the relaxational part. The physical meaning of this finding is discussed. [1] T. Scopigno, G. Ruocco, F. Sette and G. Monaco, Science 302, 849 (2003)Comment: 4 pages, 2 figures, 2 tables, 33 references. Slightly changed after refereein

A wavelet based numerical method for nonlinear partial differential equations

The purpose of this paper is to present a wavelet–Galerkin scheme for solving nonlinear elliptic partial differential equations. We select as trial spaces a nested sequence of spaces from an appropriate biorthogonal multiscale analysis. This gives rise to a nonlinear discretized system. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets to obtain knot oriented quadrature rules. Finally, Newton’s method is applied to approximate the solution in the given ansatz space. The results of some numerical experiments with different biorthogonal systems, confirming the applicability of our scheme, are presented.Instituto de Cooperação Científica e Tecnológica Internacional - Acções Integradas Luso-Alemãs (DAAD/ICCTI) - Projecto DAAD/ICCTI nº 01141

Objective measures of rollator user stability and device loading during different walking scenarios

Walking aids are widely used by older adults, however, alarmingly, their use has been linked to increased falls-risk, yet clinicians have no objective way of assessing user stability. This work aims to demonstrate the application of a novel methodology to investigate how the type of walking task, the amount of body weight supported by the device (i.e., device loading), and task performance strategy affect stability of rollator users. In this context, ten users performed six walking tasks with an instrumented rollator. The combined stability margin “SM” was calculated, which considers user and rollator as a combined system. A Friedman Test was used to investigate the effects of task on SM and a least-squares regression model was applied to investigate the relationship between device loading and SM. In addition, the effects of task performance strategy on SM were explored. As a result, it was found that: the minimum SM for straight line walking was higher than for more complex tasks (p<0.05); an increase in device loading was associated with an increase in SM (p<0.05); stepping up a kerb with at least 1 rollator wheel in ground contact at all times resulted in higher SM than lifting all four wheels simultaneously. Hence, we conclude that training should not be limited to straight line walking but should include various everyday tasks. Within person, SM informs on which tasks need practicing, and which strategy facilitates stability, thereby enabling person-specific guidance/training. The relevance of this work lies in an increase in walking aid users, and the costs arising from fall-related injuries. Supplementary data is available in Figshare

Status and Plans for the Array Control and Data Acquisition System of the Cherenkov Telescope Array

The Cherenkov Telescope Array (CTA) is the next-generation atmospheric Cherenkov gamma-ray observatory. CTA will consist of two installations, one in the northern, and the other in the southern hemisphere, containing tens of telescopes of different sizes. The CTA performance requirements and the inherent complexity associated with the operation, control and monitoring of such a large distributed multi-telescope array leads to new challenges in the field of the gamma-ray astronomy. The ACTL (array control and data acquisition) system will consist of the hardware and software that is necessary to control and monitor the CTA arrays, as well as to time-stamp, read-out, filter and store -at aggregated rates of few GB/s- the scientific data. The ACTL system must be flexible enough to permit the simultaneous automatic operation of multiple sub-arrays of telescopes with a minimum personnel effort on site. One of the challenges of the system is to provide a reliable integration of the control of a large and heterogeneous set of devices. Moreover, the system is required to be ready to adapt the observation schedule, on timescales of a few tens of seconds, to account for changing environmental conditions or to prioritize incoming scientific alerts from time-critical transient phenomena such as gamma ray bursts. This contribution provides a summary of the main design choices and plans for building the ACTL system.Comment: In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherlands. All CTA contributions at arXiv:1508.0589

Parasitic chytrids could promote copepod survival by mediating material transfer from inedible diatoms

Diatoms form large spring blooms in lakes and oceans, providing fuel for higher trophic levels at the start of the growing season. Some of the diatom blooms, however, are not grazed by filter-feeding zooplankton like Daphnia due to their large size. Several of these large diatoms are susceptible to chytrid infections. Zoospores of chytrids appeared to be excellent food for Daphnia, both in terms of size, shape, and quality (PUFAs and cholesterol). Thus, zoospores of chytrids can bridge the gap between inedible diatoms and Daphnia. In order to examine the effects of diatoms and chytrids on the survival of copepods, we performed one grazing and one survival experiment. The grazing experiment revealed that the diatom, Asterionella formosa, was not grazed by the copepod, Eudiaptomus gracilis, even after being infected by the chytrid Zygorhizidium planktonicum. However, carbon and nitrogen concentrations were significantly reduced by E. gracilis only when A. formosa was infected by Z. planktonicum, indicating that the chytrids might facilitate material transfer from inedible diatoms to the copepods. The survival experiment revealed that E. gracilis lived shorter with A. formosa than with the cryptophyta Cryptomonas pyrenoidifera. However, the survival of E. gracilis increased significantly in the treatment where A. formosa cells were infected by Z. planktonicum. Since E. gracilis could not graze A. formosa cells due to their large colonial forms, E. gracilis may acquire nutrients by grazing on the zoospores, and were so able to survive in the presence of the A. formosa. This provides new insights into the role of parasitic fungi in aquatic food webs, where chytrids may improve copepod survival during diatom blooms.