The Stability of One-Step Schemes for First-Order Two-Point Boundary Value Problems

The stability of a finite difference scheme is related explicitly to the stability of the continuous problem being solved. At times, this gives materially better estimates for the stability constant than those obtained by the standard process of appealing to the stability of the numerical scheme for the associated initial value problem

Annual Report Ant Smelt 2010: A changing role for smelt Osmerus eperlanus in the Lake IJsselmeer and Lake Markermeer foodweb? Climate- and nutrient-induced changes in ecoystem functioning

The smelt project is part of a larger research project that aims at generating, exploring and testing different possible explanations for the observed Autonomous Negative Trends (ANT) in water fowl in Lake Markermeer and Lake IJsselmeer. The smelt populations in both lakes have been in severe decline since 1990. These declines have a large impact on the conservation of water birds relying on smelt as their prey and the fishery both on smelt and on piscivorous fish relying on smelt. In winter time the Lake IJsselmeer area is home to the largest population of waterfowl in Western Europe. The area is therefore considered to be an important Natura-2000 area. Identification of the causes of the observed negative trends will help managers (RWS) to take the appropriate restoration measures and thereby improve the these lakes as habitat for waterfowl

Instrumental polarisation at the Nasmyth focus of the E-ELT

The ~39-m European Extremely Large Telescope (E-ELT) will be the largest telescope ever built. This makes it particularly suitable for sensitive polarimetric observations, as polarimetry is a photon-starved technique. However, the telescope mirrors may severely limit the polarimetric accuracy of instruments on the Nasmyth platforms by creating instrumental polarisation and/or modifying the polarisation signal of the object. In this paper we characterise the polarisation effects of the two currently considered designs for the E-ELT Nasmyth ports as well as the effect of ageing of the mirrors. By means of the Mueller matrix formalism, we compute the response matrices of each mirror arrangement for a range of zenith angles and wavelengths. We then present two techniques to correct for these effects that require the addition of a modulating device at the polarisation-free intermediate focus that acts either as a switch or as a part of a two-stage modulator. We find that the values of instrumental polarisation, Stokes transmission reduction and cross- talk vary significantly with wavelength, and with pointing, for the lateral Nasmyth case, often exceeding the accuracy requirements for proposed polarimetric instruments. Realistic ageing effects of the mirrors after perfect calibration of these effects may cause polarimetric errors beyond the requirements. We show that the modulation approach with a polarimetric element located in the intermediate focus reduces the instrumental polarisation effects down to tolerable values, or even removes them altogether. The E-ELT will be suitable for sensitive and accurate polarimetry, provided frequent calibrations are carried out, or a dedicated polarimetric element is installed at the intermediate focus.Comment: Accepted for publication in A&

A Comparison of Techniques for Sampling Web Pages

As the World Wide Web is growing rapidly, it is getting increasingly challenging to gather representative information about it. Instead of crawling the web exhaustively one has to resort to other techniques like sampling to determine the properties of the web. A uniform random sample of the web would be useful to determine the percentage of web pages in a specific language, on a topic or in a top level domain. Unfortunately, no approach has been shown to sample the web pages in an unbiased way. Three promising web sampling algorithms are based on random walks. They each have been evaluated individually, but making a comparison on different data sets is not possible. We directly compare these algorithms in this paper. We performed three random walks on the web under the same conditions and analyzed their outcomes in detail. We discuss the strengths and the weaknesses of each algorithm and propose improvements based on experimental results

L2 regularity of measurable solutions of a finite-difference equation of the circle

We show that if $\varphi$ is a lacunary Fourier series and the equation $\psi (x) -\psi (x + \alpha) = \varphi(x), x \bmod 1$ has a measurable solution $\varphi$, then in fact the equation has a solution in L2. This work of Michel Herman (1942-2000) appeared only as a preprint of the Mathematics Institute, University of Warwick, dated May 1976. It was turned into TEX format by Claire Desescures. Minor editorial work was done by Albert Fathi

Stellar Associations and their Field East of LMC 4 in the Large Magellanic Cloud

We report about the stellar content and the luminosity and mass functions of three stellar associations and their field located on the north-east edge of the super-bubble LMC 4 in the Large Magellanic Cloud.Comment: To be appeared in the meeting Proceedings of ``Modes of Star Formation and the Origin of Field Populations'', Heidelberg, Germany, October 2000; to be published in the ASP Conference Series, edited by E. K. Grebel and W. Brandne

Observations of solar scattering polarization at high spatial resolution

The weak, turbulent magnetic fields that supposedly permeate most of the solar photosphere are difficult to observe, because the Zeeman effect is virtually blind to them. The Hanle effect, acting on the scattering polarization in suitable lines, can in principle be used as a diagnostic for these fields. However, the prediction that the majority of the weak, turbulent field resides in intergranular lanes also poses significant challenges to scattering polarization observations because high spatial resolution is usually difficult to attain. We aim to measure the difference in scattering polarization between granules and intergranules. We present the respective center-to-limb variations, which may serve as input for future models. We perform full Stokes filter polarimetry at different solar limb positions with the CN band filter of the Hinode-SOT Broadband Filter Imager, which represents the first scattering polarization observations with sufficient spatial resolution to discern the granulation. Hinode-SOT offers unprecedented spatial resolution in combination with high polarimetric sensitivity. The CN band is known to have a significant scattering polarization signal, and is sensitive to the Hanle effect. We extend the instrumental polarization calibration routine to the observing wavelength, and correct for various systematic effects. The scattering polarization for granules (i.e., regions brighter than the median intensity of non-magnetic pixels) is significantly larger than for intergranules. We derive that the intergranules (i.e., the remaining non-magnetic pixels) exhibit (9.8 \pm 3.0)% less scattering polarization for 0.2<u<0.3, although systematic effects cannot be completely excluded. These observations constrain MHD models in combination with (polarized) radiative transfer in terms of CN band line formation, radiation anisotropy, and magnetic fields.Comment: Accepted for publication in A&

A composition theorem for the Fourier Entropy-Influence conjecture

The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai [FK96] seeks to relate two fundamental measures of Boolean function complexity: it states that $H[f] \leq C Inf[f]$ holds for every Boolean function $f$, where $H[f]$ denotes the spectral entropy of $f$, $Inf[f]$ is its total influence, and $C > 0$ is a universal constant. Despite significant interest in the conjecture it has only been shown to hold for a few classes of Boolean functions. Our main result is a composition theorem for the FEI conjecture. We show that if $g_1,...,g_k$ are functions over disjoint sets of variables satisfying the conjecture, and if the Fourier transform of $F$ taken with respect to the product distribution with biases $E[g_1],...,E[g_k]$ satisfies the conjecture, then their composition $F(g_1(x^1),...,g_k(x^k))$ satisfies the conjecture. As an application we show that the FEI conjecture holds for read-once formulas over arbitrary gates of bounded arity, extending a recent result [OWZ11] which proved it for read-once decision trees. Our techniques also yield an explicit function with the largest known ratio of $C \geq 6.278$ between $H[f]$ and $Inf[f]$, improving on the previous lower bound of 4.615

Evolving Strategies, Opportunistic Implementation: HIV Risk Reduction in Tanzania in the Context of an Incentive-Based HIV Prevention Intervention.

\ud Behavior change communication (BCC) interventions, while still a necessary component of HIV prevention, have not on their own been shown to be sufficient to stem the tide of the epidemic. The shortcomings of BCC interventions are partly due to barriers arising from structural or economic constraints. Arguments are being made for combination prevention packages that include behavior change, biomedical, and structural interventions to address the complex set of risk factors that may lead to HIV infection. In 2009/2010 we conducted 216 in-depth interviews with a subset of study participants enrolled in the RESPECT study - an HIV prevention trial in Tanzania that used cash awards to incentivize safer sexual behaviors. We analyzed community diaries to understand how the study was perceived in the community. We drew on these data to enhance our understanding of how the intervention influenced strategies for risk reduction. We found that certain situations provide increased leverage for sexual negotiation, and these situations facilitated opportunistic implementation of risk reduction strategies. Opportunities enabled by the RESPECT intervention included leveraging conditional cash awards, but participants also emphasized the importance of exploiting new health status knowledge from regular STI testing. Risk reduction strategies included condom use within partnerships and/or with other partners, and an unexpected emphasis on temporary abstinence. Our results highlight the importance of increasing opportunities for implementing risk reduction strategies. We found that an incentive-based intervention could be effective in part by creating such opportunities, particularly among groups such as women with limited sexual agency. The results provide new evidence that expanding regular testing of STIs is another important mechanism for providing opportunities for negotiating behavior change, beyond the direct benefits of testing. Exploiting the latent demand for STI testing should receive renewed attention as part of innovative new combination interventions for HIV prevention.\u