Theory and practice of microlensing lightcurves around fold singularities

Among all galactic microlensing events, those involving a passage of the observed source star over the caustic created by a binary lens are particularly useful in providing information about stellar atmospheres, the dynamics of stellar populations in our own and neighbouring galaxies, and the statistical properties of stellar and sub-stellar binaries. This paper presents a comprehensive guide for modelling and interpreting the lightcurves obtained in events involving fold-caustic crossings. A new general, consistent, and optimal choice of parameters provides a deep understanding of the involved features, avoids numerical difficulties and minimizes correlations between model parameters. While the photometric data of a microlensing event around a caustic crossing itself do not provide constraints on the characteristics of the underlying binary lens and does not allow predictions of the behaviour of other regions of the lightcurve, vital constraints can be obtained in an efficient way if these are combined with a few simple characteristics of data outside the caustic crossings. A corresponding algorithm containing some improvements over an earlier approach which takes into account multi-site observations is presented and discussed in detail together with the arising parameter constraints paying special attention to the role of source and background fluxes.Comment: 19 pages with 7 EPS figures embedded, LaTeX2e using mn2e.cls. Final version, tables clarifying meaning and constraints on parameters added. This is a preprint of an Article accepted for publication in Monthly Notices of the Royal Astronomical Society, (C) 2004 The Royal Astronomical Societ

Shadow Economies Around the World - Size, Causes, and Consequences

Using various methods (currency demand, physical input (electricity) method, model approach), which are discussed and criticized, estimates of the size of the shadow economy in 76 developing, transition and OECD-countries are presented. The average size of a shadow economy varies from 12 percent of GDP for OECD, to 23 percent for transition and to 39 percent for developing countries. An increasing burden of taxation and social security contributions combined with rising state regulatory activities are the drivin g forces for the increase of the shadow economy especially in OECD-countries. According to some findings, a growing shadow economy has a negative effect on official GDP growth, and a positive impact of corruption on the size of the shadow economy can be found.

Angular Radii of Stars via Microlensing

We outline a method by which the angular radii of giant and main sequence stars in the Galactic bulge can be measured to a few percent accuracy. The method combines ground-based photometry of caustic-crossing bulge microlensing events, with a handful of precise astrometric measurements of the lensed star during the event, to measure the angular radius of the source, theta_*. Dense photometric coverage of one caustic crossing yields the crossing timescale dt. Less frequent coverage of the entire event yields the Einstein timescale t_E and the angle phi of source trajectory with respect to the caustic. The photometric light curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale. A few precise astrometric measurements therefore yield theta_E, the angular Einstein ring radius. Then the angular radius of the source is obtained by theta_*=theta_E(dt/t_E) sin(phi). We argue that theta_* should be measurable to a few percent accuracy for Galactic bulge giant stars using ground-based photometry from a network of small (1m-class) telescopes, combined with astrometric observations with a precision of ~10 microarcsec to measure theta_E. We find that a factor of ~50 times fewer photons are required to measure theta_E to a given precision for binary-lens events than single-lens events. Adopting parameters appropriate to the Space Interferometry Mission (SIM), ~7 min of SIM time is required to measure theta_E to ~5% accuracy for giant sources in the bulge. For main-sequence sources, theta_E can be measured to ~15% accuracy in ~1.4 hours. With 10 hrs of SIM time, it should be possible to measure theta_* to ~5% for \~80 giant stars, or to 15% for ~7 main sequence stars. A byproduct of such a campaign is a significant sample of precise binary-lens mass measurements.Comment: 13 pages, 3 figures. Revised version, minor changes, required SIM integration times revised upward by ~60%. Accepted to ApJ, to appear in the March 20, 2003 issue (v586

Superluminal Caustics of Close, Rapidly-Rotating Binary Microlenses

The two outer triangular caustics (regions of infinite magnification) of a close binary microlens move much faster than the components of the binary themselves, and can even exceed the speed of light. When $\epsilon > 1$, where $\epsilon c$ is the caustic speed, the usual formalism for calculating the lens magnification breaks down. We develop a new formalism that makes use of the gravitational analog of the Li\'enard-Wiechert potential. We find that as the binary speeds up, the caustics undergo several related changes: First, their position in space drifts. Second, they rotate about their own axes so that they no longer have a cusp facing the binary center of mass. Third, they grow larger and dramatically so for $\epsilon >> 1$. Fourth, they grow weaker roughly in proportion to their increasing size. Superluminal caustic-crossing events are probably not uncommon, but they are difficult to observe.Comment: 12 pages, 7 ps figures, submitted to Ap

Visual Integration of Data and Model Space in Ensemble Learning

Ensembles of classifier models typically deliver superior performance and can outperform single classifier models given a dataset and classification task at hand. However, the gain in performance comes together with the lack in comprehensibility, posing a challenge to understand how each model affects the classification outputs and where the errors come from. We propose a tight visual integration of the data and the model space for exploring and combining classifier models. We introduce a workflow that builds upon the visual integration and enables the effective exploration of classification outputs and models. We then present a use case in which we start with an ensemble automatically selected by a standard ensemble selection algorithm, and show how we can manipulate models and alternative combinations.Comment: 8 pages, 7 picture

Can microlensing fold caustics reveal a second stellar limb-darkening coefficient?

Dense high-precision photometry of microlensed stars during a fold-caustic passage can be used to reveal their intensity profiles from which the temperature of the stellar atmosphere as function of fractional radius can be derived. While the capabilities of current microlensing follow-up campaigns such as PLANET allow a precise measurement of linear limb-darkening coefficients, the residual signal of a second coefficient characterizing square-root limb darkening is ~ 25 times smaller which prevents a proper determination except for unlikely cases of very high caustic-peak-to-outside relative magnifications with no adequate event being observed so far or for source stars passing over a cusp singularity. Although the presence of limb darkening can be well established from the data, a reliable measurement of the index of an underlying power-law cannot be obtained.Comment: 4 pages with 4 EPS figures embedded, LaTeX2e using mn2e.cls. Final version, minor changes. This is a preprint of an Article accepted for publication in Monthly Notices of the Royal Astronomical Society, (C) 2004 The Royal Astronomical Societ

Microlensing with advanced contour integration algorithm: Green's theorem to third order, error control, optimal sampling and limb darkening

Microlensing light curves are typically computed either by ray-shooting maps or by contour integration via Green's theorem. We present an improved version of the second method that includes a parabolic correction in Green's line integral. In addition, we present an accurate analytical estimate of the residual errors, which allows the implementation of an optimal strategy for the contour sampling. Finally, we give a prescription for dealing with limb-darkened sources reaching arbitrary accuracy. These optimizations lead to a substantial speed-up of contour integration codes along with a full mastery of the errors.Comment: 34 pages, 11 figure

Einflussfaktoren auf Soziale und Gesellschaftliche Lernprozesse im Wissenssystem Biolandbau

Improved organic farming methods that enable more sustainable use of natural resources are numerous and are applied in almost every region of this planet. However, when it comes to spreading and adapting these methods to specific ecological and socio-economic contexts, we know only little about what factors influence the learning processes involved. This study aims at a thorough assessment of factors that are enabling or hindering knowledge co-production in organic farming in general and of sustainable rice farming in particular. Following a qualitative multilevel analysis, special emphasis is placed on understanding how the socio-economic, cultural and ecological context is constituted (macro-level), how key stakeholder groups collaborate and enhance societal and social learning processes (meso-level), and to what degree these processes lead to enhancement and integration of organic rice farming methods in the farmers’ livelihood systems (micro-level). Case studies in South Korea and Cambodia show that capacity building and institutionalization of key actors such as farmer promoters and farmer researchers, as well as farmer group maintenance with diverse incentives for sustained participation are vital enabling factors

Exact and heuristic solution of the consistent vehicle-routing problem

Providing consistent service by satisfying customer demands with the same driver (driver consistency) at approximately the same time (arrival-time consistency) allows companies in last-mile distribution to stand out among competitors. The consistent vehicle-routing problem (ConVRP) is a multiday problem addressing such consistency requirements along with traditional constraints on vehicle capacity and route duration. The literature offers several heuristics but no exact method for this problem. The state-of-the-art exact technique to solve VRPs-column generation (CG) applied to route-based formulations in which columns are generated via dynamic programming-cannot be successfully extended to the ConVRP because the linear relaxation of route-based formulations is weak. We propose the first exact method for the ConVRP, which can solve medium-sized instances with five days and 30 customers. The method solves, via CG, a formulation in which each variable represents the set of routes assigned to a vehicle over the planning horizon. As an upper bounding procedure, we develop a large neighborhood search (LNS) featuring a repair procedure specifically designed to improve the arrival-time consistency of solutions. Used as stand-alone heuristic, the LNS is able to significantly improve the solution quality on benchmark instances from the literature compared with state-of-the-art heuristics