Minimum Cell Connection in Line Segment Arrangements

We study the complexity of the following cell connection problems in segment arrangements. Given a set of straight-line segments in the plane and two points a and b in different cells of the induced arrangement: [(i)] compute the minimum number of segments one needs to remove so that there is a path connecting a to b that does not intersect any of the remaining segments; [(ii)] compute the minimum number of segments one needs to remove so that the arrangement induced by the remaining segments has a single cell. We show that problems (i) and (ii) are NP-hard and discuss some special, tractable cases. Most notably, we provide a near-linear-time algorithm for a variant of problem (i) where the path connecting a to b must stay inside a given polygon P with a constant number of holes, the segments are contained in P, and the endpoints of the segments are on the boundary of P. The approach for this latter result uses homotopy of paths to group the segments into clusters with the property that either all segments in a cluster or none participate in an optimal solution

Shape reconstruction from gradient data

We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages, including high information efficiency, sensitivity, and robustness. For many applications, however, it is necessary to acquire the shape, which must be calculated from the slopes by numerical integration. Existing integration techniques show drawbacks that render them unusable in many cases. Our method is based on approximation employing radial basis functions. It can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.Comment: 16 pages, 5 figures, zip-file, submitted to Applied Optic

Euclidean TSP with few inner points in linear space

Given a set of $n$ points in the Euclidean plane, such that just $k$ points are strictly inside the convex hull of the whole set, we want to find the shortest tour visiting every point. The fastest known algorithm for the version when $k$ is significantly smaller than $n$, i.e., when there are just few inner points, works in $O(k^{11\sqrt{k}} k^{1.5} n^{3})$ time [Knauer and Spillner, WG 2006], but also requires space of order $k^{c\sqrt{k}}n^{2}$. The best linear space algorithm takes $O(k! k n)$ time [Deineko, Hoffmann, Okamoto, Woeginer, Oper. Res. Lett. 34(1), 106-110]. We construct a linear space $O(nk^2+k^{O(\sqrt{k})})$ time algorithm. The new insight is extending the known divide-and-conquer method based on planar separators with a matching-based argument to shrink the instance in every recursive call. This argument also shows that the problem admits a quadratic bikernel.Comment: under submissio

Microdeflectometry - a novel tool to acquire 3D microtopography with nanometer height resolution

We introduce "microdeflectometry", a novel technique for measuring the microtopography of specular surfaces. The primary data is the local slope of the surface under test. Measuring the slope instead of the height implies high information efficiency and extreme sensitivity to local shape irregularities. The lateral resolution can be better than one micron whereas the resulting height resolution is in the range of one nanometer. Microdeflectometry can be supplemented by methods to expand the depth of field, with the potential to provide quantitative 3D imaging with SEM-like features.Comment: 3 pages, 11 figures, latex, zip-file, accepted for publication at Optics Letter

Minimum cell connection in line segment arrangements

We study the complexity of the following cell connection problems in segment arrangements. Given a set of straight-line segments in the plane and two points a and b in different cells of the induced arrangement: (i) compute the minimum number of segments one needs to remove so that there is a path connecting a to b that does not intersect any of the remaining segments; (ii) compute the minimum number of segments one needs to remove so that the arrangement induced by the remaining segments has a single cell. We show that problems (i) and (ii) are NP-hard and discuss some special, tractable cases. Most notably, we provide a near-linear-time algorithm for a variant of problem (i) where the path connecting a to b must stay inside a given polygon P with a constant number of holes, the segments are contained in P, and the endpoints of the segments are on the boundary of P. The approach for this latter result uses homotopy of paths to group the segments into clusters with the property that either all segments in a cluster or none participate in an optimal solution

First estimation of Eurasian lynx (Lynx lynx) abundance and density using digital cameras and capture–recapture techniques in a German national park

Primera estima de la abundancia y de la densidad del lince euroasiático (Lynx lynx) utilizando cámaras digitales y técnicas de captura–recaptura en un parque nacional alemán Al lince euroasiático se le puede identificar individualmente mediante las marcas de su pelaje, que son únicas, lo que le convierte en un candidato ideal para los estudios de captura–recaptura (CMR). Hemos evaluado el uso de la fotografía digital para estimar la abundancia y la densidad de la población del lince euroasiático en el Parque Nacional Forestal Bávaro. Desde noviembre del 2008 a enero del 2009 establecimos 24 lugares de trampeo, cada uno de ellos provisto de dos cámaras encaradas entre sí, en lugares de paso frecuentados. Colocamos las unidades basándonos en una cuadrícula sistemática de 2,7 km. Capturamos cinco linces independientes y tres jóvenes, y calculamos las estimas de abundancia utilizando el programa Mark. También comparamos las estimas de densidad mediante el método MMDM (distancia media máxima recorrida) de datos telemétricos (½MMDMGPS) y de datos de las cámaras trampa (½MMDMCAM). Hallamos que en un área muestreada eficazmente de 664 km2 la densidad del lince euroasiático era de 0,9 individuos/100 km2 mediante ½MMDMCAM. La densidad del lince euroasiático calculada mediante el método ½MMDMGPS fue de 0,4 individuos/100 km2 en una zona muestreada eficazmente de 1.381 km2. Nuestros resultados sugieren que un muestreo fotográfico CMR a largo plazo y a gran escala puede ser una herramienta muy útil para monitorizar las tendencias poblacionales del lince euroasiático, según la Directiva de Hábitat, Flora y Fauna de la Unión Europea.Primera estima de la abundancia y de la densidad del lince euroasiático (Lynx lynx) utilizando cámaras digitales y técnicas de captura–recaptura en un parque nacional alemán Al lince euroasiático se le puede identificar individualmente mediante las marcas de su pelaje, que son únicas, lo que le convierte en un candidato ideal para los estudios de captura–recaptura (CMR). Hemos evaluado el uso de la fotografía digital para estimar la abundancia y la densidad de la población del lince euroasiático en el Parque Nacional Forestal Bávaro. Desde noviembre del 2008 a enero del 2009 establecimos 24 lugares de trampeo, cada uno de ellos provisto de dos cámaras encaradas entre sí, en lugares de paso frecuentados. Colocamos las unidades basándonos en una cuadrícula sistemática de 2,7 km. Capturamos cinco linces independientes y tres jóvenes, y calculamos las estimas de abundancia utilizando el programa Mark. También comparamos las estimas de densidad mediante el método MMDM (distancia media máxima recorrida) de datos telemétricos (½MMDMGPS) y de datos de las cámaras trampa (½MMDMCAM). Hallamos que en un área muestreada eficazmente de 664 km2 la densidad del lince euroasiático era de 0,9 individuos/100 km2 mediante ½MMDMCAM. La densidad del lince euroasiático calculada mediante el método ½MMDMGPS fue de 0,4 individuos/100 km2 en una zona muestreada eficazmente de 1.381 km2. Nuestros resultados sugieren que un muestreo fotográfico CMR a largo plazo y a gran escala puede ser una herramienta muy útil para monitorizar las tendencias poblacionales del lince euroasiático, según la Directiva de Hábitat, Flora y Fauna de la Unión Europea.ABC_35-2_2012 First estimation of Eurasian lynx (Lynx lynx) abundance and density using digital cameras and capture–recapture techniques in a German national park Weingarth, K., Heibl, C., Knauer, F., Zimmermann, F., Bufka, L., Heurich, M. Abstract Eurasian lynx are individually identifiable by their unique coat markings, making them ideal candidates for capture–recapture (CMR) surveys. We evaluated the use of digital photography to estimate Eurasian lynx population abundance and density within the Bavarian Forest National Park. From November 2008 to January 2009 we placed 24 camera trap sites, each with two cameras facing each other on well–used walking tracks). The units were placed based on a systematic grid of 2.7 km. We captured five independent and three juvenile lynx and calculated abundance estimates using Program Mark. We also compared density estimates based on the MMDM method (Mean Maximum Distance Moved) from telemetry data (½MMDMGPS) and from camera trapping data (½MMDMCAM). We estimated that in an effectively sampled area of 664 km2 the Eurasian lynx density was 0.9 individuals/100 km2 with ½MMDMCAM. The Eurasian lynx density calculated with ½MMDMGPS was 0.4 individuals/100 km2 in an effectively sampled area of 1,381 km2. Our results suggest that long–term photographic CMR sampling on a large scale may be a useful tool to monitor population trends of Eurasian lynx in accordance with the Fauna–Flora–Habitat Directive of the European Union

Hyperbolic odorant mixtures as a basis for more efficient signaling between flowering plants and bees

Animals use odors in many natural contexts, for example, for finding mates or food, or signaling danger. Most analyses of natural odors search for either the most meaningful components of a natural odor mixture, or they use linear metrics to analyze the mixture compositions. However, we have recently shown that the physical space for complex mixtures is ‘hyperbolic’, meaning that there are certain combinations of variables that have a disproportionately large impact on perception and that these variables have specific interpretations in terms of metabolic processes taking place inside the flower and fruit that produce the odors. Here we show that the statistics of odorants and odorant mixtures produced by inflorescences (Brassica rapa) are also better described with a hyperbolic rather than a linear metric, and that combinations of odorants in the hyperbolic space are better predictors of the nectar and pollen resources sought by bee pollinators than the standard Euclidian combinations. We also show that honey bee and bumble bee antennae can detect most components of the B. rapa odor space that we tested, and the strength of responses correlates with positions of odorants in the hyperbolic space. In sum, a hyperbolic representation can be used to guide investigation of how information is represented at different levels of processing in the CNS