Short proofs of the Kneser-Lovász coloring principle

We prove that propositional translations of the Kneser–Lovász theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs for all fixed values of k. We present a new counting-based combinatorial proof of the K neser–Lovász theorem based on the Hilton–Milner theorem; this avoids the topological arguments of prior proofs for all but finitely many base cases. We introduce new “truncated Tucker lemma” principles, which are miniaturizations of the octahedral Tucker lemma. The truncated Tucker lemma implies the Kneser–Lovász theorem. We show that the k=1 case of the truncated Tucker lemma has polynomial size extended Frege proofs.Peer ReviewedPostprint (author's final draft

First Study of Combined Blazar Light Curves with FACT and HAWC

For studying variable sources like blazars, it is crucial to achieve unbiased monitoring, either with dedicated telescopes in pointing mode or survey instruments. At TeV energies, the High Altitude Water Cherenkov (HAWC) observatory monitors approximately two thirds of the sky every day. It uses the water Cherenkov technique, which provides an excellent duty cycle independent of weather and season. The First G-APD Cherenkov Telescope (FACT) monitors a small sample of sources with better sensitivity, using the imaging air Cherenkov technique. Thanks to its camera with silicon-based photosensors, FACT features an excellent detector performance and stability and extends its observations to times with strong moonlight, increasing the duty cycle compared to other imaging air Cherenkov telescopes. As FACT and HAWC have overlapping energy ranges, a joint study can exploit the longer daily coverage given that the observatories' locations are offset by 5.3 hours. Furthermore, the better sensitivity of FACT adds a finer resolution of features on hour-long time scales, while the continuous duty cycle of HAWC ensures evenly sampled long-term coverage. Thus, the two instruments complement each other to provide a more complete picture of blazar variability. In this presentation, the first joint study of light curves from the two instruments will be shown, correlating long-term measurements with daily sampling between air and water Cherenkov telescopes. The presented results focus on the study of the variability of the bright blazars Mrk 421 and Mrk 501 during the last two years featuring various flaring activities.Comment: 6 pages, 2 figures. Contribution to the 6th International Symposium on High Energy Gamma-Ray Astronomy (Gamma2016), Heidelberg, Germany. To be published in the AIP Conference Proceeding

Terrestrial mammal three-dimensional photogrammetry : multispecies mass estimation

Assessing body mass in mammals is of importance as it influences virtually all aspects of mammal physiology, behavior and ecological parameters. However, the assessment of body mass of large mammals is potentially dangerous and logistically challenging. Photogrammetry (measurements through the use of photographs) is a well-established science. In zoology it has been used with varying success to estimate the size and mass of some marine and terrestrial mammal species. However, photogrammetric body mass estimation of terrestrial mammals has received comparatively little attention. This is largely due to species’ variable morphological attributes which complicates measurement especially if, for 3D orientation, photogrammetric models are dependent on identifiable features on the animals themselves. Ninety-two individuals belonging to 16 terrestrial mammalian species were weighed and photographed for body mass estimation using a volumetric photogrammetry method, purposely applied with commercially available software. This method is not dependent on identifiable body features for 3D orientation. Measured body mass ranged from 25 kg to 4060 kg. Photogrammetric mass estimates versus physically weighed mass was plotted and the goodness of fit assessed for each species. Body size, shape and physiological attributes influence the accuracy of body mass estimation between species (although consistent within species), largely attributed to morphological features (e.g., hair length and posture). This photogrammetric method accurately estimated the body mass of several terrestrial mammal species. It represents innovative use of photographs to create calibrated three-dimensional imagery for accurate quantification of mammalian metrics, specifically body volume and mass. Advances of a method that is not subject to species, sex or age is advantageous and suitable for wide application in our effort to model population demography.The Department of Science and Technology via the National Research Foundation (NRF) and the University of Pretoria.http://www.esajournals.orgam2016Mammal Research Institut