Good covers are algorithmically unrecognizable

A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are algorithmically unrecognizable. More precisely, the intersection pattern of a good cover can be stored in a simplicial complex called nerve which records which subfamilies of the good cover intersect. A simplicial complex is topologically d-representable if it is isomorphic to the nerve of a good cover in R^d. We prove that it is algorithmically undecidable whether a given simplicial complex is topologically d-representable for any fixed d \geq 5. The result remains also valid if we replace good covers with acyclic covers or with covers by open d-balls. As an auxiliary result we prove that if a simplicial complex is PL embeddable into R^d, then it is topologically d-representable. We also supply this result with showing that if a "sufficiently fine" subdivision of a k-dimensional complex is d-representable and k \leq (2d-3)/3, then the complex is PL embeddable into R^d.Comment: 22 pages, 5 figures; result extended also to acyclic covers in version

Cutting the same fraction of several measures

We study some measure partition problems: Cut the same positive fraction of $d+1$ measures in $\mathbb R^d$ with a hyperplane or find a convex subset of $\mathbb R^d$ on which $d+1$ given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions.Comment: 7 pages 2 figure

Complex flow in the nasal region of guitarfishes

Scent detection in an aquatic environment is dependent on the movement of water. We set out to determine the mechanisms for moving water through the olfactory organ of guitarfishes (Rhinobatidae, Chondrichthyes) with open nasal cavities. We found at least two. In the first mechanism, which we identified by observing dye movement in the nasal region of a life-sized physical model of the head of Rhinobatos lentiginosus mounted in a flume, olfactory flow is generated by the guitarfish's motion relative to water, e.g. when it swims. We suggest that the pressure difference responsible for motion-driven olfactory flow is caused by the guitarfish's nasal flaps, which create a region of high pressure at the incurrent nostril, and a region of low pressure in and behind the nasal cavity. Vortical structures in the nasal region associated with motion-driven flow may encourage passage of water through the nasal cavity and its sensory channels, and may also reduce the cost of swimming. The arrangement of vortical structures is reminiscent of aircraft wing vortices. In the second mechanism, which we identified by observing dye movement in the nasal regions of living specimens of Glaucostegus typus, the guitarfish's respiratory pump draws flow through the olfactory organ in a rhythmic (0.5-2 Hz), but continuous, fashion. Consequently, the respiratory pump will maintain olfactory flow whether the guitarfish is swimming or at rest. Based on our results, we propose a model for olfactory flow in guitarfishes with open nasal cavities, and suggest other neoselachians which this model might apply to

Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

Geometry and topology of the quasi-plane Szekeres model

This paper is a revised version of arXiv:0805.0529 and Phys.Rev. D78, 064038 (2008), taking into account the erratum published in Phys.Rev. D85, 069903(E) (2012). Geometrical and topological properties of the quasi-plane Szekeres model and of the plane symmetric dust model are discussed. Some related comments on the quasi-hyperbolical model are made. These properties include: (1) The pattern of expansion in the plane symmetric case, and the Newtonian model that imitates it; (2) The possibility of toroidal topology of the $t =$ const sections in the plane symmetric model; (3) The absence of apparent horizons in the quasi-plane and quasi-hyperbolic models (they are globally trapped); (4) Description of the toroidal topology in the Szekeres coordinates; (5) Interpretation of the mass function in the quasi-plane model.Comment: 14 pages, 6 figures; old sections 8, 10 and 11 removed, the remaining ones re-edited for consistency. This is a corrected version that takes into account the erratum published in Phys.Rev. D85, 069903(E) (2012

Motion-driven flow in an unusual piscine nasal region

Fishes have several means of moving water to effect odorant transport to their olfactory epithelium (‘olfactory flow’). Here we show that olfactory flow in the adult garpike Belone belone (Belonidae, Teleostei), a fish with an unusual nasal region, can be generated by its motion relative to water (swimming, or an external current, or both). We also show how the unusual features of the garpike’s nasal region influence olfactory flow. These features comprise a triangular nasal cavity in which the olfactory epithelium is exposed to the external environment, a papilla situated within the nasal cavity, and an elongated ventral apex. To perform our investigation we first generated life-like plastic models of garpike heads from X-ray scans of preserved specimens. We then suspended these models in a flume and flowed water over them to simulate swimming. By directing filaments of dye at the static models, we were able to visualise flow in the nasal regions at physiologically relevant Reynolds numbers (700–2,000). We found that flow of water over the heads did cause circulation in the nasal cavity. Vortices may assist in this circulation. The pattern of olfactory flow was influenced by morphological variations and the asymmetry of the nasal region. The unusual features of the nasal region may improve odorant sampling in the garpike, by dispersing flow over the olfactory epithelium and by creating favourable conditions for odorant transport (e.g. steep velocity gradients). Unexpectedly, we found that the mouth and the base of the garpike’s jaws may assist the sampling process. Thus, despite its apparent simplicity, the garpike’s nasal region is likely to act as an effective trap for odorant molecules

Technical Design Report for the PANDA Solenoid and Dipole Spectrometer Magnets

This document is the Technical Design Report covering the two large spectrometer magnets of the PANDA detector set-up. It shows the conceptual design of the magnets and their anticipated performance. It precedes the tender and procurement of the magnets and, hence, is subject to possible modifications arising during this process.Comment: 10 pages, 14MB, accepted by FAIR STI in May 2009, editors: Inti Lehmann (chair), Andrea Bersani, Yuri Lobanov, Jost Luehning, Jerzy Smyrski, Technical Coordiantor: Lars Schmitt, Bernd Lewandowski (deputy), Spokespersons: Ulrich Wiedner, Paola Gianotti (deputy

Characterization of the genetic diversity of Mycobacterium tuberculosis in São Paulo city, Brazil

<p>Abstract</p> <p>Background</p> <p>Tuberculosis is a major health problem in São Paulo, Brazil, which is the most populous and one of the most cosmopolitan cities in South America. To characterize the genetic diversity of <it>Mycobacterium tuberculosis </it>in the population of this city, the genotyping techniques of spoligotyping and MIRU were applied to 93 isolates collected in two consecutive years from 93 different tuberculosis patients residing in São Paulo city and attending the Clemente Ferreira Institute (the reference clinic for the treatment of tuberculosis).</p> <p>Findings</p> <p>Spoligotyping generated 53 different spoligotype patterns. Fifty-one isolates (54.8%) were grouped into 13 spoligotyping clusters. Seventy- two strains (77.4%) showed spoligotypes described in the international databases (SpolDB4, SITVIT), and 21 (22.6%) showed unidentified patterns. The most frequent spoligotype families were Latin American Mediterranean (LAM) (26 isolates), followed by the T family (24 isolates) and Haarlem (H) (11 isolates), which together accounted for 65.4% of all the isolates. These three families represent the major genotypes found in Africa, Central America, South America and Europe. Six Spoligo-International-types (designated SITs by the database) comprised 51.8% (37/72) of all the identified spoligotypes (SIT53, SIT50, SIT42, SIT60, SIT17 and SIT1). Other SITs found in this study indicated the great genetic diversity of <it>M. tuberculosis</it>, reflecting the remarkable ethnic diversity of São Paulo city inhabitants. The MIRU technique was more discriminatory and did not identify any genetic clusters with 100% similarity among the 93 isolates. The allelic analysis showed that MIRU loci 26, 40, 23 and 10 were the most discriminatory. When MIRU and spoligotyping techniques were combined, all isolates grouped in the 13 spoligotyping clusters were separated.</p> <p>Conclusions</p> <p>Our data indicated the genomic stability of over 50% of spoligotypes identified in São Paulo and the great genetic diversity of <it>M. tuberculosis </it>isolates in the remaining SITs, reflecting the large ethnic mix of the São Paulo city inhabitants. The results also indicated that in this city, <it>M. tuberculosis </it>isolates acquired drug resistance independently of genotype and that resistance was more dependent on the selective pressure of treatment failure and the environmental circumstances of patients.</p