Birch and Tverberg partitions are closely related concepts from discrete geometry. We show two properties for the number of Birch partitions: Evenness, and a lower bound. This implies the first non-trivial lower bound for the number of Tverberg partitions that holds for arbitrary q, where q is the number of partition blocks. The proofs are based on direct arguments, and do not use the equivaria...

If a1, a2, . . . , ak and n are positive integers such that n = a1+a2+· · ·+ak, then the sum a1 + a2 + · · ·+ ak is said to be a partition of n of length k, and a1, a2, . . . , ak are said to be the parts of the partition. Two partitions that differ only in the order of their parts are considered to be the same partition. Let Pn be the set of partitions of n, and let Pn,k be the set of partitio...

In 2009, Blagojević, Matschke & Ziegler established the first tight colored Tverberg theorem. We develop a colored version of our previous results (2008): Evenness and non-trivial lower bounds for the number of colored Tverberg partitions. Both properties follow from similar results on the number of colored Birch partitions.

The Dermatophyte Test Strip visualizes mycotic antigens by immunochromatography. It allows easy and fast detection of dermatophytes. A multicenter, single-arm, comparative clinical study was designed to evaluate the capacity of Dermatophyte Test Strip to detect dermatophytes in suspected tinea unguium specimens in comparison with direct microscopy and polymerase chain reaction (PCR). Signed con...

In this article we extend our previous work on the topic of ALS strip adjustment without GNSS/IMU trajectory data. Between overlapping strip pairs the relative orientation as a 3D affine transformation is estimated by a 3D LSM approach, which uses interpolated 2.5D grid surface models of the strips and the entire strip overlap as one big LSM window. The LSM derived relative orientations of all ...

BACKGROUND The standardized protocol for performing the strip patch test has proven to be valid, but evidence on its reliability is still missing. OBJECTIVE To estimate the parallel-test reliability of the strip patch test as compared with the conventional patch test. METHODS In this multicentre, prospective, randomized, investigator-blinded reliability study, 132 subjects were enrolled. Si...

Distance sampling is a technique for estimating the abundance of animals or other objects in a region, allowing for imperfect detection. This paper evaluates the statistical efficiency of the method when its assumptions are met, both theoretically and by simulation. The theoretical component of the paper is a derivation of the asymptotic variance penalty for the distance sampling estimator aris...

Conservation tillage has significant potential as a water management tool for cotton production on sandy, drought-prone soils. Plant residue remaining at the soil surface from prior crops serves as a vapor barrier against water loss, reduces raindrop impact energy, slows surface runoff, and often increases infiltration. By increasing infiltration, the potential for greater plant-available water...

A total of 206 urine samples collected from Hassoba Elementary schoolchildren, Afar, Ethiopia, a low Schistosoma haematobium endemic setting, was diagnosed to evaluate the performance of CCA strip using double references, urine filtration technique and urinalysis dipstick (Combur 1.0 Test) that detect schistosome eggs and blood in urine, respectively. The former was used as a gold standard refe...