Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

FISH mapping of 10 canine BAC clones harbouring genes and microsatellites in the arctic fox and the Chinese raccoon dog genomes

Cytogenetic mapping of the arctic fox and the Chinese raccoon dog were performed using a set of canine probes derived from the Bacterial Artificial Chromosome (BAC) library. Altogether, 10 BAC clones containing sequences of selected genes (PAX3, HBB, ATP2A2, TECTA, PIT1, ABCA4, ESR2, TPH1, HTR2A, MAOA) and microsatellites were mapped by fluorescence in situ hybridization (FISH) experiments to chromosomes of the canids studied. At present, the cytogenetic map on the arctic fox and Chinese raccoon dog consists of 45 loci each. Chromosomal localization of the BAC clones was in agreement with data obtained by earlier independent comparative chromosome painting. However, two events of telomere-to-centromere inversions were tentatively identified while compared with assignments in the dog karyotype.

Mapping H5N1 highly pathogenic avian influenza risk in Southeast Asia

The highly pathogenic avian influenza (HPAI) H5N1 virus that emerged in southern China in the mid-1990s has in recent years evolved into the first HPAI panzootic. In many countries where the virus was detected, the virus was successfully controlled, whereas other countries face periodic reoccurrence despite significant control efforts. A central question is to understand the factors favoring the continuing reoccurrence of the virus. The abundance of domestic ducks, in particular free-grazing ducks feeding in intensive rice cropping areas, has been identified as one such risk factor based on separate studies carried out in Thailand and Vietnam. In addition, recent extensive progress was made in the spatial prediction of rice cropping intensity obtained through satellite imagery processing. This article analyses the statistical association between the recorded HPAI H5N1 virus presence and a set of five key environmental variables comprising elevation, human population, chicken numbers, duck numbers, and rice cropping intensity for three synchronous epidemic waves in Thailand and Vietnam. A consistent pattern emerges suggesting risk to be associated with duck abundance, human population, and rice cropping intensity in contrast to a relatively low association with chicken numbers. A statistical risk model based on the second epidemic wave data in Thailand is found to maintain its predictive power when extrapolated to Vietnam, which supports its application to other countries with similar agro-ecological conditions such as Laos or Cambodia. The model’s potential application to mapping HPAI H5N1 disease risk in Indonesia is discussed.

High-precision confocal reflection measurement for two dimensional refractive index mapping of optical fibers

We introduce a new fiber-optical approach for reflection based refractive index mapping. Our approach leads to improved stability and reliability over existing free-space confocal instruments and significantly cuts alignment efforts and reduces the number of components needed. Other than properly cleaved fiber end-faces, this setup requires no additional sample preparation. The instrument is calibrated by means of a set of samples with known refractive indices. The index steps of commercially available fibers are measured accurately down to < 10⁻³. The precision limit of the instrument is currently of the order of 10⁻⁴.

Mapping Emotion Terms into Affective Space: Further Evidence for a Four-Dimensional Structure

Recent empirical work on the semantics of emotion terms across many different cultures and languages, using a theoretical componential approach, suggested that four dimensions are needed to parsimoniously describe the semantic space of the emotion domain as reflected in emotion terms (Fontaine, Scherer, Roesch, & Ellsworth, 2007; Fontaine, Scherer, & Soriano, 2013). In addition to valence, power, and arousal, a novelty dimension was discovered that mostly differentiated surprise from other emotions. Here, we further explore the existence and nature of the fourth dimension in semantic emotion space using a much larger and much more representative set of emotion terms. A group of 156 participants each rated 10 out of a set of 80 French emotion terms with respect to semantic meaning. The meaning of an emotion term was evaluated with respect to 68 emotion features representing the appraisal, action tendency, bodily reaction, expression, and feeling components of the emotion process. A principal component analysis confirmed the four-dimensional valence, power, arousal, and novelty structure. Moreover, this larger and much more representative set of emotion terms revealed that the novelty dimension not only differentiates surprise terms from other emotion terms, but also identifies substantial variation within the fear and joy emotion families.