Normal Cones and Thompson Metric

The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the linear structure. We also prove several convexity properties of $d_T$ and some results concerning the topology of $d_T$, including a brief study of the $d_T$-convergence of monotone sequences. It is shown most of the results are true without any assumption of an Archimedean-type property for $K$. One considers various completeness properties and one studies the relations between them. Since $d_T$ is defined in the context of a generic ordered linear space, with no need of an underlying topological structure, one expects to express its completeness in terms of properties of the ordering, with respect to the linear structure. This is done in this paper and, to the best of our knowledge, this has not been done yet. The Thompson metric $d_T$ and order-unit (semi)norms $|\cdot|_u$ are strongly related and share important properties, as both are defined in terms of the ordered linear structure. Although $d_T$ and $|\cdot|_u$ are only topological (and not metrical) equivalent on $K_u$, we prove that the completeness is a common feature. One proves the completeness of the Thompson metric on a sequentially complete normal cone in a locally convex space. At the end of the paper, it is shown that, in the case of a Banach space, the normality of the cone is also necessary for the completeness of the Thompson metric.Comment: 36 page

The potential of metabarcoding plant components of Malaise trap samples to enhance knowledge of plant-insect interactions

The worldwide rapid declines in insect and plant abundance and diversity that have occurred in the past decades have gained public attention and demand for political actions to counteract these declines are growing. Rapid large-scale biomonitoring can aid in observing these changes and provide information for decisions for land management and species protection. Malaise traps have long been used for insect sampling and when insects are captured in these traps, they carry traces of plants they have visited on the body surface or as digested food material in the gut contents. Metabarcoding offers a promising method for identifying these plant traces, providing insight into the plants with which insects are directly interacting at a given time. To test the efficacy of DNA metabarcoding with these sample types, 79 samples from 21 sites across Germany were analysed with the ITS2 barcode. This study, to our knowledge, is the first examination of metabarcoding plant DNA traces from Malaise trap samples. Here, we report on the feasibility of sequencing these sample types, analysis of the resulting taxa, the usage of cultivated plants by insects near nature conservancy areas and the detection of rare and neophyte species. Due to the frequency of contamination and false positive reads, isolation and PCR negative controls should be used in every reaction. Metabarcoding has advantages in efficiency and resolution over microscopic identification of pollen and is the only possible identification method for the other plant traces from Malaise traps and could provide a broad utility for future studies of plant-insect interactions

Improving insect conservation management through insect monitoring and stakeholder involvement

In recent years, the decline of insect biodiversity and the imminent loss of provided ecosystem functions and services has received public attention and raised the demand for political action. The complex, multi-causal contributors to insect decline require a broad interdisciplinary and cross-sectoral approach that addresses ecological and social aspects to find sustainable solutions. The project Diversity of Insects in Nature protected Areas (DINA) assesses insect communities in 21 nature reserves in Germany, and considers interactions with plant diversity, pesticide exposure, spatial and climatic factors. The nature reserves border on agricultural land, to investigate impacts on insect diversity. Part of the project is to obtain scientific data from Malaise traps and their surroundings, while another part involves relevant stakeholders to identify opportunities and obstacles to insect diversity conservation. Our results indicate a positive association between insect richness and biomass. Insect richness was negatively related to the number of stationary pesticides (soil and vegetation), pesticides measured in ethanol, the amount of area in agricultural production, and precipitation. Our qualitative survey along with stakeholder interviews show that there is general support for insect conservation, while at the same time the stakeholders expressed the need for more information and data on insect biodiversity, as well as flexible policy options. We conclude that conservation management for insects in protected areas should consider a wider landscape. Local targets of conservation management will have to integrate different stakeholder perspectives. Scientifically informed stakeholder dialogues can mediate conflicts of interests, knowledge, and values to develop mutual conservation scenarios

Algebraic entropy in locally linearly compact vector spaces

We introduce algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as a natural extension of the algebraic entropy for endomorphisms of discrete vector spaces studied in Giordano Bruno and Salce (Arab J Math 1:69\u201387, 2012). We show that the main properties continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem

New Protocetid Whale from the Middle Eocene of Pakistan: Birth on Land, Precocial Development, and Sexual Dimorphism

BACKGROUND: Protocetidae are middle Eocene (49-37 Ma) archaeocete predators ancestral to later whales. They are found in marine sedimentary rocks, but retain four legs and were not yet fully aquatic. Protocetids have been interpreted as amphibious, feeding in the sea but returning to land to rest. METHODOLOGY/PRINCIPAL FINDINGS: Two adult skeletons of a new 2.6 meter long protocetid, Maiacetus inuus, are described from the early middle Eocene Habib Rahi Formation of Pakistan. M. inuus differs from contemporary archaic whales in having a fused mandibular symphysis, distinctive astragalus bones in the ankle, and a less hind-limb dominated postcranial skeleton. One adult skeleton is female and bears the skull and partial skeleton of a single large near-term fetus. The fetal skeleton is positioned for head-first delivery, which typifies land mammals but not extant whales, evidence that birth took place on land. The fetal skeleton has permanent first molars well mineralized, which indicates precocial development at birth. Precocial development, with attendant size and mobility, were as critical for survival of a neonate at the land-sea interface in the Eocene as they are today. The second adult skeleton is the most complete known for a protocetid. The vertebral column, preserved in articulation, has 7 cervicals, 13 thoracics, 6 lumbars, 4 sacrals, and 21 caudals. All four limbs are preserved with hands and feet. This adult is 12% larger in linear dimensions than the female skeleton, on average, has canine teeth that are 20% larger, and is interpreted as male. Moderate sexual dimorphism indicates limited male-male competition during breeding, which in turn suggests little aggregation of food or shelter in the environment inhabited by protocetids. CONCLUSIONS/SIGNIFICANCE: Discovery of a near-term fetus positioned for head-first delivery provides important evidence that early protocetid whales gave birth on land. This is consistent with skeletal morphology enabling Maiacetus to support its weight on land and corroborates previous ideas that protocetids were amphibious. Specimens this complete are virtual 'Rosetta stones' providing insight into functional capabilities and life history of extinct animals that cannot be gained any other way

The STL model in the geometric domain

Computational geometry and its close relative image analysis are among the most promising application domains of generic programming. This insight raises the question whether, and to which extent, the concepts of the Standard Template Library (STL) are appropriate for library design in this realm. We will discuss this question in view of selected fundamental algorithms and data structures

Bildgestützte 3-D Rekonstruktion. Aspekte der Integration von digitaler Bildverarbeitung und 3-D Modellierung

Vorgestellt wird das Konzept eines hybriden 3D-Rekonstruktionsverfahrens. Zielstellung der Verfahrensentwicklung ist ein nutzerfreundliches entwicklungsfaehiges System, das interaktive Konstruktionskomponenten mit automatischen Verfahrensschritten der digitalen Bildverarbeitung verbindet. Ausgehend von den Anforderungen an ein derartiges System werden die wesentlichen Elemente eines Loesungsansatzes vorgestellt