Essential p-dimension of algebraic groups whose connected component is a torus

Following up on our earlier work and the work of N. Karpenko and A. Merkurjev, we study the essential p-dimension of linear algebraic groups G whose connected component G^0 is a torus.Comment: 23 pages, no figures. arXiv admin note: text overlap with arXiv:0910.557

Locally Maximally Entangled States of Multipart Quantum Systems

For a multipart quantum system, a locally maximally entangled (LME) state is one where each elementary subsystem is maximally entangled with its complement. This paper is a sequel to arXiv:1708.01645, which gives necessary and sufficient conditions for a system to admit LME states in terms of its subsystem dimensions $(d_1, d_2, \dots, d_n)$, and computes the dimension of the space ${\cal H}_{LME}/K$ of LME states up to local unitary transformations for all non-empty cases. In this paper, we provide a pedagogical overview and physical interpretation of the the underlying mathematics that leads to these results and give a large class of explicit constructions for LME states. In particular, we construct all LME states for tripartite systems with subsystem dimensions $(2,A,B)$ and give a general representation-theoretic construction for a special class of stabilizer LME states. The latter construction provides a common framework for many known LME states. Our results also give the dimension of the space of SLOCC equivalence classes for states with "generic" entanglement for all multipart systems since this space is equivalent to ${\cal H}_{LME}/K$. Finally, we give the dimension of the stabilizer subgroup $S \subset SL(d_1, \mathbb{C}) \times \cdots \times SL(d_n, \mathbb{C})$ for a generic state in an arbitrary multipart system and identify all cases where this stabilizer is trivial.Comment: 50 pages, 6 figures, v2: comments added in introduction and section 3.3, v3: references adde

Influence of Spring and Autumn Phenological Transitions on Forest Ecosystem Productivity

We use eddy covariance measurements of net ecosystem productivity (NEP) from 21 FLUXNET sites (153 site-years of data) to investigate relationships between phenology and productivity (in terms of both NEP and gross ecosystem photosynthesis, GEP) in temperate and boreal forests. Results are used to evaluate the plausibility of four different conceptual models. Phenological indicators were derived from the eddy covariance time series, and from remote sensing and models. We examine spatial patterns (across sites) and temporal patterns (across years); an important conclusion is that it is likely that neither of these accurately represents how productivity will respond to future phenological shifts resulting from ongoing climate change. In spring and autumn, increased GEP resulting from an ¿extra¿ day tends to be offset by concurrent, but smaller, increases in ecosystem respiration, and thus the effect on NEP is still positive. Spring productivity anomalies appear to have carry-over effects that translate to productivity anomalies in the following autumn, but it is not clear that these result directly from phenological anomalies. Finally, the productivity of evergreen needleleaf forests is less sensitive to phenology than is productivity of deciduous broadleaf forests. This has implications for how climate change may drive shifts in competition within mixed-species stands.JRC.H.5-Land Resources Managemen

Planning and Development of Social Services for Persons with Disabilities

Soziale Dienste zur Unterstützung von Menschen mit Behinderungen haben sich in den letzten Jahren dynamisch entwickelt und unterliegen auch aktuell einem erheblichen Veränderungsdruck. Die Forschungsarbeiten, die in diesem Band versammelt sind, haben die Entwicklung hin zu einer inklusionsorientierten Unterstützung in zahlreichen Projekten auf unterschiedlichen Ebenen aktiv begleitet.Social services to support persons with disabilities have developed dynamically in recent years and are currently subject to considerable pressure to change. The research work collected in this volume has actively accompanied the development towards inclusion-oriented support in numerous projects at different levels

The slice method for G-torsors

The notion of a (G,N)(G,N)-slice of a G-variety was introduced by P.I. Katsylo in the early 80's for an algebraically closed base field of characteristic 0. Slices (also known under the name of relative sections) have ever since provided a fundamental tool in invariant theory, allowing reduction of rational or regular invariants of an algebraic group G to invariants of a “simpler” group. We refine this notion for a G-scheme over an arbitrary field, and use it to get reduction of structure group results for G -torsors. Namely we show that any (G,N)(G,N)-slice of a versal G -scheme gives surjective maps H1(L,N)→H1(L,G)H1(L,N)→H1(L,G) in fppf-cohomology for infinite fields L containing F. We show that every stabilizer in general position H for a geometrically irreducible G-variety V gives rise to a (G,NG(H))(G,NG(H))-slice in our sense. The combination of these two results is applied in particular to obtain a striking new upper bound on the essential dimension of the simply connected split algebraic group of type E7E7

TRY plant trait database – enhanced coverage and open access

Plant traits - the morphological, anatomical, physiological, biochemical and phenological characteristics of plants - determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits - almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Essential dimension of algebraic tori

The essential dimension is a numerical invariant of an algebraic group G which may be thought of as a measure of complexity of G-torsors over fields. A recent theorem of N. Karpenko and A. Merkurjev gives a simple formula for the essential dimension of a finite p-group. We obtain similar formulas for the essential p-dimension of a broad class of groups, which includes all algebraic tori