Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phy

The spatial sensitivity of the spectral diversity–biodiversity relationship: an experimental test in a prairie grassland

Remote sensing has been used to detect plant biodiversity in a range of ecosystems based on the varying spectral properties of different species or functional groups. However, the most appropriate spatial resolution necessary to detect diversity remains unclear. At coarse resolution, differences among spectral patterns may be too weak to detect. In contrast, at fine resolution, redundant information may be introduced. To explore the effect of spatial resolution, we studied the scale dependence of spectral diversity in a prairie ecosystem experiment at Cedar Creek Ecosystem Science Reserve, Minnesota, USA. Our study involved a scaling exercise comparing synthetic pixels resampled from high-resolution images within manipulated diversity treatments. Hyperspectral data were collected using several instruments on both ground and airborne platforms. We used the coefficient of variation (CV) of spectral reflectance in space as the indicator of spectral diversity and then compared CV at different scales ranging from 1 mm2 to 1 m2 to conventional biodiversity metrics, including species richness, Shannon’s index, Simpson’s index, phylogenetic species variation, and phylogenetic species evenness. In this study, higher species richness plots generally had higher CV. CV showed higher correlations with Shannon’s index and Simpson’s index than did species richness alone, indicating evenness contributed to the spectral diversity. Correlations with species richness and Simpson’s index were generally higher than with phylogenetic species variation and evenness measured at comparable spatial scales, indicating weaker relationships between spectral diversity and phylogenetic diversity metrics than with species diversity metrics. High resolution imaging spectrometer data (1 mm2 pixels) showed the highest sensitivity to diversity level. With decreasing spatial resolution, the difference in CV between diversity levels decreased and greatly reduced the optical detectability of biodiversity. The optimal pixel size for distinguishing a diversity in these prairie plots appeared to be around 1 mm to 10 cm, a spatial scale similar to the size of an individual herbaceous plant. These results indicate a strong scaledependence of the spectral diversity-biodiversity relationships, with spectral diversity best able to detect a combination of species richness and evenness, and more weakly detecting phylogenetic diversity. These findings can be used to guide airborne studies of biodiversity and develop more effective large-scale biodiversity sampling methods

Preliminary data on microcharacters and chromosome number in Tornabenea species (Apiaceae) from Cape Verde islands

Tornabenea is a small Apiaceae genus that is endemic to the Cape Verde Islands. Its species differentiation is based just on a few macromorphological characters: leaf shape, number and shape of umbel bracts and mericarp ribs. These characters vary within each species and show high plasticity. Thus, in recent taxonomic data of the genus, there are different viewpoints as to the number of species. Here, in order to improve the taxonomy of the genus, microcharacters of the vegetative and reproductive structures of three taxa—T. insularis, T. annua and T. tenuissima—have been examined. The shape and arrangement of hairs on the surface of the mericarps, and the presence and structure of starch grains are the only different microcharacters noted in T. insularis and T. annua. Chromosome number of the latter two species is 2n¼18. Our preliminary results disagree with the existing classifications of the genus Tornabenea. In fact, they do not lead to a clear separation between T. insularis and T. annua. By contrast, it is easy to distinguish between these species and T. tenuissima, which possesses more peculiar microcharacter

CWRML: representing crop wild relative conservation and use data in XML

Background Crop wild relatives are wild species that are closely related to crops. They are valuable as potential gene donors for crop improvement and may help to ensure food security for the future. However, they are becoming increasingly threatened in the wild and are inadequately conserved, both in situ and ex situ. Information about the conservation status and utilisation potential of crop wild relatives is diverse and dispersed, and no single agreed standard exists for representing such information; yet, this information is vital to ensure these species are effectively conserved and utilised. The European Community-funded project, European Crop Wild Relative Diversity Assessment and Conservation Forum, determined the minimum information requirements for the conservation and utilisation of crop wild relatives and created the Crop Wild Relative Information System, incorporating an eXtensible Markup Language (XML) schema to aid data sharing and exchange. Results Crop Wild Relative Markup Language (CWRML) was developed to represent the data necessary for crop wild relative conservation and ensure that they can be effectively utilised for crop improvement. The schema partitions data into taxon-, site-, and population-specific elements, to allow for integration with other more general conservation biology schemata which may emerge as accepted standards in the future. These elements are composed of sub-elements, which are structured in order to facilitate the use of the schema in a variety of crop wild relative conservation and use contexts. Pre-existing standards for data representation in conservation biology were reviewed and incorporated into the schema as restrictions on element data contents, where appropriate. Conclusion CWRML provides a flexible data communication format for representing in situ and ex situ conservation status of individual taxa as well as their utilisation potential. The development of the schema highlights a number of instances where additional standards-development may be valuable, particularly with regard to the representation of population-specific data and utilisation potential. As crop wild relatives are intrinsically no different to other wild plant species there is potential for the inclusion of CWRML data elements in the emerging standards for representation of biodiversity data

Hyperentangled States

We investigate a new class of entangled states, which we call 'hyperentangled',that have EPR correlations identical to those in the vacuum state of a relativistic quantum field. We show that whenever hyperentangled states exist in any quantum theory, they are dense in its state space. We also give prescriptions for constructing hyperentangled states that involve an arbitrarily large collection of systems.Comment: 23 pages, LaTeX, Submitted to Physical Review

Democratic cultural policy : democratic forms and policy consequences

The forms that are adopted to give practical meaning to democracy are assessed to identify what their implications are for the production of public policies in general and cultural policies in particular. A comparison of direct, representative, democratic elitist and deliberative versions of democracy identifies clear differences between them in terms of policy form and democratic practice. Further elaboration of these differences and their consequences are identified as areas for further research

Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

Quantum value indefiniteness

The indeterministic outcome of a measurement of an individual quantum is certified by the impossibility of the simultaneous, definite, deterministic pre-existence of all conceivable observables from physical conditions of that quantum alone. We discuss possible interpretations and consequences for quantum oracles.Comment: 19 pages, 2 tables, 2 figures; contribution to PC0

The roles and values of wild foods in agricultural systems

Almost every ecosystem has been amended so that plants and animals can be used as food, fibre, fodder, medicines, traps and weapons. Historically, wild plants and animals were sole dietary components for hunter–gatherer and forager cultures. Today, they remain key to many agricultural communities. The mean use of wild foods by agricultural and forager communities in 22 countries of Asia and Africa (36 studies) is 90–100 species per location. Aggregate country estimates can reach 300–800 species (e.g. India, Ethiopia, Kenya). The mean use of wild species is 120 per community for indigenous communities in both industrialized and developing countries. Many of these wild foods are actively managed, suggesting there is a false dichotomy around ideas of the agricultural and the wild: hunter–gatherers and foragers farm and manage their environments, and cultivators use many wild plants and animals. Yet, provision of and access to these sources of food may be declining as natural habitats come under increasing pressure from development, conservation-exclusions and agricultural expansion. Despite their value, wild foods are excluded from official statistics on economic values of natural resources. It is clear that wild plants and animals continue to form a significant proportion of the global food basket, and while a variety of social and ecological drivers are acting to reduce wild food use, their importance may be set to grow as pressures on agricultural productivity increase.</jats:p

Tissue Proteome of 2-Hydroxyacyl-CoA Lyase Deficient Mice Reveals Peroxisome Proliferation and Activation of ω-Oxidation

Peroxisomal fatty acid α-oxidation is an essential pathway for the degradation of β-carbon methylated fatty acids such as phytanic acid. One enzyme in this pathway is 2-hydroxyacyl CoA lyase (HACL1), which is responsible for the cleavage of 2-hydroxyphytanoyl-CoA into pristanal and formyl-CoA. Hacl1 deficient mice do not present with a severe phenotype, unlike mice deficient in other α-oxidation enzymes such as phytanoyl-CoA hydroxylase deficiency (Refsum disease) in which neuropathy and ataxia are present. Tissues from wild-type and Hacl1−/− mice fed a high phytol diet were obtained for proteomic and lipidomic analysis. There was no phenotype observed in these mice. Liver, brain, and kidney tissues underwent trypsin digestion for untargeted proteomic liquid chromatography-mass spectrometry analysis, while liver tissues also underwent fatty acid hydrolysis, extraction, and derivatisation for fatty acid gas chromatography-mass spectrometry analysis. The liver fatty acid profile demonstrated an accumulation of phytanic and 2-hydroxyphytanic acid in the Hacl1−/− liver and significant decrease in heptadecanoic acid. The liver proteome showed a significant decrease in the abundance of Hacl1 and a significant increase in the abundance of proteins involved in PPAR signalling, peroxisome proliferation, and omega oxidation, particularly Cyp4a10 and Cyp4a14. In addition, the pathway associated with arachidonic acid metabolism was affected; Cyp2c55 was upregulated and Cyp4f14 and Cyp2b9 were downregulated. The kidney proteome revealed fewer significantly upregulated peroxisomal proteins and the brain proteome was not significantly different in Hacl1−/− mice. This study demonstrates the powerful insight brought by proteomic and metabolomic profiling of Hacl1−/− mice in better understanding disease mechanism in fatty acid α-oxidation disorders