Functions preserving nonnegativity of matrices

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every entrywise nonnegative matrix $A$ of size $n\times n$. Towards this goal, we present a complete characterization of functions preserving nonnegativity of (block) upper-triangular matrices and those preserving nonnegativity of circulant matrices. We also derive necessary conditions and sufficient conditions for entire functions that preserve nonnegativity of symmetric matrices. We also show that some of these latter conditions characterize the even or odd functions that preserve nonnegativity of symmetric matrices.Comment: 20 pages; expanded and corrected to reflect referees' remarks; to appear in SIAM J. Matrix Anal. App

Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise

The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulation Models. For this reason and due to their challenging nonlinear and anisotropic structure the Primitive Equations have recently received considerable attention from the mathematical community. In view of the complex multi-scale nature of the earth's climate system, many uncertainties appear that should be accounted for in the basic dynamical models of atmospheric and oceanic processes. In the climate community stochastic methods have come into extensive use in this connection. For this reason there has appeared a need to further develop the foundations of nonlinear stochastic partial differential equations in connection with the Primitive Equations and more generally. In this work we study a stochastic version of the Primitive Equations. We establish the global existence of strong, pathwise solutions for these equations in dimension 3 for the case of a nonlinear multiplicative noise. The proof makes use of anisotropic estimates, $L^{p}_{t}L^{q}_{x}$ estimates on the pressure and stopping time arguments.Comment: To appear in Nonlinearit

Multiple QTL-effects of wheat Gpc-B1 locus on grain protein and micronutrient concentrations

Micronutrient malnutrition afflicts over three billion peopleworldwide and the numbers are continuously increasing. Developing genetically micronutrientenriched cereals, which are the predominant source of human dietary, is essential to alleviate malnutrition worldwide. Wheat chromosome 6B derived from wild emmerwheat [Triticum turgidum ssp. dicoccoides (Körn.) Thell] was previously reported to be a source for high Zn concentration in the grain. In the present study, recombinant chromosome substitution lines (RSLs), previously constructed for genetic and physical maps of Gpc-B1 (a 250-kb locus affecting grain protein concentration), were used to identify the effects of the Gpc-B1 locus on grain micronutrient concentrations. RSLs carrying the Gpc-B1 allele of T. dicoccoides accumulated on average 12% higher concentration of Zn, 18% higher concentration of Fe, 29% higher concentration of Mn and 38% higher concentration of protein in the grain as compared with RSLs carrying the allele from cultivated wheat (Triticum durum). Furthermore, the high grain Zn, Fe and Mn concentrations were consistently expressed in five different environments with an absence of genotype by environment interaction. The results obtained in the present study also confirmed the previously reported effect of the wild-type allele of Gpc-B1 on earlier senescence of flag leaves. We suggest that the Gpc-B1 locus is involved in more efficient remobilization of protein, zinc, iron and manganese from leaves to the grains, in addition to its effect on earlier senescence of the green tissues

Tensor completion in hierarchical tensor representations

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number of measurements. Hierarchical tensors are a flexible generalization of the well-known Tucker representation, which have the advantage that the number of degrees of freedom of a low rank tensor does not scale exponentially with the order of the tensor. While corresponding tensor decompositions can be computed efficiently via successive applications of (matrix) singular value decompositions, some important properties of the singular value decomposition do not extend from the matrix to the tensor case. This results in major computational and theoretical difficulties in designing and analyzing algorithms for low rank tensor recovery. For instance, a canonical analogue of the tensor nuclear norm is NP-hard to compute in general, which is in stark contrast to the matrix case. In this book chapter we consider versions of iterative hard thresholding schemes adapted to hierarchical tensor formats. A variant builds on methods from Riemannian optimization and uses a retraction mapping from the tangent space of the manifold of low rank tensors back to this manifold. We provide first partial convergence results based on a tensor version of the restricted isometry property (TRIP) of the measurement map. Moreover, an estimate of the number of measurements is provided that ensures the TRIP of a given tensor rank with high probability for Gaussian measurement maps.Comment: revised version, to be published in Compressed Sensing and Its Applications (edited by H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral

A Study of the Residual 39Ar Content in Argon from Underground Sources

The discovery of argon from underground sources with significantly less 39Ar than atmospheric argon was an important step in the development of direct-detection dark matter experiments using argon as the active target. We report on the design and operation of a low background detector with a single phase liquid argon target that was built to study the 39Ar content of the underground argon. Underground argon from the Kinder Morgan CO2 plant in Cortez, Colorado was determined to have less than 0.65% of the 39Ar activity in atmospheric argon.Comment: 21 pages, 10 figure

Rhamnose is superior to mannitol as a monosaccharide in the dual sugar absorption test: A prospective randomized study in children with treatment-naïve celiac disease

BACKGROUND AND AIM: We sought to correlate two different measures of gut permeability [lactulose:mannitol (L:M) and lactulose:rhamnose (L:R)] to the severity of duodenal histopathology in children with and without elevated antibodies to tissue transglutaminase (tTG). A secondary objective was to correlate gut permeability with celiac disease (CD) serology and indices of inflammation and bacterial product translocation. METHODS: We prospectively randomized children undergoing endoscopy with abnormal ( RESULTS: Of the 54 cases with positive celiac serology, 31 and 69% had modified Marsh 0/1 scores or ≥3a, respectively. Circulating tTG IgA correlated with the modified Marsh score ( CONCLUSIONS: L:R, but not L:M, is associated with modified Marsh scores in children undergoing small bowel biopsy for suspected CD. Despite increased intestinal permeability, we see scant evidence of systemic exposure to gut microbes in these children. Gut permeability testing with L:R may predict which patients with abnormal celiac serology will have biopsy evidence for celiac disease and reduce the proportion of such patients undergoing endoscopy whose Marsh scores are ≤1. M should not be used as a monosaccharide for permeability testing in children

The fast and the frugal: Divergent locomotory strategies drive limb lengthening in theropod dinosaurs

Limb length, cursoriality and speed have long been areas of significant interest in theropod paleobiology, since locomotory capacity, especially running ability, is critical in the pursuit of prey and to avoid becoming prey. The impact of allometry on running ability, and the limiting effect of large body size, are aspects that are traditionally overlooked. Since several different non-avian theropod lineages have each independently evolved body sizes greater than any known terrestrial carnivorous mammal, ~1000kg or more, the effect that such large mass has on movement ability and energetics is an area with significant implications for Mesozoic paleoecology. Here, using expansive datasets that incorporate several different metrics to estimate body size, limb length and running speed, we calculate the effects of allometry on running ability. We test traditional metrics used to evaluate cursoriality in non-avian theropods such as distal limb length, relative hindlimb length, and compare the energetic cost savings of relative hindlimb elongation between members of the Tyrannosauridae and more basal megacarnivores such as Allosauroidea or Ceratosauridae. We find that once the limiting effects of body size increase is incorporated there is no significant correlation to top speed between any of the commonly used metrics, including the newly suggested distal limb index (Tibia + Metatarsus/ Femur length). The data also shows a significant split between large and small bodied theropods in terms of maximizing running potential suggesting two distinct strategies for promoting limb elongation based on the organisms’ size. For small and medium sized theropods increased leg length seems to correlate with a desire to increase top speed while amongst larger taxa it corresponds more closely to energetic efficiency and reducing foraging costs. We also find, using 3D volumetric mass estimates, that the Tyrannosauridae show significant cost of transport savings compared to more basal clades, indicating reduced energy expenditures during foraging and likely reduced need for hunting forays. This suggests that amongst theropods, hindlimb evolution was not dictated by one particular strategy. Amongst smaller bodied taxa the competing pressures of being both a predator and a prey item dominant while larger ones, freed from predation pressure, seek to maximize foraging ability. We also discuss the implications both for interactions amongst specific clades and Mesozoic paleobiology and paleoecological reconstructions as a whole

Effective Interactions and Volume Energies in Charged Colloids: Linear Response Theory

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out from the partition function the degrees of freedom of all microions, and assuming linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the DLVO screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy -- a natural consequence of the one-component reduction -- contributes to the total free energy and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.Comment: 14 pages, including 3 figure

Social representations and the politics of participation

Recent work has called for the integration of different perspectives into the field of political psychology (Haste, 2012). This chapter suggests that one possible direction that such efforts can take is studying the role that social representations theory (SRT) can play in understanding political participation and social change. Social representations are systems of common-sense knowledge and social practice; they provide the lens through which to view and create social and political realities, mediate people's relations with these sociopolitical worlds and defend cultural and political identities. Social representations are therefore key for conceptualising participation as the activity that locates individuals and social groups in their sociopolitical world. Political participation is generally seen as conditional to membership of sociopolitical groups and therefore is often linked to citizenship. To be a citizen of a society or a member of any social group one has to participate as such. Often political participation is defined as the ability to communicate one's views to the political elite or to the political establishment (Uhlaner, 2001), or simply explicit involvement in politics and electoral processes (Milbrath, 1965). However, following scholars on ideology (Eagleton, 1991; Thompson, 1990) and social knowledge (Jovchelovitch, 2007), we extend our understanding of political participation to all social relations and also develop a more agentic model where individuals and groups construct, develop and resist their own views, ideas and beliefs. We thus adopt a broader approach to participation in comparison to other political-psychological approaches, such as personality approaches (e.g. Mondak and Halperin, 2008) and cognitive approaches or, more recently, neuropsychological approaches (Hatemi and McDermott, 2012). We move away from a focus on the individual's political behaviour and its antecedents and outline an approach that focuses on the interaction between psychological and political phenomena (Deutsch and Kinnvall, 2002) through examining the politics of social knowledge

DOMINO – Synthesis of Soil Management Strategies Integrating Plant and Waste Based Alternative Fertilizers

The project DOMINO (http://www.domino-coreorganic.eu/) focused on the evaluation of alternative fertilisers based on locally available wastes, legume-based materials and vermicompost extracts as alternatives to animal-based fertilizers from conventional agriculture in apple orchards. The project included incubation experiments, pot and field experiments in different European countries. In addition, a survey on nutrient budgets and soil nutrient status in organic fruit orchards was conducted in Germany. The evaluation of the fertilizers encompassed also their impact on soil nematodes and microbial activity and biodiversity. Considering all pros and cons, there is no single ideal solution for fertilization. An integrated approach using fertilizers based on legumes in combination with stillages that provide N early in the season can enhance farm internal N cycles leading to an overall higher N efficiency