Concentration and localization of zinc during seed development and germination in wheat

In a field experiment, the effect of foliar Zn applications on the concentration of Zn in seeds of a bread wheat cultivar (Triticum aestivum L. cv. Balatilla) was studied during different stages of seed development. In addition, a staining method using dithizone (DTZ: diphenyl thiocarbazone) was applied to (1) study the localization of Zn in seeds, (2) follow the remobilization of Zn during germination, and (3) develop a rapid visual Zn screening method for seed and flour samples. In all seed development stages, foliar Zn treatments were effective in increasing seed Zn concentration. The highest Zn concentration in the seeds was found in the first stage of seed development (around the early milk stage); after this, seed Zn concentration gradually decreased until maturity. When reacting with Zn, DTZ forms a redcolored complex. The DTZ staining of seed samples revealed that Zn is predominantly located in the embryo and aleurone parts of the seeds. After 36 h of germination, the coleoptile and roots that emerged from seeds showed very intensive red color formation and had Zn concentrations up to 200 mg kg1, indicating a substantial remobilization of Zn from seed pools into the developing roots (radicle) and coleoptile. The DTZ staining method seems to be useful in ranking flour samples for their Zn concentrations. There was a close relationship between the seed Zn concentrations and spectral absorbance of the methanol extracts of the flour samples stained with DTZ. The results suggest that (1) accumulation of Zn in seeds is particularly high during early seed development, (2) Zn is concentrated in the embryo and aleurone parts, and (3) the DTZ staining method can be used as a rapid, semiquantitative method to estimate Zn concentrations of flour and seed samples and to screen genotypes for their Zn concentrations in seeds

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

Folding and unfolding phylogenetic trees and networks

Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network $N$ can be "unfolded" to obtain a MUL-tree $U(N)$ and, conversely, a MUL-tree $T$ can in certain circumstances be "folded" to obtain a phylogenetic network $F(T)$ that exhibits $T$. In this paper, we study properties of the operations $U$ and $F$ in more detail. In particular, we introduce the class of stable networks, phylogenetic networks $N$ for which $F(U(N))$ is isomorphic to $N$, characterise such networks, and show that they are related to the well-known class of tree-sibling networks.We also explore how the concept of displaying a tree in a network $N$ can be related to displaying the tree in the MUL-tree $U(N)$. To do this, we develop a phylogenetic analogue of graph fibrations. This allows us to view $U(N)$ as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in $U(N)$ and reconcilingphylogenetic trees with networks

Wegner estimate for discrete alloy-type models

We study discrete alloy-type random Schr\"odinger operators on $\ell^2(\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis.Comment: Accepted for publication in AHP. For an earlier version see http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=09-10

On Alternative Supermatrix Reduction

We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible superconformal-like transformations. The features of even- and odd-reduced supermatrices are investigated on a par. They can be unified into some kind of "sandwich" semigroups. Also we define a special module over even- and odd-reduced supermatrix sets, and the generalized Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced supermatrices represent semigroup bands and Rees matrix semigroups over a unit group.Comment: 22 pages, Standard LaTeX with AmS font

Unusual past dry and wet rainy seasons over Southern Africa and South America from a climate perspective

Southern Africa and Southern South America have experienced recent extremes in dry and wet rainy seasons which have caused severe socio-economic damages. Selected past extreme events are here studied, to estimate how human activity has changed the risk of the occurrence of such events, by applying an event attribution approach (Stott et al., 2004)comprising global climate models of Coupled Model Intercomparison Project 5 (CMIP5). Our assessment shows that models' representation of mean precipitation variability over Southern South America is not adequate to make a robust attribution statement about seasonal rainfall extremes in this region. Over Southern Africa, we show that unusually dry austral summers as occurred during 2002/2003 have become more likely, whereas unusually wet austral summers like that of 1999/2000 have become less likely due to anthropogenic climate change. There is some tentative evidence that the risk of extreme high 5-day precipitation totals (as observed in 1999/2000) have increased in the region. These results are consistent with CMIP5 models projecting a general drying trend over SAF during December–January–February (DJF) but also an increase in atmospheric moisture availability to feed heavy rainfall events when they do occur. Bootstrapping the confidence intervals of the fraction of attributable risk has demonstrated estimates of attributable risk are very uncertain, if the events are very rare. The study highlights some of the challenges in making an event attribution study for precipitation using seasonal precipitation and extreme 5-day precipitation totals and considering natural drivers such as ENSO in coupled ocean–atmosphere models

Mean Curvature Flow on Ricci Solitons

We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazzawhich will treat the case of non-solitonic backgrounds \cite{a_14}.Comment: 19 page

Ricci Solitons and Einstein-Scalar Field Theory

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a free massless scalar field with nonzero cosmological constant are associated to shrinking or expanding Ricci solitons. We exhibit examples, including an explicit family of complete expanding solitons which can be thought of as a Ricci flow for a complete Lorentzian metric. The possible generalization to Ricci-flat stationary metrics leads us to consider an alternative to Ricci flow.Comment: 17 pages, 1 figure; Revised version (organizational changes, other minor revisions and corrections, citations corrected and added), to appear in CQ