A concentration phenomenon for semilinear elliptic equations

For a domain \Omega\subset\dR^N we consider the equation -\Delta u + V(x)u = Q_n(x)\abs{u}^{p-2}u with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $\Omega$ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\in\Omega$ as $n\to\infty$. We show that if $u_n$ is a nontrivial solution corresponding to $Q_n$, then the sequence $(u_n)$ concentrates at $x_0$ with respect to the $H^1$ and certain $L^q$-norms. We also show that if the sets $\{Q_n>0\}$ shrink to two points and $u_n$ are ground state solutions, then they concentrate at one of these points

Global bifurcation for asymptotically linear Schr\"odinger equations

We prove global asymptotic bifurcation for a very general class of asymptotically linear Schr\"odinger equations \begin{equation}\label{1} \{{array}{lr} \D u + f(x,u)u = \lam u \quad \text{in} \ {\mathbb R}^N, u \in H^1({\mathbb R}^N)\setmimus\{0\}, \quad N \ge 1. {array}. \end{equation} The method is topological, based on recent developments of degree theory. We use the inversion $u\to v:= u/\Vert u\Vert_X^2$ in an appropriate Sobolev space $X=W^{2,p}({\mathbb R}^N)$, and we first obtain bifurcation from the line of trivial solutions for an auxiliary problem in the variables (\lambda,v) \in {\mathbb R} \x X. This problem has a lack of compactness and of regularity, requiring a truncation procedure. Going back to the original problem, we obtain global branches of positive/negative solutions 'bifurcating from infinity'. We believe that, for the values of $\lambda$ covered by our bifurcation approach, the existence result we obtain for positive solutions of \eqref{1} is the most general so fa

Homoeologous chromosomal location of the genes encoding thionins in wheat and rye

Thionins are high sulphur basic polypeptides present in the endosperm of Gramineae. In wheat there are three thionins encoded by genes located in the long arms of chromosomes 1A, 1B and 1D. Rye has one thionin encoded by a gene which has been assigned to chromosome 1R after analysis of the Imperial-Chinese Spring rye-wheat disomic addition lines. Commercial varieties and experimental stocks with a 1B/1R substitution carry the thionin from rye ( R) instead of the B thionin from wheat. The R thionin gene is not located in the large chromosomal segment representing most of the short arm of chromosome 1R

Unrelated donor hematopoietic cell transplantation after nonmyeloablative conditioning for patients with poor risk, relapsed or refractory multiple myeloma

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Ulcerative Colitis Physician Team-Work in the Treatment

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68011/2/10.1177_000992286400300203.pd

Treatment of patients (pts) with chemotherapy-refractory chronic lymphocytic leukemia (CLL) with nonmyeloablative (NM) conditioning and hematopoietic cell transplantation (HCT) from HLA-matched related (MRD) or unrelated donors (URD)

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Reptiles as food: Predation of Australian reptiles by introduced red foxes compounds and complements predation by cats

Context: Invasive species are a major cause of biodiversity loss across much of the world, and a key threat to Australia’s diverse reptile fauna. There has been no previous comprehensive analysis of the potential impact of the introduced European red fox, Vulpes vulpes, on Australian reptiles. Aims: We seek to provide an inventory of all Australian reptile species known to be consumed by the fox, and identify characteristics of squamate species associated with such predation. We also compare these tallies and characteristics with reptile species known to be consumed by the domestic cat, Felis catus, to examine whether predation by these two introduced species is compounded (i.e. affecting much the same set of species) or complementary (affecting different groups of species). Methods: We collated records of Australian reptiles consumed by foxes in Australia, with most records deriving from fox dietary studies (tallying >35 000 samples). We modelled presence or absence of fox predation records against a set of biological and other traits, and population trends, for squamate species. Key results: In total, 108 reptile species (~11% of Australia’s terrestrial reptile fauna) have been recorded as consumed by foxes, fewer than that reported for cats (263 species). Eighty-six species have been reported to be eaten by both predators. More Australian turtle species have been reported as consumed by foxes than by cats, including many that suffer high levels of predation on egg clutches. Twenty threatened reptile species have been reported as consumed by foxes, and 15 by cats. Squamate species consumed by foxes are more likely to be undergoing population decline than those not known to be consumed by foxes. The likelihood of predation by foxes increased with squamate species’ adult body mass, in contrast to the relationship for predation by cats, which peaked at ~217 g. Foxes, but not cats, were also less likely to consume venomous snakes. Conclusions: The two introduced, and now widespread, predators have both compounding and complementary impacts on the Australian reptile fauna. Implications: Enhanced and integrated management of the two introduced predators is likely to provide substantial conservation benefits to much of the Australian reptile fauna

Counting the bodies: Estimating the numbers and spatial variation of Australian reptiles, birds and mammals killed by two invasive mesopredators

Aim Introduced predators negatively impact biodiversity globally, with insular fauna often most severely affected. Here, we assess spatial variation in the number of terrestrial vertebrates (excluding amphibians) killed by two mammalian mesopredators introduced to Australia, the red fox (Vulpes vulpes) and feral cat (Felis catus). We aim to identify prey groups that suffer especially high rates of predation, and regions where losses to foxes and/or cats are most substantial. Location Australia. Methods We draw information on the spatial variation in tallies of reptiles, birds and mammals killed by cats in Australia from published studies. We derive tallies for fox predation by (i) modelling continental-scale spatial variation in fox density, (ii) modelling spatial variation in the frequency of occurrence of prey groups in fox diet, (iii) analysing the number of prey individuals within dietary samples and (iv) discounting animals taken as carrion. We derive point estimates of the numbers of individuals killed annually by foxes and by cats and map spatial variation in these tallies. Results Foxes kill more reptiles, birds and mammals (peaking at 1071 km−2 year−1) than cats (55 km−2 year−1) across most of the unmodified temperate and forested areas of mainland Australia, reflecting the generally higher density of foxes than cats in these environments. However, across most of the continent – mainly the arid central and tropical northern regions (and on most Australian islands) – cats kill more animals than foxes. We estimate that foxes and cats together kill 697 million reptiles annually in Australia, 510 million birds and 1435 million mammals. Main conclusions This continental-scale analysis demonstrates that predation by two introduced species takes a substantial and ongoing toll on Australian reptiles, birds and mammals. Continuing population declines and potential extinctions of some of these species threatens to further compound Australia's poor contemporary conservation record

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page