Geometry of Banach spaces and biorthogonal systems

A separable Banach space X contains $\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal system

Serial nuclear magnetic resonance imaging in acute myocardial infarction

Recent studies show that proton nuclear magnetic resonance (NMR) imaging can detect myocardial ischemia and acute myocardial infarction (AMI) in animal models1-3 and in humans.4-6 The area of AMI appears as increased signal intensity on the spin-echo NMR images and most likely reflects the regional edema associated with tissue necrosis.1 Thus, the time course of regional edema and the evolution of infarct healing may be revealed by serial NMR studies. In a recent canine study, Pflugfelder et al7 examined the time course of the increased NMR signal intensity associated with AMI. They found that the relative signal intensity increased between the day of AMI and 2 weeks after AMI and subsequently decreased by the 20th day. We examined the early time course of NMR changes in humans.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26729/1/0000279.pd

Convexity in partial cubes: the hull number

We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves some earlier results in the literature. On the other hand we provide a polynomial-time algorithm to determine the hull number of planar partial cube quadrangulations. Instances of the hull number problem for partial cubes described include poset dimension and hitting sets for interiors of curves in the plane. To obtain the above results, we investigate convexity in partial cubes and characterize these graphs in terms of their lattice of convex subgraphs, improving a theorem of Handa. Furthermore we provide a topological representation theorem for planar partial cubes, generalizing a result of Fukuda and Handa about rank three oriented matroids.Comment: 19 pages, 4 figure

CD-independent subsets in meet-distributive lattices

A subset $X$ of a finite lattice $L$ is CD-independent if the meet of any two incomparable elements of $X$ equals 0. In 2009, Cz\'edli, Hartmann and Schmidt proved that any two maximal CD-independent subsets of a finite distributive lattice have the same number of elements. In this paper, we prove that if $L$ is a finite meet-distributive lattice, then the size of every CD-independent subset of $L$ is at most the number of atoms of $L$ plus the length of $L$. If, in addition, there is no three-element antichain of meet-irreducible elements, then we give a recursive description of maximal CD-independent subsets. Finally, to give an application of CD-independent subsets, we give a new approach to count islands on a rectangular board.Comment: 14 pages, 4 figure

Attitudes to in vitro meat:A survey of potential consumers in the United States

Positivity towards meat consumption remains strong, despite evidence of negative environmental and ethical outcomes. Although awareness of these repercussions is rising, there is still public resistance to removing meat from our diets. One potential method to alleviate these effects is to produce in vitro meat: meat grown in a laboratory that does not carry the same environmental or ethical concerns. However, there is limited research examining public attitudes towards in vitro meat, thus we know little about the capacity for it be accepted by consumers. This study aimed to examine perceptions of in vitro meat and identify potential barriers that might prevent engagement. Through conducting an online survey with US participants, we identified that although most respondents were willing to try in vitro meat, only one third were definitely or probably willing to eat in vitro meat regularly or as a replacement for farmed meat. Men were more receptive to it than women, as were politically liberal respondents compared with conservative ones. Vegetarians and vegans were more likely to perceive benefits compared to farmed meat, but they were less likely to want to try it than meat eaters. The main concerns were an anticipated high price, limited taste and appeal and a concern that the product was unnatural. It is concluded that people in the USA are likely to try in vitro meat, but few believed that it would replace farmed meat in their diet

Viral population estimation using pyrosequencing

The diversity of virus populations within single infected hosts presents a major difficulty for the natural immune response as well as for vaccine design and antiviral drug therapy. Recently developed pyrophosphate based sequencing technologies (pyrosequencing) can be used for quantifying this diversity by ultra-deep sequencing of virus samples. We present computational methods for the analysis of such sequence data and apply these techniques to pyrosequencing data obtained from HIV populations within patients harboring drug resistant virus strains. Our main result is the estimation of the population structure of the sample from the pyrosequencing reads. This inference is based on a statistical approach to error correction, followed by a combinatorial algorithm for constructing a minimal set of haplotypes that explain the data. Using this set of explaining haplotypes, we apply a statistical model to infer the frequencies of the haplotypes in the population via an EM algorithm. We demonstrate that pyrosequencing reads allow for effective population reconstruction by extensive simulations and by comparison to 165 sequences obtained directly from clonal sequencing of four independent, diverse HIV populations. Thus, pyrosequencing can be used for cost-effective estimation of the structure of virus populations, promising new insights into viral evolutionary dynamics and disease control strategies.Comment: 23 pages, 13 figure