Rolle's Theorem for Complex Polynomials with Real Coefficients

Let p(z) be an algebraic polynomial of degree n ¸ 2 with real coefficients and p(i) = p(¡i). According to Grace-Heawood Theorem, at least one zero of the derivative p0(z) is on the disk with center in the origin and radius cot(¼=n). In this paper is found the smallest domain containing at leas one zero of the derivative p0(z).

(Table 1) Number of alleles per locus and heterozygosity of Arctic charr (Salvelinus alpinus) populations in Iceland

The ecological theory of adaptive radiation predicts that the evolution of phenotypic diversity within species is generated by divergent natural selection arising from different environments and competition between species. Genetic connectivity among populations is likely also to have an important role in both the origin and maintenance of adaptive genetic diversity. Our goal was to evaluate the potential roles of genetic connectivity and natural selection in the maintenance of adaptive phenotypic differences among morphs of Arctic charr, Salvelinus alpinus, in Iceland. At a large spatial scale, we tested the predictive power of geographic structure and phenotypic variation for patterns of neutral genetic variation among populations throughout Iceland. At a smaller scale, we evaluated the genetic differentiation between two morphs in Lake Thingvallavatn relative to historically explicit, coalescent-based null models of the evolutionary history of these lineages. At the large spatial scale, populations are highly differentiated, but weakly structured, both geographically and with respect to patterns of phenotypic variation. At the intralacustrine scale, we observe modest genetic differentiation between two morphs, but this level of differentiation is nonetheless consistent with strong reproductive isolation throughout the Holocene. Rather than a result of the homogenizing effect of gene flow in a system at migration-drift equilibrium, the modest level of genetic differentiation could equally be a result of slow neutral divergence by drift in large populations. We conclude that contemporary and recent patterns of restricted gene flow have been highly conducive to the evolution and maintenance of adaptive genetic variation in Icelandic Arctic charr.

GSP-1 genes are linked to the grain hardness locus (Ha) on wheat chromosome 5D.

An important determinant of wheat grain quality is the hardness of the grain. The trait is controlled by a major locus, Ha, on the short arm of chromosome 5D. Purified starch granules from soft-grained wheats have associated with them 15-kDa polypeptides called grain softness proteins (GSPs) or "friabilins." Genes that encode one family of closely related GSP polypeptides - GSP-1 genes - were mapped using chromosome substitution lines to the group 5 chromosomes. An F2 population segregating for hard and soft alleles at the Ha locus on a near-isogenic background was used in a single-seed study of the inheritance of grain softness and of GSP-1 alleles. Grain softness versus grain hardness was inherited in a 3:1 ratio. The presence versus absence of GSPs in single seed starch preparations was coinherited with grain softness versus hardness. This showed that grain softness is primarily determined by seed, and not by maternal, genotype. In addition, no recombination was detected in 44 F2 plants between GSP-1 restriction fragment length polymorphisms and Ha alleles. Differences between hard and soft wheat grains in membrane structure and lipid extractability have been described and, of the three characterized proteins that are part of the mixture of 15-kDa polypeptides called GSPs, at least two, and probably all three, are proteins that bind polar lipids. The data are interpreted to suggest that the Ha locus may encode one or more members of a large family of lipid-binding proteins.

Self-referencing and consumer evaluations of larger-sized female models : a weight locus of control perspective

In two experiments, we show that the beliefs women have about the controllability of their weight (i.e., weight locus of control) influences their responses to advertisements featuring a larger-sized female model or a slim female model. Further, we examine self-referencing as a mechanism for these effects. Specifically, people who believe they can control their weight (“internals”), respond most favorably to slim models in advertising, and this favorable response is mediated by self-referencing. In contrast, people who feel powerless about their weight (“externals”), self-reference larger-sized models, but only prefer larger-sized models when the advertisement is for a non-fattening product. For fattening products, they exhibit a similar preference for larger-sized models and slim models. Together, these experiments shed light on the effect of model body size and the role of weight locus of control in influencing consumer attitudes.

Combining Cartesian and polar coordinates in IBVS

Image-based visual servo (IBVS) is a simple, efficient and robust technique for vision-based control. Although technically a local method in practice it demonstrates almost global convergence. However IBVS performs very poorly for cases that involve large rotations about the optical axis. It is well known that re-parameterizing the problem by using polar, instead of Cartesian coordinates, of feature points overcomes this limitation. First, simulation and experimental results are presented to show the complementarity of these two parameter-izations. We then describe a new hybrid visual servo strategy based on combining polar and Cartesian image Jacobians. © 2009 IEEE.

Evolving a locus based gait for a humanoid robot

This paper describes a process for evolving a stable humanoid walking gait that is based around parameterised loci of motion. The parameters of the loci are chosen by an evolutionary process based on the criteria that the robot's ZMP (zero moment point) follows a desirable path. The paper illustrates the evolution of a straight line walking gait. The gait has been tested on a 1.2 m tall humanoid robot (GuRoo). The results, apart form illustrating a successful walk, illustrate the effectiveness of the ZMP path criterion in not only ensuring a stable walk, but also in achieving efficient use of the actuators.

Reduction of functionalized graphite oxides by trioctylphosphine in non-polar organic solvents

Graphene, functionalized with oleylamine (OA) and soluble in non-polar organic solvents, was produced on a large scale with a high yield by combining the Hummers process for graphite oxidation, an amine-coupling process to make OA-functionalized graphite oxide (OA-GO), and a novel reduction process using trioctylphosphine (TOP). TOP acts as both a reducing agent and an aggregation-prevention surfactant in the reduction of OA-GO in 1,2-dichlorobenzene (DCB). The reduction of OA-GO is confirmed by X-ray photoelectron spectroscopy, Fourier-transform infrared spectroscopy, X-ray diffraction, thermogravimetric analysis, and Raman spectroscopy. The exfoliation of GO, OA GO, and OA-functionalized graphene (OA-G) is verified by atomic force microscopy. The conductivity of TOP-reduced OA G, which is deduced from the current–voltage characteristics of a vacuum-filtered thin film, shows that the reduction of functionalized GO by TOP is as effective as the reduction of GO by hydrazine.

High-resolution DNA melt curve analysis of the clustered, regularly interspaced short-palindromic-repeat locus of Campylobacter jejuni

A novel method for genotyping the clustered, regularly interspaced short-palindromic-repeat (CRISPR) locus of Campylobacter jejuni is described. Following real-time PCR, CRISPR products were subjected to high-resolution melt (HRM) analysis, a new technology that allows precise melt profile determination of amplicons. This investigation shows that the CRISPR HRM assay provides a powerful addition to existing C. jejuni genotyping methods and emphasizes the potential of HRM for genotyping short sequence repeats in other species

Two SusD-like proteins encoded within a polysaccharide utilisation locus of an uncultured ruminant bacteroidetes bind strongly to cellulose

We demonstrate that two characteristic Sus-like proteins encoded within a Polysaccharide Utilisation Locus (PUL) bind strongly to cellulosic substrates and interact with plant primary cell walls. This shows associations between uncultured Bacteroidetes-affiliated lineages and cellulose in the rumen, and thus presents new PUL-derived targets to pursue regarding plant biomass degradation.