On the Nonexistence of Singular Equilibria in the Four-vortex Problem

In this paper we provide a partial answer to a question recently posed by Hassan Aref et. al. in their article Vortex Crystals, namely whether there are certain singular equilibria of point vortices. We prove that there are no such equilibria in the four-vortex case

Seven-body central configurations: a family of central configurations in the spatial seven-body problem

The main result of this paper is the existence of a new family of central configurations in the Newtonian spatial seven-body problem. This family is unusual in that it is a simplex stacked central configuration, i.e the bodies are arranged as concentric three and two dimensional simplexes.Comment: 15 pages 5 figure

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Power, Ownership and Tourism in Small Islands: evidence from Indonesia

This paper examines the political economy of tourism development in islands and uses Gili Trawangan, Indonesia as a case study. A longitudinal study drawing from fieldwork contributes to the discussion of how different types of power shape community development, and how the effects of hosting international tourism play an explicit role. Analysis using Barnett and Duvall’s Taxonomy of Power model reveals the interplay between the types of power over time and its effects on different actors. Results raise questions for Less Developed Countries, and particularly islands, concerning the social costs of using tourism for development

Identification of Differential Gene Expression in Brassica rapa Nectaries through Expressed Sequence Tag Analysis

BACKGROUND: Nectaries are the floral organs responsible for the synthesis and secretion of nectar. Despite their central roles in pollination biology, very little is understood about the molecular mechanisms underlying nectar production. This project was undertaken to identify genes potentially involved in mediating nectary form and function in Brassica rapa. METHODOLOGY AND PRINCIPAL FINDINGS: Four cDNA libraries were created using RNA isolated from the median and lateral nectaries of B. rapa flowers, with one normalized and one non-normalized library being generated from each tissue. Approximately 3,000 clones from each library were randomly sequenced from the 5' end to generate a total of 11,101 high quality expressed sequence tags (ESTs). Sequence assembly of all ESTs together allowed the identification of 1,453 contigs and 4,403 singleton sequences, with the Basic Localized Alignment Search Tool (BLAST) being used to identify 4,138 presumptive orthologs to Arabidopsis thaliana genes. Several genes differentially expressed between median and lateral nectaries were initially identified based upon the number of BLAST hits represented by independent ESTs, and later confirmed via reverse transcription polymerase chain reaction (RT PCR). RT PCR was also used to verify the expression patterns of eight putative orthologs to known Arabidopsis nectary-enriched genes. CONCLUSIONS/SIGNIFICANCE: This work provided a snapshot of gene expression in actively secreting B. rapa nectaries, and also allowed the identification of differential gene expression between median and lateral nectaries. Moreover, 207 orthologs to known nectary-enriched genes from Arabidopsis were identified through this analysis. The results suggest that genes involved in nectar production are conserved amongst the Brassicaceae, and also supply clones and sequence information that can be used to probe nectary function in B. rapa

Systems analyses of key metabolic modules of floral and extrafloral nectaries of cotton

Nectar is a primary reward mediating plant-animal mutualisms to improve plant fitness and reproductive success. In Gossypium hirsutum (cotton), four distinct trichomatic nectaries develop, one floral and three extrafloral. The secreted floral and extrafloral nectars serve different purposes, with the floral nectar attracting bees to promote pollination and the extrafloral nectar attracting predatory insects as a means of indirect resistance from herbivores. Cotton therefore provides an ideal system to contrast mechanisms of nectar production and nectar composition between floral and extrafloral nectaries. Here, we report the transcriptome, ultrastructure, and metabolite spatial distribution using mass spectrometric imaging of the four cotton nectary types throughout development. Additionally, the secreted nectar metabolomes were defined and were jointly composed of 197 analytes, 60 of which were identified. Integration of theses datasets support the coordination of merocrine-based and eccrine-based models of nectar synthesis. The nectary ultrastructure supports the merocrine-based model due to the abundance of rough endoplasmic reticulum positioned parallel to the cell walls and profusion of vesicles fusing to the plasma membranes. The eccrine-based model which consist of a progression from starch synthesis to starch degradation and to sucrose biosynthesis was supported by gene expression data. This demonstrates conservation of the eccrine-based model for the first time in both trichomatic and extrafloral nectaries. Lastly, nectary gene expression data provided evidence to support de novo synthesis of amino acids detected in the secreted nectars

PIN6 is required for nectary auxin response and short stamen development

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98417/1/tpj12184-sup-0001-FigS1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98417/2/tpj12184.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98417/3/tpj12184-sup-0004-FigS4.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98417/4/tpj12184-sup-0003-FigS3.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98417/5/tpj12184-sup-0002-FigS2.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98417/6/tpj12184-sup-0005-FigS5.pd