Combinatorics of reductions between equivalence relations

We discuss combinatorial conditions for the existence of various types of reductions between equivalence relations, and in particular identify necessary and sufficient conditions for the existence of injective reductions.Comment: 7 pages, 2 figure

Direct Detection of Giant Close-In Planets Around the Source Stars of Caustic-Crossing Microlensing Events

We propose a direct method to detect close-in giant planets orbiting stars in the Galactic bulge. This method uses caustic-crossing binary microlensing events discovered by survey teams monitoring the bulge to measure light from a planet orbiting the source star. When the planet crosses the caustic, it is more magnified than the source star; its light is magnified by two orders of magnitude for Jupiter size planets. If the planet is a giant close to the star, it may be bright enough to make a significant deviation in the light curve of the star. Detection of this deviation requires intensive monitoring of the microlensing light curve using a 10-meter class telescope for a few hours after the caustic. This is the only method yet proposed to directly detect close-in planets around stars outside the solar neighborhood.Comment: 4 pages, 2 figures. Submitted to ApJ Letter

The Meat-Farming Ants: Predatory Mutualism Between Melissotarsus Ants (Hymenoptera: Formicidae) and Armored Scale Insects (Hemiptera: Diaspididae)

Ant agricultural mutualisms are common, well studied, and receive attention from scientific and public spheres due to shared similarities with human agriculture (i.e. ant/fungus ‘crop farming’ and ant/insect ‘dairy farming’). They also serve as important model systems for studying many facets of mutualism. This study reveals that the repertoire of ant agriculture may also include ‘meat farming’. Predatory mutualisms occur between Melissotarsus ants and various species of armored scale insects. This dissertation employs a multi-disciplinary approach to investigate the evolutionary history and nature of ant/diaspidid mutualisms. Chapter 1 reviews the current state of knowledge regarding species composition of these associations and includes descriptions of three new diaspidid species. Also included is a discussion on new observations of foraging behaviors gathered from multiple colonies of Melissotarsus emeryi in South Africa. Chapter 2 reconstructs the phylogeny of the Aspidiotini tribe of armored scale insects from molecular data for 127 species from 31 genera. Nearly all known ant-associated diaspidids belong to the tribe Aspidiotini. The majority of aspidiotine genera are found to be paraphyletic as currently defined and recommendations to increase taxonomic stability for this tribe are provided. Myrmecophily among diaspidids has evolved no fewer than six times independently, four times within the Aspidiotini and two additional origins recorded from the Diaspidini. Relationships between ants/diaspidids are labile at the species level and partnerships can shift. However, several clades of ant-specialized diaspidids have evolved indicating that some relationships can be stable on an evolutionary timescale. Chapter 3 investigates the diet and relative trophic position of Melissotarsus ants by analyzing stable isotopic enrichment of δ15N and δ13C, and by assaying ant gut contents for diaspidid COI mtDNA fragments. Diaspidid DNA is consistently amplified from gut contents of worker ants. Isotopic analyses indicate a strong positive relationship between δ15N and δ13C isotopes of worker ants and associated diaspidids; most variation in worker isotopes can be explained by variation in diaspidid isotopes. Worker ants are calculated to be approximately one trophic level above associated diaspidids. These dietary studies indicate that Melissotarsus ants are predators of mutualistically associated diaspidids. Predation plays a central role in the establishment and maintenance of ant/diaspidid mutualisms

Magnification as a Tool in Weak Lensing

Weak lensing surveys exploit measurements of galaxy ellipticities. These measurements are subject to errors which degrade the cosmological information that can be extracted from the surveys. Here we propose a way of using the galaxy data themselves to calibrate the measurement errors. In particular, the cosmic shear field, which causes the galaxies to appear elliptical, also changes their sizes and fluxes. Information about the sizes and fluxes of the galaxies can be added to the shape information to obtain more robust information about the cosmic shear field. The net result will be tighter constraints on cosmological parameters such as those which describe dark energy.Comment: 4 pages, 2 figure

Liver Transplantation to Provide Low-Density-Lipoprotein Receptors and Lower Plasma Cholesterol in a Child with Homozygous Familial Hypercholesterolemia

A six-year-old girl with severe hypercholesterolemia and atherosclerosis had two defective genes at the low-density-lipoprotein (LDL) receptor locus, as determined by biochemical studies of cultured fibroblasts. One gene, inherited from the mother, produced no LDL receptors; the other gene, inherited from the father, produced a receptor precursor that was not transported to the cell surface and was unable to bind LDL. The patient degraded intravenously administered 125I-LDL at an extremely low rate, indicating that her high plasma LDL-cholesterol level was caused by defective receptor-mediated removal of LDL from plasma. After transplantation of a liver and a heart from a normal donor, the patient's plasma LDL-cholesterol level declined by 81 per cent, from 988 to 184 mg per deciliter. The fractional catabolic rate for intravenously administered 125I-LDL, a measure of functional LDL receptors in vivo, increased by 2.5-fold. Thus, the transplanted liver, with its normal complement of LDL receptors, was able to remove LDL cholesterol from plasma at a nearly normal rate. We conclude that a genetically determined deficiency of LDL receptors can be largely reversed by liver transplantation. These data underscore the importance of hepatic LDL receptors in controlling the plasma level of LDL cholesterol in human beings. (N Engl J Med 1984; 311: 1658–64.). © 1984, Massachusetts Medical Society. All rights reserved