Ricci flow for homogeneous compact models of the universe

Using quaternions, we give a concise derivation of the Ricci tensor for homogeneous spaces with topology of the 3-dimensional sphere. We derive explicit and numerical solutions for the Ricci flow PDE and discuss their properties. In the collapse (or expansion) of these models, the interplay of the various components of the Ricci tensor are studied. We dedicate this paper to honor the work of Josh Goldberg.Comment: 18 pages, 2 figure

Herd-level risk factors associated with the presence of Phage type 21/28 E. coli O157 on Scottish cattle farms

<p>Background: E. coli O157 is a bacterial pathogen that is shed by cattle and can cause severe disease in humans. Phage type (PT) 21/28 is a subtype of E. coli O157 that is found across Scotland and is associated with particularly severe human morbidity.</p> <p>Methods: A cross-sectional survey of Scottish cattle farms was conducted in the period Feb 2002-Feb 2004 to determine the prevalence of E. coli O157 in cattle herds. Data from 88 farms on which E. coli O157 was present were analysed using generalised linear mixed models to identify risk factors for the presence of PT 21/28 specifically.</p> <p>Results: The analysis identified private water supply, and northerly farm location as risk factors for PT 21/28 presence. There was a significant association between the presence of PT 21/28 and an increased number of E. coli O157 positive pat samples from a farm, and PT 21/28 was significantly associated with larger E. coli O157 counts than non-PT 21/28 E. coli O157.</p> <p>Conclusion: PT 21/28 has significant risk factors that distinguish it from other phage types of E. coli O157. This finding has implications for the control of E. coli O157 as a whole and suggests that control could be tailored to target the locally dominant PT.</p&gt

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

The effects of dietary fish oil on hepatic high density and low density lipoprotein receptor activities in the rat

AbstractRats were fed either a standard ration diet or that diet supplemented with 8% by wt of a marine fish oil or safflower oil. After 10 days, plasma triacylglycerols, total cholesterol, high density lipoprotein (HDL) cholesterol, hepatic cholesterol and fatty acid synthesis and hepatic low density lipoprotein (LDL) receptor activity were significantly depressed while HDL receptor activity was significantly increased in rats fed fish oil. Fish oil-induced effects on cholesterol metabolism in the rat therefore include reciprocal changes in the activities of hepatic LDL and HDL receptors

Predicting the public health benefit of vaccinating cattle against Escherichia coli O157

Identifying the major sources of risk in disease transmission is key to designing effective controls. However, understanding of transmission dynamics across species boundaries is typically poor, making the design and evaluation of controls particularly challenging for zoonotic pathogens. One such global pathogen is Escherichia coli O157, which causes a serious and sometimes fatal gastrointestinal illness. Cattle are the main reservoir for E. coli O157, and vaccines for cattle now exist. However, adoption of vaccines is being delayed by conflicting responsibilities of veterinary and public health agencies, economic drivers, and because clinical trials cannot easily test interventions across species boundaries, lack of information on the public health benefits. Here, we examine transmission risk across the cattle–human species boundary and show three key results. First, supershedding of the pathogen by cattle is associated with the genetic marker stx2. Second, by quantifying the link between shedding density in cattle and human risk, we show that only the relatively rare supershedding events contribute significantly to human risk. Third, we show that this finding has profound consequences for the public health benefits of the cattle vaccine. A naïve evaluation based on efficacy in cattle would suggest a 50% reduction in risk; however, because the vaccine targets the major source of human risk, we predict a reduction in human cases of nearly 85%. By accounting for nonlinearities in transmission across the human–animal interface, we show that adoption of these vaccines by the livestock industry could prevent substantial numbers of human E. coli O157 cases

Interactions of asbestos-activated macrophages with an experimental fibrosarcoma

Supernatants from in vivo asbestos-activated macrophages failed to show any cytostatic activity against a syngeneic fibrosarcoma cell line in vitro. UICC chrysotile-induced peritoneal exudate cells also failed to demonstrate any growth inhibitory effect on the same cells in Winn assays of tumor growth. Mixing UICC crocidolite with inoculated tumor cells resulted in a dose-dependent inhibition of tumor growth; this could, however, be explained by a direct cytostatic effect on the tumor cells of high doses of crocidolite, which was observed in vitro

Ricci flow and black holes

Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the canonical ensemble for gravity in a box. At high temperature the action has three saddle points: hot flat space and a large and small black hole. Adding a time direction, these also give static 5-dimensional Kaluza-Klein solutions, whose potential energy equals the 4-dimensional action. The small black hole has a Gross-Perry-Yaffe-type negative mode, and is therefore unstable under Ricci flow. We numerically simulate the two flows seeded by this mode, finding that they lead to the large black hole and to hot flat space respectively, in the latter case via a topology-changing singularity. In the context of string theory these flows are world-sheet renormalization group trajectories. We also use them to construct a novel free energy diagram for the canonical ensemble.Comment: 31 pages, 14 color figures. v2: Discussion of the metric on the space of metrics corrected and expanded, references adde

Controlling magnetic order and quantum disorder in molecule-based magnets.

We investigate the structural and magnetic properties of two molecule-based magnets synthesized from the same starting components. Their different structural motifs promote contrasting exchange pathways and consequently lead to markedly different magnetic ground states. Through examination of their structural and magnetic properties we show that [Cu(pyz)(H 2 O)(gly) 2 ](ClO 4 ) 2 may be considered a quasi-one-dimensional quantum Heisenberg antiferromagnet whereas the related compound [Cu(pyz)(gly)](ClO 4 ) , which is formed from dimers of antiferromagnetically interacting Cu 2+ spins, remains disordered down to at least 0.03 K in zero field but shows a field-temperature phase diagram reminiscent of that seen in materials showing a Bose-Einstein condensation of magnons

Controlling magnetic order and quantum disorder in molecule-based magnets

We investigate the structural and magnetic properties of two molecule-based magnets synthesized from the same starting components. Their different structural motifs promote contrasting exchange pathways and consequently lead to markedly different magnetic ground states. Through examination of their structural and magnetic properties we show that [Cu(pyz)(H2O)(gly)2](ClO4)2 may be considered a quasi-one-dimensional quantum Heisenberg antiferromagnet whereas the related compound [Cu(pyz)(gly)](ClO4), which is formed from dimers of antiferromagnetically interacting Cu2+ spins, remains disordered down to at least 0.03 K in zero field but shows a field-temperature phase diagram reminiscent of that seen in materials showing a Bose-Einstein condensation of magnons