Ricci flows with unbounded curvature

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference

Ricci flows with bursts of unbounded curvature

Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time [GT11]. In the case that the underlying Riemann surface supports a hyperbolic metric, this Ricci flow always exists for all time and converges (after scaling by a factor 1/2t ) to this hyperbolic metric [GT11], i.e. our Ricci flow geometrises the surface. In this paper we show that there exist complete, bounded curvature initial metrics, including those conformal to a hyperbolic metric, which have subsequent Ricci flows developing unbounded curvature at certain intermediate times. In particular, when coupled with the uniqueness from [Top13], we find that any complete Ricci flow starting with such initial metrics must develop unbounded curvature over some intermediate time interval, but that nevertheless, the curvature must later become bounded and the flow must achieve geometrisation as t → ∞, even though there are other conformal deformations to hyperbolic metrics that do not involve unbounded curvature. Another consequence of our constructions is that while our Ricci flow from [GT11] must agree initially with the classical flow of Hamilton and Shi in the special case that the initial surface is complete and of bounded curvature, by uniqueness, it is now clear that our flow lasts for a longer time interval in general, with Shi’s flow stopping when the curvature blows up, but our flow continuing strictly beyond in these situations. All our constructions of unbounded curvature developing and then disappearing are in two dimensions. Generalisations to higher dimensions are then immediate

Decision Trees

The object of this paper is to inform those concerned with the administration of justice in Ethiopia – particularly, criminal justice – about a new and simple procedure which may assist in procuring uniform interpretation and application of laws and regulations. The problem of uniform interpretation and application is particularly severe where, as in Ethiopia, new laws must be interpreted and applied by persons who have not yet had the opportunity of formal legal education. For these persons the discovery of the relevant code articles and the understanding of their interrelationships and application must be very difficult indeed. One possible result of this unfortunate state of affairs is that the codes will not be fully, effectively, or consistently applied throughout the Empire. If, on the other hand, administrators try to avoid this problem by assigning the Empire\u27s comparatively few legally trained persons to such jobs as public prosecutor, woreda court judge, etc., then the result may be waste of legal resources. No one of these jobs is, in national perspective, of the very greatest importance; overall inefficiency of performance in them, on the other hand, can markedly reduce the quality of Ethiopian justice

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

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

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

How predation and landscape fragmentation affect vole population dynamics

Background: Microtine species in Fennoscandia display a distinct north-south gradient from regular cycles to stable populations. The gradient has often been attributed to changes in the interactions between microtines and their predators. Although the spatial structure of the environment is known to influence predator-prey dynamics of a wide range of species, it has scarcely been considered in relation to the Fennoscandian gradient. Furthermore, the length of microtine breeding season also displays a north-south gradient. However, little consideration has been given to its role in shaping or generating population cycles. Because these factors covary along the gradient it is difficult to distinguish their effects experimentally in the field. The distinction is here attempted using realistic agent-based modelling. Methodology/Principal Findings: By using a spatially explicit computer simulation model based on behavioural and ecological data from the field vole (Microtus agrestis), we generated a number of repeated time series of vole densities whose mean population size and amplitude were measured. Subsequently, these time series were subjected to statistical autoregressive modelling, to investigate the effects on vole population dynamics of making predators more specialised, of altering the breeding season, and increasing the level of habitat fragmentation. We found that fragmentation as well as the presence of specialist predators are necessary for the occurrence of population cycles. Habitat fragmentation and predator assembly jointly determined cycle length and amplitude. Length of vole breeding season had little impact on the oscillations. Significance: There is good agreement between our results and the experimental work from Fennoscandia, but our results allow distinction of causation that is hard to unravel in field experiments. We hope our results will help understand the reasons for cycle gradients observed in other areas. Our results clearly demonstrate the importance of landscape fragmentation for population cycling and we recommend that the degree of fragmentation be more fully considered in future analyses of vole dynamics

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