Convergence of Markov processes near saddle fixed points.

We consider sequences (XtN)t≥0 of Markov processes in two dimensions whose fluid limit is a stable solution of an ordinary differential equation of the form ẋt=b(xt), where for some λ, μ>0 and τ(x)=O(|x|2). Here the processes are indexed so that the variance of the fluctuations of XtN is inversely proportional to N. The simplest example arises from the OK Corral gunfight model which was formulated by Williams and McIlroy [Bull. London Math. Soc. 30 (1998) 166–170] and studied by Kingman [Bull. London Math. Soc. 31 (1999) 601–606]. These processes exhibit their most interesting behavior at times of order logN so it is necessary to establish a fluid limit that is valid for large times. We find that this limit is inherently random and obtain its distribution. Using this, it is possible to derive scaling limits for the points where these processes hit straight lines through the origin, and the minimum distance from the origin that they can attain. The power of N that gives the appropriate scaling is surprising. For example if T is the time that XtN first hits one of the lines y=x or y=−x, then Nμ/{(2(λ+μ))}|XTN| ⇒ |Z|μ/{(λ+μ)}, for some zero mean Gaussian random variable Z

A quantitative probabilistic investigation into the accumulation of rounding errors in numerical ODE solution.

We examine numerical rounding errors of some deterministic solvers for systems of ordinary differential equations (ODEs) from a probabilistic viewpoint. We show that the accumulation of rounding errors results in a solution which is inherently random and we obtain the theoretical distribution of the trajectory as a function of time, the step size and the numerical precision of the computer. We consider, in particular, systems which amplify the effect of the rounding errors so that over long time periods the solutions exhibit divergent behaviour. By performing multiple repetitions with different values of the time step size, we observe numerically the random distributions predicted theoretically. We mainly focus on the explicit Euler and fourth order Runge–Kutta methods but also briefly consider more complex algorithms such as the implicit solvers VODE and RADAU5 in order to demonstrate that the observed effects are not specific to a particular method

The impact on the Scottish economy of reducing greenhouse gas emissions in Scotland: Illustrative findings from an experimental computable general equilibrium model for Scotland: Final Report October 2008

First paragraph: This project uses an experimental energy-economy-environment computable general equilibrium (CGE) model of the Scottish economy (AMOSENVI) to conduct illustrative simulations of the economic and environmental impacts of various options to reduce the generation of CO2 emissions (as the main greenhouse gas) in Scotland. These simulations are illustrative in nature because the process of appropriate database development and model specification for a comprehensive and accurate analysis of climate change policy issues for Scotland, while advanced relative to many regional (and even national) economies, is still in its very early stages. One of the key objectives of this project is to illustrate the potential value-added to Scotland's analytical capacity if further investment is made (by both the policy community, particularly in terms of data provision, and the research community, with public support, for example by seeking support from the research councils) in developing an appropriate CGE modelling framework

A feasibility study into the production of a mussel matrix reference material for the cyanobacterial toxins microcystins and nodularins.

Microcystins and nodularins, produced naturally by certain species of cyanobacteria, have been found to accumulate in aquatic foodstuffs such as fish and shellfish, resulting in a risk to the health of the seafood consumer. Monitoring of toxins in such organisms for risk management purposes requires the availability of certified matrix reference materials to aid method development, validation and routine quality assurance. This study consequently targeted the preparation of a mussel tissue reference material incurred with a range of microcystin analogues and nodularins. Nine targeted analogues were incorporated into the material as confirmed through liquid chromatography with tandem mass spectrometry (LC-MS/MS), with an additional 15 analogues detected using LC coupled to non-targeted high resolution mass spectrometry (LC-HRMS). Toxins in the reference material and additional source tissues were quantified using LC-MS/MS, two different enzyme-linked immunosorbent assay (ELISA) methods and with an oxidative-cleavage method quantifying 3-methoxy-2-methyl-4-phenylbutyric acid (MMPB). Correlations between the concentrations quantified using the different methods were variable, likely relating to differences in assay cross-reactivities and differences in the abilities of each method to detect bound toxins. A consensus concentration of total soluble toxins determined from the four independent test methods was 2425 ± 575 µg/kg wet weight. A mean 43 ± 9% of bound toxins were present in addition to the freely extractable soluble form (57 ± 9%). The reference material produced was homogenous and stable when stored in the freezer for six months without any post-production stabilization applied. Consequently, a cyanotoxin shellfish reference material has been produced which demonstrates the feasibility of developing certified seafood matrix reference materials for a large range of cyanotoxins and could provide a valuable future resource for cyanotoxin risk monitoring, management and mitigation

Two Rare Magnetic Cataclysmic Variables with Extreme Cyclotron Features Identified in the Sloan Digital Sky Survey

Two newly identified magnetic cataclysmic variables discovered in the Sloan Digital Sky Survey (SDSS), SDSSJ155331.12+551614.5 and SDSSJ132411.57+032050.5, have spectra showing highly prominent, narrow, strongly polarized cyclotron humps with amplitudes that vary on orbital periods of 4.39 and 2.6 hrs, respectively. In the former, the spacing of the humps indicates the 3rd and 4th harmonics in a magnetic field of ~60 MG. The narrowness of the cyclotron features and the lack of strong emission lines imply very low temperature plasmas and very low accretion rates, so that the accreting area is heated by particle collisions rather than accretion shocks. The detection of rare systems like these exemplifies the ability of the SDSS to find the lowest accretion rate close binaries.Comment: Accepted for publication in the Astrophysical Journal, vol. 583, February 1, 2003; slight revisions and additions in response to referee's comments; 17 pages, 6 figures, AASTeX v4.

Sri Lankan tsunami refugees: a cross sectional study of the relationships between housing conditions and self-reported health

BACKGROUND: On the 26th December 2004 the Asian tsunami devastated the Sri Lankan coastline. More than two years later, over 14,500 families were still living in transitional shelters. This study compares the health of the internally displaced people (IDP), living in transitional camps with those in permanent housing projects provided by government and non-government organisations in Sri Lanka. METHODS: This study was conducted in seven transitional camps and five permanent housing projects in the south west of Sri Lanka. Using an interviewer-led questionnaire, data on the IDPs' self-reported health and housing conditions were collected from 154 participants from transitional camps and 147 participants from permanent housing projects. Simple tabulation with non-parametric tests and logistic regression were used to identify and analyse relationships between housing conditions and the reported prevalence of specific symptoms. RESULTS: Analysis showed that living conditions were significantly worse in transitional camps than in permanent housing projects for all factors investigated, except 'having a leaking roof'. Transitional camp participants scored significantly lower on self-perceived overall health scores than those living in housing projects. After controlling for gender, age and marital status, living in a transitional camp compared to a housing project was found to be a significant risk factor for the following symptoms; coughs OR: 3.53 (CI: 2.11-5.89), stomach ache 4.82 (2.19-10.82), headache 5.20 (3.09-8.76), general aches and pains 6.44 (3.67-11.33) and feeling generally unwell 2.28 (2.51-7.29). Within transitional camp data, the only condition shown to be a significant risk factor for any symptom was household population density, which increased the risk of stomach aches 1.40 (1.09-1.79) and headaches 1.33 (1.01-1.77). CONCLUSION: Internally displaced people living in transitional camps are a vulnerable population and specific interventions need to be targeted at this population to address the health inequalities that they report to be experiencing. Further studies need to be conducted to establish which aspects of their housing environment predispose them to poorer health

Identification and Selection of Cases and Controls in the Pneumonia Etiology Research for Child Health Project

Methods for the identification and selection of patients (cases) with severe or very severe pneumonia and controls for the Pneumonia Etiology Research for Child Health (PERCH) project were needed. Issues considered include eligibility criteria and sampling strategies, whether to enroll hospital or community controls, whether to exclude controls with upper respiratory tract infection (URTI) or nonsevere pneumonia, and matching criteria, among others. PERCH ultimately decided to enroll community controls and an additional human immunodeficiency virus (HIV)–infected control group at high HIV-prevalence sites matched on age and enrollment date of cases; controls with symptoms of URTI or nonsevere pneumonia will not be excluded. Systematic sampling of cases (when necessary) and random sampling of controls will be implemented. For each issue, we present the options that were considered, the advantages and disadvantages of each, the rationale for the methods selected for PERCH, and remaining implications and limitations

From the Yellow Springs to the Land of Immortality

The Yellow Springs is a vivid metaphorical reference to the final destination of a mortal being and the dwelling place of a departed one in ancient China. In the writings of philosophers, historians, and poets during the long period of Chinese history, the Yellow Springs is not only considered as an underground physical locus where a grave is situated, but also an emotionally charged space invoke grieving, longing, and memory for the departed loved ones. The subterranean dwelling at the Yellow Springs is both a destination for a departed mortal being and an intermediary place to an ideal and imaginative realm, the land of immortality where the soul would enjoy eternity. From the Yellow Springs to the Land of Immortality is an exhibition that highlights sixteen carefully selected artworks from Gettysburg College’s Special Collections; each object embodies the perceptions and ritual practices of the rich funerary culture in the historical period in China, ranging from the late second millennium BCE to the beginning of the early twentieth century. These artifacts represent various artistic traditions and fabrication techniques — including jade carving, bronze casting, glazed pottery making — and most importantly, offer a glimpse of how art and artifacts are employed as a means to connect the living with the soul of the departed one in the Yellow Springs. Archaeo- logical discoveries in the past four decades in China have provided rich information that helps contextualize the sixteen artworks, as well as intimate knowledge about how the objects might “perform” in the life and afterlife of the individuals in the past. The practice of burying goods alongside departed loved ones has had a long tradition in China. The artworks included in this exhibition catalogue, encompassing the major dynasties in Chinese history, epitomize such a practice from a historical point of view. The bronze jue of the Shang dynasty (mid-16th c.-1046 BCE), and the miniature bell, a replica of yong bronze bell of the Zhou dynasty (1045-256 BCE), are not only ceremonial paraphernalia used by elites in ancestral sacrifices during the Bronze Age, but also material manifestations of ritual and music, the very foundations of ancient Chinese civilization. Comparable examples found in Bronze Age tombs illustrate the idea to connect the deceased, often the owner of these ritual objects, to the ancestors in the netherworld as they themselves were transitioned into the role of ancestors through a series of funerary ceremonies. [excerpt]https://cupola.gettysburg.edu/artcatalogs/1034/thumbnail.jp

Model-based evaluation of the long-term cost-effectiveness of systematic case-finding for COPD in primary care

Introduction'One-off' systematic case-finding for COPD using a respiratory screening questionnaire is more effective and cost-effective than routine care at identifying new cases. However, it is not known whether early diagnosis and treatment is beneficial in the longer term. We estimated the long-term cost-effectiveness of a regular case-finding programme in primary care.MethodsA Markov decision analytic model was developed to compare the cost-effectiveness of a 3-yearly systematic case-finding programme targeted to ever smokers aged ≥50 years with the current routine diagnostic process in UK primary care. Patient-level data on case-finding pathways was obtained from a large randomised controlled trial. Information on the natural history of COPD and treatment effects was obtained from a linked COPD cohort, UK primary care database and published literature. The discounted lifetime cost per quality-adjusted life-year (QALY) gained was calculated from a health service perspective.ResultsThe incremental cost-effectiveness ratio of systematic case-finding versus current care was £16 596 per additional QALY gained, with a 78% probability of cost-effectiveness at a £20 000 per QALY willingness-to-pay threshold. The base case result was robust to multiple one-way sensitivity analyses. The main drivers were response rate to the initial screening questionnaire and attendance rate for the confirmatory spirometry test.DiscussionRegular systematic case-finding for COPD using a screening questionnaire in primary care is likely to be cost-effective in the long-term despite uncertainties in treatment effectiveness. Further knowledge of the natural history of case-found patients and the effectiveness of their management will improve confidence to implement such an approach