The max-plus Martin boundary

We develop an idempotent version of probabilistic potential theory. The goal is to describe the set of max-plus harmonic functions, which give the stationary solutions of deterministic optimal control problems with additive reward. The analogue of the Martin compactification is seen to be a generalisation of the compactification of metric spaces using (generalised) Busemann functions. We define an analogue of the minimal Martin boundary and show that it can be identified with the set of limits of ``almost-geodesics'', and also the set of (normalised) harmonic functions that are extremal in the max-plus sense. Our main result is a max-plus analogue of the Martin representation theorem, which represents harmonic functions by measures supported on the minimal Martin boundary. We illustrate it by computing the eigenvectors of a class of translation invariant Lax-Oleinik semigroups. In this case, we relate the extremal eigenvectors to the Busemann points of a normed space.Comment: 37 pages; 8 figures v1: December 20, 2004. v2: June 7, 2005. Section 12 adde

How to find horizon-independent optimal strategies leading off to infinity: a max-plus approach

A general problem in optimal control consists of finding a terminal reward that makes the value function independent of the horizon. Such a terminal reward can be interpreted as a max-plus eigenvector of the associated Lax-Oleinik semigroup. We give a representation formula for all these eigenvectors, which applies to optimal control problems in which the state space is non compact. This representation involves an abstract boundary of the state space, which extends the boundary of metric spaces defined in terms of Busemann functions (the horoboundary). Extremal generators of the eigenspace correspond to certain boundary points, which are the limit of almost-geodesics. We illustrate our results in the case of a linear quadratic problem.Comment: 13 pages, 5 figures, To appear in Proc. 45th IEEE Conference on Decision and Contro

Higher-order Fourier analysis of Fpn\mathbb{F}_p^n and the complexity of systems of linear forms

Consider a subset $A$ of $\mathbb{F}_p^n$ and a decomposition of its indicator function as the sum of two bounded functions $1_A=f_1+f_2$. For every family of linear forms, we find the smallest degree of uniformity $k$ such that assuming that $\|f_2\|_{U^k}$ is sufficiently small, it is possible to discard $f_2$ and replace $1_A$ with $f_1$ in the average over this family of linear forms, affecting it only negligibly. Previously, Gowers and Wolf solved this problem for the case where $f_1$ is a constant function. Furthermore, our main result solves Problem 7.6 in [W. T. Gowers and J. Wolf. Linear forms and higher-degree uniformity for functions on $\mathbb{F}_p^n$. Geom. Funct. Anal., 21(1):36--69, 2011] regarding the analytic averages that involve more than one subset of $\mathbb{F}_p^n$.] regarding the analytic averages that involve more than one subset of $\mathbb{F}_p^n$.Comment: final version, 25 page

Diabetes-related knowledge, attitude and practices (KAP) of adult patients with type 2 diabetes mellitus in the Free State province, South Africa

Introduction: Type 2 diabetes mellitus (T2DM) is a global health problem with high morbidity and mortality in patients who are mostly still economically active. The growing incidence and health implications for those affected make T2DM a major public health issue. Objectives: To compile a demographic, anthropometric and knowledge, attitude and practices (KAP) profile of adult patients with T2DM in the public health sector of the Free State province, South Africa. Design: A descriptive observational study was conducted. Setting: A total of 255 participants attending public health facilities in the Free State were interviewed. Outcome Measures: Questionnaires were completed in an interview to determine demographics and KAP. Anthropometric measurements were obtained by standard techniques. Results: The majority of the participants (n = 222; 87.1%) were black women from urban areas, who were overweight and obese. The median age at diagnosis was 48 years (range 15–80 years), and 25 participants (9.8%) lacked formal schooling. In 212 participants (83.1%), a waist circumference above cut-off points was observed. Only half of the participants knew the normal range for blood glucose. Approximately 80% felt that they would be a different person if they did not have diabetes. Although 96.1% of participants were knowledgeable about the benefits of physical exercise, only 31.0% reported exercising on a daily basis. A statistically significant association was found between knowledge and attitudes, indicating that better knowledge about diabetes could be associated with a more positive attitude towards diabetes. Conclusion: Poor knowledge, a negative attitude and poor practices related to diabetes were observed in a very high percentage of participants, which may contribute to morbidity and mortality. The fact that knowledge was associated with attitude indicates that interventions aimed at improving knowledge could benefit patients in more than one way. Interventions to equip patients to successfully manage their condition are urgently required

Recent Common Ancestry of Ebola Zaire Virus Found in a Bat Reservoir

No abstract available

Evaluation of the protective potential of antibody and T cell responses elicited by a novel preventative vaccine towards respiratory syncytial virus small hydrophobic protein

The small hydrophobic (SH) glycoprotein of human respiratory syncytial virus (RSV) is a transmembrane protein that is poorly accessible by antibodies on the virion but has an ectodomain (SHe) that is accessible and expressed on infected cells. The SHe from RSV strain A has been formulated in DPX, a unique delivery platform containing an adjuvant, and is being evaluated as an RSV vaccine candidate. The proposed mechanism of protection is the immune-mediated clearance of infected cells rather than neutralization of the virion. Our phase I clinical trial data dearly showed that vaccination resulted in robust antibody responses, but it was unclear if these immune responses have any correlation to immune responses to natural infection with RSV. Therefore, we embarked on this study to examine these immune responses in older adults with confirmed RSV infection. We compared vaccine-induced (DPX-RSV(A)) immune responses from participants in a Phase 1 clinical trial to paired acute and convalescent titers from older adults with symptomatic laboratory-confirmed RSV infection. Serum samples were tested for anti-SHe IgG titers and the isotypes determined. T cell responses were evaluated by IFN-gamma ELISPOT. Anti-SHe titers were detected in 8 of 42 (19%) in the acute phase and 16 of 42 (38%) of convalescent serum samples. IgG1, IgG3, and IgA were the prevalent isotypes generated by both vaccination and infection. Antigen-specific T cell responses were detected in 9 of 16 (56%) of vaccinated participants. Depletion of CD4(+) but not CD8(+) T cells abrogated the IFN-gamma ELISPOT response supporting the involvement of CD4(+) T cells in the immune response to vaccination. The data showed that an immune response like that induced by DPX-RSV(A) could be seen in a subset of participants with confirmed RSV infection. These findings show that older adults with clinically significant infection as well as vaccinated adults generate a humoral response to SHe. The induction of both SHe-specific antibody and cellular responses support further clinical development of the DPX-RSV(A) vaccine

Aeromedical retrieval services characteristics globally: a scoping review

Background Aeromedical emergency retrieval services play an important role in supporting patients with critical and often life-threatening clinical conditions. Aeromedical retrieval services help to provide fast access to definitive care for critically ill patients in under-served regions. Typically, fixed-wing aeromedical retrieval becomes the most viable transport option compared with rotary-wing aircraft when distances away from centres of definitive care extend beyond 200 kms. To our knowledge, there are no studies that have investigated fixed-wing aeromedical services in the member countries of the organisation for economic cooperation and development (OECD). A description of the global characteristics of aeromedical services will inform international collaboration to optimise clinical outcomes for patients. Aim In this scoping review, we aimed to describe the features of government- and not-for-profit organisation-owned fixed-wing aeromedical retrieval services in some of the member countries of the OECD. Methods We followed scoping review methodology based on the grey literature search strategy identified in earlier studies. This mostly involved internet-based searches of the websites of fixed-wing aeromedical emergency retrieval services affiliated with the OECD member countries. Results We identified 460 potentially relevant records after searching Google Scholar (n = 24) and Google search engines (n = 436). After removing ineligible and duplicate information, this scoping review identified 86 government-and not-for-profit-operated fixed-wing aeromedical retrieval services as existing in 17 OECD countries. Concentrations of the services were greatest in the USA followed by Australia, Canada, and the UK. The most prevalent business models used across the identified OECD member countries comprised the government, not-for-profit, and hybrid models. Three-quarters of the not-for-profit and two-fifths of the hybrid business models were in the USA compared to other countries studied. The government or state-funded business model was most common in Australia (11/24, 46%), Canada (4/24, 17%), and the UK (4/24, 17%). The frequently used service delivery models adopted for patients of all ages included primary/secondary retrievals, secondary retrievals only, and service specialisation models. Of these service models, primary/secondary retrieval involving the transportation of adults and children from community clinics and primary health care facilities to centres of definitive care comprised the core tasks performed by most of the aeromedical retrieval services studied. The service specialisation model provided an extra layer of specialist health care dedicated to the transportation of neonates and paediatrics. At least eight aeromedical retrieval services catered solely for children from birth to 16 years of age. One aeromedical service, the royal flying doctor service in Australia also provided primary health care and telehealth services in addition to primary retrieval and interhospital transfer of patients. The doctor and registered nurse/paramedic (Franco-German model) and the nurse and/or paramedic (Anglo-American model) configurations were the most common staffing models used across the aeromedical services studied. Conclusions The development and composition of fixed-wing aeromedical emergency retrieval services operated by not-for-profit organisations and governments in the OECD countries showed diversity in terms of governance arrangements, services provided, and staffing models used. We do not fully understand the impact of these differences on the quality of service provision, including equitable service access, highlighting a need for further research.publishedVersio