Cyclic projectors and separation theorems in idempotent convex geometry

Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold cartesian product of the max-plus semiring it is known that one can separate a vector from a closed subsemimodule that does not contain it. We establish here a more general separation theorem, which applies to any finite collection of closed semimodules with a trivial intersection. In order to prove this theorem, we investigate the spectral properties of certain nonlinear operators called here idempotent cyclic projectors. These are idempotent analogues of the cyclic nearest-point projections known in convex analysis. The spectrum of idempotent cyclic projectors is characterized in terms of a suitable extension of Hilbert's projective metric. We deduce as a corollary of our main results the idempotent analogue of Helly's theorem.Comment: 20 pages, 1 figur

Perceptions of childhood immunization in a minority community: Qualitative study

This is the author's accepted manuscript. The final published article is available from the link below. Published article copyright @ The Royal Society of Medicine.Objective - To assess reasons for low uptake of immunization amongst orthodox Jewish families. Design - Qualitative interviews with 25 orthodox Jewish mothers and 10 local health care workers. Setting - The orthodox Jewish community in North East London. Main outcome measures - Identification of views on immunization in the orthodox Jewish community. Results - In a community assumed to be relatively insulated from direct media influence, word of mouth is nevertheless a potent source of rumours about vaccination dangers. The origins of these may lie in media scares that contribute to anxieties about MMR. At the same time, close community cohesion leads to a sense of relative safety in relation to tuberculosis, with consequent low rates of BCG uptake. Thus low uptake of different immunizations arises from enhanced feelings of both safety and danger. Low uptake was not found to be due to the practical difficulties associated with large families, or to perceived insensitive cultural practices of health care providers. Conclusions - The views and practices of members of this community are not homogeneous and may change over time. It is important that assumptions concerning the role of religious beliefs do not act as an obstacle for providing clear messages concerning immunization, and community norms may be challenged by explicitly using its social networks to communicate more positive messages about immunization. The study provides a useful example of how social networks may reinforce or challenge misinformation about health and risk and the complex nature of decision making about children's health.City and Hackney Teaching Primary Care Trus

The level set method for the two-sided eigenproblem

We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a finite union of intervals, can be computed in pseudo-polynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introduction of a spectral function, which we interpret in terms of the least Chebyshev distance between Ax and lambda Bx. The spectrum is obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we explain relation to mean-payoff games and discrete event systems, and show that the reconstruction of spectrum is pseudopolynomia

Detecting Features from Confusion Matrices using Generalized Formal Concept Analysis

We claim that the confusion matrices of multiclass problems can be analyzed by means of a generalization of Formal Concept Analysis to obtain symbolic information about the feature sets of the underlying classification task.We prove our claims by analyzing the confusion matrices of human speech perception experiments and comparing our results to those elicited by experts.This work has been supported by Spanish Government-Comisión Interministerial de Ciencia y Tecnología TEC2008-02473/TEC y TEC2008-06382/TEC.Publicad

Under-vaccinated groups in Europe and their beliefs, attitudes and reasons for non-vaccination; two systematic reviews

BackgroundDespite effective national immunisation programmes in Europe, some groups remain incompletely or un-vaccinated ('under-vaccinated'), with underserved minorities and certain religious/ideological groups repeatedly being involved in outbreaks of vaccine preventable diseases (VPD). Gaining insight into factors regarding acceptance of vaccination of 'under-vaccinated groups' (UVGs) might give opportunities to communicate with them in a trusty and reliable manner that respects their belief system and that, maybe, increase vaccination uptake. We aimed to identify and describe UVGs in Europe and to describe beliefs, attitudes and reasons for non-vaccination in the identified UVGs.MethodsWe defined a UVG as a group of persons who share the same beliefs and/or live in socially close-knit communities in Europe and who have/had historically low vaccination coverage and/or experienced outbreaks of VPDs since 1950. We searched MEDLINE, EMBASE and PsycINFO databases using specific search term combinations. For the first systematic review, studies that described a group in Europe with an outbreak or low vaccination coverage for a VPD were selected and for the second systematic review, studies that described possible factors that are associated with non-vaccination in these groups were selected.ResultsWe selected 48 articles out of 606 and 13 articles out of 406 from the first and second search, respectively. Five UVGs were identified in the literature: Orthodox Protestant communities, Anthroposophists, Roma, Irish Travellers, and Orthodox Jewish communities. The main reported factors regarding vaccination were perceived non-severity of traditional "childhood" diseases, fear of vaccine side-effects, and need for more information about for example risk of vaccination.ConclusionsWithin each UVG identified, there are a variety of health beliefs and objections to vaccination. In addition, similar factors are shared by several of these groups. Communication strategies regarding these similar factors such as educating people about the risks associated with being vaccinated versus not being vaccinated, addressing their concerns, and countering vaccination myths present among members of a specific UVG through a trusted source, can establish a reliable relationship with these groups and increase their vaccination uptake. Furthermore, other interventions such as improving access to health care could certainly increase vaccination uptake in Roma and Irish travellers