The horofunction boundary of the Hilbert geometry

We investigate the horofunction boundary of the Hilbert geometry defined on an arbitrary finite-dimensional bounded convex domain D. We determine its set of Busemann points, which are those points that are the limits of `almost-geodesics'. In addition, we show that any sequence of points converging to a point in the horofunction boundary also converges in the usual sense to a point in the Euclidean boundary of D. We prove that all horofunctions are Busemann points if and only if the set of extreme sets of the polar of D is closed in the Painleve-Kuratowski topology.Comment: 24 pages, 2 figures; minor changes, examples adde

Asymptotic behaviour of random Markov chains with tridiagonal generators

Continuous-time discrete-state random Markov chains generated by a random linear differential equation with a random tridiagonal matrix are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of probability vectors. The proof uses comparison theorems for Carath\'eodory random differential equations and the fact that the linear cocycle generated by the Markov chain is a uniformly contractive mapping of the positive cone into itself with respect to the the Hilbert projective metric. It does not involve probabilistic properties of the sample path and is thus equally valid in the nonautonomous deterministic context of Markov chains with, say, periodically varying transitions probabilities, in which case the attractor is a periodic path.Comment: 11 pages, 15 bibliography references, added bibliography, minor change

High-frequency oscillatory ventilation in pediatric acute hypoxemic respiratory failure: disease-specific morbidity survival analysis.

BackgroundMultiple ventilatory strategies for acute hypoxemic respiratory failure (AHRF) in children have been advocated, including high-frequency oscillatory ventilation (HFOV). Despite the frequent deployment of HFOV, randomized controlled trials remain elusive and currently there are no pediatric trials looking at its use. Our longitudinal study analyzed the predictive clinical outcome of HFOV in pediatric AHRF given disease-specific morbidity.MethodsA retrospective 8-year review on pediatric intensive care unit admissions with AHRF ventilated by HFOV was performed. Primary outcomes included survival, morbidity, length of stay (LOS), and factors associated with survival or mortality.ResultsA total of 102 patients underwent HFOV with a 66 % overall survival rate. Survivors had a greater LOS than nonsurvivors (p = 0.001). Mortality odds ratio (OR) for patients without bronchiolitis was 8.19 (CI = 1.02, 65.43), and without pneumonia it was 3.07 (CI = 1.12, 8.39). A lower oxygenation index (OI) after HFOV commencement and at subsequent time points analyzed predicted survival. After 24 h, mortality was associated with an OI > 35 [OR = 31.11 (CI = 3.25, 297.98)]. Sepsis-related mortality was associated with a higher baseline FiO(2) (0.88 vs. 0.65), higher OI (42 vs. 22), and augmented metabolic acidosis (pH of 7.25 vs. 7.32) evaluated 4 h on HFOV (p < 0.05).ConclusionHigh-frequency oscillatory ventilation may be safely utilized. It has a 66 % overall survival rate in pediatric AHRF of various etiologies. Patients with morbidity limited to the respiratory system and optimized oxygenation indices are most likely to survive on HFOV

Some Guidance on Conducting and Reporting Qualitative Studies

This paper sets out to address the problem of the imbalance between the number of quantitative and qualitative articles published in highly ranked research journals, by providing guidelines for the design, implementation and reporting of qualitative research. Clarification is provided of key terms (such as quantitative and qualitative) and the interrelationships between them. The relative risks and benefits of using guidelines for qualitative research are considered, and the importance of using any such guidelines flexibly is highlighted. The proposed guidelines are based on a synthesis of existing guidelines and syntheses of guidelines from a range of fields

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on $n$ letters, where $n$ is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.Comment: 36 pages, 1 fugur

Ten myths about character, virtue and virtue education – plus three well-founded misgivings

Initiatives to cultivate character and virtue in moral education at school continue to provoke sceptical responses. Most of those echo familiar misgivings about the notions of character, virtue and education in virtue – as unclear, redundant, old-fashioned, religious, paternalistic, anti-democratic, conservative, individualistic, relative and situation dependent. I expose those misgivings as ‘myths’, while at the same time acknowledging three better-founded historical, methodological and practical concerns about the notions in question

Women\u2019s human rights when experiencing humanitarian crises and conflicts: the impact of United Nations Security Council Resolutions on women, peace, security, and the CEDAW General Recommendation no. 30.

Violence and insecurity are strictly linked to unequal political, social, and economic power. However, the continuity of violence is obscured by masculinist and patriarchal rules of security within gendered structures, especially inside the division of public/private dimensions and spaces, of production-reproduction activities, and of conflicts of war/peace. Nowadays, there is a general perception of the gendered dimensions of humanitarian emergencies in public policy outcomes and more in general in institutional contexts where the central role of women in security and maintaining peace, at all levels of decision making, both prior to, during, and after the conflict stage, hostilities, and peace-keeping and peace-building stages, as well as in trying to pursue a condition of reconciliation and reconstruction, has been formally recognized at international level. Nevertheless, it is necessary to focus on some problems related to the conceptualization of and legal provision for \u2018gender based security\u2019 and its subsequent effects upon accountability, with particular reference to transitional justice and post-conflict societies. It is important to assess a range of contemporary issues implicated for women and security, such as violence and other forms of harassment in times of post-conflict

Research on ICT in K-12 schools e A review of experimental and survey-based studies in computers & education 2011 to 2015

International audienceWhat is the role of a journal? Is it to follow the research or lead it? For the former, it is to serve as an archival record of the scholarship in a field. It can serve to permit the research community to engage with each other via the written record. But, for the latter, it can serve the research community by pointing out gaps in the research based on the archival record. This review is intended to do just that

Educating for Autonomy: Liberalism and Autonomy in the Capabilities Approach

Martha Nussbaum grounds her version of the capabilities approach in political liberalism. In this paper, we argue that the capabilities approach, insofar as it genuinely values the things that persons can actually do and be, must be grounded in a hybrid account of liberalism: in order to show respect for adults, its justification must be political; in order to show respect for children, however, its implementation must include a commitment to comprehensive autonomy, one that ensures that children develop the skills necessary to make meaningful choices about whether or not to exercise their basic capabilities. Importantly, in order to show respect for parents who do not necessarily recognize autonomy as a value, we argue that the liberal state, via its system of public education, should take on the role of ensuring that all children within the state develop a sufficient degree of autonomy

Normal Cones and Thompson Metric

The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the linear structure. We also prove several convexity properties of $d_T$ and some results concerning the topology of $d_T$, including a brief study of the $d_T$-convergence of monotone sequences. It is shown most of the results are true without any assumption of an Archimedean-type property for $K$. One considers various completeness properties and one studies the relations between them. Since $d_T$ is defined in the context of a generic ordered linear space, with no need of an underlying topological structure, one expects to express its completeness in terms of properties of the ordering, with respect to the linear structure. This is done in this paper and, to the best of our knowledge, this has not been done yet. The Thompson metric $d_T$ and order-unit (semi)norms $|\cdot|_u$ are strongly related and share important properties, as both are defined in terms of the ordered linear structure. Although $d_T$ and $|\cdot|_u$ are only topological (and not metrical) equivalent on $K_u$, we prove that the completeness is a common feature. One proves the completeness of the Thompson metric on a sequentially complete normal cone in a locally convex space. At the end of the paper, it is shown that, in the case of a Banach space, the normality of the cone is also necessary for the completeness of the Thompson metric.Comment: 36 page