Cylindrical Algebraic Sub-Decompositions

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem. We define two new types of sub-CAD: variety sub-CADs which are those cells in a CAD lying on a designated variety; and layered sub-CADs which have only those cells of dimension higher than a specified value. We present algorithms to produce these and describe how the two approaches may be combined with each other and the recent theory of truth-table invariant CAD. We give a complexity analysis showing that these techniques can offer substantial theoretical savings, which is supported by experimentation using an implementation in Maple.Comment: 26 page

Anomalous isotopic predissociation in the F³Πu(v=1) state of O₂

Using a tunable, narrow-bandwidth vacuum-ultraviolet source based on third-harmonic generation from excimer-pumped dye-laser radiation, the F³Πu←X³Σg-(1,0)photoabsorption cross sections of ¹⁶O₂ and ¹⁸O₂ have been recorded in high resolution. Rotational analyses have been performed and the resultant F(v=1) term values fitted to the ³Π Hamiltonian of Brown and Merer [J. Mol. Spectrosc. 74, 488 (1979)]. A large rotationless isotope effect is observed in the F(v=1)predissociation, wherein the Lorentzian linewidth component for ¹⁸O₂ is a factor of ∼50 smaller than the corresponding ¹⁶O₂linewidth. This effect, a consequence of the nonadiabatic rotationless predissociation mechanism, is described using a coupled-channel treatment of the strongly Rydberg-valence-mixed 3Πu states. Significant J, e/f-parity, and sublevel dependencies observed in the isotopic F(v=1) rotational widths are found to derive from an indirect predissociation mechanism involving an accidental degeneracy with the E³Σ−u(v=3) level, itself strongly predissociated by ³Σ−u Rydberg-valence interactions, together with L-uncoupling (rotational) interactions between the Rydberg components of the F and E states. Transitions into the E(v=3) level are observed directly for the first time, specifically in the ¹⁸O₂ spectrumPartial support was provided by an NSF International Opportunities for Scientists and Engineers Program Grant No. INT-9513350, and Visiting Fellowships for G.S. and J.B.W. at the Australian National University

Deaf and hearing children's picture naming Impact of age of acquisition and language modality on representational gesture

Stefanini, Bello, Caselli, Iverson, & Volterra (2009) reported that Italian 24-36 month old children use a high proportion of representational gestures to accompany their spoken responses when labelling pictures. The two studies reported here used the same naming task with (1) typically developing 24-46-month-old hearing children acquiring English and (2) 24-63-month-old deaf children of deaf and hearing parents acquiring British Sign Language (BSL) and spoken English. In Study 1 children scored within the range of correct spoken responses previously reported, but produced very few representational gestures. However, when they did gesture, they expressed the same action meanings as reported in previous research. The action bias was also observed in deaf children of hearing parents in Study 2, who labelled pictures with signs, spoken words and gestures. The deaf group with deaf parents used BSL almost exclusively with few additional gestures. The function of representational gestures in spoken and signed vocabulary development is considered in relation to differences between native and non-native sign language acquisition

Safety drain system for fluid reservoir

A safety drain system includes a plurality of drain sections, each of which defines distinct fluid flow paths. At least a portion of the fluid flow paths commence at a side of the drain section that is in fluid communication with a reservoir's fluid. Each fluid flow path at the side communicating with the reservoir's fluid defines an opening having a smallest dimension not to exceed approximately one centimeter. The drain sections are distributed over at least one surface of the reservoir. A manifold is coupled to the drain sections

On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins

This paper brings together analytic and simulation-based approaches to reserve risk in general (P&C) insurance, applied to the traditional actuarial view of risk over the lifetime of the liabilities and to the one-year view of Solvency II. It also connects the lifetime and one-year views of risk. The framework of the model in Mack (1993) is used throughout, although the results have wider applicability. The advantages of a simulation-based approach are highlighted, giving a full predictive distribution, which is used to estimate risk margins under Solvency II and risk adjustments under IFRS 17. We discuss methods for obtaining capital requirements in a cost-of-capital risk margin, and methods for estimating risk adjustments using risk measures applied to a simulated distribution of the outstanding liabilities over their lifetime

The Leadership Role of Psychiatrists in the NHS

This article explores leadership in the context of psychiatry in the NHS. It identifies considerable policy challenges facing psychiatry such as recent attempts to upgrade mental health services and bring them up to par with other services. It suggests it will become increasingly necessary for the profession to respond to such challengers by engaging with leadership at various levels. The article suggests there may be merit in exploring one particular approach to leadership, namely transformational leadership, given its emphasis on dealing with change. Psychiatrists may find the behaviours associated with this approach of particular relevance. However, it suggests that there may need to adopt a particular variant of transformational leadership that acknowledges both the achievement of objectives and showing genuine concern for followers. The latter is important given the on going problem of clinical engagement in the NHS. The article concludes with the developmental implications in adopting this leadership approach

Reviewing research evidence and the case of participation in sport and physical recreation by black and minority ethnic communities

The paper addresses the implications of using the process of systematic review in the many areas of leisure where there is a dearth of material that would be admitted into conventional Cochrane Reviews. This raises important questions about what constitutes legitimate knowledge, questions that are of critical import not just to leisure scholars, but to the formulation of policy. The search for certainty in an area that lacks conceptual consensus results in an epistemological imperialism that takes a geocentric form. While clearly, there is a need for good research design whatever the style of research, we contend that the wholesale rejection of insightful research is profligate and foolhardy. A mechanism has to be found to capitalise on good quality research of whatever form. In that search, we draw upon our experience of conducting a review of the material available on participation in sport and physical recreation by people from Black and minority ethnic groups. The paper concludes with a proposal for a more productive review process that makes better use of the full panoply of good quality research available. © 2012 © 2012 Taylor & Francis

Dynamics of gene expression and the regulatory inference problem

From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription factor molecules to regulatory DNA. Here, we construct stochastic models of gene expression dynamics and test them on experimental time-series data of messenger-RNA concentrations. The models are used to infer biophysical parameters of gene transcription, including the statistics of transcription factor-DNA binding and the target genes controlled by a given transcription factor.Comment: revised version to appear in Europhys. Lett., new titl