Involution products in Coxeter groups

For W a Coxeter group, let = {w ∈ W | w = xy where x, y ∈ W and x 2 = 1 = y 2}. It is well known that if W is finite then W = . Suppose that w ∈ . Then the minimum value of ℓ(x) + ℓ(y) – ℓ(w), where x, y ∈ W with w = xy and x 2 = 1 = y 2, is called the excess of w (ℓ is the length function of W). The main result established here is that w is always W-conjugate to an element with excess equal to zero

Study protocol: Delayed intervention randomised controlled trial within the Medical Research Council (MRC) Framework to assess the effectiveness of a new palliative care service

Background: Palliative care has been proposed to help meet the needs of patients who suffer progressive non-cancer conditions but there have been few evaluations of service development initiatives. We report here a novel protocol for the evaluation of a new palliative care service in this context. Methods/Design: Using the MRC Framework for the Evaluation of Complex Interventions we modelled a new palliative care and neurology service for patients severely affected by Multiple Sclerosis (MS). We conducted qualitative interviews with patients, families and staff, plus a literature review to model and pilot the service. Then we designed a delayed intervention randomised controlled trial to test its effectiveness as part of phase II of the MRC framework. Inclusion criteria for the trial were patients identified by referring clinicians as having unresolved symptoms or psychological concerns. Referrers were advised to use a score of greater than 8 on the Expanded Disability Scale was a benchmark. Consenting patients newly referred to the new service were randomised to either receive the palliative care service immediately (fast-track) or after a 12-week wait (standard best practice). Face to face interviews were conducted at baseline (before intervention), and at 4–6, 10–12 (before intervention for the standard-practice group), 16– 18 and 22–24 weeks with patients and their carers using standard questionnaires to assess symptoms, palliative care outcomes, function, service use and open comments. Ethics committee approval was granted separately for the qualitative phase and then for the trial. Discussion: We publish the protocol trial here, to allow methods to be reviewed in advance of publication of the results. The MRC Framework for the Evaluation of Complex Interventions was helpful in both the design of the service, methods for evaluation in convincing staff and the ethics committee to accept the trial. The research will provide valuable information on the effects of palliative care among non-cancer patients and a method to evaluate palliative care in this context

The monopole mass in the three-dimensional Georgi-Glashow model

We study the three-dimensional Georgi-Glashow model to demonstrate how magnetic monopoles can be studied fully non-perturbatively in lattice Monte Carlo simulations, without any assumptions about the smoothness of the field configurations. We examine the apparent contradiction between the conjectured analytic connection of the `broken' and `symmetric' phases, and the interpretation of the mass (i.e., the free energy) of the fully quantised 't Hooft-Polyakov monopole as an order parameter to distinguish the phases. We use Monte Carlo simulations to measure the monopole free energy and its first derivative with respect to the scalar mass. On small volumes we compare this to semi-classical predictions for the monopole. On large volumes we show that the free energy is screened to zero, signalling the formation of a confining monopole condensate. This screening does not allow the monopole mass to be interpreted as an order parameter, resolving the paradox.Comment: 12 pages, 7 figures, uses revtex. Minor changes made to the text to match with the published version at http://link.aps.org/abstract/PRD/v65/e12500

Theory of Networked Minority Games based on Strategy Pattern Dynamics

We formulate a theory of agent-based models in which agents compete to be in a winning group. The agents may be part of a network or not, and the winning group may be a minority group or not. The novel feature of the present formalism is its focus on the dynamical pattern of strategy rankings, and its careful treatment of the strategy ties which arise during the system's temporal evolution. We apply it to the Minority Game (MG) with connected populations. Expressions for the mean success rate among the agents and for the mean success rate for agents with $k$ neighbors are derived. We also use the theory to estimate the value of connectivity $p$ above which the Binary-Agent-Resource system with high resource level goes into the high-connectivity state.Comment: 24 pages, 3 figures, submitted to PR

Love, rights and solidarity: studying children's participation using Honneth's theory of recognition

Recent attempts to theorize children’s participation have drawn on a wide range of ideas, concepts and models from political and social theory. The aim of this article is to explore the specific usefulness of Honneth’s theory of a ‘struggle for recognition’ in thinking about this area of practice. The article identifies what is distinctive about Honneth’s theory of recognition, and how it differs from other theories of recognition. It then considers the relevance of Honneth’s conceptual framework to the social position of children, including those who may be involved in a variety of ‘participatory’ activities. It looks at how useful Honneth’s ideas are in direct engagement with young people’s praxis, drawing on ethnographic research with members of a children and young people’s forum. The article concludes by reflecting on the implications of this theoretical approach and the further questions which it opens up for theories of participation and of adult–child relations more generally

The spectrum of screening masses near T_c: predictions from universality

We discuss the spectrum of screening masses in a pure gauge theory near the deconfinement temperature from the point of view of the dimensionally reduced model describing the spontaneous breaking of the center symmetry. Universality arguments can be used to predict the values of the mass ratios in the scaling region of the deconfined phase when the transition is of second order. One such prediction is that the scalar sector of the screening spectrum in SU(2) pure gauge theory contains a bound state of the fundamental excitation, corresponding through universality to the bound state found in the 3D Ising model and phi^4 theory in the broken symmetry phase. A Monte Carlo evaluation of the screening masses in the gauge theory confirms the validity of the prediction. We briefly discuss the possibility of using similar arguments for first order deconfinement transitions, and in particular for the physically relevant case of SU(3).Comment: 12 pages, 3 figures. Some changes in the discussion, added references, results unchanged. Version to appear in Phys. Rev.

Light scalars in strongly-coupled extra-dimensional theories

The low-energy dynamics of five-dimensional Yang-Mills theories compactified on S^1 can be described by a four-dimensional gauge theory coupled to a scalar field in the adjoint representation of the gauge group. Perturbative calculations suggest that the mass of this elementary scalar field is protected against power divergences, and is controlled by the size of the extra dimension R. As a first step in the study of this phenomenon beyond perturbation theory, we investigate the phase diagram of a SU(2) Yang-Mills theory in five dimensions regularized on anisotropic lattices and we determine the ratios of the relevant physical scales. The lattice system shows a dimensionally reduced phase where the four-dimensional correlation length is much larger than the size of the extra dimension, but still smaller than the four-dimensional volume. In this region of the bare parameter space, at energies below 1/R, the non-perturbative spectrum contains a \emph{light} scalar state. This state has a mass that is independent of the cut-off, and a small overlap with glueball operators. Our results suggest that light scalar fields can be introduced in a lattice theory using compactified extra dimensions, rather than fine tuning the bare mass parameter.Comment: 38 pages (7 pages of Appendix), 10 tables, 21 figures. Minor corrections. Version accepted for publication in JHE

Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit

Squeezing of quantum fluctuations by means of entanglement is a well recognized goal in the field of quantum information science and precision measurements. In particular, squeezing the fluctuations via entanglement between two-level atoms can improve the precision of sensing, clocks, metrology, and spectroscopy. Here, we demonstrate 3.4 dB of metrologically relevant squeezing and entanglement for ~ 10^5 cold cesium atoms via a quantum nondemolition (QND) measurement on the atom clock levels. We show that there is an optimal degree of decoherence induced by the quantum measurement which maximizes the generated entanglement. A two-color QND scheme used in this paper is shown to have a number of advantages for entanglement generation as compared to a single color QND measurement.Comment: 6 pages+suppl, PNAS forma