Collineation group as a subgroup of the symmetric group

Let $\Psi$ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension $\ge 3$ over a field. Let $H$ be a closed (in the pointwise convergence topology) subgroup of the permutation group $\mathfrak{S}_{\Psi}$ of the set $\Psi$. Suppose that $H$ contains the projective group and an arbitrary self-bijection of $\Psi$ transforming a triple of collinear points to a non-collinear triple. It is well-known from \cite{KantorMcDonough} that if $\Psi$ is finite then $H$ contains the alternating subgroup $\mathfrak{A}_{\Psi}$ of $\mathfrak{S}_{\Psi}$. We show in Theorem \ref{density} below that $H=\mathfrak{S}_{\Psi}$, if $\Psi$ is infinite.Comment: 9 page

Efficacy of social cognition and interaction training in outpatients with schizophrenia spectrum disorders: randomized controlled trial

Given the relationship between social cognition and functional outcome in schizophrenia, a number of social cognitive interventions have been developed, including Social Cognition Interaction Training (SCIT), a group-based, comprehensive, manualized intervention. In the current trial, we examined SCIT efficacy as well as potential moderators of treatment effects. Fifty-one outpatients were randomized to SCIT or a wait-list-control (WLC), with assessments of social cognition, neurocognition, self-report, symptoms, and functioning conducted at baseline and end of the active phase. Relative to WLC, we did not find significant improvements for SCIT on neurocognition, social cognition, self-report, or symptoms, though there was a trend-level, medium effect favoring the SCIT condition on interpersonal and instrumental role function. Post-hoc analyses indicated that baseline neurocognition did not impact degree of social cognitive or functional change. Shorter duration of illness was significantly associated with better post-training neurocognition and self-esteem and, at trend-level with better symptoms and social functioning. We discuss the importance of outcome measure selection and the need for continued evaluation of potential treatment moderators in order to better match people to existing treatments. Clinical trial registration: Clinicaltrials.gov, Identifier NCT00587561

Localized anomalies in orbifold gauge theories

We apply the path-integral formalism to compute the anomalies in general orbifold gauge theories (including possible non-trivial Scherk-Schwarz boundary conditions) where a gauge group G is broken down to subgroups H_f at the fixed points y=y_f. Bulk and localized anomalies, proportional to \delta(y-y_f), do generically appear from matter propagating in the bulk. The anomaly zero-mode that survives in the four-dimensional effective theory should be canceled by localized fermions (except possibly for mixed U(1) anomalies). We examine in detail the possibility of canceling localized anomalies by the Green-Schwarz mechanism involving two- and four-forms in the bulk. The four-form can only cancel anomalies which do not survive in the 4D effective theory: they are called globally vanishing anomalies. The two-form may cancel a specific class of mixed U(1) anomalies. Only if these anomalies are present in the 4D theory this mechanism spontaneously breaks the U(1) symmetry. The examples of five and six-dimensional Z_N orbifolds are considered in great detail. In five dimensions the Green-Schwarz four-form has no physical degrees of freedom and is equivalent to canceling anomalies by a Chern-Simons term. In all other cases, the Green-Schwarz forms have some physical degrees of freedom and leave some non-renormalizable interactions in the low energy effective theory. In general, localized anomaly cancellation imposes strong constraints on model building.Comment: 30 pages, 4 figures. v2: reference adde

SUSY GUT Model Building

I discuss an evolution of SUSY GUT model building, starting with the construction of 4d GUTs, to orbifold GUTs and finally to orbifold GUTs within the heterotic string. This evolution is an attempt to obtain realistic string models, perhaps relevant for the LHC. This review is in memory of the sudden loss of Julius Wess, a leader in the field, who will be sorely missed.Comment: 24 pages, 14 figures, lectures given at PiTP 2008, Institute for Advanced Study, Princeton, to be published in the European Physical Journal

Model Building with Gauge-Yukawa Unification

In supersymmetric theories with extra dimensions, the Higgs and matter fields can be part of the gauge multiplet, so that the Yukawa interactions can arise from the gauge interactions. This leads to the possibility of gauge-Yukawa coupling unification, g_i=y_f, in the effective four dimensional theory after the initial gauge symmetry and the supersymmetry are broken upon orbifold compactification. We consider gauge-Yukawa unified models based on a variety of four dimensional symmetries, including SO(10), SU(5), Pati-Salam symmetry, trinification, and the Standard Model. Only in the case of Pati-Salam and the Standard Model symmetry, we do obtain gauge-Yukawa unification. Partial gauge-Yukawa unification is also briefly discussed.Comment: 23 page

Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for "observed" particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg to gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD beta function in the FDH and dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include

Sport for Yes? The role of sporting issues in pro-independence political discourse during the Scottish independence referendum campaign

This article critically considers the extent to which sporting issues were harnessed by pro-independence political campaigners during the Scottish independence referendum campaign. Developments such as the inclusion of sport within the Scottish Government’s White Paper on Scottish independence, the establishment of the ‘Working Group on Scottish Sport’ and the establishment of the ‘Sport for Yes’ campaign group demonstrate the harnessing of sporting issues as an additional, if somewhat peripheral, debate point in the referendum campaigns (Lafferty 2014, Scottish Government 2013, Working Group on Scottish Sport and Scottish Government 2013, 2014). The latter of these developments, the establishment of the ‘Sport for Yes’ campaign group, is of particular interest, offering evidence of the explicit political mobilisation of past and present athletes in support of the ‘Yes Scotland’ pro-independence campaign. The use of sport within pro-independence political discourse is therefore scrutinised, drawing upon the principles of critical discourse analysis to explore the ideological assumptions underpinning the discursive representation of sport in relation to Scottish independence

Impact of Chlamydia trachomatis in the reproductive setting: British Fertility Society Guidelines for practice

Chlamydia trachomatis infection of the genital tract is the most common sexually transmitted infection and has a world-wide distribution. The consequences of infection have an adverse effect on the reproductive health of women and are a common cause of infertility. Recent evidence also suggests an adverse effect on male reproduction. There is a need to standardise the approach in managing the impact of C. trachomatis infection on reproductive health. We have surveyed current UK practice towards screening and management of Chlamydia infections in the fertility setting. We found that at least 90% of clinicians surveyed offered screening. The literature on this topic was examined and revealed a paucity of solid evidence for estimating the risks of long-term reproductive sequelae following lower genital tract infection with C. trachomatis. The mechanism for the damage that occurs after Chlamydial infections is uncertain. However, instrumentation of the uterus in women with C. trachomatis infection is associated with a high risk of pelvic inflammatory disease, which can be prevented by appropriate antibiotic treatment and may prevent infected women from being at increased risk of the adverse sequelae, such as ectopic pregnancy and tubal factor infertility. Recommendations for practice have been proposed and the need for further studies is identified