Enumeration of Hypermaps of a Given Genus

This paper addresses the enumeration of rooted and unrooted hypermaps of a given genus. For rooted hypermaps the enumeration method consists of considering the more general family of multirooted hypermaps, in which darts other than the root dart are distinguished. We give functional equations for the generating series counting multirooted hypermaps of a given genus by number of darts, vertices, edges, faces and the degrees of the vertices containing the distinguished darts. We solve these equations to get parametric expressions of the generating functions of rooted hypermaps of low genus. We also count unrooted hypermaps of given genus by number of darts, vertices, hyperedges and faces.Comment: 42 page

The big Dehn surgery graph and the link of S^3

In a talk at the Cornell Topology Festival in 2005, W. Thurston discussed a graph which we call "The Big Dehn Surgery Graph", B. Here we explore this graph, particularly the link of S^3, and prove facts about the geometry and topology of B. We also investigate some interesting subgraphs and pose what we believe are important questions about B.Comment: 15 pages, 4 figures, 4 ancillary files. Reorganized and shortened from previous versions, while correcting one error in the proof of Theorem 5.4. Also, ancillary files detailing our computations with the computer program ORB have been provide

Using HINODE/Extreme-Ultraviolet Imaging Spectrometer to confirm a seismologically inferred coronal temperature

The Extreme-Ultraviolet Imaging Spectrometer on board the HINODE satellite is used to examine the loop system described in Marsh et al. (2009) by applying spectroscopic diagnostic methods. A simple isothermal mapping algorithm is applied to determine where the assumption of isothermal plasma may be valid, and the emission measure locii technique is used to determine the temperature profile along the base of the loop system. It is found that, along the base, the loop has a uniform temperature profile with a mean temperature of 0.89 +- 0.09 MK which is in agreement with the temperature determined seismologically in Marsh et al. (2009), using observations interpreted as the slow magnetoacoustic mode. The results further strengthen the slow mode interpretation, propagation at a uniform sound speed, and the analysis method applied in Marsh et al. (2009). It is found that it is not possible to discriminate between the slow mode phase speed and the sound speed within the precision of the present observations

HeI in the central Giant HII Region of NGC 5253. A 2D observational approach to collisional and radiative transfer effects

ABRIDGED: NGC5253 is an ideal laboratory for detailed studies of starburst galaxies. We present for the first time in a starburst galaxy a 2D study of the spatial behavior of collisional and radiative transfer effects in He^+. The HeI lines are analysed based on data obtained with FLAMES and GMOS. Collisional effects are negligible for transitions in the singlet cascade while relatively important for those in the triplet cascade. In particular, they can contribute up to 20% of the flux in the HeIl7065 line. Radiative transfer effects are important over an extended and circular area of 30pc in diameter centered at the Super Star Clusters. HeI abundance, y^+, has been mapped using extinction corrected fluxes of six HeI lines, realistic assumptions for T_e, n_e, and the stellar absorption equivalent width as well as the most recent emissivities. We found a mean of 10^3 y^+ ~80.3 over the mapped area. The relation between the excitation and the total helium abundance, y_tot, is consistent with no abundance gradient. Uncertainties in the derivation of He abundances are dominated by the adopted assumptions. We illustrated the difficulty of detecting a putative He enrichment due to the presence of Wolf-Rayet stars in the main GHIIR. Data are marginally consistent with an excess in the N/He ratio in the N enriched area of the order of both, the atmospheric N/He ratios in WR stars and the uncertainties estimated for the N/He ratios.Comment: Accepted in Astronomy and Astrophysics; the emissivities presented in the Corrigendum, Porter et al. 2013, arXiv:1303.5115, have been include

Effective patient–clinician interaction to improve treatment outcomes for patients with psychosis: a mixed-methods design

BACKGROUND:At least 100,000 patients with schizophrenia receive care from community mental health teams (CMHTs) in England. These patients have regular meetings with clinicians, who assess them, engage them in treatment and co-ordinate care. As these routine meetings are not commonly guided by research evidence, a new intervention, DIALOG, was previously designed to structure consultations. Using a hand-held computer, clinicians asked patients to rate their satisfaction with eight life domains and three treatment aspects, and to indicate whether or not additional help was needed in each area, with responses being graphically displayed and compared with previous ratings. In a European multicentre trial, the intervention improved patients’ quality of life over a 1-year period. The current programme builds on this research by further developing DIALOG in the UK. RESEARCH QUESTIONS:(1) How can the practical procedure of the intervention be improved, including the software used and the design of the user interface? (2) How can elements of resource-oriented interventions be incorporated into a clinician manual and training programme for a new, more extensive ‘DIALOG+’ intervention? (3) How effective and cost-effective is the new DIALOG+ intervention in improving treatment outcomes for patients with schizophrenia or a related disorder? (4) What are the views of patients and clinicians regarding the new DIALOG+ intervention? METHODS:We produced new software on a tablet computer for CMHTs in the NHS, informed by analysis of videos of DIALOG sessions from the original trial and six focus groups with 18 patients with psychosis. We developed the new ‘DIALOG+’ intervention in consultation with experts, incorporating principles of solution-focused therapy when responding to patients’ ratings and specifying the procedure in a manual and training programme for clinicians. We conducted an exploratory cluster randomised controlled trial with 49 clinicians and 179 patients with psychosis in East London NHS Foundation Trust, comparing DIALOG+ with an active control. Clinicians working as care co-ordinators in CMHTs (along with their patients) were cluster randomised 1 : 1 to either DIALOG+ or treatment as usual plus an active control, to prevent contamination. Intervention and control were to be administered monthly for 6 months, with data collected at baseline and at 3, 6 and 12 months following randomisation. The primary outcome was subjective quality of life as measured on the Manchester Short Assessment of Quality of Life; secondary outcomes were also measured. We also established the cost-effectiveness of the DIALOG intervention using data from the Client Service Receipt Inventory, which records patients’ retrospective reports of using health- and social-care services, including hospital services, outpatient services and medication, in the 3 months prior to each time point. Data were supplemented by the clinical notes in patients’ medical records to improve accuracy. We conducted an exploratory thematic analysis of 16 video-recorded DIALOG+ sessions and measured adherence in these videos using a specially developed adherence scale. We conducted focus groups with patients (n = 19) and clinicians (n = 19) about their experiences of the intervention, and conducted thematic analyses. We disseminated the findings and made the application (app), manual and training freely available, as well as producing a protocol for a definitive trial. RESULTS:Patients receiving the new intervention showed more favourable quality of life in the DIALOG+ group after 3 months (effect size: Cohen’s d = 0.34), after 6 months (Cohen’s d = 0.29) and after 12 months (Cohen’s d = 0.34). An analysis of video-recorded DIALOG+ sessions showed inconsistent implementation, with adherence to the intervention being a little over half of the possible score. Patients and clinicians from the DIALOG+ arm of the trial reported many positive experiences with the intervention, including better self-expression and improved efficiency of meetings. Difficulties reported with the intervention were addressed by further refining the DIALOG+ manual and training. Cost-effectiveness analyses found a 72% likelihood that the intervention both improved outcomes and saved costs. LIMITATIONS:The research was conducted solely in urban east London, meaning that the results may not be broadly generalisable to other settings. CONCLUSIONS:(1) Although services might consider adopting DIALOG+ based on the existing evidence, a definitive trial appears warranted; (2) applying DIALOG+ to patient groups with other mental disorders may be considered, and to groups with physical health problems; (3) a more flexible use with variable intervals might help to make the intervention even more acceptable and effective; (4) more process evaluation is required to identify what mechanisms precisely are involved in the improvements seen in the intervention group in the trial; and (5) what appears to make DIALOG+ effective is that it is not a separate treatment and not a technology that is administered by a specialist; rather, it changes and utilises the existing therapeutic relationship between patients and clinicians in CMHTs to initiate positive change, helping the patients to improve their quality of life. FUTURE RESEARCH:Future studies should include a definitive trial on DIALOG+ and test the effectiveness of the intervention with other populations, such as people with depression. TRIAL REGISTRATION:Current Controlled Trials ISRCTN34757603. FUNDING:The National Institute for Health Research Programme Grants for Applied Research programme

The Phase Diagram of 1-in-3 Satisfiability Problem

We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause. Random 1-in-3 Satisfiability and Exact 3-Cover are special cases of this ensemble. We interpolate between these cases from a region where satisfiability can be typically decided for all connectivities in polynomial time to a region where deciding satisfiability is hard, in some interval of connectivities. We derive several rigorous results in the first region, and develop the one-step--replica-symmetry-breaking cavity analysis in the second one. We discuss the prediction for the transition between the almost surely satisfiable and the almost surely unsatisfiable phase, and other structural properties of the phase diagram, in light of cavity method results.Comment: 30 pages, 12 figure