Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

‘Because it’s our culture!’ (Re)negotiating the meaning of lobola in Southern African secondary schools

Payment of bridewealth or lobola is a significant element of marriage among the Basotho of Lesotho and the Shona of Zimbabwe. However, the functions and meanings attached to the practice are constantly changing. In order to gauge the interpretations attached to lobola by young people today, this paper analyses a series of focus group discussions conducted among senior students at two rural secondary schools. It compares the interpretations attached by the students to the practice of lobola with academic interpretations (both historical and contemporary). Among young people the meanings and functions of lobola are hotly contested, but differ markedly from those set out in the academic literature. While many students see lobola as a valued part of ‘African culture’, most also view it as a financial transaction which necessarily disadvantages women. The paper then seeks to explain the young people’s interpretations by reference to discourses of ‘equal rights’ and ‘culture’ prevalent in secondary schools. Young people make use of these discourses in (re)negotiating the meaning of lobola, but the limitations of the discourses restrict the interpretations of lobola available to them

A randomised controlled trial of treatments of childhood anxiety disorder in the context of maternal anxiety disorder: clinical and cost-effectiveness outcomes

Background: This study evaluated whether clinical and economic outcomes from CBT for child anxiety disorders in the context of maternal anxiety disorders are improved by adding treatment focused on (i) maternal anxiety disorders, or (ii) mother-child interactions. Methods: 211 children (7 – 12 years, 85% White British, 52% female) with a primary anxiety disorder, whose mothers also had a current anxiety disorder, were randomised to receive (i) child-focused CBT with non-specific control interventions (CCBT+Con), (ii) CCBT with CBT for the maternal anxiety disorder (CCBT+MCBT), or (iii) CCBT with an intervention targeting the mother-child interaction (CCBT+MCI). A cost-utility analysis from a societal perspective was conducted using mother/child combined Quality Adjusted Life Years (QALYs). [Trial registration: https://doi.org/10.1186/ISRCTN19762288]. Results: MCBT was associated with immediate reductions in maternal anxiety compared to the non-specific control; however, after children had also received CCBT, maternal outcomes in the CCBT+MCI and CCBT+Con arms improved and CCBT+MCBT was no longer superior. Neither CCBT+MCBT nor CCBT+MCI conferred a benefit over CCBT+Con in terms of child anxiety disorder diagnoses post-treatment [primary outcome] (adj RR: 1.22 (95% CI 0.88, 1.67), p = .23; adj RR: 1.21 (95% CI 0.88, 1.65), p = .24 respectively) or global improvement ratings (adj RR 1.25 (95% CI 0.99, 1.57), p = .06; adj RR 1.18 (95% CI 0.93, 1.50), p = .17) or six and 12 months later. No significant differences between the groups were found on the main economic outcome measures (child/mother combined QALY mean difference: CCBT+MCBT vs CCBT+Con: -0.04 (95% CI -0.12, 0.04), p = 0.29; CCBT+MCI vs CCBT+Con: 0.02 (95% CI -0.05, -0.09), p = 0.54). CCBT+MCI was associated with non-significantly higher costs than CCBT (mean difference: £154 (95% CI -£1239, £1547), p = 0.83) but, when taking into account sampling uncertainty, it may be cost-effective compared with CCBT alone. Conclusions: Good outcomes were achieved for children and their mothers across treatment arms. There was no evidence of significant clinical benefit from supplementing CCBT with either CBT for the maternal anxiety disorder or treatment focussed on mother-child interactions, but the addition of MCI (and not MCBT) may be cost-effective. Keywords: Child; anxiety; mother; parent-child interaction; CBT

Quark-Squark Alignment Revisited

We re-examine the possibility that the solution to the supersymmetric flavor problem is related to small mixing angles in gaugino couplings induced by approximate horizontal Abelian symmetries. We prove that, for a large class of models, there is a single viable structure for the down quark mass matrix with four holomorphic zeros. Consequently, we are able to obtain both lower and upper bounds on the supersymmetric mixing angles and predict the contributions to various flavor changing neutral current processes. We find that the most likely signals for alignment are $\Delta m_D$ close to the present bound, significant CP violation in $D^0-\bar{D^0}$ mixing, and shifts of order a few percent in various CP asymmetries in $B^0$ and $B_s$ decays. In contrast, the modifications to radiative B decays, to $\epsilon^\prime/\epsilon$ and to $K\to\pi\nu\bar\nu$ decays are small. We further investigate a new class of alignment models, where supersymmetric contributions to flavor changing processes are suppressed by both alignment and RGE-induced degeneracy.Comment: 20 pages, 3 figure

“It’s my dream to work with Olympic athletes”: Neophyte sport psychologists’ expectations and initial experiences regarding service delivery

We examined trainee practitioners' initial experiences of applied sport psychology practice. Semi-structured interviews (4) were conducted over 6 months with 7 full-time MSc students before, during, and after the applied sport psychology module, when they were working with clients. Participants also kept reflective diaries over an 8-week period whilst working with clients. Findings included: (a) motivations and expectations of an ASP practice career, (b) perceptions of service delivery, (c) emotional demands, and (d) pivotal experiences. Findings extend previous literature on the initial stages of practitioner development, providing micro-level detail on aspects of the intense development process during this pivotal perio

Adjoint bulk scalars and supersymmetric unification in the presence of extra dimensions

There are several advantages of introducing adjoint superfields at intermediate energies around $M=10^{13}$ GeV. Such as (i) gauge couplings still unify (ii) neutrino masses and mixings are produced (iii) primordial lepton asymmetry can be produced. We point out that if adjoint scalars have bulk excitations along with gauge bosons whereas fermions and the doublet scalar live on boundary then N=2 supersymmetric beta functions $\tilde{b_i}$ vanish. Thus even if extra dimensions open up at an intermediate scale $\mu_0$ and all N=2 Yang-Mills fields as well as N=2 matter fields in the adjoint representation propagate in the bulk, still gauge couplings renormalize beyond $\mu_0$ just like they do in 4-dimensions with adjoint scalars. Consequently unification is achieved in the presence to extra dimensions, mass scales are determined uniquely via Renormalization Group Equations(RGE) and unification scale remains high enough to suppress proton decay. This scenario can be falsified if we get signatures of extra dimensions at low energy.Comment: New references added. This version will appear in Phys. Rev.

Bottom Production

We review the prospects for bottom production physics at the LHC.Comment: 74 pages, Latex, 71 figures, to appear in the Report of the ``1999 CERN Workshop on SM physics (and more) at the LHC'', P. Nason, G. Ridolfi, O. Schneider G.F. Tartarelli, P. Vikas (conveners

Democracy and governance networks: compatible or not?

The relationship between representative democracy and governance networks is investigated at a theoretical level. Four conjectures about the relationship are defined. The incompatibility conjectures rests on the primacy of politics and sees governance networks as a threat. The complementarity conjecture presents governance networks as a means of enabling greater participation in the policy process and sensitivity in programme implementation. The transitional conjecture posits a wider evolution of governance forms towards network relationships. The instrumental conjecture views governance networks as a powerful means through which dominant interests can achieve their goals. Illustrative implications for theory and practice are identified, in relation to power in the policy process, the public interest, and the role of public managers. The heuristic potential of the conjectures is demonstrated through the identification of an outline research agenda

Amine Containing Analogs of Sulindac for Cancer Prevention

Background: Sulindac belongs to the chemically diverse family of Non-Steroidal Anti-Inflammatory Drugs (NSAIDs) that effectively prevent adenomatous colorectal polyps and colon cancer, especially in patients with familial adenomatous polyposis. Sulindac sulfide amide (SSA), an amide analog of sulindac sulfide, shows insignificant COX-related activity and toxicity while enhancing anticancer activity in vitro and demonstrating in vivo xenograft activity. Objective: Develop structure-activity relationships in the sulindac amine series and identify analogs with promising anticancer activities. Method: A series of sulindac amine analogs were designed and synthesized and then further modified in a “libraries from libraries” approach to produce amide, sulfonamide and N,N-disubstituted sulindac amine sub-libraries. All analogs were screened against three cancer cell lines (prostate, colon and breast). Results: Several active compounds were identified viain vitro cancer cell line screening with the most potent compound (26) in the nanomolar range. Conclusion: Compound 26 and analogs showing the most potent inhibitory activity may be considered for further design and optimization efforts as anticancer hit scaffolds