Boxicity of graphs on surfaces

The boxicity of a graph $G=(V,E)$ is the least integer $k$ for which there exist $k$ interval graphs $G_i=(V,E_i)$, $1 \le i \le k$, such that $E=E_1 \cap ... \cap E_k$. Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface $\Sigma$ of genus $g$ is at most $5g+3$. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces.Comment: 9 pages, 2 figure

Axial Involvement in Psoriatic Arthritis cohort (AXIS): the protocol of a joint project of the Assessment of SpondyloArthritis international Society (ASAS) and the Group for Research and Assessment of Psoriasis and Psoriatic Arthritis (GRAPPA)

Background: Involvement of the axial skeleton (sacroiliac joints and spine) is a relatively frequent manifestation associated with psoriatic skin disease, mostly along with involvement of peripheral musculoskeletal structures (peripheral arthritis, enthesitis, dactylitis), which are referred to as psoriatic arthritis (PsA). Data suggest that up to 30% of patients with psoriasis have PsA. Depending on the definition used, the prevalence of axial involvement varies from 25% to 70% of patients with PsA. However, there are currently no widely accepted criteria for axial involvement in PsA.Objective: The overarching aim of the Axial Involvement in Psoriatic Arthritis (AXIS) study is to systematically evaluate clinical and imaging manifestations indicative of axial involvement in patients with PsA and to develop classification criteria and a unified nomenclature for axial involvement in PsA that would allow defining a homogeneous subgroup of patients for research.Design: Prospective, multicenter, multinational, cross-sectional study.Methods and analyses: In this multicenter, multinational, cross-sectional study, eligible patients [adult patients diagnosed with PsA and fulfilling Classification Criteria for Psoriatic Arthritis (CASPAR) with musculoskeletal symptom duration of <= 10 years not treated with biological or targeted synthetic disease-modifying anti-rheumatic drugs] will be recruited prospectively. They will undergo study-related clinical and imaging examinations. Imaging will include radiography and magnetic resonance imaging examinations of sacroiliac joints and spine. Local investigators will evaluate for the presence of axial involvement based on clinical and imaging information which will represent the primary outcome of the study. In addition, imaging will undergo evaluation by central review. Finally, the central clinical committee will determine the presence of axial involvement based on all available information.Ethics: The study will be performed according to the ethical principles of the Declaration of Helsinki and International Council for Harmonisation Good Clinical Practice guidelines. The study protocol will be approved by the individual Independent Ethics Committee / Institutional Review Board of participating centers. Written informed consent will be obtained from all included patients.Pathophysiology and treatment of rheumatic disease

More Please

More Please was the result of a collaboration with the Core company members - Moving memory, which mapped their development as a company and as developing choreographers/performance making. The show was performed at the Theatre Royal Margate and the Gulbenkian in 201