Coexistency on Hilbert space effect algebras and a characterisation of its symmetry transformations

The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig's formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of coexistence plays an important role in this theory, as it expresses when two quantum events can be measured together by applying a suitable apparatus. This paper's first goal is to answer a very natural question about this relation, namely, when two effects are coexistent with exactly the same effects? The other main aim is to describe all automorphisms of the effect algebra with respect to the relation of coexistence. In particular, we will see that they can differ quite a lot from usual standard automorphisms, which appear for instance in Ludwig's theorem. As a byproduct of our methods we also strengthen a theorem of Molnar

Results of the worldwide, cross-sectional ASAS-PerSpA study

Objectives: To characterise peripheral musculoskeletal involvement in patients with spondyloarthritis (SpA) including psoriatic arthritis (PsA), across the world. Methods: Cross-sectional study with 24 participating countries. Patients with a diagnosis of axial SpA (axSpA), peripheral SpA (pSpA) or PsA according to their rheumatologist were included. The investigators were asked which diagnosis out of a list of six (axSpA, PsA, pSpA, inflammatory bowel disease-associated SpA, reactive arthritis or juvenile SpA (Juv-SpA)) fitted the patient best. Peripheral manifestations (ie, peripheral joint disease, enthesitis, dactylitis and root joint disease), their localisation and treatments were evaluated. Results: A total of 4465 patients were included (61% men, mean age 44.5 years) from four geographic areas: Latin America (n=538), Europe plus North America (n=1677), Asia (n=975) and the Middle East plus North Africa (n=1275). Of those, 78% had ever suffered from at least one peripheral musculoskeletal manifestation; 57% had peripheral joint disease, 44% had enthesitis and 15% had dactylitis. Latin American had far more often peripheral joint disease (80%) than patients from other areas. Patients with PsA had predominantly upper limb and small joint involvement (52%). Hip and shoulder involvement was found in 34% of patients. The prevalence of enthesitis ranged between 41% in patients with axSpA and 65% in patients with Juv-SpA. Dactylitis was most frequent among patients with PsA (37%). Conclusion: These results suggest that all peripheral features can be found in all subtypes of SpA, and that differences are quantitative rather than qualitative. In a high proportion of patients, axial and peripheral manifestations coincided. These findings reconfirm SpA clinical subtypes are descendants of the same underlying disease, called SpA.publishersversionpublishe

A cluster analysis in the worldwide ASAS-PerSpA study

Objective To identify clusters of peripheral involvement according to the specific location of peripheral manifestations (ie, arthritis, enthesitis and dactylitis) in patients with spondyloarthritis (SpA) including psoriatic arthritis (PsA), and to evaluate whether these clusters correspond with the clinical diagnosis of a rheumatologist. Methods Cross-sectional study with 24 participating countries. Consecutive patients diagnosed by their rheumatologist as PsA, axial SpA or peripheral SpA were enrolled. Four different cluster analyses were conducted: one using information on the specific location from all the peripheral manifestations, and a cluster analysis for each peripheral manifestation, separately. Multiple correspondence analyses and k-means clustering methods were used. Distribution of peripheral manifestations and clinical characteristics were compared across the different clusters. Results The different cluster analyses performed in the 4465 patients clearly distinguished a predominantly axial phenotype (cluster 1) and a predominantly peripheral phenotype (cluster 2). In the predominantly axial phenotype, hip involvement and lower limb large joint arthritis, heel enthesitis and lack of dactylitis were more prevalent. In the predominantly peripheral phenotype, different subgroups were distinguished based on the type and location of peripheral involvement: a predominantly involvement of upper versus lower limbs joints, a predominantly axial enthesitis versus peripheral enthesitis, and predominantly finger versus toe involvement in dactylitis. A poor agreement between the clusters and the rheumatologist € s diagnosis as well as with the classification criteria was found. Conclusion These results suggest the presence of two main phenotypes (predominantly axial and predominantly peripheral) based on the presence and location of the peripheral manifestations.publishersversionpublishe

Isometric rigidity of Wasserstein tori and spheres

We prove isometric rigidity for p-Wasserstein spaces over finite-dimensional tori and spheres for all p. We present a unified approach to proving rigidity that relies on the robust method of recovering measures from their Wasserstein potentials

Prevalence and distribution of peripheral musculoskeletal manifestations in spondyloarthritis including psoriatic arthritis: results of the worldwide, cross-sectional ASAS-PerSpA study

Objectives To characterise peripheral musculoskeletal involvement in patients with spondyloarthritis (SpA) including psoriatic arthritis (PsA), across the world.Methods Cross-sectional study with 24 participating countries. Patients with a diagnosis of axial SpA (axSpA), peripheral SpA (pSpA) or PsA according to their rheumatologist were included. The investigators were asked which diagnosis out of a list of six (axSpA, PsA, pSpA, inflammatory bowel disease-associated SpA, reactive arthritis or juvenile SpA (Juv-SpA)) fitted the patient best. Peripheral manifestations (ie, peripheral joint disease, enthesitis, dactylitis and root joint disease), their localisation and treatments were evaluated.Results A total of 4465 patients were included (61% men, mean age 44.5 years) from four geographic areas: Latin America (n=538), Europe plus North America (n=1677), Asia (n=975) and the Middle East plus North Africa (n=1275). Of those, 78% had ever suffered from at least one peripheral musculoskeletal manifestation; 57% had peripheral joint disease, 44% had enthesitis and 15% had dactylitis. Latin American had far more often peripheral joint disease (80%) than patients from other areas. Patients with PsA had predominantly upper limb and small joint involvement (52%).Hip and shoulder involvement was found in 34% of patients. The prevalence of enthesitis ranged between 41% in patients with axSpA and 65% in patients with Juv-SpA. Dactylitis was most frequent among patients with PsA (37%).Conclusion These results suggest that all peripheral features can be found in all subtypes of SpA, and that differences are quantitative rather than qualitative. In a high proportion of patients, axial and peripheral manifestations coincided. These findings reconfirm SpA clinical subtypes are descendants of the same underlying disease, called SpA