Fuchsian convex bodies: basics of Brunn--Minkowski theory

The hyperbolic space \H^d can be defined as a pseudo-sphere in the $(d+1)$ Minkowski space-time. In this paper, a Fuchsian group $\Gamma$ is a group of linear isometries of the Minkowski space such that \H^d/\Gamma is a compact manifold. We introduce Fuchsian convex bodies, which are closed convex sets in Minkowski space, globally invariant for the action of a Fuchsian group. A volume can be associated to each Fuchsian convex body, and, if the group is fixed, Minkowski addition behaves well. Then Fuchsian convex bodies can be studied in the same manner as convex bodies of Euclidean space in the classical Brunn--Minkowski theory. For example, support functions can be defined, as functions on a compact hyperbolic manifold instead of the sphere. The main result is the convexity of the associated volume (it is log concave in the classical setting). This implies analogs of Alexandrov--Fenchel and Brunn--Minkowski inequalities. Here the inequalities are reversed

Systemic phenotype related to primary Sjögren's syndrome in 279 patients carrying isolated anti-La/SSB antibodies

Objective. To evaluate the systemic phenotype associated with the presence of isolated anti-La/SSB antibodies in a large international registry of patients with primary Sjögren's syndrome (pSS) fulfilling the 2002 classification criteria. Methods. The Big Data Sjögren Project Consortium is an international, multicentre registry created in 2014. Baseline clinical information from leading centres on clinical research in SS of the 5 continents was collected. Combination patterns of anti-Ro/SSA-La/SSB antibodies at the time of diagnosis defined the following four immu-nological phenotypes: Double positive (combined Ro/SSA and La/SSB,) isolated anti-Ro/SSA, isolated anti-La/ SSB, and immunonegative. Results. The cohort included 12,084 patients (11,293 females, mean 52.4 years) with recorded ESSDAI scores available. Among them, 279 (2.3%) had isolated anti-La/SSB antibodies. The mean total ESSDAI score at diagnosis of patients with pSS carrying isolated anti-La/SSB was 6.0, and 80.4% of patients had systemic activity (global ESSDAI score ≥ 1) at diagnosis. The domains with the highest frequency of active patients were the biological (42.8%), glandular (36.8%) and articular (31.2%) domains. Patients with isolated anti-La/ SSB showed a higher frequency of active patients in all ESSDAI domains but two (articular and peripheral nerve) in com-parison with immune-negative patients, and even a higher absolute frequency in six clinical ESSDAI domains in comparison with patients with isolated anti-Ro/ SSA. In addition, patients with isolated anti-La/SSB showed a higher frequency of active patients in two ESSDAI domains (pulmonary and glandular) with respect to the most active immunological subset (double-positive antibodies). Meanwhile, systemic activity detected in patients with isolated anti-La/SSB was overwhelmingly low. Even in ESSDAI domains where patients with isolated anti-La/SSB had the highest frequencies of systemic activity (lymphadenopathy and muscular), the percentage of patients with moderate or high activity was lower in comparison with the combined Ro/SSA and La/SSB group. Conclusion. Patients carrying isolated La/SSB antibodies represent a very small subset of patients with a systemic SS phenotype characterised by a significant frequency of active patients in most clinical ESSDAI domains but with a relative low frequency of the highest severe organ-specific involvements. Primary SS still remains the best clinical diagnosis for this subset of patients

Characterization and outcomes of 414 patients with primary SS who developed haematological malignancies

Objective: To characterize 414 patients with primary SS who developed haematological malignancies and to analyse how the main SS- and lymphoma-related features can modify the presentation patterns and outcomes. Methods: By January 2021, the Big Data Sjögren Project Consortium database included 11 966 patients fulfilling the 2002/2016 classification criteria. Haematological malignancies diagnosed according to the World Health Organization (WHO) classification were retrospectively identified. Results: There were 414 patients (355 women, mean age 57 years) with haematological malignancies (in 43, malignancy preceded at least one year the SS diagnosis). A total of 376 (91%) patients had mature B-cell malignancy, nearly half had extranodal marginal zone lymphoma (MZL) of mucosa-associated lymphoid tissue (MALT lymphoma) (n = 197), followed by diffuse large B-cell lymphoma (DLBCL) (n = 67), nodal MZL lymphoma (n = 29), chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL) (n = 19) and follicular lymphoma (FL) (n = 17). Rates of complete response, relapses and death were 80%, 34% and 13%, respectively, with a 5-year survival rate of 86.5% after a mean follow-up of 8 years. There were significant differences in age at diagnosis (younger in MALT, older in CLL/SLL), predominant clinical presentation (glandular enlargement in MALT lymphoma, peripheral lymphadenopathy in nodal MZL and FL, constitutional symptoms in DLBCL, incidental diagnosis in CLL/SLL), therapeutic response (higher in MALT lymphoma, lower in DLBCL) and survival (better in MALT, nodal MZL and FL, worse in DLBCL). Conclusion: In the largest reported study of haematological malignancies complicating primary SS, we confirm the overwhelming predominance of B-cell lymphomas, especially MALT, with the salivary glands being the primary site of involvement. This highly-specific histopathological scenario is linked with the overall good prognosis with a 5-year survival rate of nearly 90%