The class of n-entire operators

We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1,1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized sense due to M. G. Krein. We show that these classes of operators have several distinctive properties, some of them related to the spectra of their canonical selfadjoint extensions. In particular, we provide necessary and sufficient conditions on the spectra of two canonical selfadjoint extensions of an operator for it to belong to one of our classes. Our discussion is based on some recent results in the theory of de Branges spaces.Comment: 33 pages. Typos corrected. Changes in the wording of Section 2. References added. Examples added. arXiv admin note: text overlap with arXiv:1104.476

Applications of M.G. Krein's Theory of Regular Symmetric Operators to Sampling Theory

The classical Kramer sampling theorem establishes general conditions that allow the reconstruction of functions by mean of orthogonal sampling formulae. One major task in sampling theory is to find concrete, non trivial realizations of this theorem. In this paper we provide a new approach to this subject on the basis of the M. G. Krein's theory of representation of simple regular symmetric operators having deficiency indices (1,1). We show that the resulting sampling formulae have the form of Lagrange interpolation series. We also characterize the space of functions reconstructible by our sampling formulae. Our construction allows a rigorous treatment of certain ideas proposed recently in quantum gravity.Comment: 15 pages; v2: minor changes in abstract, addition of PACS numbers, changes in some keywords, some few changes in the introduction, correction of the proof of the last theorem, and addition of some comments at the end of the fourth sectio

Transancestral mapping and genetic load in systemic lupus erythematosus

Systemic lupus erythematosus (SLE) is an autoimmune disease with marked gender and ethnic disparities. We report a large transancestral association study of SLE using Immunochip genotype data from 27,574 individuals of European (EA), African (AA) and Hispanic Amerindian (HA) ancestry. We identify 58 distinct non-HLA regions in EA, 9 in AA and 16 in HA (B50% of these regions have multiple independent associations); these include 24 novel SLE regions (Po5 10 8), refined association signals in established regions, extended associations to additional ancestries, and a disentangled complex HLA multigenic effect. The risk allele count (genetic load) exhibits an accelerating pattern of SLE risk, leading us to posit a cumulative hit hypothesis for autoimmune disease. Comparing results across the three ancestries identifies both ancestry-dependent and ancestry-independent contributions to SLE risk. Our results are consistent with the unique and complex histories of the populations sampled, and collectively help clarify the genetic architecture and ethnic disparities in SL

Rivaroxaban or aspirin for patent foramen ovale and embolic stroke of undetermined source: a prespecified subgroup analysis from the NAVIGATE ESUS trial

Background: Patent foramen ovale (PFO) is a contributor to embolic stroke of undetermined source (ESUS). Subgroup analyses from previous studies suggest that anticoagulation could reduce recurrent stroke compared with antiplatelet therapy. We hypothesised that anticoagulant treatment with rivaroxaban, an oral factor Xa inhibitor, would reduce the risk of recurrent ischaemic stroke compared with aspirin among patients with PFO enrolled in the NAVIGATE ESUS trial. Methods: NAVIGATE ESUS was a double-blinded, randomised, phase 3 trial done at 459 centres in 31 countries that assessed the efficacy and safety of rivaroxaban versus aspirin for secondary stroke prevention in patients with ESUS. For this prespecified subgroup analysis, cohorts with and without PFO were defined on the basis of transthoracic echocardiography (TTE) and transoesophageal echocardiography (TOE). The primary efficacy outcome was time to recurrent ischaemic stroke between treatment groups. The primary safety outcome was major bleeding, according to the criteria of the International Society of Thrombosis and Haemostasis. The primary analyses were based on the intention-to-treat population. Additionally, we did a systematic review and random-effects meta-analysis of studies in which patients with cryptogenic stroke and PFO were randomly assigned to receive anticoagulant or antiplatelet therapy. Findings: Between Dec 23, 2014, and Sept 20, 2017, 7213 participants were enrolled and assigned to receive rivaroxaban (n=3609) or aspirin (n=3604). Patients were followed up for a mean of 11 months because of early trial termination. PFO was reported as present in 534 (7·4%) patients on the basis of either TTE or TOE. Patients with PFO assigned to receive aspirin had a recurrent ischaemic stroke rate of 4·8 events per 100 person-years compared with 2·6 events per 100 person-years in those treated with rivaroxaban. Among patients with known PFO, there was insufficient evidence to support a difference in risk of recurrent ischaemic stroke between rivaroxaban and aspirin (hazard ratio [HR] 0·54; 95% CI 0·22–1·36), and the risk was similar for those without known PFO (1·06; 0·84–1·33; pinteraction=0·18). The risks of major bleeding with rivaroxaban versus aspirin were similar in patients with PFO detected (HR 2·05; 95% CI 0·51–8·18) and in those without PFO detected (HR 2·82; 95% CI 1·69–4·70; pinteraction=0·68). The random-effects meta-analysis combined data from NAVIGATE ESUS with data from two previous trials (PICSS and CLOSE) and yielded a summary odds ratio of 0·48 (95% CI 0·24–0·96; p=0·04) for ischaemic stroke in favour of anticoagulation, without evidence of heterogeneity. Interpretation: Among patients with ESUS who have PFO, anticoagulation might reduce the risk of recurrent stroke by about half, although substantial imprecision remains. Dedicated trials of anticoagulation versus antiplatelet therapy or PFO closure, or both, are warranted. Funding: Bayer and Janssen

Characteristics of joint involvement and relationships with systemic inflammation in systemic sclerosis: results from the EULAR Scleroderma Trial and Research Group (EUSTAR) database

OBJECTIVE: To determine the prevalence of and independent factors associated with joint involvement in a large population of patients with systemic sclerosis (SSc). METHODS: This study was cross-sectional, based on data collected on patients included in the European League Against Rheumatism (EULAR) Scleroderma Trials and Research (EUSTAR) registry. We queried this database to extract data regarding global evaluation of patients with SSc and the presence of any clinical articular involvement: synovitis (tender and swollen joints), tendon friction rubs (rubbing sensation detected as the tendon was moved), and joint contracture (stiffness of the joints that decreased their range of motion). Overall joint involvement was defined by the occurrence of synovitis and/or joint contracture and/or tendon friction rubs. RESULTS: We recruited 7286 patients with SSc; their mean age was 56 +/- 14 years, disease duration 10 +/- 9 years, and 4210 (58%) had a limited cutaneous disease subset. Frequencies of synovitis, tendon friction rubs, and joint contractures were 16%, 11%, and 31%, respectively. Synovitis, tendon friction rubs, and joint contracture were more prevalent in patients with the diffuse cutaneous subset and were associated together and with severe vascular, muscular, renal, and interstitial lung involvement. Moreover, synovitis had the highest strength of association with elevated acute-phase reactants taken as the dependent variable. CONCLUSION: Our results highlight the striking level of articular involvement in SSc, as evaluated by systematic examination in a large cohort of patients with SSc. Our data also show that synovitis, joint contracture, and tendon friction rubs are associated with a more severe disease and with systemic inflammation

Transancestral mapping and genetic load in systemic lupus erythematosus

Systemic lupus erythematosus (SLE) is an autoimmune disease with marked gender and ethnic disparities. We report a large transancestral association study of SLE using Immunochip genotype data from 27,574 individuals of European (EA), African (AA) and Hispanic Amerindian (HA) ancestry. We identify 58 distinct non-HLA regions in EA, 9 in AA and 16 in HA (similar to 50% of these regions have multiple independent associations); these include 24 novel SLE regions (P < 5 x 10(-8)), refined association signals in established regions, extended associations to additional ancestries, and a disentangled complex HLA multigenic effect. The risk allele count (genetic load) exhibits an accelerating pattern of SLE risk, leading us to posit a cumulative hit hypothesis for autoimmune disease. Comparing results across the three ancestries identifies both ancestry-dependent and ancestry-independent contributions to SLE risk. Our results are consistent with the unique and complex histories of the populations sampled, and collectively help clarify the genetic architecture and ethnic disparities in SLE.We gratefully acknowledge the Alliance for Lupus Research for funding and support. The research was supported in part by awards from the Arthritis Research UK Special Strategic Award (ref. 19289) and from George Koukis (T.J.V.). In addition, the research was funded/supported by the National Institute for Health Research (NIHR) Biomedical Research Centre based at Guy's and St Thomas' NHS Foundation Trust and King's College London (T.J.V.). The work would not be possible without funding from the NIH grants AR049084 (RPK, EEB); the International Consortium on the Genetics of Systemic Lupus Erythematosus (SLEGEN) AI083194 (J.B.H.); CA141700, AR058621 Proyecto de Excelencia, Consejeria de Andalucia (M.E.A.R.); AR043814 and AR-065626 (B.P.T.); AR060366, MD007909, AI107176 (S.K.N.); AR-057172 (C.O.J.); RC2 AR058959, U19 A1082714, R01 AR063124, P30 GM110766, R01 AR056360 (P.M.G.); P60 AR053308 (L.A.C.), MUSC part is from UL1RR029882 (G.S.G., D.L.K.) and 5P60AR062755 (G.S.G., D.L.K., P.R.R.). Oklahoma Samples U19AI082714, U01AI101934, P30GM103510, U54GM104938 and P30AR053483 (J.A.J., J.M.G.); Northwestern P60 AR066464 and 1U54TR001018 (R.R.G.); This study was supported by the US National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health (NIH) under Award Numbers K01 AR067280 and P60 AR062755 (PSR); N01AR22265 (funded collection of APPLE samples) (LES) and the APPLE Investigators; R01AR43727, NIH AR 043727 and 069572 (M.P.); NIAMS/NIH P50-AR055503 (D.R.K.). We would like to also thank the RILITE foundation for financial support (C.D.L.). Additional funding for Immunochip genotyping was provided by Genentech.Peer reviewe

Characteristics of joint involvement and relationship with systemic inflammation in systemic sclerosis: result from the EULAR scleroderma trial and research (EUSTAR) database.

To determine the prevalence of and independent factors associated with joint involvement in a large population of patients with systemic sclerosis (SSc). METHODS: This study was cross-sectional, based on data collected on patients included in the European League Against Rheumatism (EULAR) Scleroderma Trials and Research (EUSTAR) registry. We queried this database to extract data regarding global evaluation of patients with SSc and the presence of any clinical articular involvement: synovitis (tender and swollen joints), tendon friction rubs (rubbing sensation detected as the tendon was moved), and joint contracture (stiffness of the joints that decreased their range of motion). Overall joint involvement was defined by the occurrence of synovitis and/or joint contracture and/or tendon friction rubs. RESULTS: We recruited 7286 patients with SSc; their mean age was 56 +/- 14 years, disease duration 10 +/- 9 years, and 4210 (58%) had a limited cutaneous disease subset. Frequencies of synovitis, tendon friction rubs, and joint contractures were 16%, 11%, and 31%, respectively. Synovitis, tendon friction rubs, and joint contracture were more prevalent in patients with the diffuse cutaneous subset and were associated together and with severe vascular, muscular, renal, and interstitial lung involvement. Moreover, synovitis had the highest strength of association with elevated acute-phase reactants taken as the dependent variable. CONCLUSION: Our results highlight the striking level of articular involvement in SSc, as evaluated by systematic examination in a large cohort of patients with SSc. Our data also show that synovitis, joint contracture, and tendon friction rubs are associated with a more severe disease and with systemic inflammation

Characteristics of joint involvement and relationships with systemic inflammation in systemic sclerosis: results from the EULAR Scleroderma Trial and Research Group (EUSTAR) database

OBJECTIVE: To determine the prevalence of and independent factors associated with joint involvement in a large population of patients with systemic sclerosis (SSc). METHODS: This study was cross-sectional, based on data collected on patients included in the European League Against Rheumatism (EULAR) Scleroderma Trials and Research (EUSTAR) registry. We queried this database to extract data regarding global evaluation of patients with SSc and the presence of any clinical articular involvement: synovitis (tender and swollen joints), tendon friction rubs (rubbing sensation detected as the tendon was moved), and joint contracture (stiffness of the joints that decreased their range of motion). Overall joint involvement was defined by the occurrence of synovitis and/or joint contracture and/or tendon friction rubs. RESULTS: We recruited 7286 patients with SSc; their mean age was 56 +/- 14 years, disease duration 10 +/- 9 years, and 4210 (58%) had a limited cutaneous disease subset. Frequencies of synovitis, tendon friction rubs, and joint contractures were 16%, 11%, and 31%, respectively. Synovitis, tendon friction rubs, and joint contracture were more prevalent in patients with the diffuse cutaneous subset and were associated together and with severe vascular, muscular, renal, and interstitial lung involvement. Moreover, synovitis had the highest strength of association with elevated acute-phase reactants taken as the dependent variable. CONCLUSION: Our results highlight the striking level of articular involvement in SSc, as evaluated by systematic examination in a large cohort of patients with SSc. Our data also show that synovitis, joint contracture, and tendon friction rubs are associated with a more severe disease and with systemic inflammation