Characteristic Function, Schur Parameters and Pseudocontinuation of Schur functions

In [19] there is an approach to the investigation of the pseudocontinuability of Schur functions in terms of Schur parameters. In particular, there was obtained a criterion for the pseudocontinuability of Schur functions and the Schur parameters of rational Schur functions were described. This approach is based on the description in terms of the Schur parameters of the relative position of the largest shift and the largest coshift in a completely nonunitary contraction. It should be mentioned that these results received a further development in [8, 21-24]. This paper is aimed to give a survey about essential results on this direction. The main object in the approach is based on considering a Schur function as characteristic function of a contraction (see Section 1.2). This enables us outgoing from Schur parameters to construct a model of the corresponding contraction (see Section 2). In this model, the relative position of the largest shift and the largest coshift in a completely nonunitary contraction is described in Section 3 and then, based on this model, to find characteristics which are responsible for the pseudocontinuability of Schur functions (see Sections 4 and 5). The further parts of this paper (see Sections 6-8) admit applications of the above results to the study of properties of Schur functions and questions related with them.Comment: arXiv admin note: text overlap with arXiv:1003.167

Characteristic Function, Schur Interpolation Problem and Darlington Synthesis

In this paper we would like to show the interrelation between the different mathematical theories concerning the Schur interpolation problem, contractions in Hilbert spaces, pseudocontinuation and Darlington synthesis. The main objects of this article are contractive functions holomorphic in the unit disc (Schur functions). Here they are considered, on the one hand, as characteristic functions of contractions in Hilbert spaces and, on the other hand, as transfer functions of open systems

The search for the Holy Grail: autoantigenic targets in primary sclerosing cholangitis associated with disease phenotype and neoplasia

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Identification of chitinase-3-like protein 1 as a novel neutrophil antigenic target in Crohn’s disease

Background and Aims There is an increasing incidence of inflammatory bowel disease [IBD]. Autoimmune responses are involved in the pathophysiology of IBD, but their underlying pathways and target antigens have not yet been fully elucidated. Methods Autoantigenic targets in IBD were identified after separation of whole cell proteins isolated from neutrophils using two-dimensional electrophoresis and matrix assisted laser desorption ionization – time of flight mass spectrometry-based protein identification of the spots that displayed Western blotting signals with anti-neutrophil cytoplasmic antibody-positive sera. The prevalence of IgG, IgA and secretory IgA [sIgA] to chitinase 3-like protein 1 [CHI3L1] was analysed by enzyme-linked immunosorbent assays using recombinant CHI3L1 in 110 patients with Crohn’s disease [CD], 95 with ulcerative colitis [UC], 126 with coeliac disease [CeD] and 86 healthy controls [HCs]. Results The 18-glycosylhydrolase family member CHI3L1 was identified as a neutrophil autoantigenic target. CD patients displayed significantly higher levels of IgG to CHI3L1 than patients with UC and CeD (p < 0.0001, respectively). IgA and sIgA to CHI3L1 was significantly higher in CD than in UC, CeD and HCs [p < 0.0001, respectively]. IgA and sIgA to CHI3L1 demonstrated the highest prevalence in CD [25.5%, 28/110; and 41.8%%, 46/110] compared to HCs [2.3%, 2/86; and 4.7%%, 4/86; p = 0.0015 and p < 0.0001] and are associated with a more complicated progression of CD. Conclusion CHI3L1 is a novel neutrophil autoantigenic target in CD. IgA and sIgA to CHI3L1 may serve as novel markers for CD and may facilitate the serological diagnosis of IBD

The search for the Holy Grail: autoantigenic targets in primary sclerosing cholangitis associated with disease phenotype and neoplasia

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Autoantikörpernachweis mittels indirekter Immunfluoreszenz an HEp-2-Zellen

Systemic autoimmune diseases are characterized by the presence of antinuclear autoantibodies (ANAs). Diluted patient sera are typically used to screen for the presence of ANAs by immunofluorescence microscopy with fixed HEp-2 cells. Despite high quality test kits, reports of different laboratories frequently present controversial results. This study presents a recommendation for a unified processing and interpretation of HEp-2 based screening for autoantibodies. We provide suggestions for selection of high quality test kits, optimized processing, and diagnostic procedures. For good laboratory practice, in addition to a relevant clinical diagnosis and an experienced laboratory specialist, the following procedure is highly recommended: initial HEp-2 based screening by indirect immunofluorescence, starting with a 1:80 serum dilution and evaluation in a bright fluorescence microscope, pathological values from a titer of 1:160, internal quality checks, and unified interpretation. We aim to improve diagnostics and care for patients with autoimmune diseases as a central focus of the European Autoimmunity Standardization Initiative (EASI)

PR3-ANCAs Detected by Third-Generation ELISA Predicts Severe Disease and Poor Survival in Primary Sclerosing Cholangitis

A highly sensitive detection of anti-neutrophil cytoplasmic antibodies to serine proteinase-3 (PR3-ANCAs) aids in the serological diagnosis of autoimmune liver disorders and the prediction of severity in primary sclerosing cholangitis (PSC). Here, we evaluate a novel thirdgeneration ELISA for the detection of PR3-ANCAs. In total, 309 patients with PSC, 51 with primary biliary cholangitis (PBC), and 120 healthy blood donors (BD) were analyzed. For the survival analysis in PSC, the outcome was defined as liver-transplantation-free survival during the followup. Positive PR3-ANCA levels were found in 74/309 (24.0%) of patients with PSC. No BDs and one patient with PBC demonstrated PR3-ANCA positivity. PR3-ANCAs were revealed as independent predictors for a poor PSC outcome (study endpoint: liver transplantation/death, log-rank test, p = 0.02). PR3-ANCA positivity, lower albumin levels, and higher bilirubin concentrations were independent risks of a poor survival (Cox proportional-hazards regression analysis, p < 0.05). The Mayo risk score for PSC was associated with PR3-ANCA positivity (p = 0.01) and the disease severity assessed with a model of end-stage liver disease (MELD) and extended MELD-Na (p < 0.05). PR3-ANCAs detected by a third-generation ELISA are diagnostic and prognostic markers for PSC. Their wider use could help to identify patients who are at-risk of a more severe disease

Spatio-temporal Analysis of the Genetic Diversity of Arctic Rabies Viruses and Their Reservoir Hosts in Greenland

There has been limited knowledge on spatio-temporal epidemiology of zoonotic arctic fox rabies among countries bordering the Arctic, in particular Greenland. Previous molecular epidemiological studies have suggested the occurrence of one particular arctic rabies virus (RABV) lineage (arctic-3), but have been limited by a low number of available samples preventing in-depth high resolution phylogenetic analysis of RABVs at that time. However, an improved knowledge of the evolution, at a molecular level, of the circulating RABVs and a better understanding of the historical perspective of the disease in Greenland is necessary for better direct control measures on the island. These issues have been addressed by investigating the spatio-temporal genetic diversity of arctic RABVs and their reservoir host, the arctic fox, in Greenland using both full and partial genome sequences. Using a unique set of 79 arctic RABV full genome sequences from Greenland, Canada, USA (Alaska) and Russia obtained between 1977 and 2014, a description of the historic context in relation to the genetic diversity of currently circulating RABV in Greenland and neighboring Canadian Northern territories has been provided. The phylogenetic analysis confirmed delineation into four major arctic RABV lineages (arctic 1-4) with viruses from Greenland exclusively grouping into the circumpolar arctic-3 lineage. High resolution analysis enabled distinction of seven geographically distinct subclades (3.I - 3.VII) with two subclades containing viruses from both Greenland and Canada. By combining analysis of full length RABV genome sequences and host derived sequences encoding mitochondrial proteins obtained simultaneously from brain tissues of 49 arctic foxes, the interaction of viruses and their hosts was explored in detail. Such an approach can serve as a blueprint for analysis of infectious disease dynamics and virus-host interdependencies. The results showed a fine-scale spatial population structure in Greenland arctic foxes based on mitochondrial sequences, but provided no evidence for independent isolated evolutionary development of RABV in different arctic fox lineages. These data are invaluable to support future initiatives for arctic fox rabies control and elimination in Greenland