Selfadjoint extensions of relations whose domain and range are orthogonal

© 2020 Authors. The authors retain the copyright for their papers published in MFAT under the terms of the Creative Commons Attribution-ShareAlike License (CC BY-SA).fi=vertaisarvioitu|en=peerReviewed

Boundary relations and generalized resolvents of symmetric operators

The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint exit space extensions of a, not necessarily densely defined, symmetric operator, in terms of maximal dissipative (in \dC_+) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of a boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct the generalized resolvents from the given parameter family. The general version of the coupling method is introduced and the role of boundary relations and their Weyl families for the Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page

Prospective study of immunological factors in non-inflammatory bowel disease enterocutaneous fistulas

© 2011 The Authors. Published by BMC, part of Springer Nature. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1186/1471-2482-11-12Background: Enterocutaneous fistulas (ECF) are debilitating and usually result following complex abdominal surgery. While there is an association with inflammatory bowel disease (IBD), a large number of fistulas occur after surgery not related to IBD. The consequences of ECF include short bowel syndrome and the need for long term parenteral nutrition. ECF can heal spontaneously and in the case of IBD can be cured by medical therapy in some instances. Those that do not resolve spontaneously have to be cured by surgery which is complex and associated with a high morbidity. It is not considered traditional treatment to use the same medical therapy as in IBD to cure ECF caused by other conditions. A small case series has reported three patients with persistent ECF not related to IBD to have healed following use of Infliximab which is the treatment commonly used for ECF caused by IBD. Infliximab acts by inhibiting the activity of the inflammatory cytokine TNF- alpha. It is not known if this cytokine is present in ECF tissue in the absence of IBD. The aim of this study is to demonstrate the presence of inflammatory markers in tissue surrounding non-IBD ECF and in particular to quantify the presence of the cytokine TNF- alpha. We hypothesise that TNF - alpha levels are raised in non-IBD ECF. Methods/Design. Tissue and serum from ECF of IBD and non-IBD patients will be prospectively collected at St. Mark's Hospital Intestinal Failure Unit. The control group will consist of patients undergoing colonoscopy for bowel cancer screening, with normal findings. Biopsies of the terminal ileum will be obtained from this group during colonoscopy. The fistula tract and serum cytokine profiles of interleukins (IL)-1a, IL-1b, IL-2, IL-4, IL-6, IL-8, IL-10, TNF- alpha, IFN-y, MCP-1, EGF and VEGF will be assessed. Discussion. This study aims to assess the presence or absence of TNF- alpha expression in the ECF tissue in non-IBD origin. If our hypothesis is correct we would then be able to study the use of the TNF- alpha inhibitor Infliximab as a therapeutic option in the treatment of non-IBD ECF. Secondary aims include assessing the spectrum of inflammatory cytokines and markers present in tissue and serum of non-IBD ECF when compared with IBD ECF and normal controls. © 2011 Rahbour et al; licensee BioMed Central Ltd.The study has secured funding from Bowel Disease Research Foundation (BDRF).Published versio

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

Lost therapeutic potential of monocyte-derived dendritic cells through lost tissue homing: Stable restoration of gut specificity with retinoic acid

© 2013 The Authors. Published by Wiley. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1111/cei.12118Summary: Human monocyte-derived dendritic cells (DC) (MoDC) are utilized for immunotherapy. However, in-vitro immunological effects are often not mirrored in vivo. We studied the tissue-homing potential of MoDC. Circulating monocytes and DC expressed different tissue-homing markers and, during in-vitro development of MoDC, homing marker expression was lost resulting in a 'homeless' phenotype. Retinoic acid (RA) induced gut-homing markers (β7 and CCR9) and a regulatory phenotype and function [decreased human leucocyte antigen D-related (HLA-DR) and increased ILT3 and fluorescein isothiocyanate (FITC-dextran uptake) in MoDC]. RA-MoDC were less stimulatory and primed conditioned T cells with a gut-homing profile (β7+CLA-). Unlike the normal intestinal microenvironment, that from inflamed colon of ulcerative colitis (UC) patients did not induce regulatory properties in MoDC. However, RA-MoDC maintained their regulatory gut-specific properties even in the presence of UC microenvironment. Therefore, MoDC may be ineffectual for immunotherapy because they lack tissue-homing and tissue-imprinting specificity. However, MoDC rehabilitation with gut-homing potential by RA could be useful in promoting immunotherapy in pathologies such as UC. © 2013 The Authors. Clinical and Experimental Immunology published by John Wiley & Sons Ltd on behalf of British. Society for Immunology.This work was supported by Marie Curie Intra European Fellowship (FP7‐people‐IEF‐2008‐235993), St Mark's Hospital Foundation the Brigid Balfour Fund and the BBSRC (WMNI P33458).Published versio

Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions

© 2020 The Authors. Mathematische Nachrichten published by Wiley‐VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.fi=vertaisarvioitu|en=peerReviewed

Skin- and gut-homing molecules on human circulating gamma delta T cells and their dysregulation in inflammatory bowel disease

Changes in phenotype and function of γδ T cells have been reported in inflammatory bowel disease (IBD), including Crohn's disease (CD) and ulcerative colitis (UC). Dysregulation of lymphocyte migration plays a key role in IBD pathogenesis; however, data on migratory properties of γδ T cells are scarce. Human circulating γδ T cells from healthy controls (n = 27), patients with active CD (n = 15), active UC (n = 14) or cutaneous manifestations of IBD (n = 2) were characterized by flow cytometry. Circulating γδ T cells in healthy controls were CD3(hi) and expressed CD45RO. They expressed gut-homing molecule β7 but not gut-homing molecule corresponding chemokine receptors (CCR)9, or skin-homing molecules cutaneous lymphocyte-associated antigen (CLA) and CCR4, despite conventional T cells containing populations expressing these molecules. CCR9 expression was increased on γδ T cells in CD and UC, while skin-homing CLA was expressed aberrantly on γδ T cells in patients with cutaneous manifestations of IBD. Lower levels of CD3 expression were found on γδ T cells in CD but not in UC, and a lower proportion of γδ T cells expressed CD45RO in CD and UC. Enhanced expression of gut-homing molecules on circulating γδ T cells in IBD and skin-homing molecules in cutaneous manifestations of IBD may be of clinical relevance