An invariant analytic orthonormalization procedure with an application to coherent states

We discuss a general strategy which produces an orthonormal set of vectors, stable under the action of a given set of unitary operators $A_j$, $j=1,2,...,n$, starting from a fixed normalized vector in \Hil and from a set of unitary operators. We discuss several examples of this procedure and, in particular, we show how a set of {\em coherent-like} vectors can be produced and in which condition over the lattice spacing this can be done

Some invariant biorthogonal sets with an application to coherent states

We show how to construct, out of a certain basis invariant under the action of one or more unitary operators, a second biorthogonal set with similar properties. In particular, we discuss conditions for this new set to be also a basis of the Hilbert space, and we apply the procedure to coherent states. We conclude the paper considering a simple application of our construction to pseudo-hermitian quantum mechanics.Comment: in press in Journal of Mathematical Analysis and Applications. arXiv admin note: text overlap with arXiv:0904.088

Coordinate representation for non Hermitian position and momentum operators

In this paper we undertake an analysis of the eigenstates of two non self-adjoint operators $\hat q$ and $\hat p$ similar, in a suitable sense, to the self-adjoint position and momentum operators $\hat q_0$ and $\hat p_0$ usually adopted in ordinary quantum mechanics. In particular we discuss conditions for these eigenstates to be {\em biorthogonal distributions}, and we discuss few of their properties. We illustrate our results with two examples, one in which the similarity map between the self-adjoint and the non self-adjoint is bounded, with bounded inverse, and the other in which this is not true. We also briefly propose an alternative strategy to deal with $\hat q$ and $\hat p$, based on the so-called {\em quasi *-algebras}.Comment: Accepted in Proceedings of the Royal Society

Pathogenesis of polymyalgia rheumatica

Polymyalgia rheumatica (PMR) is a chronic, inflammatory disorder of unknown cause, almost exclusively occurring in people aged over 50 and often associated with giant cell arteritis. The evidence that PMR occurs almost exclusively in individuals aged over 50 may indicate that age-related immune alterations in genetically predisposed subjects contribute to development of the disease. Several infectious agents have been investigated as possible triggers of PMR even though the results are inconclusive. Activation of the innate and adaptive immune systems has been proved in PMR patients as demonstrated by the activation of dendritic cells and monocytes/macrophages and the altered balance between Th17 and Treg cells. Disturbed B cell distribution and function have been also demonstrated in PMR patients suggesting a pathogenesis more complex than previously imagined. In this review we will discuss the recent findings regarding the pathogenesis of PMR

Intestinal dysbiosis and innate immune responses in axial spondyloarthritis

Purpose of review Inflammatory innate and adaptive immune cell responses to commensal bacteria underlie the pathogenesis of human chronic inflammatory diseases. Intestinal dysbiosis has been described in patients with spondyloarthritis (SpA) and seems to be correlated with histologic and immunologic alterations. Purpose of this review is to discuss the relationship occurring between intestinal dysbiosis and innate immune responses in patients with axial SpA. Recent findings Intestinal dysbiosis and differential activation of intestinal immune responses in patients with SpA have been demonstrated. Furthermore, innate cells that appear to be involved in the pathogenesis of SpA may control intestinal homeostasis through induction of apoptotic cell death and deletion of activated commensal bacteria-specific T cells. Summary Although the evidence shows that dysbiosis occurs in SpA, it is not clear the role of dysbiosis in regulating innate immune responses in SpA. Relationships between cause and effect remain to be answered

Maximal extensions of a linear functional

Extensions of a positive hermitian linear functional ω, defined on a dense *-subalgebra A0 of a topological *-algebra A[τ] are analyzed. It turns out that their maximal extensions as linear functionals or hermitian linear functionals are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [2] is revisited from this point of view. Examples mostly taken from the theory of integration are discussed

Blocking CD248 molecules in perivascular stromal cells of patients with systemic sclerosis strongly inhibits their differentiation toward myofibroblasts and proliferation: A new potential target for antifibrotic therapy

Background: Fibrosis may be considered the hallmark of systemic sclerosis (SSc), the end stage triggered by different pathological events. Transforming growth factor-β (TGF-β) and platelet-derived growth factor BB (PDGF-BB) are profibrotic molecules modulating myofibroblast differentiation and proliferation, respectively. There is evidence linking CD248 with these two molecules, both highly expressed in patients with SSc, and suggesting that CD248 may be a therapeutic target for several diseases. The aim of this work was to evaluate the expression of CD248 in SSc skin and its ability to modulate SSc fibrotic process. Methods: After ethical approval was obtained, skin biopsies were collected from 20 patients with SSc and 10 healthy control subjects (HC). CD248 expression was investigated in the skin, as well as in bone marrow mesenchymal stem cells (MSCs) treated with TGF-β or PDGF-BB, by immunofluorescence, qRT-PCR, and Western blotting. Finally, in SSc-MSCs, the CD248 gene was silenced by siRNA. Results: Increased expression of CD248 was found in endothelial cells and perivascular stromal cells of SSc skin. In SSc-MSCs, the levels of CD248 and α-smooth muscle actin expression were significantly higher than in HC-MSCs. In both SSc- and HC-MSCs, PDGF-BB induced increased expression of Ki-67 when compared with untreated cells but was unable to modulate CD248 levels. After CD248 silencing, both TGF-β and PDGF-BB signaling were inhibited in SSc-MSCs. Conclusions: CD248 overexpression may play an important role in the fibrotic process by modulating the molecular target, leading to perivascular cells differentiation toward myofibroblasts and interfering with its expression, and thus might open a new therapeutic strategy to inhibit myofibroblast generation during SSc

Adult-onset Still's disease: Evaluation of prognostic tools and validation of the systemic score by analysis of 100 cases from three centers

Background: Adult-onset Still's disease (AOSD) is rare inflammatory disease of unknown etiology that usually affects young adults. The more common clinical manifestations are spiking fevers, arthritis, evanescent rash, elevated liver enzymes, lymphadenopathy, hepatosplenomegaly, and serositis. The multi-visceral involvement of the disease and the different complications, such as macrophage activation syndrome, may strongly decrease the life expectancy of AOSD patients. Methods: This study aimed to identify the positive and negative features correlated with the outcome of patients. A retrospective analysis of AOSD patients prospectively admitted to three rheumatologic centers was performed to identify the clinical features present at the time of diagnosis and to predict the possible outcome. Furthermore, we investigated the as yet to be validated prognostic value of the systemic score previously proposed. Results: One hundred consecutive AOSD patients were enrolled. The mean systemic score showed that the majority of patients had a multi-organ involvement. Sixteen patients showed different complications, mainly the macrophage activation syndrome. A strong increase of inflammatory markers was observed. All patients received steroids at different dosages, 55 patients in association with immunosuppressive drugs and 32 in association with biologic agents. Sixteen patients died during the follow-up. Regression analysis showed that the higher values of the systemic score and the presence of AOSD-related complications, assessed at the time of diagnosis, were significantly correlated with patient mortality. A prognostic impact of the systemic score of 65 7.0 was reported. Conclusions: Our study showed that a higher systemic score and the presence of AOSD-related complications at the time of diagnosis were significantly associated with mortality. Of note, a cut-off at 7.0 of the systemic score showed a strong prognostic impact in identifying patients at risk of AOSD-related death