On the Convergence of Ritz Pairs and Refined Ritz Vectors for Quadratic Eigenvalue Problems

For a given subspace, the Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the angle between the subspace and the desired eigenvector converges to zero. We prove that there is a Ritz value that converges to the desired eigenvalue unconditionally but the Ritz vector converges conditionally and may fail to converge. To remedy the drawback of possible non-convergence of the Ritz vector, we propose a refined Ritz vector that is mathematically different from the Ritz vector and is proved to converge unconditionally. We construct examples to illustrate our theory.Comment: 20 page

Rapid Accumulation of CD14+CD11c+ Dendritic Cells in Gut Mucosa of Celiac Disease after in vivo Gluten Challenge

Of antigen-presenting cells (APCs) expressing HLA-DQ molecules in the celiac disease (CD) lesion, CD11c(+) dendritic cells (DCs) co-expressing the monocyte marker CD14 are increased, whereas other DC subsets (CD1c(+) or CD103(+)) and CD163(+)CD11c(-) macrophages are all decreased. It is unclear whether these changes result from chronic inflammation or whether they represent early events in the gluten response. We have addressed this in a model of in vivo gluten challenge.Treated HLA-DQ2(+) CD patients (n = 12) and HLA-DQ2(+) gluten-sensitive control subjects (n = 12) on a gluten-free diet (GFD) were orally challenged with gluten for three days. Duodenal biopsies obtained before and after gluten challenge were subjected to immunohistochemistry. Single cell digests of duodenal biopsies from healthy controls (n = 4), treated CD (n = 3) and untreated CD (n = 3) patients were analyzed by flow cytometry.In treated CD patients, the gluten challenge increased the density of CD14(+)CD11c(+) DCs, whereas the density of CD103(+)CD11c(+) DCs and CD163(+)CD11c(-) macrophages decreased, and the density of CD1c(+)CD11c(+) DCs remained unchanged. Most CD14(+)CD11c(+) DCs co-expressed CCR2. The density of neutrophils also increased in the challenged mucosa, but in most patients no architectural changes or increase of CD3(+) intraepithelial lymphocytes (IELs) were found. In control tissue no significant changes were observed.Rapid accumulation of CD14(+)CD11c(+) DCs is specific to CD and precedes changes in mucosal architecture, indicating that this DC subset may be directly involved in the immunopathology of the disease. The expression of CCR2 and CD14 on the accumulating CD11c(+) DCs indicates that these cells are newly recruited monocytes

Functional interplay between p63 and p53 controls RUNX1 function in the transition from proliferation to differentiation in human keratinocytes

The interfollicular epidermis is continuously renewed, thanks to a regulated balance between proliferation and differentiation. The ΔNp63 transcription factor has a key role in the control of this process. It has been shown that ΔNp63 directly regulates Runt-related transcription factor 1 (RUNX1) transcription factor expression in mouse keratinocytes. The present study showed for the first time that RUNX1 is expressed in normal human interfollicular epidermis and that its expression is tightly regulated during the transition from proliferation to differentiation. It demonstrated that ΔNp63 directly binds two different RUNX1 regulatory DNA sequences and modulates RUNX1 expression differentially in proliferative or differentiated human keratinocytes. It also showed that the regulation of RUNX1 expression by ΔNp63 is dependent on p53 and that this coregulation relies on differential binding and activation of RUNX1 regulatory sequences by ΔNp63 and p53. We also found that RUNX1 inhibits keratinocyte proliferation and activates directly the expression of KRT1, a critical actor in early keratinocyte differentiation. Finally, we described that RUNX1 expression, similar to ΔNp63 and p53, was strongly expressed and downregulated in basal cell carcinomas and squamous cell carcinomas respectively. Taken together, these data shed light on the importance of tight control of the functional interplay between ΔNp63 and p53 in regulating RUNX1 transcription factor expression for proper regulation of interfollicular epidermal homeostasis

The human keratins: biology and pathology

The keratins are the typical intermediate filament proteins of epithelia, showing an outstanding degree of molecular diversity. Heteropolymeric filaments are formed by pairing of type I and type II molecules. In humans 54 functional keratin genes exist. They are expressed in highly specific patterns related to the epithelial type and stage of cellular differentiation. About half of all keratins—including numerous keratins characterized only recently—are restricted to the various compartments of hair follicles. As part of the epithelial cytoskeleton, keratins are important for the mechanical stability and integrity of epithelial cells and tissues. Moreover, some keratins also have regulatory functions and are involved in intracellular signaling pathways, e.g. protection from stress, wound healing, and apoptosis. Applying the new consensus nomenclature, this article summarizes, for all human keratins, their cell type and tissue distribution and their functional significance in relation to transgenic mouse models and human hereditary keratin diseases. Furthermore, since keratins also exhibit characteristic expression patterns in human tumors, several of them (notably K5, K7, K8/K18, K19, and K20) have great importance in immunohistochemical tumor diagnosis of carcinomas, in particular of unclear metastases and in precise classification and subtyping. Future research might open further fields of clinical application for this remarkable protein family

Editorial Approaches to Wittgenstein’s Nachlass: Towards a Historical Appreciation

Building on the unpublished correspondence between Ludwig Wittgenstein's literary executors Rush Rhees, Elizabeth Anscombe and Georg Henrik von Wright, this paper sketches the historical development of different editorial approaches to Wittgenstein's Nachlass. Using the metaphor of a ladder, it is possible to distinguish seven significant “rungs” or “steps” in the history of editing Wittgenstein's writings. The paper focuses particularly on the first four rungs, elucidating how Rhees, Anscombe and von Wright developed different editorial approaches that resulted in significant differences in their editions. The paper sheds light on how these editorial differences are grounded in the editors' divergent understandings of their task. It is suggested that future research may investigate the development of editorial approaches to Wittgenstein's Nachlass as a human story of philosophical inheritance