Denjoy-Carleman differentiable perturbation of polynomials and unbounded operators

Let $t\mapsto A(t)$ for $t\in T$ be a $C^M$-mapping with values unbounded operators with compact resolvents and common domain of definition which are self-adjoint or normal. Here $C^M$ stands for C^\om (real analytic), a quasianalytic or non-quasianalytic Denjoy-Carleman class, $C^\infty$, or a H\"older continuity class C^{0,\al}. The parameter domain $T$ is either $\mathbb R$ or $\mathbb R^n$ or an infinite dimensional convenient vector space. We prove and review results on $C^M$-dependence on $t$ of the eigenvalues and eigenvectors of $A(t)$.Comment: 8 page

Microsatellite instability, KRAS mutations and cellular distribution of TRAIL-receptors in early stage colorectal cancer.

Thus, we evaluated the immunofluorescence pattern of TRAIL-receptors and E-cadherin to assess the fraction of membrane-bound TRAIL-receptors in 231 selected patients with early-stage CRC undergoing surgical treatment only. Moreover, we investigated whether membrane staining for TRAIL-receptors as well as the presence of KRAS mutations or of microsatellite instability (MSI) had an effect on survival and thus a prognostic effect. The fact that the receptors for the TNF-related apoptosis inducing ligand (TRAIL) are almost invariably expressed in colorectal cancer (CRC) represents the rationale for the employment of TRAIL-receptors targeting compounds for the therapy of patients affected by this tumor. Yet, first reports on the use of these bioactive agents provided disappointing results. We therefore hypothesized that loss of membrane-bound TRAIL-R might be a feature of some CRC and that the evaluation of membrane staining rather than that of the overall expression of TRAIL-R might predict the response to TRAIL-R targeting compounds in this tumor. As expected, almost all CRC samples stained positive for TRAIL-R1 and 2. Instead, membrane staining for these receptors was positive in only 71% and 16% of samples respectively. No correlation between KRAS mutation status or MSI-phenotype and prognosis could be detected. TRAIL-R1 staining intensity correlated with survival in univariate analysis, but only membranous staining of TRAIL-R1 and TRAIL-R2 on cell membranes was an independent predictor of survival (cox multivariate analysis: TRAIL-R1: p = 0.019, RR 2.06[1.12-3.77]; TRAIL-R2: p = 0.033, RR 3.63[1.11-11.84]). In contrast to the current assumptions, loss of membrane staining for TRAIL-receptors is a common feature of early stage CRC which supersedes the prognostic significance of their staining intensity. Failure to achieve therapeutic effects in recent clinical trials using TRAIL-receptors targeting compounds might be due to insufficient selection of patients bearing tumors with membrane-bound TRAIL-receptors

An algebraic approach to manifold-valued generalized functions

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and validity of this approach, we see that this generalized version on algebra isomorphisms in turn implies the classical result on algebras of smooth functions.Comment: 7 page

Un-reduction

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was originally concieved for an application to image dynamics, uses Lagrangian reduction by symmetry in reverse. A deeper understanding of un-reduction leads to new developments in image matching which serve to illustrate the mathematical power of the technique.Comment: 25 pages, revised versio

A p38 Mitogen‐Activated Protein Kinase Inhibitor Arrests Active Alveolar Bone Loss in a Rat Periodontitis Model

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141943/1/jper1992.pd

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

High-precision molecular dynamics simulation of UO2-PuO2: superionic transition in uranium dioxide

Our series of articles is devoted to high-precision molecular dynamics simulation of mixed actinide-oxide (MOX) fuel in the rigid ions approximation using high-performance graphics processors (GPU). In this article we assess the 10 most relevant interatomic sets of pair potential (SPP) by reproduction of the Bredig superionic phase transition (anion sublattice premelting) in uranium dioxide. The measurements carried out in a wide temperature range from 300K up to melting point with 1K accuracy allowed reliable detection of this phase transition with each SPP. The {\lambda}-peaks obtained are smoother and wider than it was assumed previously. In addition, for the first time a pressure dependence of the {\lambda}-peak characteristics was measured, in a range from -5 GPa to 5 GPa its amplitudes had parabolic plot and temperatures had linear (that is similar to the Clausius-Clapeyron equation for melting temperature).Comment: 7 pages, 6 figures, 1 tabl

CD133 expression is an independent prognostic marker for low survival in colorectal cancer

Colon cancer cells have previously been demonstrated to contain a subpopulation of CD133+ tumour cells that have the ability to initiate tumour growth and are thus referred to as colon cancer-initiating cells or colon cancer stem cells (CSCs). As CD133 is currently one of the best markers to characterise colon CSCs, we analysed CD133+ tumour cells in colorectal cancer specimens using immunohistochemistry. We show that CD133 detection is specific and that the CD133 antigen is localised on the glandular-luminal surface of colon cancer cells, whereas undifferentiated tumour cells at the front of invasion are CD133−. In addition, CD133+ cells are characterised in situ by lack of CK20 expression, whereas they are positive for EpCAM. Moreover, we show that CD133 expression in colorectal cancer is an independent prognostic marker that correlates with low survival in a stratified patient collective. Our results indicate that in colorectal cancer, the CD133+ tumour cells can be detected by immunohistochemistry, which facilitates their further characterisation in situ

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

TRAIL receptor I (DR4) polymorphisms C626G and A683C are associated with an increased risk for hepatocellular carcinoma (HCC) in HCV-infected patients

<p>Abstract</p> <p>Background</p> <p>Tumour surveillance via induction of TRAIL-mediated apoptosis is a key mechanism, how the immune system prevents malignancy. To determine if gene variants in the TRAIL receptor I (<it>DR4</it>) gene affect the risk of hepatitis C virus (HCV)-induced liver cancer (HCC), we analysed <it>DR4 </it>mutations C626G (rs20575) and A683C (rs20576) in HCV-infected patients with and without HCC.</p> <p>Methods</p> <p>Frequencies of <it>DR4 </it>gene polymorphisms were determined by LightSNiP assays in 159 and 234 HCV-infected patients with HCC and without HCC, respectively. 359 healthy controls served as reference population.</p> <p>Results</p> <p>Distribution of C626G and A683C genotypes were not significantly different between healthy controls and HCV-positive patients without HCC. <it>DR4 </it>variants 626C and 683A occurred at increased frequencies in patients with HCC. The risk of HCC was linked to carriage of the 626C allele and the homozygous 683AA genotype, and the simultaneous presence of the two risk variants was confirmed as independent HCC risk factor by Cox regression analysis (Odds ratio 1.975, 95% CI 1.205-3.236; p = 0.007). Furthermore HCV viral loads were significantly increased in patients who simultaneously carried both genetic risk factors (2.69 ± 0.36 × 10⁶ IU/ml vs. 1.81 ± 0.23 × 10⁶ IU/ml, p = 0.049).</p> <p>Conclusions</p> <p>The increased prevalence of patients with a 626C allele and the homozygous 683AA genotype in HCV-infected patients with HCC suggests that these genetic variants are a risk factor for HCC in chronic hepatitis C.</p