Representation Theorems for Indefinite Quadratic Forms Revisited

The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring the second representation theorem to hold is proved. A new simple and explicit example of a self-adjoint operator for which the second representation theorem does not hold is also provided.Comment: This work is supported in part by the Deutsche Forschungsgemeinschaf

A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered.Comment: 38 pages, Proposition 2.2 and its proof corrected, Remarks 2.5, 3.4, and 3.12 extended, details added in subsections 2.3 and 4.2, section 6 rearranged, typos corrected, references adde

The cholesterol-lowering effect of oats and oat beta glucan: modes of action and potential role of bile acids and the microbiome

Consumption of sufficient quantities of oat products has been shown to reduce host cholesterol and thereby modulate cardiovascular disease risk. The effects are proposed to be mediated by the gel-forming properties of oat β-glucan which modulates host bile acid and cholesterol metabolism and potentially removes intestinal cholesterol for excretion. However, the gut microbiota has emerged as a major factor regulating cholesterol metabolism in the host. Oat β-glucan has been shown to modulate the gut microbiota, particularly those bacterial species that influence host bile acid metabolism and production of short chain fatty acids, factors which are regulators of host cholesterol homeostasis. Given a significant role for the gut microbiota in cholesterol metabolism it is likely that the effects of oat β-glucan on the host are multifaceted and involve regulation of microbe-host interactions at the gut interface. Here we consider the potential for oat β-glucan to influence microbial populations in the gut with potential consequences for bile acid metabolism, reverse cholesterol transport (RCT), short-chain fatty acid (SCFA) production, bacterial metabolism of cholesterol and microbe-host signaling

Auswirkungen dynamischer Lasteinträge landwirtschaftlicher Radfahrzeuge auf die physikalischen Eigenschaften von Lößböden

Im Rahmen eines vom Bundesministerium für Ernährung, Landwirtschaft und Verbraucherschutz (BMELV) geförderten Verbundprojektes wurde in Zusammenarbeit des Institutes für Pflanzenernährung und Bodenkunde der CAU zu Kiel und der landtechnischen Abteilung der Fachhochschule Südwestfalen auf zwei Versuchsflächen in Nordrheinwestfalen Spannungsausbreitung und Deformation unterschiedlich bearbeiteter Ackerböden unter definierten Belastungssituationen (Radlasten 3,3, 6,3 und 7,5Mg) untersucht. Ziel der gemeinsamen Experimente war die flächenhafte Bestimmung der Bodenstabilität und der Bodenfunktionen, sowie deren Beeinflussung durch technogene Belastung landwirtschaftlicher Radfahrzeuge. In Kombination von Beprobungen, bodenphysikalischen Laboruntersuchungen und dynamischen Belastungsversuchen im Freiland, war es möglich für die unterschiedlichen Bodenbearbeitungssysteme (konventionell wendend zu Mulch- bzw. Frässohlensaat) definierte Basisstabilitäten zu ermitteln und diese den gemessenen Spannungseinträgen bewertend gegenüber zu stellen. Anhand auflastabhängiger Vergleiche ausgewählter Bodenfunktionskennwerte (kf, Pv, LK) konnte eine Einordnung des Gefährdungspotentials definierter Lastsituationen für das Bodenausgangssubstrat Lösslehm erfolgen. Die Ergebnisse der Überfahrungsexperimente zeigen hinsichtlich der gemessenen Spannungseinträge eine auflastabhängige bodenschonende Wirkungen der konservierenden Bodenbearbeitung. Für Radlasten über 3,3Mg wurde in der horizontspezifischen Gegenüberstellung der Bodenstabilität und des Spannungseintrages, trotz bodenschonender Maßnahmen, eine Verdichtungsgefährdung für den Unterboden ermittelt. Die Untersuchungen der Bodenfunktionskennwerte weisen unter mechanischer Belastung einen signifikanten Anstieg der Vorbelastung sowie Abnahmen der Luftkapazität und eine Beeinträchtigung der hydraulischen Leitfähigkeit auf. Mehrfach wiederholte Lasteinträge bzw. zunehmende Überfahrungshäufigkeit zeigten eine weitaus deutlichere negative Beeinflussung der Bodenfunktion als einmalige Überfahrten

Linezolid Resistance Genes and Mutations among Linezolid-Susceptible Enterococcus spp.—A Loose Cannon?

The National Reference Centre for Enterococci receives an increasing number of linezolid-resistant Enterococcus isolates. Linezolid (LIN) resistance is mediated by G2576T 23S rDNA gene mutations and/or acquisition of resistance genes (cfr, optrA, poxtA). There are anecdotal reports that those resistance traits may be present in phenotypically linezolid-susceptible isolates. We aimed to determine the prevalence of LIN resistance genes and mutations in enterococci with a LIN MIC of 4 mg/L in broth microdilution (EUCAST = susceptible) isolated from German hospital patients 2019-2021. LIN MICs were additionally determined by ETEST (R) and VITEK2. Selected strains were subjected to LIN selective pressure and growth was monitored with increasing antibiotic concentrations. We received 195 isolates (LIN MIC = 4 mg/L). In total, 78/195 (40%) isolates contained either a putative resistance gene, the G2576T mutation, or a combination thereof. Very major error was high for broth microdilution. The ability to predict phenotypic resistance from genotypic profile was highest for G2576T-mediated resistance. Selection experiments revealed that, in particular, E. faecium isolates with resistance gene mutations or poxtA rapidly adapt to MICs above the clinical breakpoint. In conclusion, LIN resistance genes and mutations can be observed in phenotypically linezolid-susceptible enterococci. Those isolates may rapidly develop resistance under LIN selective pressure potentially leading to treatment failure

Abstract kinetic equations with positive collision operators

We consider "forward-backward" parabolic equations in the abstract form $Jd \psi / d x + L \psi = 0$, $0< x < \tau \leq \infty$, where $J$ and $L$ are operators in a Hilbert space $H$ such that $J=J^*=J^{-1}$, $L=L^* \geq 0$, and $\ker L = 0$. The following theorem is proved: if the operator $B=JL$ is similar to a self-adjoint operator, then associated half-range boundary problems have unique solutions. We apply this theorem to corresponding nonhomogeneous equations, to the time-independent Fokker-Plank equation $\mu \frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2 \psi}{\partial \mu^2} (x, \mu)$, $0<x<\tau$, $\mu \in \R$, as well as to other parabolic equations of the "forward-backward" type. The abstract kinetic equation $T d \psi/dx = - A \psi (x) + f(x)$, where $T=T^*$ is injective and $A$ satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in the introductio

C/EBPβ regulates homeostatic and oncogenic gastric cell proliferation

Cancer of the stomach is among the leading causes of death from cancer worldwide. The transcription factor C/EBPβ is frequently overexpressed in gastric cancer and associated with the suppression of the differentiation marker TFF1. We show that the murine C/EBP{beta} knockout stomach displays unbalanced homeostasis and reduced cell proliferation and that tumorigenesis of human gastric cancer xenograft is inhibited by knockdown of C/EBPβ. Cross-species comparison of gene expression profiles between C/EBPβ-deficient murine stomach and human gastric cancer revealed a subset of tumors with a C/EBPβ signature. Within this signature, the RUNX1t1 tumor suppressor transcript was down-regulated in 38% of gastric tumor samples. The RUNX1t1 promoter was frequently hypermethylated and ectopic expression of RUNX1t1 in gastric cancer cells inhibited proliferation and enhanced TFF1 expression. These data suggest that the tumor suppressor activity of both RUNX1t1 and TFF1 are mechanistically connected to C/EBPβ and that cross-regulation between C/EBPβ-RUNX1t1-TFF1 plays an important role in gastric carcinogenesis

Five years MIQE guidelines: The case of the Arabian countries

The quantitative real time polymerase chain reaction (qPCR) has become a key molecular enabling technology with an immense range of research, clinical, forensic as well as diagnostic applications. Its relatively moderate instrumentation and reagent requirements have led to its adoption by numerous laboratories, including those located in the Arabian world, where qPCR, which targets DNA, and reverse transcription qPCR (RT-qPCR), which targets RNA, are widely used for region-specific biotechnology, agricultural and human genetic studies. However, it has become increasingly apparent that there are significant problems with both the quality of qPCR-based data as well as the transparency of reporting. This realisation led to the publication of the Minimum Information for Publication of Quantitative Real-Time PCR Experiments (MIQE) guidelines in 2009 and their more widespread adoption in the last couple of years. An analysis of the performance of biomedical research in the Arabian world between 2001-2005 suggests that the Arabian world is producing fewer biomedical publications of lower quality than other Middle Eastern countries. Hence we have analysed specifically the quality of RT-qPCR-based peer-reviewed papers published since 2009 from Arabian researchers using a bespoke iOS/Android app developed by one of the authors. Our results show that compliance with 15 essential MIQE criteria was low (median of 40%, range 0-93%) and few details on RNA quality controls (22% compliance), assays design (12%), RT strategies (32%), amplification efficiencies (30%) and the normalisation process (3%). These data indicate that one of the reasons for the poor performance of Arabian world biomedical research may be the low standard of any supporting qPCR experiments and identify which aspects of qPCR experiments require significant improvements

Amplification efficiency: linking baseline and bias in the analysis of quantitative PCR data

Despite the central role of quantitative PCR (qPCR) in the quantification of mRNA transcripts, most analyses of qPCR data are still delegated to the software that comes with the qPCR apparatus. This is especially true for the handling of the fluorescence baseline. This article shows that baseline estimation errors are directly reflected in the observed PCR efficiency values and are thus propagated exponentially in the estimated starting concentrations as well as ‘fold-difference’ results. Because of the unknown origin and kinetics of the baseline fluorescence, the fluorescence values monitored in the initial cycles of the PCR reaction cannot be used to estimate a useful baseline value. An algorithm that estimates the baseline by reconstructing the log-linear phase downward from the early plateau phase of the PCR reaction was developed and shown to lead to very reproducible PCR efficiency values. PCR efficiency values were determined per sample by fitting a regression line to a subset of data points in the log-linear phase. The variability, as well as the bias, in qPCR results was significantly reduced when the mean of these PCR efficiencies per amplicon was used in the calculation of an estimate of the starting concentration per sample