Categorification of the Kauffman bracket skein module of I-bundles over surfaces

Khovanov defined graded homology groups for links L in R^3 and showed that their polynomial Euler characteristic is the Jones polynomial of L. Khovanov's construction does not extend in a straightforward way to links in I-bundles M over surfaces F not D^2 (except for the homology with Z/2 coefficients only). Hence, the goal of this paper is to provide a nontrivial generalization of his method leading to homology invariants of links in M with arbitrary rings of coefficients. After proving the invariance of our homology groups under Reidemeister moves, we show that the polynomial Euler characteristics of our homology groups of L determine the coefficients of L in the standard basis of the skein module of M. Therefore, our homology groups provide a `categorification' of the Kauffman bracket skein module of M. Additionally, we prove a generalization of Viro's exact sequence for our homology groups. Finally, we show a duality theorem relating cohomology groups of any link L to the homology groups of the mirror image of L.Comment: Version 2 was obtained by merging math.QA/0403527 (now removed) with Version 1. This version is published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-52.abs.htm

Conformally Einstein Products and Nearly K\"ahler Manifolds

In the first part of this note we study compact Riemannian manifolds (M,g) whose Riemannian product with R is conformally Einstein. We then consider compact 6--dimensional almost Hermitian manifolds of type W_1+W_4 in the Gray--Hervella classification admitting a parallel vector field and show that (under some regularity assumption) they are obtained as mapping tori of isometries of compact Sasaki-Einstein 5-dimensional manifolds. In particular, we obtain examples of inhomogeneous locally (non-globally) conformal nearly K\"ahler compact manifolds

Persistent clinical efficacy and safety of anti-tumour necrosis factor \textgreeka therapy with infliximab in patients with ankylosing spondylitis over 5 years: evidence for different types of response

Background: There is insufficient evidence for the long-term efficacy and safety of anti-tumour necrosis factor therapy in patients with ankylosing spondylitis (AS). This is the first report on the treatment with infliximab over 5 years.Methods: As part of a multicentre randomised trial, 69 patients with active AS at baseline (BL) have been continuously treated with infliximab (5 mg/kg i.v. every 6 weeks)---except for a short discontinuation after 3 years (FU1). The primary outcome of this extension was remission according to the ASsessment in Ankylosing Spondylitis (ASAS) criteria at the end of year 5 of the study (FU2).Results: Of the 43 patients who completed year 3, 42 agreed to continue, 38 of which (90.5%) finished year 5 (55% of 69 initially). Partial clinical remission was achieved in 13 of 38 patients (34.2%) at FU1 and FU2. At FU2, the mean Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) was 2.5±1.9 (BL:6.4, FU1:2.5). BASDAI values <4 were seen in 79% of patients at both, FU1 and FU2. ASAS 20% and 40% responses were seen in 32 (84%) and 24 (63%) patients at FU2, respectively. Most patients classified as non-responders at FU2 were part-time responders, as all but one patient achieved an ASAS 20% response at least once within the last 2 years. Three types of responders were identified. No major side effects occurred during years 4 and 5 of infliximab therapy.Conclusions: Infliximab is safe and efficacious in AS patients over 5 years. The majority of the patients remained on treatment and had rather persistent levels of low disease activity. Different response types could be identified

Investigating the missing data mechanism in quality of life outcomes: a comparison of approaches

Background: Missing data is classified as missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR). Knowing the mechanism is useful in identifying the most appropriate analysis. The first aim was to compare different methods for identifying this missing data mechanism to determine if they gave consistent conclusions. Secondly, to investigate whether the reminder-response data can be utilised to help identify the missing data mechanism. Methods: Five clinical trial datasets that employed a reminder system at follow-up were used. Some quality of life questionnaires were initially missing, but later recovered through reminders. Four methods of determining the missing data mechanism were applied. Two response data scenarios were considered. Firstly, immediate data only; secondly, all observed responses (including reminder-response). Results: In three of five trials the hypothesis tests found evidence against the MCAR assumption. Logistic regression suggested MAR, but was able to use the reminder-collected data to highlight potential MNAR data in two trials. Conclusion: The four methods were consistent in determining the missingness mechanism. One hypothesis test was preferred as it is applicable with intermittent missingness. Some inconsistencies between the two data scenarios were found. Ignoring the reminder data could potentially give a distorted view of the missingness mechanism. Utilising reminder data allowed the possibility of MNAR to be considered.The Chief Scientist Office of the Scottish Government Health Directorate. Research Training Fellowship (CZF/1/31

Aseptic meningitis in a patient taking etanercept for rheumatoid arthritis: a case report

Background \ud We report a case of a 53 year old lady recently commenced on etanercept, an anti-TNF (tumour necrosis factor) therapy for rheumatoid arthritis presenting with \ud confusion, pyrexia and an erythematous rash. \ud \ud Case presentation \ud A lumbar puncture was highly suggestive of bacterial meningitis, but CSF cultures produced no growth, and polymerase chain reactions (PCR) for all previously reported bacterial, fungal and viral causes of meningitis were negative. \ud \ud Conclusions \ud This case report describes aseptic meningitis as a previously unreported complication of etanercept therapy, and serves as a reminder of the rare but potentially lifethreatening risk of serious infections in patients taking anti-TNF therapy for a variety of conditions

Änderung der Sickerwassermengen und Nährstofffrachten durch verschiedene Pflanzenkohlesubstrate in einem Kulturversuch auf einem sandigen Waldstandort

Die Wälder auf den sandigen Standorten im Hessischen Ried sind besonders exponiert gegenüber klimatischen Extremsituationen die zukünftig vermehrt auftreten werden. Bereits heute können Auflösungserscheinungen der Wälder beobachtet werden. Pflanzungen sind im Hinblick auf die Sicherung der Waldfunktionen daher unerlässlich. Um diese Forstkulturen gegenüber den klimatischen Extremereignissen zu stabilisieren und den Anwuchserfolg zu sichern, kann das Einbringen von Pflanzenkohle ein erfolgversprechender Weg sein. Es wird erwartet, dass diese Pflanzenkohlen einen stabilisierenden Einfluss auf den Wasserhaushalt während Phasen extremer Trockenheit haben. Die Wälder sind besonders in der dicht besiedelten Rhein-Main-Ebene wichtige Gebiete der Grundwasserneubildung. Daher wird in diesem Beitrag der Blick auf mögliche Änderungen in Menge und Nährstoffbelastung des Sickerwassers zwischen den Versuchsvarianten gelenkt, die mit der Bodenbearbeitung und Kohleneinbringung zusammenhängen. In einem randomisierten Blockversuch wurden sechs verschiedene Kohlesubstrate im Hessischen Ried ausgebracht. Die Kohlen unterschieden sich im Ausgangssubstrat und in der Vorbehandlung (aufgesprühte Nährstofflösung, Kompostierung). Auf den mit Hainbuchen und Kiefern bepflanzen Parzellen wurden Saugkerzen installiert, um die Nährstoffkonzentrationen im Sickerwasser zu untersuchen. Nach Modellierung der Sickerwasserraten mit Brook90 werden die mit dem Sickerwasser verlagerten Nährstoffmengen berechnet. Die Beprobung des Sickerwassers zeigt deutliche Unterschiede in der Nährstoffkonzentration während der ersten Nichtvegetationszeit nach Kohleeinbringung. Besonders die Nitratkonzentrationen des Sickerwassers unter vorbehandelten Kohlevarianten sind im Vergleich zur Kontrolle erhöht. In der zweiten und dritten Nichtvegetationszeit sind die Unterschiede in den Nitratkonzentrationen weniger stark ausgeprägt. Die Ergebnisse zeigen, dass sich durch die Einbringung von Kohlesubstraten die jährliche Sickerwassermenge an diesem Standort um etwa 100 mm verringert. Zusätzlich erfahren die Konzentrationen von Nitrat und Ammonium im Sickerwasser je nach Vorbehandlung der Pflanzenkohle eine deutlich Veränderung, so dass sie zeitweise über den Grundwassergrenzwerten liegen