Differential and holomorphic differential operators on noncommutative algebras

Abstract This paper deals with sheaves of differential operators on noncommutative algebras, in a manner related to the classical theory of D-modules. The sheaves are defined by quotienting the tensor algebra of vector fields (suitably deformed by a covariant derivative). As an example we can obtain enveloping algebra like relations for Hopf algebras with differential structures which are not bicovariant. Symbols of differential operators are defined, but not studied. These sheaves are shown to be in the center of a category of bimodules with flat bimodule covariant derivatives. Also holomorphic differential operators are considered

The Serre spectral sequence of a noncommutative fibration for de Rham cohomology

For differential calculi on noncommutative algebras, we construct a twisted de Rham cohomology using flat connections on modules. This has properties similar, in some respects, to sheaf cohomology on topological spaces. We also discuss generalised mapping properties of these theories, and relations of these properties to corings. Using this, we give conditions for the Serre spectral sequence to hold for a noncommutative fibration. This might be better read as giving the definition of a fibration in noncommutative differential geometry. We also study the multiplicative structure of such spectral sequences. Finally we show that some noncommutative homogeneous spaces satisfy the conditions to be such a fibration, and in the process clarify the differential structure on these homogeneous spaces. We also give two explicit examples of differential fibrations: these are built on the quantum Hopf fibration with two different differential structures.Comment: LaTeX, 33 page

Increasing the frequency of hand washing by healthcare workers does not lead to commensurate reductions in staphylococcal infection in a hospital ward

Hand hygiene is generally considered to be the most important measure that can be applied to prevent the spread of healthcare-associated infection (HAI). Continuous emphasis on this intervention has lead to the widespread opinion that HAI rates can be greatly reduced by increased hand hygiene compliance alone. However, this assumes that the effectiveness of hand hygiene is not constrained by other factors and that improved compliance in excess of a given level, in itself, will result in a commensurate reduction in the incidence of HAI. However, several researchers have found the law of diminishing returns to apply to hand hygiene, with the greatest benefits occurring in the first 20% or so of compliance, and others have demonstrated that poor cohorting of nursing staff profoundly influences the effectiveness of hand hygiene measures. Collectively, these findings raise intriguing questions about the extent to which increasing compliance alone can further reduce rates of HAI. In order to investigate these issues further, we constructed a deterministic Ross-Macdonald model and applied it to a hypothetical general medical ward. In this model the transmission of staphylococcal infection was assumed to occur after contact with the transiently colonized hands of HCWs, who, in turn, acquire contamination only by touching colonized patients. The aim of the study was to evaluate the impact of imperfect hand cleansing on the transmission of staphylococcal infection and to identify, whether there is a limit, above which further hand hygiene compliance is unlikely to be of benefit. The model demonstrated that if transmission is solely via the hands of HCWs, it should, under most circumstances, be possible to prevent outbreaks of staphylococcal infection from occurring at a hand cleansing frequencies <50%, even with imperfect hand hygiene. The analysis also indicated that the relationship between hand cleansing efficacy and frequency is not linear - as efficacy decreases, so the hand cleansing frequency required to ensure R0<1 increases disproportionately. Although our study confirmed hand hygiene to be an effective control measure, it demonstrated that the law of diminishing returns applies, with the greatest benefit derived from the first 20% or so of compliance. Indeed, our analysis suggests that there is little benefit to be accrued from very high levels of hand cleansing and that in most situations compliance >40% should be enough to prevent outbreaks of staphylococcal infection occurring, if transmission is solely via the hands of HCWs. Furthermore we identified a non-linear relationship between hand cleansing efficacy and frequency, suggesting that it is important to maximise the efficacy of the hand cleansing process

Involutive Categories and Monoids, with a GNS-correspondence

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the so-called Gelfand-Naimark-Segal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive categories

Letter to Editor: Carpal tunnel syndrome due to an atypical deep soft tissue leiomyoma: The risk of misdiagnosis and mismanagement

A response to Chalidis et al: Carpal tunnel syndrome due to an atypical deep soft tissue leiomyoma: The risk of misdiagnosis and mismanagement. World J Surg Oncol 2007, 5:92

Alternative job search strategies in remote rural and peri-urban labour markets: the role of social networks

This paper examines the importance of informal methods (especially social networking) to the job search strategies used by unemployed people. It compares three areas: a small rural town; a larger, more sparsely populated, remote rural area; and a centrally-located, peri-urban labour market. The analysis is based first on survey research undertaken with 490 job seekers across the study areas. Emerging issues were then followed up during a series of twelve focus groups. The survey research showed that job seekers in the rural study areas were significantly more likely to use social networks to look for work. However, those who had experienced repeated or long-term periods out of work, the unskilled and young people were significantly less likely to use such networks. Focus groups confirmed the perceived importance of social networking to the job search process in rural areas, in contrast to the more marginal role such methods appear to play in peri-urban settings. For many rural job seekers, formal job search activities conducted through Jobcentres were seen as largely symbolic, lacking the practical value of social networking. These results suggest that service providers seeking to assist unemployed people in rural areas need to address the problems faced by many disadvantaged job seekers who are currently caught between their lack of social network relations and the absence of local public employment service facilities in more remote communities

Point-occurrence self-similarity in crackling-noise systems and in other complex systems

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.Comment: Submitted to J. Stat. Mech. for the proceedings of UPON 2008 (Lyon), topic: crackling nois

From exercise intolerance to functional improvement: The second wind phenomenon in the identification of McArdle disease

McArdle disease is the most common of the glycogen storage diseases. Onset of symptoms is usually in childhood with muscle pain and restricted exercise capacity. Signs and symptoms are often ignored in children or put down to 'growing pains' and thus diagnosis is often delayed. Misdiagnosis is not uncommon because several other conditions such as muscular dystrophy and muscle channelopathies can manifest with similar symptoms. A simple exercise test performed in the clinic can however help to identify patients by revealing the second wind phenomenon which is pathognomonic of the condition. Here a patient is reported illustrating the value of using a simple 12 minute walk test.RSS is funded by Ciências sem Fronteiras/CAPES Foundation. The authors would like to thank the Association for Glycogen Storage Disease (UK), the EUROMAC Registry funded by the European Union, the Muscular Dystrophy Campaign, the NHS National Specialist Commissioning Group and the Myositis Support Group for funding

The First Detections of the Extragalactic Background Light at 3000, 5500, and 8000A (II): Measurement of Foreground Zodiacal Light

We present a measurement of the absolute surface brightness of the zodiacal light (3900-5100A) toward a fixed extragalactic target at high ecliptic latitude based on moderate resolution (~1.3A per pixel) spectrophotometry obtained with the du Pont 2.5m telescope at Las Campanas Observatory in Chile. This measurement and contemporaneous Hubble Space Telescope data from WFPC2 and FOS comprise a coordinated program to measure the mean flux of the diffuse extragalactic background light (EBL). The zodiacal light at optical wavelengths results from scattering by interplanetary dust, so that the zodiacal light flux toward any extragalactic target varies seasonally with the position of the Earth. This measurement of zodiacal light is therefore relevant to the specific observations (date and target field) under discussion. To obtain this result, we have developed a technique that uses the strength of the zodiacal Fraunhofer lines to identify the absolute flux of the zodiacal light in the multiple-component night sky spectrum. Statistical uncertainties in the result are 0.6% (1 sigma). However, the dominant source of uncertainty is systematic errors, which we estimate to be 1.1% (1 sigma). We discuss the contributions included in this estimate explicitly. The systematic errors in this result contribute 25% in quadrature to the final error in our coordinated EBL measurement, which is presented in the first paper of this series.Comment: Accepted for publication in ApJ, 22 pages using emulateapj.sty, version with higher resolution figures available at http://www.astro.lsa.umich.edu/~rab/publications.html or at http://nedwww.ipac.caltech.edu/level5/Sep01/Bernstein2/frames.htm