Difference schemes with point symmetries and their numerical tests

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new difference schemes are tested as numerical methods. The obtained numerical solutions are shown to be much more accurate than those obtained by standard methods without an increase in cost. For an example involving a solution with a singularity in the integration region the symmetry preserving scheme, contrary to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure

Salmonella enterica bacteraemia: a multi-national population-based cohort study

<p>Abstract</p> <p>Background</p> <p><it>Salmonella enterica </it>is an important emerging cause of invasive infections worldwide. However, population-based data are limited. The objective of this study was to define the occurrence of <it>S. enterica </it>bacteremia in a large international population and to evaluate temporal and regional differences.</p> <p>Methods</p> <p>We conducted population-based laboratory surveillance for all salmonella bacteremias in six regions (annual population at risk 7.7 million residents) in Finland, Australia, Denmark, and Canada during 2000-2007.</p> <p>Results</p> <p>A total of 622 cases were identified for an annual incidence of 1.02 per 100,000 population. The incidence of typhoidal (serotypes Typhi and Paratyphi) and non-typhoidal (other serotypes) disease was 0.21 and 0.81 per 100,000/year. There was major regional and moderate seasonal and year to year variability with an increased incidence observed in the latter years of the study related principally to increasing rates of non-typhoidal salmonella bacteremias. Advancing age and male gender were significant risk factors for acquiring non-typhoidal salmonella bacteremia. In contrast, typhoidal salmonella bacteremia showed a decreasing incidence with advancing age and no gender-related excess risk.</p> <p>Conclusions</p> <p><it>Salmonella enterica </it>is an important emerging pathogen and regional determinants of risk merits further investigation.</p

Rationale for and protocol of a multi-national population-based bacteremia surveillance collaborative

<p>Abstract</p> <p>Background</p> <p>Bloodstream infections are frequent causes of human illness and cause major morbidity and death. In order to best define the epidemiology of these infections and to track changes in occurrence, adverse outcome, and resistance rates over time, population based methodologies are optimal. However, few population-based surveillance systems exist worldwide, and because of differences in methodology inter-regional comparisons are limited. In this report we describe the rationale and propose first practical steps for developing an international collaborative approach to the epidemiologic study and surveillance for bacteremia.</p> <p>Findings</p> <p>The founding collaborative participants represent six regions in four countries in three continents with a combined annual surveillance population of more than 8 million residents.</p> <p>Conclusion</p> <p>Future studies from this collaborative should lead to a better understanding of the epidemiology of bloodstream infections.</p

The Jacobi last multiplier for difference equations

We present a discretization of the Jacobi last multiplier, with some applications to the computation of solutions of difference equations.Comment: 9 page

Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I

We propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability properties of such discretization. This method should provide, in particular, useful and concrete informations on how good is any numerical scheme used to integrate a given integrable PDE. The procedure, illustrated on a fairly general 10-parameter family of discretizations of the nonlinear Schroedinger equation, consists of the following three steps: i) the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in epsilon, following the Degasperis - Manakov - Santini procedure; ii) the application, to such expansion, of the Degasperis - Procesi (DP) integrability test, to test the asymptotic integrability properties of the discrete system and its ``distance'' from its continuous limit; iii) the use of the main output of the DP test to construct infinitely many approximate symmetries and constants of motion of the discrete system, through novel and simple formulas.Comment: 34 pages, no figur

When Do Objects Become Landmarks? A VR Study of the Effect of Task Relevance on Spatial Memory

We investigated how objects come to serve as landmarks in spatial memory, and more specifically how they form part of an allocentric cognitive map. Participants performing a virtual driving task incidentally learned the layout of a virtual town and locations of objects in that town. They were subsequently tested on their spatial and recognition memory for the objects. To assess whether the objects were encoded allocentrically we examined pointing consistency across tested viewpoints. In three experiments, we found that spatial memory for objects at navigationally relevant locations was more consistent across tested viewpoints, particularly when participants had more limited experience of the environment. When participants’ attention was focused on the appearance of objects, the navigational relevance effect was eliminated, whereas when their attention was focused on objects’ locations, this effect was enhanced, supporting the hypothesis that when objects are processed in the service of navigation, rather than merely being viewed as objects, they engage qualitatively distinct attentional systems and are incorporated into an allocentric spatial representation. The results are consistent with evidence from the neuroimaging literature that when objects are relevant to navigation, they not only engage the ventral “object processing stream”, but also the dorsal stream and medial temporal lobe memory system classically associated with allocentric spatial memory

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

Faecal pharmacokinetics of orally administered vancomycin in patients with suspected Clostridium difficile infection

<p>Abstract</p> <p>Background</p> <p>Oral vancomycin (125 mg qid) is recommended as treatment of severe <it>Clostridium difficile </it>infection (CDI). Higher doses (250 or 500 mg qid) are sometimes recommended for patients with very severe CDI, without supporting clinical evidence. We wished to determine to what extent faecal levels of vancomycin vary according to diarrhoea severity and dosage, and whether it is rational to administer high-dose vancomycin to selected patients.</p> <p>Methods</p> <p>We recruited hospitalized adults suspected to have CDI for whom oral vancomycin (125, 250 or 500 mg qid) had been initiated. Faeces were collected up to 3 times/day and levels were measured with the AxSYM fluorescence polarization immunoassay.</p> <p>Results</p> <p>Fifteen patients (9 with confirmed CDI) were treated with oral vancomycin. Patients with ≥4 stools daily presented lower faecal vancomycin levels than those with a lower frequency. Higher doses of oral vancomycin (250 mg or 500 mg qid) led to consistently higher faecal levels (> 2000 mg/L), which were 3 orders of magnitude higher than the MIC₉₀of vancomycin against <it>C. difficile</it>. One patient receiving 125 mg qid had levels below 50 mg/L during the first day of treatment.</p> <p>Conclusions</p> <p>Faecal levels of vancomycin are proportional to the dosage administered and, even in patients with increased stool frequency, much higher than the MIC₉₀. Patients given the standard 125 mg qid dosage might have low faecal levels during the first day of treatment. A loading dose of 250 mg or 500 mg qid during the first 24-48 hours followed by the standard dosage should be evaluated in larger studies, since it might be less disruptive to the colonic flora and save unnecessary costs.</p