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

Lagrangian Curves in a 4-dimensional affine symplectic space

Lagrangian curves in R4 entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify La- grangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R4 and determine Lagrangian geodesic

Bezlotoxumab for Prevention of Recurrent Clostridium difficile Infection

BACKGROUND Clostridium difficile is the most common cause of infectious diarrhea in hospitalized patients. Recurrences are common after antibiotic therapy. Actoxumab and bezlotoxumab are human monoclonal antibodies against C. difficile toxins A and B, respectively. METHODS We conducted two double-blind, randomized, placebo-controlled, phase 3 trials, MODIFY I and MODIFY II, involving 2655 adults receiving oral standard-of-care antibiotics for primary or recurrent C. difficile infection. Participants received an infusion of bezlotoxumab (10 mg per kilogram of body weight), actoxumab plus bezlotoxumab (10 mg per kilogram each), or placebo; actoxumab alone (10 mg per kilogram) was given in MODIFY I but discontinued after a planned interim analysis. The primary end point was recurrent infection (new episode after initial clinical cure) within 12 weeks after infusion in the modified intention-to-treat population. RESULTS In both trials, the rate of recurrent C. difficile infection was significantly lower with bezlotoxumab alone than with placebo (MODIFY I: 17% [67 of 386] vs. 28% [109 of 395]; adjusted difference, −10.1 percentage points; 95% confidence interval [CI], −15.9 to −4.3; P<0.001; MODIFY II: 16% [62 of 395] vs. 26% [97 of 378]; adjusted difference, −9.9 percentage points; 95% CI, −15.5 to −4.3; P<0.001) and was significantly lower with actoxumab plus bezlotoxumab than with placebo (MODIFY I: 16% [61 of 383] vs. 28% [109 of 395]; adjusted difference, −11.6 percentage points; 95% CI, −17.4 to −5.9; P<0.001; MODIFY II: 15% [58 of 390] vs. 26% [97 of 378]; adjusted difference, −10.7 percentage points; 95% CI, −16.4 to −5.1; P<0.001). In prespecified subgroup analyses (combined data set), rates of recurrent infection were lower in both groups that received bezlotoxumab than in the placebo group in subpopulations at high risk for recurrent infection or for an adverse outcome. The rates of initial clinical cure were 80% with bezlotoxumab alone, 73% with actoxumab plus bezlotoxumab, and 80% with placebo; the rates of sustained cure (initial clinical cure without recurrent infection in 12 weeks) were 64%, 58%, and 54%, respectively. The rates of adverse events were similar among these groups; the most common events were diarrhea and nausea. CONCLUSIONS Among participants receiving antibiotic treatment for primary or recurrent C. difficile infection, bezlotoxumab was associated with a substantially lower rate of recurrent infection than placebo and had a safety profile similar to that of placebo. The addition of actoxumab did not improve efficacy. (Funded by Merck; MODIFY I and MODIFY II ClinicalTrials.gov numbers, NCT01241552 and NCT01513239.

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

Accuracy and generalizability of using automated methods for identifying adverse events from electronic health record data: a validation study protocol

BACKGROUND: Adverse events (AEs) in acute care hospitals are frequent and associated with significant morbidity, mortality, and costs. Measuring AEs is necessary for quality improvement and benchmarking purposes, but current detection methods lack in accuracy, efficiency, and generalizability. The growing availability of electronic health records (EHR) and the development of natural language processing techniques for encoding narrative data offer an opportunity to develop potentially better methods. The purpose of this study is to determine the accuracy and generalizability of using automated methods for detecting three high-incidence and high-impact AEs from EHR data: a) hospital-acquired pneumonia, b) ventilator-associated event and, c) central line-associated bloodstream infection. METHODS: This validation study will be conducted among medical, surgical and ICU patients admitted between 2013 and 2016 to the Centre hospitalier universitaire de Sherbrooke (CHUS) and the McGill University Health Centre (MUHC), which has both French and English sites. A random 60% sample of CHUS patients will be used for model development purposes (cohort 1, development set). Using a random sample of these patients, a reference standard assessment of their medical chart will be performed. Multivariate logistic regression and the area under the curve (AUC) will be employed to iteratively develop and optimize three automated AE detection models (i.e., one per AE of interest) using EHR data from the CHUS. These models will then be validated on a random sample of the remaining 40% of CHUS patients (cohort 1, internal validation set) using chart review to assess accuracy. The most accurate models developed and validated at the CHUS will then be applied to EHR data from a random sample of patients admitted to the MUHC French site (cohort 2) and English site (cohort 3)—a critical requirement given the use of narrative data –, and accuracy will be assessed using chart review. Generalizability will be determined by comparing AUCs from cohorts 2 and 3 to those from cohort 1. DISCUSSION: This study will likely produce more accurate and efficient measures of AEs. These measures could be used to assess the incidence rates of AEs, evaluate the success of preventive interventions, or benchmark performance across hospitals

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

High spatial overlap but diverging age-related trajectories of cortical magnetic resonance imaging markers aiming to represent intracortical myelin and microstructure

ABSTRACT: Statistical effects of cortical metrics derived from standard T1- and T2-weighted magnetic resonance imaging (MRI) images, such as gray–white matter contrast (GWC), boundary sharpness coefficient (BSC), T1-weighted/T2-weighted ratio (T1w/T2w), and cortical thickness (CT), are often interpreted as representing or being influenced by intracortical myelin content with little empirical evidence to justify these interpretations. We first examined spatial correspondence with more biologically specific microstructural measures, and second compared between-marker age-related trends with the underlying hypothesis that different measures primarily driven by similar changes in myelo- and microstructural underpinnings should be highly related. Cortical MRI markers were derived from MRI images of 127 healthy subjects, aged 18–81, using cortical surfaces that were generated with the CIVET 2.1.0 pipeline. Their gross spatial distributions were compared with gene expression-derived cell-type densities, histology-derived cytoarchitecture, and quantitative R1 maps acquired on a subset of participants. We then compared between-marker age-related trends in their shape, direction, and spatial distribution of the linear age effect. The gross anatomical distributions of cortical MRI markers were, in general, more related to myelin and glial cells than neuronal indicators. Comparing MRI markers, our results revealed generally high overlap in spatial distribution (i.e., group means), but mostly divergent age trajectories in the shape, direction, and spatial distribution of the linear age effect. We conclude that the microstructural properties at the source of spatial distributions of MRI cortical markers can be different from microstructural changes that affect these markers in aging

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