The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus

We present necessary and sufficient conditions for the generic rigidity of body-bar frameworks on the three-dimensional fixed torus. These frameworks correspond to infinite periodic body-bar frameworks in $\mathbb{R}^3$ with a fixed periodic lattice.Comment: 31 pages, 12 figure

Predictors of long-term pain and disability in patients with low back pain investigated by magnetic resonance imaging: A longitudinal study

<p>Abstract</p> <p>Background</p> <p>It is possible that clinical outcome of low back pain (LBP) differs according to the presence or absence of spinal abnormalities on magnetic resonance imaging (MRI), in which case there could be value in using MRI findings to refine case definition of LBP in epidemiological research. We therefore conducted a longitudinal study to explore whether spinal abnormalities on MRI for LBP predict prognosis after 18 months.</p> <p>Methods</p> <p>A consecutive series of patients aged 20-64 years, who were investigated by MRI because of mechanical LBP (median duration of current episode 16.2 months), were identified from three radiology departments, and those who agreed completed self-administered questionnaires at baseline and after a mean follow-up period of 18.5 months (a mean of 22.2 months from MRI investigation). MRI scans were assessed blind to other clinical information, according to a standardised protocol. Associations of baseline MRI findings with pain and disability at follow-up, adjusted for treatment and for other potentially confounding variables, were assessed by Poisson regression and summarised by prevalence ratios (PRs) with their 95% confidence intervals (CIs).</p> <p>Results</p> <p>Questionnaires were completed by 240 (74%) of the patients who had agreed to be followed up. Among these 111 men and 129 women, 175 (73%) reported LBP in the past four weeks, 89 (37%) frequent LBP, and 72 (30%) disabling LBP. In patients with initial disc degeneration there was an increased risk of frequent (PR 1.3, 95%CI 1.0-1.9) and disabling LBP (PR 1.7, 95%CI 1.1-2.5) at follow-up. No other associations were found between MRI abnormalities and subsequent outcome.</p> <p>Conclusions</p> <p>Our findings suggest that the MRI abnormalities examined are not major predictors of outcome in patients with LBP. They give no support to the use of MRI findings as a way of refining case definition for LBP in epidemiological research.</p

The vaginal microbiota associates with the regression of untreated cervical intraepithelial neoplasia 2 lesions

Emerging evidence suggests associations between the vaginal microbiota (VMB) composition, human papillomavirus (HPV) infection, and cervical intraepithelial neoplasia (CIN); however, causal inference remains uncertain. Here, we use bacterial DNA sequencing from serially collected vaginal samples from a cohort of 87 adolescent and young women aged 16–26 years with histologically confirmed, untreated CIN2 lesions to determine whether VMB composition affects rates of regression over 24 months. We show that women with a Lactobacillus-dominant microbiome at baseline are more likely to have regressive disease at 12 months. Lactobacillus spp. depletion and presence of specific anaerobic taxa including Megasphaera, Prevotella timonensis and Gardnerella vaginalis are associated with CIN2 persistence and slower regression. These findings suggest that VMB composition may be a future useful biomarker in predicting disease outcome and tailoring surveillance, whilst it may offer rational targets for the development of new prevention and treatment strategies