Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

Cap inflammation leads to higher plaque cap strain and lower cap stress: An MRI-PET/CT-based FSI modeling approach.

Plaque rupture may be triggered by extreme stress/strain conditions. Inflammation is also implicated and can be imaged using novel imaging techniques. The impact of cap inflammation on plaque stress/strain and flow shear stress were investigated. A patient-specific MRI-PET/CT-based modeling approach was used to develop 3D fluid-structure interaction models and investigate the impact of inflammation on plaque stress/strain conditions for better plaque assessment. 18FDG-PET/CT and MRI data were acquired from 4 male patients (average age: 66) to assess plaque characteristics and inflammation. Material stiffness for the fibrous cap was adjusted lower to reflect cap weakening causing by inflammation. Setting stiffness ratio (SR) to be 1.0 (fibrous tissue) for baseline, results for SR=0.5, 0.25, and 0.1 were obtained. Thin cap and hypertension were also considered. Combining results from the 4 patients, mean cap stress from 729 cap nodes was lowered by 25.2% as SR went from 1.0 to 0.1. Mean cap strain value for SR=0.1 was 0.313, 114% higher than that from SR=1.0 model. The thin cap SR=0.1 model had 40% mean cap stress decrease and 81% cap strain increase compared with SR=1.0 model. The hypertension SR=0.1 model had 19.5% cap stress decrease and 98.6% cap strain increase compared with SR=1.0 model. Differences of flow shear stress with 4 different SR values were limited (<10%). Cap inflammation may lead to large cap strain conditions when combined with thin cap and hypertension. Inflammation also led to lower cap stress. This shows the influence of inflammation on stress/strain calculations which are closely related to plaque assessment.This work was supported in part by NIH grants NIH/NIBIB R01 EB004759, NIH/NHLBI R01 HL071021, and National Natural Sciences Foundation of China grant 11672001, 11171030

The foramen magnum meningioma: 3 consecutive cases with particular association with multiple aneurysms

Intracranial meningioma represent a quite frequent pathology but those located in the foramen magnum are quite rare. We have described a small number of cases with their singularities – FMM associated with vagal disorders and associated with multiple aneurysms - operated in a short period of time along with reviewing the literature concerning the topic – frequency, type of approach, clinic signs

Spread of imipenem-resistant Acinetobacter baumannii co-expressing OXA-23 and GES-11 carbapenemases in Lebanon

© 2015 The Authors. Objectives: The acquisition of carbapenemases by Acinetobacter baumannii is reported increasingly worldwide, but data from Lebanon are limited. The aims of this study were to evaluate the prevalence of imipenem-resistant A. baumannii in Lebanon, identify resistance determinants, and detect clonal relatedness. Methods: Imipenem-resistant A. baumannii were collected from nine Lebanese hospitals during 2012. Antimicrobial susceptibility, the cloxacillin effect, and ethylenediaminetetraacetic acid (EDTA) synergy were determined. Genes encoding carbapenemases and insertion sequence IS. Aba1 were screened via PCR sequencing. IS. Aba1 position relative to genes encoding Acinetobacter-derived cephalosporinases (ADCs) and OXA-23 was studied by PCR mapping. Clonal linkage was examined by enterobacterial repetitive intergenic consensus PCR (ERIC-PCR). Results: Out of 724 A. baumannii isolated in 2012, 638 (88%) were imipenem-resistant. Of these, 142 were analyzed. Clavulanic acid-imipenem synergy suggested carbapenem-hydrolyzing extended-spectrum β-lactamase. A positive cloxacillin test indicated ADCs, while EDTA detection strips were negative. Genotyping indicated that 90% of isolates co-harbored blaOXA-23 and blaGES-11. The remaining strains had blaOXA-23, blaOXA-24, blaGES-11, or blaOXA-24 with blaGES-11. ISAba1 was located upstream of blaADC and blaOXA-23 in 97% and 100% of isolates, respectively. ERIC-PCR fingerprinting revealed 18 pulsotypes spread via horizontal gene transfer and clonal dissemination. Conclusion: This survey established baseline evidence of OXA-23 and GES-11-producing A. baumannii in Lebanon, indicating the need for further surveillance

Countrywide spread of OXA-48 carbapenemase in Lebanon: Surveillance and genetic characterization of carbapenem-non-susceptible Enterobacteriaceae in 10 hospitals over a one-year period

© 2014 The Authors. Objectives: To detect, characterize, and assess the genetic clonality of carbapenem-non-susceptible Enterobacteriaceae in 10 Lebanese hospitals in 2012. Methods: Selected Enterobacteriaceae isolates with reduced susceptibility to carbapenems were subject to phenotypic study including antibiotic susceptibility, cloxacillin effect, modified Hodge test, and activity of efflux pump inhibitor. Carbapenemase genes were detected using PCR; clonal relatedness was studied by pulsed field gel electrophoresis. Results: Out of 8717 Enterobacteriaceae isolated in 2012, 102 (1.2%) showed reduced susceptibility to carbapenems. Thirty-one (70%) of the 44 studied clinical isolates harbored blaOXA-48, including 15 Klebsiella pneumoniae, eight Escherichia coli, four Serratia marcescens, three Enterobacter cloacae, and one Morganella morganii. The majority of OXA-48 producers co-secreted an extended-spectrum beta-lactamase, while one had an acquired AmpC of the ACC type. In the non-OXA-48 producers, carbapenem resistance was attributed to the production of acquired AmpC cephalosporinases of MOX or CIT type, outer membrane impermeability, and/or efflux pump overproduction. DNA fingerprints revealed that OXA-48 producers were different, except for clonal relatedness among four K. pneumoniae, two E. coli, two E. cloacae, and three S. marcescens. Conclusions: Nosocomial carbapenem-non-susceptible Enterobacteriaceae are moderately spread in Lebanon and the predominant mechanism is OXA-48 production

Epstein-Barr virus infection and chronic lymphocytic leukemia: a possible progression factor?

Epstein-Barr virus is pathogenically associated with a well defined group of lymphoid and epithelial tumors in which the virus directly drives transformation of infected cells. Recent evidence however indicates that this virus may infect a subpopulation of tumor cells in patients with chronic lymphocytic leukemia (CLL) and EBV infection has been also associated with Richter transformation in a fraction of cases. We herein review available data suggesting a possible role of EBV as a direct or micro-environmental progression factor in a subset of CLL

Effect of calcification on the mechanical stability of plaque based on a three-dimensional carotid bifurcation model

Background: This study characterizes the distribution and components of plaque structure by presenting a three-dimensional blood-vessel modelling with the aim of determining mechanical properties due to the effect of lipid core and calcification within a plaque. Numerical simulation has been used to answer how cap thickness and calcium distribution in lipids influence the biomechanical stress on the plaque.Method: Modelling atherosclerotic plaque based on structural analysis confirms the rationale for plaque mechanical examination and the feasibility of our simulation model. Meaningful validation of predictions from modelled atherosclerotic plaque model typically requires examination of bona fide atherosclerotic lesions. To analyze a more accurate plaque rupture, fluid-structure interaction is applied to three-dimensional blood-vessel carotid bifurcation modelling

Eradicating the burden of atherosclerotic cardiovascular disease by lowering apolipoprotein B lipoproteins earlier in life

Jennifer G. Robinson, Kevin Jon Williams, Samuel Gidding, Jan Borén, Ira Tabas, Edward A. Fisher, Chris Packard, Michael Pencina, Zahi A. Fayad, Venkatesh Mani, Kerry Anne Rye, Børge G. Nordestgaard, Anne Tybjærg-Hansen, Pamela S. Douglas, Stephen J. Nicholls, Neha Pagidipati, Allan Sniderma