Isoperimetric Inequalities in Simplicial Complexes

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In particular, we present a Cheeger-type inequality, and a high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach, we obtain a connection between spectral properties of complexes and Gromov's notion of geometric overlap. Using the work of Gunder and Wagner, we give an estimate for the combinatorial expansion and geometric overlap of random Linial-Meshulam complexes

The Bifidobacterium dentium Bd1 Genome Sequence Reflects Its Genetic Adaptation to the Human Oral Cavity

Bifidobacteria, one of the relatively dominant components of the human intestinal microbiota, are considered one of the key groups of beneficial intestinal bacteria (probiotic bacteria). However, in addition to health-promoting taxa, the genus Bifidobacterium also includes Bifidobacterium dentium, an opportunistic cariogenic pathogen. The genetic basis for the ability of B. dentium to survive in the oral cavity and contribute to caries development is not understood. The genome of B. dentium Bd1, a strain isolated from dental caries, was sequenced to completion to uncover a single circular 2,636,368 base pair chromosome with 2,143 predicted open reading frames. Annotation of the genome sequence revealed multiple ways in which B. dentium has adapted to the oral environment through specialized nutrient acquisition, defences against antimicrobials, and gene products that increase fitness and competitiveness within the oral niche. B. dentium Bd1 was shown to metabolize a wide variety of carbohydrates, consistent with genome-based predictions, while colonization and persistence factors implicated in tissue adhesion, acid tolerance, and the metabolism of human saliva-derived compounds were also identified. Global transcriptome analysis demonstrated that many of the genes encoding these predicted traits are highly expressed under relevant physiological conditions. This is the first report to identify, through various genomic approaches, specific genetic adaptations of a Bifidobacterium taxon, Bifidobacterium dentium Bd1, to a lifestyle as a cariogenic microorganism in the oral cavity. In silico analysis and comparative genomic hybridization experiments clearly reveal a high level of genome conservation among various B. dentium strains. The data indicate that the genome of this opportunistic cariogen has evolved through a very limited number of horizontal gene acquisition events, highlighting the narrow boundaries that separate commensals from opportunistic pathogens

The development and validation of a scoring tool to predict the operative duration of elective laparoscopic cholecystectomy

Background: The ability to accurately predict operative duration has the potential to optimise theatre efficiency and utilisation, thus reducing costs and increasing staff and patient satisfaction. With laparoscopic cholecystectomy being one of the most commonly performed procedures worldwide, a tool to predict operative duration could be extremely beneficial to healthcare organisations. Methods: Data collected from the CholeS study on patients undergoing cholecystectomy in UK and Irish hospitals between 04/2014 and 05/2014 were used to study operative duration. A multivariable binary logistic regression model was produced in order to identify significant independent predictors of long (> 90 min) operations. The resulting model was converted to a risk score, which was subsequently validated on second cohort of patients using ROC curves. Results: After exclusions, data were available for 7227 patients in the derivation (CholeS) cohort. The median operative duration was 60 min (interquartile range 45–85), with 17.7% of operations lasting longer than 90 min. Ten factors were found to be significant independent predictors of operative durations > 90 min, including ASA, age, previous surgical admissions, BMI, gallbladder wall thickness and CBD diameter. A risk score was then produced from these factors, and applied to a cohort of 2405 patients from a tertiary centre for external validation. This returned an area under the ROC curve of 0.708 (SE = 0.013, p  90 min increasing more than eightfold from 5.1 to 41.8% in the extremes of the score. Conclusion: The scoring tool produced in this study was found to be significantly predictive of long operative durations on validation in an external cohort. As such, the tool may have the potential to enable organisations to better organise theatre lists and deliver greater efficiencies in care

Sustained increases in atmospheric oxygen and marine productivity in the Neoproterozoic and Palaeozoic eras

A geologically rapid Neoproterozoic oxygenation event is commonly linked to the appearance of marine animal groups in the fossil record. However, there is still debate about what evidence from the sedimentary geochemical record—if any—provides strong support for a persistent shift in surface oxygen immediately preceding the rise of animals. We present statistical learning analyses of a large dataset of geochemical data and associated geological context from the Neoproterozoic and Palaeozoic sedimentary record and then use Earth system modelling to link trends in redox-sensitive trace metal and organic carbon concentrations to the oxygenation of Earth’s oceans and atmosphere. We do not find evidence for the wholesale oxygenation of Earth’s oceans in the late Neoproterozoic era. We do, however, reconstruct a moderate long-term increase in atmospheric oxygen and marine productivity. These changes to the Earth system would have increased dissolved oxygen and food supply in shallow-water habitats during the broad interval of geologic time in which the major animal groups first radiated. This approach provides some of the most direct evidence for potential physiological drivers of the Cambrian radiation, while highlighting the importance of later Palaeozoic oxygenation in the evolution of the modern Earth system