Definable orthogonality classes in accessible categories are small

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Levy hierarchy. For example, the statement that, for a class S of morphisms in a locally presentable category C of structures, the orthogonal class of objects is a small-orthogonality class (hence reflective) is provable in ZFC if S is \Sigma_1, while it follows from the existence of a proper class of supercompact cardinals if S is \Sigma_2, and from the existence of a proper class of what we call C(n)-extendible cardinals if S is \Sigma_{n+2} for n bigger than or equal to 1. These cardinals form a new hierarchy, and we show that Vopenka's principle is equivalent to the existence of C(n)-extendible cardinals for all n. As a consequence, we prove that the existence of cohomological localizations of simplicial sets, a long-standing open problem in algebraic topology, is implied by the existence of arbitrarily large supercompact cardinals. This result follows from the fact that cohomology equivalences are \Sigma_2. In contrast with this fact, homology equivalences are \Sigma_1, from which it follows (as is well known) that the existence of homological localizations is provable in ZFC.Comment: 38 pages; some results have been improved and former inaccuracies have been correcte

A Generalization of Martin's Axiom

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the literature before.Comment: 36 page

Definable orthogonality classes in accessible categories are small

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopěnka's principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Lévy hierarchy. For example, the statement that, for a class S of morphisms in a locally presentable category C of structures, the orthogonal class of objects is a small-orthogonality class (hence reflective) can be proved in ZFC if S is Σ1, while it follows from the existence of a proper class of supercompact cardinals if S is Σ2, and from the existence of a proper class of what we call C(n)-extendible cardinals if S is Σn+2 for n≥1. These cardinals form a new hierarchy, and we show that Vopěnka's principle is equivalent to the existence of C(n)-extendible cardinals for all n. As a consequence of our approach, we prove that the existence of cohomological localizations of simplicial sets, a long-standing open problem in algebraic topology, is implied by the existence of arbitrarily large supercompact cardinals. This follows from the fact that E∗-equivalence classes are Σ2, where E denotes a spectrum treated as a parameter. In contrast with this fact, E∗-equivalence classes are Σ1, from which it follows (as is well known) that the existence of homological localizations is provable in ZFC

Health Impacts of Catastrophic Climate Change: Expert Workshop. Avoid Dangerous Climate Change (AVOID)

Climate change is likely to have serious and significant impacts on human population health. The mechanisms by which climate change may affect health are becoming better understood. Current quantitative methods of estimating future health impacts rely on disease-specific models that primarily describe relationships between mean values of weather variables and health outcomes and do not address the impacts of extreme events or weather disasters. Extreme events have the potential to disrupt community function, which is of concern for decision-makers. Estimating the magnitude and extent of impacts from low probability high impact events is challenging because there is often no analogue that can provide relevant evidence and that take into account the complexity of factors determining future vulnerability and health impacts (the social determinants of health)

Real-Time Cytotoxicity Assay for Rapid and Sensitive Detection of Ricin from Complex Matrices

BACKGROUND: In the context of a potential bioterrorist attack sensitive and fast detection of functionally active toxins such as ricin from complex matrices is necessary to be able to start timely countermeasures. One of the functional detection methods currently available for ricin is the endpoint cytotoxicity assay, which suffers from a number of technical deficits. METHODOLOGY/FINDINGS: This work describes a novel online cytotoxicity assay for the detection of active ricin and Ricinus communis agglutinin, that is based on a real-time cell electronic sensing system and impedance measurement. Characteristic growth parameters of Vero cells were monitored online and used as standardized viability control. Upon incubation with toxin the cell status and the cytotoxic effect were visualized using a characteristic cell index-time profile. For ricin, tested in concentrations of 0.06 ng/mL or above, a concentration-dependent decrease of cell index correlating with cytotoxicity was recorded between 3.5 h and 60 h. For ricin, sensitive detection was determined after 24 h, with an IC50 of 0.4 ng/mL (for agglutinin, an IC50 of 30 ng/mL was observed). Using functionally blocking antibodies, the specificity for ricin and agglutinin was shown. For detection from complex matrices, ricin was spiked into several food matrices, and an IC50 ranging from 5.6 to 200 ng/mL was observed. Additionally, the assay proved to be useful in detecting active ricin in environmental sample materials, as shown for organic fertilizer containing R. communis material. CONCLUSIONS/SIGNIFICANCE: The cell-electrode impedance measurement provides a sensitive online detection method for biologically active cytotoxins such as ricin. As the cell status is monitored online, the assay can be standardized more efficiently than previous approaches based on endpoint measurement. More importantly, the real-time cytotoxicity assay provides a fast and easy tool to detect active ricin in complex sample matrices

Evaluation of cell-free DNA approaches for multi-cancer early detection

In the Circulating Cell-free Genome Atlas (NCT02889978) substudy 1, we evaluate several approaches for a circulating cell-free DNA (cfDNA)-based multi-cancer early detection (MCED) test by defining clinical limit of detection (LOD) based on circulating tumor allele fraction (cTAF), enabling performance comparisons. Among 10 machine-learning classifiers trained on the same samples and independently validated, when evaluated at 98% specificity, those using whole-genome (WG) methylation, single nucleotide variants with paired white blood cell background removal, and combined scores from classifiers evaluated in this study show the highest cancer signal detection sensitivities. Compared with clinical stage and tumor type, cTAF is a more significant predictor of classifier performance and may more closely reflect tumor biology. Clinical LODs mirror relative sensitivities for all approaches. The WG methylation feature best predicts cancer signal origin. WG methylation is the most promising technology for MCED and informs development of a targeted methylation MCED test

Medical Therapies for Uterine Fibroids - A Systematic Review and Network Meta-Analysis of Randomised Controlled Trials

BACKGROUND: Uterine fibroids are common, often symptomatic and a third of women need repeated time off work. Consequently 25% to 50% of women with fibroids receive surgical treatment, namely myomectomy or hysterectomy. Hysterectomy is the definitive treatment as fibroids are hormone dependent and frequently recurrent. Medical treatment aims to control symptoms in order to replace or delay surgery. This may improve the outcome of surgery and prevent recurrence. PURPOSE: To determine whether any medical treatment can be recommended in the treatment of women with fibroids about to undergo surgery and in those for whom surgery is not planned based on currently available evidence. STUDY SELECTION: Two authors independently identified randomised controlled trials (RCT) of all pharmacological treatments aimed at the treatment of fibroids from a list of references obtained by formal search of MEDLINE, EMBASE, Cochrane library, Science Citation Index, and ClinicalTrials.gov until December 2013. DATA EXTRACTION: Two authors independently extracted data from identified studies. DATA SYNTHESIS: A Bayesian network meta-analysis was performed following the National Institute for Health and Care Excellence-Decision Support Unit guidelines. Odds ratios, rate ratios, or mean differences with 95% credible intervals (CrI) were calculated. RESULTS AND LIMITATIONS: A total of 75 RCT met the inclusion criteria, 47 of which were included in the network meta-analysis. The overall quality of evidence was very low. The network meta-analysis showed differing results for different outcomes. CONCLUSIONS: There is currently insufficient evidence to recommend any medical treatment in the management of fibroids. Certain treatments have future promise however further, well designed RCTs are needed

Set Theory and Structures

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure