Logarithmic Hennings invariants for restricted quantum sl(2)

We construct a Hennings type logarithmic invariant for restricted quantum $\mathfrak{sl}(2)$ at a $2\mathsf{p}$-th root of unity. This quantum group $U$ is not braided, but factorizable. The invariant is defined for a pair: a 3-manifold $M$ and a colored link $L$ inside $M$. The link $L$ is split into two parts colored by central elements and by trace classes, or elements in the $0^{\text{th}}$ Hochschild homology of $U$, respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of $U$, and the modified trace introduced by the third author with his collaborators and computed on tensor powers of the regular representation. Our invariant is a colored extension of the logarithmic invariant constructed by Jun Murakami

Abelian complexity of fixed point of morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1

We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds applications in several fields such as combinatorics on words; for example, in pattern avoidance it is often used to construct infinite words avoiding given patterns. It has been shown that the factor complexity of vtm, i.e., the number of factors of length n, is Θ(n); in fact, it is bounded by ¹⁰⁄₃n for all n, and it reaches that bound precisely when n can be written as 3 times a power of 2. In this paper, we show that the abelian complexity of vtm, i.e., the number of Parikh vectors of length n, is O(log n) with constant approaching ¾ (assuming base 2 logarithm), and it is Ω(1) with constant 3 (and these are the best possible bounds). We also prove some results regarding factor indices in vtm."F. Blanchet-Sadri and Nathan Fox’s research was supported by the National Science Foundation under Grant No. DMS–1060775." "James D. Currie and Narad Rampersad’s research was supported by NSERC Discovery grants.

Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories

In this paper we construct invariants of 3-manifolds "\`a la Reshetikhin-Turaev" in the setting of non-semi-simple ribbon tensor categories. We give concrete examples of such categories which lead to a family of 3-manifold invariants indexed by the integers. We prove this family of invariants has several notable features, including: they can be computed via a set of axioms, they distinguish homotopically equivalent manifolds that the standard Reshetikhin-Turaev-Witten invariants do not, and they allow the statement of a version of the Volume Conjecture and a proof of this conjecture for an infinite class of links.Comment: 46 pages, 45 figures, new introduction, some misprints corrected and an example detailed. An appendix added to correct a proo

Systematic review of the evidence on the effectiveness of sexual and reproductive health interventions in humanitarian crises

Objectives This systematic review aims to evaluate evidence on the effectiveness of sexual and reproductive health (SRH) interventions delivered in humanitarian crises.Setting Crisis affected low-income or middle-income countries.Participants Crisis-affected populations in low-income or middle-income countries.Method Peer-reviewed and grey literature sources were systematically searched for relevant papers detailing interventions from 1 January 1980 until the search date on 30 April 2013. Data from included studies were then extracted, and the papers’ quality evaluated using criteria based on modified STROBE and CONSORT checklists.Primary and secondary outcome measures Primary outcomes include, but are not limited to, changes in morbidity, mortality, sexually transmitted infection (STI) diagnosis or gender-based violence. Secondary outcomes include, but are not limited to, reported condom use or skilled attendance at birth. Primary outputs include, but are not limited to, condoms distributed or education courses taught.Results Of 7149 returned citations, 15 studies met the inclusion criteria. Only one randomised controlled trial was identified. The remaining observational studies were of moderate quality, demonstrating limited use of controls and inadequate attempts to address bias. Evidence of effectiveness was available for the following interventions: impregnated bed nets for pregnant women, subsidised refugee healthcare, female community health workers, and tiered community reproductive health services.Conclusions The limited evidence base for SRH interventions highlights the need for improved research on the effectiveness of public health interventions in humanitarian crises. While interventions proven efficacious in stable settings are being used in humanitarian efforts, more evidence is required to demonstrate the effectiveness of delivering and scaling-up such interventions in humanitarian crises

Integrated high-content quantification of intracellular ROS levels and mitochondrial morphofunction

Oxidative stress arises from an imbalance between the production of reactive oxygen species (ROS) and their removal by cellular antioxidant systems. Especially under pathological conditions, mitochondria constitute a relevant source of cellular ROS. These organelles harbor the electron transport chain, bringing electrons in close vicinity to molecular oxygen. Although a full understanding is still lacking, intracellular ROS generation and mitochondrial function are also linked to changes in mitochondrial morphology. To study the intricate relationships between the different factors that govern cellular redox balance in living cells, we have developed a high-contentmicroscopy-based strategy for simultaneous quantification of intracellular ROS levels and mitochondrial morphofunction. Here, we summarize the principles of intracellular ROS generation and removal, and we explain the major considerations for performing quantitative microscopy analyses of ROS and mitochondrial morphofunction in living cells. Next, we describe our workflow, and finally, we illustrate that a multiparametric readout enables the unambiguous classification of chemically perturbed cells as well as laminopathy patient cells

AI is a viable alternative to high throughput screening: a 318-target study

: High throughput screening (HTS) is routinely used to identify bioactive small molecules. This requires physical compounds, which limits coverage of accessible chemical space. Computational approaches combined with vast on-demand chemical libraries can access far greater chemical space, provided that the predictive accuracy is sufficient to identify useful molecules. Through the largest and most diverse virtual HTS campaign reported to date, comprising 318 individual projects, we demonstrate that our AtomNet® convolutional neural network successfully finds novel hits across every major therapeutic area and protein class. We address historical limitations of computational screening by demonstrating success for target proteins without known binders, high-quality X-ray crystal structures, or manual cherry-picking of compounds. We show that the molecules selected by the AtomNet® model are novel drug-like scaffolds rather than minor modifications to known bioactive compounds. Our empirical results suggest that computational methods can substantially replace HTS as the first step of small-molecule drug discovery