Software tools for green and sustainable chemistry

In this review, we consider green chemistry metrics, related software tools, and the opportunities and challenges for their use in research laboratories. We provide an overview of state-of-the-art software designed both to aid researchers in planning and conducting chemical experiments and to assess sustainability of individual reactions and synthetic routes. The increasing digitalisation of research means that there is great opportunity for more extensive use of computational tools by synthetic chemists and for closer integration of green chemistry principles into the routine work of chemical laboratories. We discuss the scope for using software tools in the laboratory and assisting synthetic chemists in the adoption of green and sustainable chemistry approaches that are suitable for their specific purposes.     

Electrodeposition of zinc oxide nanoparticles on multiwalled carbon nanotube-modified electrode for determination of caffeine in wastewater effluent

We report on the development of an electrochemical sensor based on electrodepositing zinc oxide on multiwalled carbon nanotube-modified glassy carbon electrode for the detection of caffeine in pharmaceutical wastewater effluents. The measurements were carried out using cyclic voltammetry, electrochemical impedance spectroscopy, chronoamperometry and differential pulse voltammetry (DPV). DPV measurements showed a linear relationship between oxidation peak current and concentration of caffeine in 0.1 M HClO₄ (pH 1.0) over the concentration range 0.00388–4.85 mg/L and a detection limit of 0.00194 mg/L. The diffusion coefficient and Langmuir adsorption constant for caffeine were calculated to be 3.25 × 10^?6 cm² s^?1 and 1.10 × 10³ M^?1, respectively. The sensor showed satisfactory results when applied to the detection of caffeine in wastewater effluents.     

Rigidity and curvature estimates for graphical self-shrinkers

Self-shrinkers are hypersurfaces that shrink homothetically under mean curvature flow; these solitons model the singularities of the flow. It is presently known that an entire self-shrinking graph must be a hyperplane. In this paper we show that the hyperplane is rigid in an even stronger sense, namely: for \(2\le n \le 6\), any smooth, complete self-shrinker \(\Sigma ^n\subset \mathbf {R}^{n+1}\) that is graphical inside a large, but compact, set must be a hyperplane. In fact, this rigidity holds within a larger class of almost stable self-shrinkers. A key component of this paper is the procurement of linear curvature estimates for almost stable shrinkers, and it is this step that is responsible for the restriction on n. Our methods also yield uniform curvature bounds for translating solitons of the mean curvature flow.     

Novel total synthesis of anserinone A and B

Anserinones A and B are natural products that have been shown to have potential anticancer, antifungal, and antibacterial properties. This work entails the novel synthesis of these natural products.     

Diagonal-preserving ring ⁎-isomorphisms of Leavitt path algebras

The graph groupoids of directed graphs E and F are topologically isomorphic if and only if there is a diagonal-preserving ring ?-isomorphism between the Leavitt path algebras of E and F.     

On separating a fixed point from zero by invariants

Assume a fixed point v∈V^G can be separated from zero by a homogeneous invariant f∈𝕜[V]^G of degree p^rd, where p>0 is the characteristic of the ground field 𝕜 and p,d are coprime. We show that then v can also be separated from zero by an invariant of degree p^r, which we obtain explicitly from f. It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power.     

Efficient Computation of the Joint Sample Frequency Spectra for Multiple Populations

A wide range of studies in population genetics have employed the sample frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a sample of DNA sequences and provides a highly efficient dimensional reduction of large-scale population genomic variation data. Recently, there has been much interest in analyzing the joint SFS data from multiple populations to infer parameters of complex demographic histories, including variable population sizes, population split times, migration rates, admixture proportions, and so on. SFS-based inference methods require accurate computation of the expected SFS under a given demographic model. Although much methodological progress has been made, existing methods suffer from numerical instability and high computational complexity when multiple populations are involved and the sample size is large. In this article, we present new analytic formulas and algorithms that enable accurate, efficient computation of the expected joint SFS for thousands of individuals sampled from hundreds of populations related by a complex demographic model with arbitrary population size histories (including piecewise-exponential growth). Our results are implemented in a new software package called momi (MOran Models for Inference). Through an empirical study, we demonstrate our improvements to numerical stability and computational complexity.     

Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogenous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school. Supplementary material for this article is available online.