Montecrinanes A–C: Triterpenes with an Unprecedented Rearranged Tetracyclic Skeleton from Celastrus vulcanicola. Insights into Triterpenoid Biosynthesis Based on DFT Calculations

Three new triterpenoids with an unprecedented 6/6/6/6‐fused tetracyclic carbon skeleton, montecrinanes A–C ( 1 – 3 ), were isolated from the root bark of Celastrus vulcanicola, along with known D:B‐friedobaccharanes ( 4 – 6 ), and lupane‐type triterpenes ( 7 – 12 ). The stereostructures of the new metabolites were elucidated based on spectroscopic (1D and 2D NMR) and spectrometric (HR‐EIMS and HR‐ESIMS) techniques. Their absolute configurations were determined by both NMR spectroscopy, with (R)‐(?)‐α‐methoxyphenylacetic acid as a chiral derivatizing agent, and biogenetic considerations. Biogenetic pathways for montecrinane and D:B‐friedobaccharane skeletons were proposed and studied by DFT methods. The theoretical results support the energetic feasibility of the putative biogenetic pathways, in which the 1,2‐methyl shift from the secondary baccharenyl cation represents a novel and key reaction step for a new montecrinane skeleton.     

Pedagogical challenges in making mathematics relevant for Indigenous Australians

After the invasion and occupation of their land by Europeans, Indigenous Australians were expected to benefit from a Western education system based on that of the dominant Europeans. Gradually educators realized that Aboriginal children learn differently and that Indigenous culture and pedagogy has validity and strength. Of course, educators also need to be acutely aware of the diversity of Indigenous cultures in Australia and that there is not a monolithic sense of Aboriginal identity or Aboriginal pedagogy. Dispossession and alienation, poor health and few employment opportunities must also affect educational interest, attendance, application and performance. In this paper the characteristics of Indigenous learners are examined and pedagogical strategies to assist in both students' learning and teachers' delivery are explored. The message conveyed in this paper has particular relevance for teaching mathematics to Aboriginal learners. It is also of considerable value in teaching mathematics to nonAboriginal students, in Australia and elsewhere.     

Wide binaries as a critical test of classical gravity

Modified gravity scenarios where a change of regime appears at acceleration scales a<a ₀ have been proposed. Since for 1M _⊙ systems the acceleration drops below a ₀ at scales of around 7000 AU, a statistical survey of wide binaries with relative velocities and separations reaching 10⁴ AU and beyond should prove useful to the above debate. We apply the proposed test to the best currently available data. Results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude, in analogy with galactic flat rotation curves in the same a<a ₀ acceleration regime. Our results are suggestive of a breakdown of Kepler’s third law beyond a≈a ₀ scales, in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond.     

One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Optimisation of sensor positions in random linear arrays based on statistical relations between geometry and performance

Due to the widespread use of acoustic arrays, optimisation techniques for array design, focused on improving array performance, have been widely published. This paper exploits the statistical relation between different measures of sidelobe levels and the spacing of elements in random linear arrays made up of a small number of sensors. This paper defines the methodology to obtain maximum probability functions, associating array geometry and performance. These maximum probability functions allow a pre-selection of those array geometries that are more likely to be associated to specified sidelobe level values. This pre-selection results in a significantly reduced computational burden.     

Simplified model for mass diffusivity estimation based on dynamic pendant drop volume analysis

We present a simplified correlation for calculating the dissolved gas moles in a pendant drop during the diffusion time, for several drop shapes. After this correlation is determined, the Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) dynamic pendant drop volume analysis (DPDVA) method for calculation of mass diffusivity from the pendant drop volume variation against time can be used. We solved the differential equation in cylindrical coordinates for the mass transfer model of the gas diffusion into the liquid inside the pendant drop, using a different characteristic length (L_C), instead of the outer radius of the syringe needle (r_n) used in Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) for defining the dimensionless variables. L_C is the relationship between the pendant drop volume and its mass transfer surface area at the initial conditions. The generalized correlation saves time, simplifies the method application and the deviations in the diffusion coefficient calculation respect to the complete Yang and Gu model are below 6%.     

Simultaneous Determination of Barbital and Thiobarbituric Acid by Derivative Spectrophotometry

A new method for the simultaneous determination of barbital and thiobarbituric acid by derivative spectrophotometry is proposed. The method allows the resolution of mixtures of the two components over the concentration ranges 0.37–4.70 μg/ml (barbital) and 0.40–4.50 μg/ml (thiobarbituric acid) provided the ratio between their concentrations does not exceed 5:1. It was applied to the determination of the two compounds in synthetic samples and blood serum.     

Unravelling the Time Scale of Conformational Plasticity and Allostery in Glycan Recognition by Human Galectin-1

The interaction of human galectin-1 with a variety of oligosaccharides, from di-(N-acetyllactosamine) to tetra-saccharides (blood B type-II antigen) has been scrutinized by using a combined approach of different NMR experiments, molecular dynamics (MD) simulations, and isothermal titration calorimetry. Ligand- and receptor-based NMR experiments assisted by computational methods allowed proposing three-dimensional structures for the different complexes, which explained the lack of enthalpy gain when increasing the chemical complexity of the glycan. Interestingly, and independently of the glycan ligand, the entropy term does not oppose the binding event, a rather unusual feature for protein-sugar interactions. CLEANEX-PM and relaxation dispersion experiments revealed that sugar binding affected residues far from the binding site and described significant changes in the dynamics of the protein. In particular, motions in the microsecond-millisecond timescale in residues at the protein dimer interface were identified in the presence of high affinity ligands. The dynamic process was further explored by extensive MD simulations, which provided additional support for the existence of allostery in glycan recognition by human galectin-1.     

Luminescent Graphene-Based Materials via Europium Complexation on Dipyridylpyridazine-Functionalized Graphene Sheets

Graphene-based materials exhibit outstanding physical properties and so are potentially applicable in a great variety of fields. Unlike their corresponding oxides, graphite and graphene are not prone to functionalization. Diels–Alder reactions are among the scarce reactions that they can occur without disrupting their conjugated sp² systems. Herein, the reaction between graphite and 3,6-di(2-pyridyl)-1,2,4,5-tetrazine under different conditions affords several graphene-based materials consisting of dipyridylpyridazine-functionalized few-layer graphene, multilayer graphene and graphite, the sheets of which act as ligands for the grafting of a europium complex. These three materials show strong red emission under 365 nm UV radiation. Their emitting particles can be visualized by confocal microscopy. The rich coordination chemistry of dipyridylpyridazine ligands has potential novel properties for similarly functionalized graphene-based materials grafted with other metal complexes.