Enzyme Design from the Bottom Up: An Active Nickel Electrocatalyst with a Structured Peptide Outer Coordination Sphere

Catalytic, peptide‐containing metal complexes with a well‐defined peptide structure have the potential to enhance molecular catalysts through an enzyme‐like outer coordination sphere. Here, we report the synthesis and characterization of an active, peptide‐based metal complex built upon the well‐characterized hydrogen production catalyst [Ni(P^Ph₂N^Ph)₂]²⁺ (P^Ph₂N^Ph=1,3,6‐triphenyl‐1‐aza‐3,6‐diphosphacycloheptane). The incorporated peptide maintains its β‐hairpin structure when appended to the metal core, and the electrocatalytic activity of the peptide‐based metal complex (≈100,000 s^?1) is enhanced compared to the parent complex ([Ni(P^Ph₂N^APPA)₂]²⁺; ≈50,500 s^‐1). The combination of an active molecular catalyst with a structured peptide provides a scaffold that permits the incorporation of features of an enzyme‐like outer‐coordination sphere necessary to create molecular electrocatalysts with enhanced functionality.     

Relative acidities and structure analysis of cis and trans isomers of 1,5‐oxazaspiro[5.5] undecane derivatives by multinuclear magnetic resonance

The relative acidities of the cis and trans isomers of a series of 1,5‐oxazaspiro[5.5]undecane derivatives were determined by measuring ΔpK in acid‐base titrations followed by ¹ H NMR. Relative structural stabilities were determined by measuring substituent chemical shift and γ‐gauche effects in ¹³C, ¹⁵N, and ¹⁷O NMR. Crystallographic characterization of a model spiro[5.5]undecane is presented to support the basicity in solid state. Copyright © 2010 John Wiley & Sons, Ltd.     

Characterizing STEM Teacher Education: Affordances and Constraints of Explicit STEM Preparation for Elementary Teachers

Although science, technology, engineering, and mathematics (STEM) education sits at the center of a national conversation, comparatively little attention has been given to growing need for STEM teacher preparation, particularly at the elementary level. This study analyzes the outcomes of a novel, preservice STEM teacher education model. Building on both general and STEM‐specific teacher preparation principles, this program combined two traditional mathematics and science methods courses into one STEM block. Analysis compared preservice teachers in the traditional courses with those enrolled in the STEM block, investigating STEM teaching efficacy, reported and exhibited pedagogical practices, and STEM literacies using a pre‐post survey as well as analysis of lesson planning products. Linear regression models indicated that substantial growth was seen in both approaches but STEM block preservice teachers reported significantly greater gains in STEM teaching efficacy as compared with traditional‐route teachers. Lesson planning artifacts also demonstrated increased facilitation of STEM literacies, with specific attention to content integration, engineering and design, and arts inclusion. Technology and computational thinking emerged as areas for further growth and clarification in STEM teacher education models. Findings contribute to a growing research base on developing the STEM teacher workforce.     

Twisted Surfaces with Null Rotation Axis in Minkowski 3-Space

We examine curvature properties of twisted surfaces with null rotation axis in Minkowski 3-space. That is, we study surfaces that arise when a planar curve is subject to two synchronized rotations, possibly at different speeds, one in its supporting plane and one of this supporting plane about an axis in the plane. Moreover, at least one of the two rotation axes is a null axis. As is clear from its construction, a twisted surface generalizes the concept of a surface of revolution. We classify flat, constant Gaussian curvature, minimal and constant mean curvature twisted surfaces with a null rotation axis. Aside from pseudospheres, pseudohyperbolic spaces and cones, we encounter B-scrolls in these classifications. The appearance of B-scrolls in these classifications is of course the result of the rotation about a null axis. As for the cones in the classification of flat twisted surfaces, introducing proper coordinates, we prove that they are determined by so-called Clelia curves. With a Clelia curve we mean a curve that has linear dependent spherical coordinates.     

Simplified,interpretable graph convolutional neural networks for small molecule activity prediction

Journal of Computer-Aided Molecular Design - We here present a streamlined, explainable graph convolutional neural network (gCNN) architecture for small molecule activity prediction. We first...     

Numerical treatment of retarded boundary integral equations by sparse panel clustering

Stefan Sauter Institute for Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland ^{We consider the wave equation in a boundary integral formulation.The discretization in time is done by using convolution quadraturetechniques and a Galerkin boundary element method for the spatialdiscretization. In a previous paper, we have introduced a sparseapproximation of the system matrix by cut-off, in order to reducethe storage costs. In this paper, we extend this approach byintroducing a panel clustering method to further reduce thesecosts.}     

Joint Distribution of Rises and Falls

The marginal distributions of the number of rises and the number of falls have been used successfully in various areas of statistics, especially in non-parametric statistical inference. Carlitz (1972, Duke Math. J. 39, 268–269) showed that the generating function of the joint distribution for the numbers of rises and falls satisfies certain complex combinatorial equations, and pointed out that he had been unable to derive the explicit formula for the joint distribution from these equations. After more than two decades, this latter problem remains unsolved. In this article, the joint distribution is obtained via the probabilistic method of finite Markov chain imbedding for random permutations. A numerical example is provided to illustrate the theoretical results and the corresponding computational procedures.