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Electrophoretic deposition (EPD) of colloidal particles is a practical system for the study of crystallization and related physical phenomena. The aggregation is driven by the electroosmotic flow fields and induced dipole moments generated by the polarization of the electrode‐particle‐electrolyte interface. Here, the electrochemical control of aggregation and repulsion in the electrophoretic deposition of colloidal microspheres is reported. The nature of the observed transition depended on the composition of the solvent, switching from electrode‐driven aggregation in water to electrical field‐driven repulsion in ethanol for otherwise identical systems of colloidal microspheres. This work uses optical microscopy‐derived particles and a recently developed particle insertion method approach to extract model‐free, effective interparticle potentials to describe the ensemble behavior of the particles as a function of the solvent and electrode potential at the electrode interface. This approach can be used to understand the phase behavior of these systems based on the observable particle positions rather than a detailed understanding of the electrode‐electrolyte microphysics. This approach enables simple predictability of the static and dynamic behaviors of functional colloid‐electrode interfaces.

 

The catalytic hydroboration of imines, nitriles, and carbodiimides is a powerful method of preparing amines which are key synthetic intermediates in the synthesis of many value-added products. Imine hydroboration has perennially featured in notable reports while nitrile and carbodiimide hydroboration have gained attention recently. Initial developments in catalytic hydroboration of imines and nitriles employed precious metals and typically required harsh reaction conditions. More recent advances have shifted toward the use of base metal and main group element catalysis and milder reaction conditions. In this survey, we review metal and nonmetal catalyzed hydroboration of these unsaturated organic molecules and group them into three distinct categories: precious metals, base metals, and main group catalysts. The TON and TOF of imine hydroboration catalysts are reported and summarized with a brief overview of recent advances in the field. Mechanistic and kinetic studies of some of these protocols are also presented. 

One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied studies have turned to data that varies in time. A time-varying collection of metric spaces as formed, for example, by a moving school of fish or flock of birds, can contain a vast amount of information. There is often a need to simplify or summarize the dynamic behavior. We provide an introduction to topological summaries of time-varying metric spaces including vineyards [19], crocker plots [55], and multiparameter rank functions [37]. We then introduce a new tool to summarize time-varying metric spaces: a crocker stack. Crocker stacks are convenient for visualization, amenable to machine learning, and satisfy a desirable continuity property which we prove. We demonstrate the utility of crocker stacks for a parameter identification task involving an influential model of biological aggregations [57]. Altogether, we aim to bring the broader applied mathematics community up-to-date on topological summaries of time-varying metric spaces.

 

Umbrella-sampling density functional theory molecular dynamics (DFT-MD) has been employed to study the full catalytic cycle of the allylic oxidation of cyclohexene using a Cu(II) 7-amino-6-((2- hydroxybenzylidene)amino)quinoxalin-2-ol complex in acetonitrile to create cyclohexenone and H2O as products. After the initial H-atom abstraction step, two different reaction pathways have been identified that are distinguished by the participation of alkyl hydroperoxide (referred to as the “open” cycle) versus the methanol side-product (referred to as the “closed” cycle) within the catalyst recovery process. Importantly, both pathways involve dehydrogenation and re-hydrogenation of the -NH2 group bound to the Cu-site - a feature that is revealed from the ensemble sampling of configurations of the reactive species that are stabilized within the explicit solvent environment of the simulation. Estimation of the energy span from the experimental turnover frequency yields an approximate value of 22.7 kcal/mol at 350 K. Whereas the closed cycle value is predicted to be 26.2 kcal/mol, the open cycle value at 16.5 kcal/mol. Both pathways are further consistent with the equilibrium between Cu(II) and Cu(III) than what has previously been observed. In comparison to prior static DFT calculations, the ensemble of of both solute and solvent configurations has helped to reveal a breadth of processes that underpin the full catalytic cycle yielding a more comprehensive understanding of the importance of radical reactions and catalysis recovery. 

Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as the three-circle model for 3 × 3 pixel patches from natural images, or the configuration space of the cyclo-octane molecule, which is a sphere with a Klein bottle attached via two circles of singularity. In these studies of global shape, short persistent homology bars are disregarded as sampling noise. More recently, however, persistent homology has been used to address questions about the local geometry of data. For instance, how can local geometry be vectorized for use in machine learning problems? Persistent homology and its vectorization methods, including persistence landscapes and persistence images, provide popular techniques for incorporating both local geometry and global topology into machine learning. Our meta-hypothesis is that the short bars are as important as the long bars for many machine learning tasks. In defense of this claim, we survey applications of persistent homology to shape recognition, agent-based modeling, materials science, archaeology, and biology. Additionally, we survey work connecting persistent homology to geometric features of spaces, including curvature and fractal dimension, and various methods that have been used to incorporate persistent homology into machine learning.