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Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to find the low-dimensional structure of data. Dimension reduction for large, high-dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high-dimensional point clouds and allow one to visualize, denoise, and interpret them. This review presents the underlying principles of ML, its representative methods, and their statistical foundations, all from a practicing statistician's perspective. It describes the trade-offs and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 11 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates. 

Our synthesis method yields FeCo nanostructures of varied dimensions, validated by simulations. In addition, our findings highlight enhanced coercivity in these structures. 

Abstract Microtubules and catalytic motor proteins underlie the microscale actuation of living materials, and they have been used in reconstituted systems to harness chemical energy to drive new states of organization of soft matter (e.g., liquid crystals (LCs)). Such materials, however, are fragile and challenging to translate to technological contexts. Rapid (sub‐second) and reversible changes in the orientations of LCs at room temperature using reactions between gaseous hydrogen and oxygen that are catalyzed by Pd/Au surfaces are reported. Surface chemical analysis and computational chemistry studies confirm that dissociative adsorption of H₂on the Pd/Au films reduces preadsorbed O and generates 1 ML of adsorbed H, driving nitrile‐containing LCs from a perpendicular to a planar orientation. Subsequent exposure to O₂leads to oxidation of the adsorbed H, reformation of adsorbed O on the Pd/Au surface, and a return of the LC to its initial orientation. The roles of surface composition and reaction kinetics in determining the LC dynamics are described along with a proof‐of‐concept demonstration of microactuation of beads. These results provide fresh ideas for utilizing chemical energy and catalysis to reversibly actuate functional LCs on the microscale. 

Even though extensive studies have developed various eco-driving strategies for vehicle platoon to travel on urban roads with traffic signals, most of them focus on vehicle-level trajectory planning or speed advisory rather than real-time platoon-level closed-loop control. In addition, majority of existing efforts neglect the traffic and vehicle dynamic uncertainties to avoid the modeling and solution complexity. To make up these research gaps, this study develops a system optimal vehicle platooning control for eco-driving (SO-ED), which can guide a mixed flow platoon to smoothly run on the urban roads and pass the signalized intersections without sudden deceleration or red idling. The SO-ED is mathematically implemented by a hybrid model predictive control (MPC) system, including three MPC controllers and an MINLP platoon splitting switching signal. Based on the features of the system, this study uses active set method to solve the large-scale MPC controllers in real time. The numerical experiments validate the merits of the proposed SO-ED in smoothing the traffic flow and reducing energy consumption and emission at urban signalized intersections.