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Abstract Determining suitable dopants with optimized doping concentration is critical to design efficient water splitting photocatalysts. However, there is currently a lack of fundamental knowledge to guide this process. Herein, we examine the impact of Al³⁺, Mg²⁺, and Ga³⁺on the photocatalytic performance of SrTiO₃and propose a defect compensation model to understand the doping effect. Doped SrTiO₃crystals were grown hydrothermally and treated in molten SrCl₂. The hydrogen production rates from 50 catalysts produced in this way were measured with a high‐throughput parallelized and automated photochemical reactor (PAPCR). The investigation revealed that all three dopants significantly enhance the photocatalytic reactivity. According to Brouwer diagrams computed using available reaction constants, the optimum reactivity is achieved when the concentration of acceptor dopants fully compensates the oxygen vacancy donors. The improved reactivity can be attributed to the reduction in free electron concentration, resulting in a space charge layer that is 1000 times longer. Consequently, this situation enhances the number of photogenerated charge carriers capable of being separated by the band bending and transported to the surface. 

In modern machine learning systems, distributed algorithms are deployed across applications to ensure data privacy and optimal utilization of computational resources. This work offers a fresh perspective to model, analyze, and design distributed optimization algorithms through the lens of stochastic multi-rate feedback control. We show that a substantial class of distributed algorithms—including popular Gradient Tracking for decentralized learning, and FedPD and Scaffold for federated learning—can be modeled as a certain discrete-time stochastic feedback-control system, possibly with multiple sampling rates. This key observation allows us to develop a generic framework to analyze the convergence of the entire algorithm class. It also enables one to easily add desirable features such as differential privacy guarantees, or to deal with practical settings such as partial agent participation, communication compression, and imperfect communication in algorithm design and analysis. 

Summary Tfap2b, a pivotal transcription factor, plays critical roles within neural crest cells and their derived lineage. To unravel the intricate lineage dynamics and contribution of these Tfap2b+ cells during craniofacial development, we established aTfap2b‐CreER^T2knock‐in transgenic mouse line using the CRISPR‐Cas9‐mediated homologous direct repair. By breeding with tdTomato reporter mice and initiating Cre activity through tamoxifen induction at distinct developmental time points, we show theTfap2blineage within the key neural crest‐derived domains, such as the facial mesenchyme, midbrain, cerebellum, spinal cord, and limbs. Notably, the migratory neurons stemming from the dorsal root ganglia are visible subsequent to Cre activity initiated at E8.5. Intriguingly, Tfap2b+ cells, serving as the progenitors for limb development, show activity predominantly commencing at E10.5. Across the mouse craniofacial landscape, Tfap2b exhibits a widespread presence throughout the facial organs. Here we validate its role as a marker of progenitors in tooth development and have confirmed that this process initiates from E12.5. Our study not only validates theTfap2b‐CreER^T2transgenic line, but also provides a powerful tool for lineage tracing and genetic targeting ofTfap2b‐expressing cells and their progenitor in a temporally and spatially regulated manner during the intricate process of development and organogenesis. 

Abstract BaTiO₃heated in an excess of SrCl₂at 1150 °C converts to SrTiO₃through an ion exchange reaction. The SrTiO₃synthesized by ion exchange produces hydrogen from pH 7 water at a rate more than twice that of conventional SrTiO₃treated identically. The apparent quantum yield for hydrogen production in pure water of the ion exchanged SrTiO₃is 11.4% under 380 nm illumination. The catalyst resulting from ion‐exchange differs from conventional SrTiO₃by having ≈2% residual Ba, inhomogeneous Cl‐doping at a concentration less than 1%, Kirkendall voids in the centers of particles that result from the unequal rates of Sr and Ba diffusion together with the transport of Ti and O, and nanoscale regions near the surface that have lattice spacings consistent with the Sr‐excess phase Sr₂TiO₄. The increased photochemical efficiency of this nonequilibrium structure is most likely related to the Sr‐excess, which is known to compensate donor defects that can act as charge traps and recombination centers.