Quantization avoids saddle points in distributed optimization.

Distributed nonconvex optimization underpins key functionalities of numerous distributed systems, ranging from power systems, smart buildings, cooperative robots, vehicle networks to sensor networks. Recently, it has also merged as a promising solution to handle the enormous growth in data and model sizes in deep learning. A fundamental problem in distributed nonconvex optimization is avoiding convergence to saddle points, which significantly degrade optimization accuracy. We find that the process of quantization, which is necessary for all digital communications, can be exploited to enable saddle-point avoidance. More specifically, we propose a stochastic quantization scheme and prove that it can effectively escape saddle points and ensure convergence to a second-order stationary point in distributed nonconvex optimization. With an easily adjustable quantization granularity, the approach allows a user to control the number of bits sent per iteration and, hence, to aggressively reduce the communication overhead. Numerical experimental results using distributed optimization and learning problems on benchmark datasets confirm the effectiveness of the approach.

Highly Selective Photocatalytic CO2 Methanation with Water Vapor on Single-Atom Platinum-Decorated Defective Carbon Nitride.

Solar-driven CO2 methanation with water is an important route to simultaneously address carbon neutrality and produce fuels. It is challenging to achieve high selectivity in CO2 methanation due to competing reactions. Nonetheless, aspects of the catalyst design can be controlled with meaningful effects on the catalytic outcomes. We report highly selective CO2 methanation with water vapor using a photocatalyst that integrates polymeric carbon nitride (CN) with single Pt atoms. As revealed by experimental characterization and theoretical simulations, the widely explored Pt-CN catalyst is adapted for selective CO2 methanation with our rationally designed synthetic method. The synthesis creates defects in CN along with formation of hydroxyl groups proximal to the coordinated Pt atoms. The photocatalyst exhibits high activity and carbon selectivity (99 %) for CH4 production in photocatalytic CO2 reduction with pure water. This work provides atomic scale insight into the design of photocatalysts for selective CO2 methanation.

Altering Hydrogenation Pathways in Photocatalytic Nitrogen Fixation by Tuning Local Electronic Structure of Oxygen Vacancy with Dopant.

To avoid the energy-consuming step of direct N≡N bond cleavage, photocatalytic N2 fixation undergoing the associative pathways has been developed for mild-condition operation. However, it is a fundamental yet challenging task to gain comprehensive understanding on how the associative pathways (i.e., alternating vs. distal) are influenced and altered by the fine structure of catalysts, which eventually holds the key to significantly promote the practical implementation. Herein, we introduce Fe dopants into TiO2 nanofibers to stabilize oxygen vacancies and simultaneously tune their local electronic structure. The combination of in situ characterizations with first-principles simulations reveals that the modulation of local electronic structure by Fe dopants turns the hydrogenation of N2 from associative alternating pathway to associative distal pathway. This work provides fresh hints for rationally controlling the reaction pathways toward efficient photocatalytic nitrogen fixation.

Recent advances in engineering active sites for photocatalytic CO2 reduction.

The photocatalytic conversion of green-house gas CO2 into high value-added carbonaceous fuels and chemicals through harvesting solar energy is a great promising strategy for simultaneously tackling global environmental issues and the energy crisis. Considering the vital role of active sites in determining the activity and selectivity in photocatalytic CO2 reduction reactions, great efforts have been directed toward engineering active sites for fabricating efficient photocatalysts. This review highlights recent advances in the strategies for engineering active sites on surfaces and in open frameworks toward photocatalytic CO2 reduction, referring to surface vacancies, doped heteroatoms, functional groups, loaded metal nanoparticles, crystal facets, heterogeneous/homogeneous single-site catalysts and metal nodes/organic linkers in metal organic frameworks.

Sulfur Atomically Doped Bismuth Nanobelt Driven by Electrochemical Self-Reconstruction for Boosted Electrocatalysis.

Recent years have witnessed various in-depth research efforts on self-reconstruction behavior toward electrocatalysis. Tracking the phase transformation and evolution of true active sites is of great significance for the development of self-reconstructed electrocatalysts. Here, the optimized atomic sulfur-doped bismuth nanobelt (S-Bi) is fabricated via an electrochemical self-reconstruction evolved from Bi2S3. Advanced technologies have demonstrated that the nonmetallic S atoms have been doped into the lattice Bi frame, leading to the reconstruction of local electronic structure of Bi. The as-prepared S-Bi nanobelt exhibits a remarkable NH3 generation rate of 10.28 µg h-1 mg-1 and Faradaic efficiency of 10.48%. Density functional theory calculations prove that the S doping can significantly lower the energy barrier of the rate-determining step and enlarge the N≡N bond for further dissociation toward N2 fixation. This work not only establishes insights into the evolution process of electrochemically derived self-reconstruction but also unravels the root of the N2 reduction reaction mechanism associated with the atomic nonmetal dopants.

Scalable Fabrication of Highly Active and Durable Membrane Electrodes toward Water Oxidation.

The electrocatalytic oxygen evolution reaction (OER) is a highly important reaction that requires a relatively high overpotential and determines the rate of water splitting-a process for producing hydrogen. The overall OER performance is often largely limited by uncontrollable interface when active catalysts are loaded on conductive supports, for which polymer binders are widely used, but inevitably block species transportation channels. Here, a scalable fabrication approach to freestanding graphitized carbon nanofiber networks is reported, which provides abundant sites for in situ growing Fe/Ni catalysts with the improved interface. The fabricated hybrid membrane exhibits high activity and durability toward OER, with an overpotential of 280 mV at a geometrical current density of 10 mA cm-2 and a Tafel slope of 30 mV dec-1 in alkaline medium. As implemented as a freestanding electrode, the 3D hybrid structure achieves further enhanced OER performance with an overpotential down to 215 mV at 10 mA cm-2 . This work provides fresh insights into rationally fabricating OER electrocatalysts from the angle of electrode design.