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This paper introduces a game-theoretical strategy for optimal dispatch of building thermal loads, based on a marginal price model derived from an actual dispatch curve. A non-cooperative game is formulated, and the existence and uniqueness of the Nash equilibrium solution are proved aided by the variational inequality theory. A game solution algorithm is presented in this paper to solve the control problem with guaranteed convergence. The proposed game-theoretical control technique was evaluated against a baseline energy minimization strategy and a socially optimal solution, through a simulation test of a virtual market comprised of six buildings. The results show that the proposed game-theoretical strategy could achieve performance very close to the social optimum with a Price of Anarchy of 1.0041 and a 24% cost reduction compared to the baseline energy-priority strategy. 

Abstract Repairing fractured metals to extend their useful lifetimes advances sustainability and mitigates carbon emissions from metal mining and processing. While high‐temperature techniques are being used to repair metals, the increasing ubiquity of digital manufacturing and “unweldable” alloys, as well as the integration of metals with polymers and electronics, call for radically different repair approaches. Herein, a framework for effective room‐temperature repair of fractured metals using an area‐selective nickel electrodeposition process refered to as electrochemical healing is presented. Based on a model that links geometric, mechanical, and electrochemical parameters to the recovery of tensile strength, this framework enables 100% recovery of tensile strength in nickel, low‐carbon steel, two “unweldable” aluminum alloys, and a 3D‐printed difficult‐to‐weld shellular structure using a single common electrolyte. Through a distinct energy‐dissipation mechanism, this framework also enables up to 136% recovery of toughness in an aluminum alloy. To facilitate practical adoption, this work reveals scaling laws for the energetic, financial, and time costs of healing, and demonstrates the restoration of a functional level of strength in a fractured standard steel wrench. Empowered with this framework, room‐temperature electrochemical healing can open exciting possibilities for the effective, scalable repair of metals in diverse applications. 

Abstract Extracellular vesicles (EVs) – nanoscale membranous particles that carry multiple proteins and nucleic acid cargoes from their mother cells of origin into circulation – have enormous potential as biomarkers. However, devices appropriately scaled to the nanoscale to match the size of EVs (30–200 nm) have orders of magnitude too low throughput to process clinical samples (10¹²EVs mL⁻¹in serum). To address this challenge, we develop a novel approach that incorporates billions of nanomagnetic sorters that act in parallel to precisely isolate sparse EVs based on immunomagnetic labeling directly from clinical samples at flow rates billions of times greater than that of a single nanofluidic device. To fabricate these chips, the ferromagnetic metals are electro‐deposited into a self‐assembled microlattice, achieving >10⁹nanoscale magnetophoretic sorting devices in a 3D postage stamp‐sized lattice with >70x magnetic traps and >20x enrichment of magnetic nanoparticles versus our previous work. The immunomagnetically labeled EVs are isolated and achieve a ≈100% increase in yield as well as increased purity compared to conventional methods. Building on the proof‐of‐concept demonstrations in this manuscript, this new approach has the potential to enhance the future clinical translation of EV biomarkers by enabling rapid, sensitive, and specific isolation of EV subpopulations from clinical samples.