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We consider the Ising perceptron model with N spins and M = N*alpha patterns, with a general activation function U that is bounded above. For U bounded away from zero, or U a onesided threshold function, it was shown by Talagrand (2000, 2011) that for small densities alpha, the free energy of the model converges in the largeN limit to the replica symmetric formula conjectured in the physics literature (Krauth–Mezard 1989, see also Gardner–Derrida 1988). We give a new proof of this result, which covers the more general class of all functions U that are bounded above and satisfy a certain variance bound. The proof uses the (first and second) moment method conditional on the approximate message passing iterates of the model. In order to deduce our main theorem, we also prove a new concentration result for the perceptron model in the case where U is not bounded away from zero.

Selfhealing triboelectric nanogenerators (SHTENGs) with fast selfhealing, high output performance, and wearing comfort have wide and promising applications in wearable electronic devices. This work presents a highperformance hydrogelbased SHTENG, which consists of a high dielectric triboelectric layer (HDTL), a selfhealing hydrogel electrode layer (SHEL), and a physical crosslinking layer (PCLL). Carbon nanotubes (CNTs), obtained by a chemical vapor deposition (CVD) method, were added into polydimethylsiloxane (PDMS) to produce the HDTL. Compared with pure PDMS, the shortcircuit transferred charge (44 nC) and the open circuit voltage (132 V) are doubled for PDMS with 0.01 wt% CNTs. Glycerin, polydopamine particles (PDAP) and graphene were added to poly (vinyl alcohol) (PVA) to prepare the selfhealing hydrogel electrode layer. SHEL can physically selfheal in ~1 min when exposed to air. The selfhealing efficiency reaches up to 98%. The PCLL is made of poly(methylhydrosiloxane) (PMHS) and PDMS. It forms a good physical bond between the hydrophilic hydrogel and hydrophobic PDMS layers. The electric output performance of the SHTENG can reach 94% of the undamaged one in 1 min. The SHTENG (6 × 6 cm2) exhibits good stability and superior electrical performance, enabling it to power 37 LEDs simultaneously.

Spinorbit coupling (SOC), the interaction between the electron spin and the orbital angular momentum, can unlock rich phenomena at interfaces, in particular interconverting spin and charge currents. Conventional heavy metals have been extensively explored due to their strong SOC of conduction electrons. However, spinorbit effects in classes of materials such as epitaxial 5 d electron transitionmetal complex oxides, which also host strong SOC, remain largely unreported. In addition to strong SOC, these complex oxides can also provide the additional tuning knob of epitaxy to control the electronic structure and the engineering of spintocharge conversion by crystalline symmetry. Here, we demonstrate roomtemperature generation of spinorbit torque on a ferromagnet with extremely high efficiency via the spinHall effect in epitaxial metastable perovskite SrIrO 3 . We first predict a large intrinsic spinHall conductivity in orthorhombic bulk SrIrO 3 arising from the Berry curvature in the electronic band structure. By manipulating the intricate interplay between SOC and crystalline symmetry, we control the spinHall torque ratio by engineering the tilt of the cornersharing oxygen octahedra in perovskite SrIrO 3 through epitaxial strain. This allows the presence of an anisotropic spinHall effect due to a characteristic structural anisotropy in SrIrO 3 with orthorhombic symmetry. Ourmore »