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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 one-sided threshold function, it was shown by Talagrand (2000, 2011) that for small densities alpha, the free energy of the model converges in the large-N 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. 

Self-healing triboelectric nanogenerators (SH-TENGs) with fast self-healing, high output performance, and wearing comfort have wide and promising applications in wearable electronic devices. This work presents a high-performance hydrogel-based SH-TENG, which consists of a high dielectric triboelectric layer (HDTL), a self-healing hydrogel electrode layer (SHEL), and a physical cross-linking 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 short-circuit 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 self-healing hydrogel electrode layer. SHEL can physically self-heal in ~1 min when exposed to air. The self-healing 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 SH-TENG can reach 94% of the undamaged one in 1 min. The SH-TENG (6 × 6 cm2) exhibits good stability and superior electrical performance, enabling it to power 37 LEDs simultaneously. 

Spin-orbit 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, spin-orbit effects in classes of materials such as epitaxial 5 d -electron transition-metal 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 spin-to-charge conversion by crystalline symmetry. Here, we demonstrate room-temperature generation of spin-orbit torque on a ferromagnet with extremely high efficiency via the spin-Hall effect in epitaxial metastable perovskite SrIrO 3 . We first predict a large intrinsic spin-Hall 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 spin-Hall torque ratio by engineering the tilt of the corner-sharing oxygen octahedra in perovskite SrIrO 3 through epitaxial strain. This allows the presence of an anisotropic spin-Hall effect due to a characteristic structural anisotropy in SrIrO 3 with orthorhombic symmetry. Our experimental findings demonstrate the heteroepitaxial symmetry design approach to engineer spin-orbit effects. We therefore anticipate that these epitaxial 5 d transition-metal oxide thin films can be an ideal building block for low-power spintronics.