A symplectic dynamics approach to the spatial isosceles three-body problem

We study the spatial isosceles three-body problem from the perspective of Symplectic Dynamics. For certain choices of mass ratio, angular momentum, and energy, the dynamics on the energy surface is equivalent to a Reeb flow on the tight three-sphere. We find a Hopf link formed by the Euler orbit and a symmetric brake orbit, which spans an open book decomposition whose pages are annulus-like global surfaces of section. In the case of large mass ratios, the Hopf link is non-resonant, forcing the existence of infinitely many periodic orbits. The rotation number of the Euler orbit plays a fundamental role in the existence of periodic orbits and their symmetries. We explore such symmetries in the Hill region and show that the Euler orbit is negative hyperbolic for an open set of parameters while it can never be positive hyperbolic. Finally, we address convexity and determine for each parameter whether the energy surface is strictly convex, convex, or non-convex. Dynamical consequences of this fact are then discussed.Comment: 66 pages, 15 figure

Differentiable Genetic Programming for High-dimensional Symbolic Regression

Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the dominator in solving SR problems. However, as the scale of SR problems increases, GP often poorly demonstrates and cannot effectively address the real-world high-dimensional problems. This limitation is mainly caused by the stochastic evolutionary nature of traditional GP in constructing the trees. In this paper, we propose a differentiable approach named DGP to construct GP trees towards high-dimensional SR for the first time. Specifically, a new data structure called differentiable symbolic tree is proposed to relax the discrete structure to be continuous, thus a gradient-based optimizer can be presented for the efficient optimization. In addition, a sampling method is proposed to eliminate the discrepancy caused by the above relaxation for valid symbolic expressions. Furthermore, a diversification mechanism is introduced to promote the optimizer escaping from local optima for globally better solutions. With these designs, the proposed DGP method can efficiently search for the GP trees with higher performance, thus being capable of dealing with high-dimensional SR. To demonstrate the effectiveness of DGP, we conducted various experiments against the state of the arts based on both GP and deep neural networks. The experiment results reveal that DGP can outperform these chosen peer competitors on high-dimensional regression benchmarks with dimensions varying from tens to thousands. In addition, on the synthetic SR problems, the proposed DGP method can also achieve the best recovery rate even with different noisy levels. It is believed this work can facilitate SR being a powerful alternative to interpretable ML for a broader range of real-world problems

Surface engineering of perovskite oxide for bifunctional oxygen electrocatalysis

Perovskite oxide, a low‐cost bifunctional oxygen evolution reaction (OER) and oxygen reduction reaction (ORR) electrocatalyst, has acquired a rapidly growing research interest in the areas of energy conversion and storage, owing to its significant surface structure‐induced catalytic performance. Here, recent progress on the electrocatalytic performance of La0.6Sr0.4Co0.2Fe0.8O3–δ (LSCF) is built by engineering its surface defect structure through a versatile, effective, and controllable lithium reduction strategy. It is established that the lithium reduction treatment causes the formation of a structurally disordered layer at the surface of LSCF nanoparticles. The treated nanoparticles demonstrate significantly enhanced OER and ORR performance, especially for 5 wt% lithium‐reduced LSCF, whose OER potential decreases from 1.66 to 1.55 V at current density of 10 mA cm−2, and ORR onset potential increases from 0.70 to 0.84 V. This work provides the foundation for the optimization of catalytic performance of perovskite oxide (LSCF). Moreover, such defective materials are promising candidates for energy conversion and storage applications

Surface engineering of perovskite oxide for bifunctional oxygen electrocatalysis

Perovskite oxide, a low‐cost bifunctional oxygen evolution reaction (OER) and oxygen reduction reaction (ORR) electrocatalyst, has acquired a rapidly growing research interest in the areas of energy conversion and storage, owing to its significant surface structure‐induced catalytic performance. Here, recent progress on the electrocatalytic performance of La0.6Sr0.4Co0.2Fe0.8O3–δ (LSCF) is built by engineering its surface defect structure through a versatile, effective, and controllable lithium reduction strategy. It is established that the lithium reduction treatment causes the formation of a structurally disordered layer at the surface of LSCF nanoparticles. The treated nanoparticles demonstrate significantly enhanced OER and ORR performance, especially for 5 wt% lithium‐reduced LSCF, whose OER potential decreases from 1.66 to 1.55 V at current density of 10 mA cm−2, and ORR onset potential increases from 0.70 to 0.84 V. This work provides the foundation for the optimization of catalytic performance of perovskite oxide (LSCF). Moreover, such defective materials are promising candidates for energy conversion and storage applications

Differentiable Genetic Programming for High-dimensional Symbolic Regression

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