“Classical approaches retain high-order accuracy and strong computational efficiency for single-instance problems... Physics-informed neural networks (PINNs) are also able to reproduce qualitative solutions but are generally less accurate and less efficient in low dimensions than classical solvers.”

“The paper introduces two complementary high-order strategies for triangular elements: a reduced quadrilateralization approach and a triangle based spectral element method based on Dubiner polynomials.”

“The SMC-HOCBF framework constitutes a strong candidate for safety-critical control for small marine robots and surface vessels with limited onboard computational resources.”

“The paper validates the numerical approaches by successfully reproducing standard vacuum test cases and achieving long-term stable evolutions of stationary black holes, including Kerr black holes with extreme spin.”

“HGMem extends the concept of memory beyond simple storage into a dynamic, expressive structure for complex reasoning and global understanding.”

“The high-order cumulant ratios $R_{n2}$ ($n>2$) exhibit non-monotonic variations across the chiral phase transition... These structures gradually weaken and eventually vanish at high chemical potential as they compete with the sharpening of the chiral phase transition.”

“The paper proposes to use a standard reduced basis method (RBM) to construct this low-order rational function. Algorithmically, this procedure is an iterative greedy approach, where the greedy objective is evaluated through an error estimator that exploits the linearity of the frequency domain representation.”

“The results confirm the high-order accuracy of the model through convergence studies and demonstrate a substantial speed-up over low-order numerical schemes.”

“The reduced-order model preserves a semi-discrete energy balance inherited from the full-order model, and avoids the need for additional interface enrichment.”

“The quantum Fisher information scales as $ \mathcal{F}_Q \sim L^{2p}$ (with L the lattice size and p the order of band touching) and $\mathcal{F}_Q \sim N^2 L^{2p}$ (with N the number of particles).”

“The theory enables predictive design of bright, high-photon-number quantum states at tunable frequencies.”

“GM-QAOA exhibits monotonic performance improvement with circuit depth and achieves superior results for HUBO problems.”

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“All logarithms arising in the loop expansion of the single soft current can be reabsorbed in the scale choices for the $d$-dimensional coupling, casting some doubt on the need for a logarithmic celestial theory.”

“The research focuses on the 'generation of hollow vector beams by high-order cylindrical vector beams.'”

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“LGAN is an efficient high-order graph neural network via the Line Graph Aggregation.”

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