“The funding is being used to accelerate Harmonic’s momentum in developing Aristotle, which the company claims is the world’s […]”

“The trilinear equivalence only requires an averaging over grids, which converts a difficult exponential sum into an oscillatory integral with periodic amplitude.”

“The main new input is a hypersingular sparse domination principle combined with Bourgain's interpolation method, which provides a flexible mechanism to establish critical-line (and endpoint) estimates.”

“The tracking of multiple, unknown targets is formulated as a harmonic extension problem on a cellular sheaf, accommodating nonlinear dynamics and external disturbances for all agents.”

“Including quantum anharmonicity simplifies the free-energy landscape and is essential for correct stability rankings, that is especially important for high-temperature phases that could be missed in classical 0 K CSP.”

“The paper investigates the Gelfand theory of the algebra and discusses properties of the Fourier transform of operators arising from the Gelfand transform.”

“The inclusion of higher-order response in calculating optimal protocols provides marginal improvement in effectiveness despite incurring a significant computational expense, while introducing the possibility of predicting arbitrarily low and unphysical negative excess work.”

“Closed-form formulas for electron current and HHG spectra are presented. Based on the developed theory, we provide an analytic explanation for key features of HHG yield and show that the interband mechanism of HHG prevails over the intraband one.”

“The paper emphasizes the simplicity and platform independence of the Gaussian (phase-space) framework.”

“The results show that the amount of entanglement generated in this setup is extremely small, highlighting the experimental challenges of observing gravitationally induced quantum effects.”

“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.”

“The multimodal Transformer achieves RMSE = 0.90 mm and R^2 = 0.97 on the test set on the eastern Ireland tile (E32N34).”

“The evaluation protocol jointly measures average accuracy, average cost, and throughput, and builds a ranking score from the harmonic mean of normalized cost and accuracy to enable comparison across router configurations and cost budgets.”

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

“The paper proves the "log-log" blowup rate and describes the mass concentration behavior near the blowup time. It also finds that increasing the repulsive potential can lead to global solutions.”

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“The paper demonstrates that excited meson states are populated abundantly for typical parton configurations expected in jets.”

“The main results describe graded module structures of orbit harmonics quotients for the rook, partial transformation, and full transformation monoids.”

“The paper identifies four necessary conditions: noncoplanarity of the spin texture, contribution from both spin bands, different band-specific densities of states, and higher harmonics in the CPR.”

“The paper introduces a Biorthogonal Graph Fourier Transform (BGFT) adapted to directed diffusion.”

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“The article likely details the specific iterative learning algorithm and how it interacts with the anharmonic lattice dynamics calculations. It would also likely present results demonstrating the improved accuracy of the predictions compared to other methods.”

“The research focuses on Hölder-Lipschitz functions on fundamental domains of lattices in $\mathbb{R}^{d}$.”

“The context provided indicates the article covers the initialization, launch, and testing of a polyharmonic cascade.”

“The research focuses on a gold-polymer hybrid metasurface.”

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“The article's context provides information about computational procedures and differentiation.”

“Propagators of singular anharmonic oscillators with quasi-equidistant spectra.”

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“The paper focuses on Weighted K-Harmonic Means Clustering and its applications to Wireless Communications.”

“The article proposes a 'Biorthogonal Laplacian Framework for Non-Normal Graphs'.”

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