“The discrete period matrix admits the same canonical decomposition $Π= rac{1}{2} H + i T$ as in the smooth setting, where $H$ encodes the topological type and $T$ is purely imaginary.”

“The paper determines the splitting field and a set of 68 linearly independent generators for the Mordell--Weil lattice of the elliptic surface.”

“The algorithm minimizes a discretized version of the energy using finite elements, generalizing existing TV-minimization methods.”

“Learning curves can better capture the effects of multi-task learning and their multi-task extensions can delineate pairwise and contextual transfer effects in foundation models.”

“The exttt{Mgformer}-based module is superior in performance and flexibility. Its representative recall and precision values are 0.79 and 0.76, respectively, and can be modified by adjusting the threshold.”

“The optimal model achieves 97.23% accuracy when trained on complete energy spectra.”

“The paper introduces skein-type identities expressing cluster variables associated with incompatible curves on a surface in terms of cluster variables corresponding to compatible arcs.”

“Observational upper limits on the mass enclosed in central galactic regions can probe both attractive and repulsive self-interactions with strengths $λ\sim \pm 10^{-96} - 10^{-95}$.”

“The paper builds examples of real space sextics with 64 and 120 totally real tritangents.”

“The Hilbert-VLM model achieves a Dice score of 82.35 percent on the BraTS2021 segmentation benchmark, with a diagnostic classification accuracy (ACC) of 78.85 percent.”

“The resulting augmented excess free-energy functional quantitatively reproduces equilibrium density profiles, coexistence curves, and surface tensions across a broad temperature range, and accurately predicts contact angles and droplet shapes far beyond the training regime.”

“The delayed wind model provides a consistent explanation for the observed radio phenomenology, successfully reproducing events both with and without delayed radio flares.”

“The model reproduced quite well both the inner rise and outer flat regions of the observed rotation curves using the observed baryonic mass profiles only.”

“The proposed model achieves convergence on large test systems (e.g., IEEE 118 bus) in seconds and is validated against exact AC solutions.”

“The paper explains the appearance of singularities of dual curves and considers applications to the Clairaut differential equation.”

“KANO provides a transparent and structured representation of the latent degradation fitting process.”

“"Vector graphic, flat corporate tech design. Background: 100% solid uniform dark navy blue color (Hex #050A14), absolutely zero texture. Visuals: Sleek, translucent blue vector curves on the far left and right edges only. Style: Adobe Illustrator export, lossless SVG, smooth digital gradients. Center: Large empty solid color space. NO noise, NO film grain, NO dithering, NO vignette, NO texture, NO realistic lighting, NO 3D effects. 16:9 aspect ratio."”

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“The article is a scientific research paper, so there are no direct quotes suitable for this field.”

“The article is based on a research paper from ArXiv, suggesting it's a preliminary publication or a pre-print.”

“The article is from ArXiv, indicating it is a pre-print publication.”

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“The paper investigates the cohomology of compactified Jacobians for locally planar integral curves.”

“An inequality discovered and proved in collaboration with AI.”

“The article's topic is mentioned on Hacker News.”

“The article's key fact would be related to the specific learning or hurdle encountered.”

“Emergent abilities often occur for “hard” evaluation metrics, such as exact match or multiple-choice accuracy, which don’t award credit for partially correct answers.”

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