“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.”

“BandiK employs a Multi-Armed Bandit (MAB) framework for each task, where the arms correspond to the performance of candidate auxiliary sets realized as multiple output neural networks over train-test data set splits.”

“The paper constructs 3-fold blocking sets of conjectured size, obtained as the disjoint union of three linear blocking sets of Rédei type, and they lie on the same orbit of the projectivity (x:y:z)↦(z:x:y).”

“The paper finds a partial extension of Poincaré duality theorem to hypersurfaces obtained by non-primitive Viro's combinatorial patchworking.”

“The algorithm achieves linear time complexity when the number of colors is greater than 3.637 times the maximum degree plus 1.”

“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.”

“The paper introduces 'incremental certificate learning' to maximize work in sound linear relaxation and invoke exact piecewise-linear reasoning only when relaxations become inconclusive.”

“The paper identifies three equilibrium phases: a mixed phase where rings interpenetrate, and two segregated phases (expanded and collapsed).”

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

“The paper demonstrates that a previously proposed condition for consistency does not hold and provides new characterizations and conditions.”

“The framework yields UNSAT certificates for a collection of anchored subfamilies. We also report pronounced runtime variability across configurations, including heavy-tailed behavior that currently dominates the computational effort and motivates further encoding refinements.”

“The policy was successfully deployed to see a 4.5% revenue increase during an A/B test.”

“LIMO achieves superior solution quality and faster time-to-solution on instances up to 85,900 cities compared to prior hardware annealers.”

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“INTERACT-CMIL achieves consistent improvements over CNN and foundation-model (FM) baselines, with relative macro F1 gains up to 55.1% (WHO4) and 25.0% (vertical spread).”

“The article's focus is on words of length $N = 3M$ with a three-letter alphabet.”

“The algorithm solves weighted MaxCut instances with up to 1000 vertices using only 10 qubits, and numerical results indicate that it consistently outperforms the Goemans-Williamson algorithm.”

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“The authors introduce a linear programming witness for network nonlocality built from five classes of linear constraints.”

“The proposed approach integrates classical MARL algorithms with quantum-inspired optimization techniques, leveraging variational quantum circuits VQCs as the core structure and employing the Quantum Approximate Optimization Algorithm QAOA as a representative VQC based method for combinatorial optimization.”

“The paper proves that $χ\leq f(ω),$ where $f$ is a polynomial of degree $2j-2i-4.$”

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“The research is sourced from ArXiv.”

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“The research is sourced from ArXiv, indicating it's a peer-reviewed research paper.”

“The research focuses on the combinatorial explosion problem in deformable medical image registration.”

“Regular Cyclic (q+1)-Arcs in PG(3,2^m): Spectral Rigidity, Descent, and an MDS Criterion”

“The article is a survey of the orienteering problem.”

“The paper focuses on using a clustering-based variable ordering framework.”

“The paper is published on ArXiv.”

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“The article is an academic paper from ArXiv, implying a focus on theoretical foundations rather than practical applications.”

“The study proposes a systemic pathological network model and combinatorial intervention strategies.”

“The article doesn't contain a direct quote.”