“The article uses the term 'people weak at verbalization' not as a put-down, but as a label for those who find it challenging to articulate thoughts and intentions clearly from the start.”

“This approach shifts the focus from directly instructing to collaboratively exploring the knowledge space, ultimately leading to higher quality outputs.”

“This requires access to the original article content, which is not provided. Without the actual article content a key quote cannot be formulated.”

“Our approach relies on a unified formulation of the distance from a point to a hyperplane on the considered spaces.”

“The user's frustration is evident in their statement: "How is it possible that chatGPT still fails at simple Excel formulas, yet can produce thousands of lines of Python code without mistakes?"”

“"RAG (Retrieval-Augmented Generation) is a representative mechanism for solving these problems."”

“The paper identifies physical theories as least fixed points of admissibility constraints derived from Galois connections.”

“The paper formulates the covariant hydrodynamics equations as an intersection problem on an infinite dimensional symplectic manifold associated with spacetime.”

“The paper derives explicit expressions for the joint Laplace-Stieltjes transform, probability density function, and governing differential equations of the multivariate gamma subordinator.”

“The best solution approach for a practical path-based model reduces the IP gap by an average of 26.5% and 22.5% for the two largest instance groups, compared to solving the reformulation alone.”

“The paper revisits the process of eigenvalue approximation from the perspective of computational spectral geometry.”

“The paper develops a general convergence analysis based on a reformulation of the operators by means of a fixed-point equation, providing a list of hypotheses related to the regularization properties of the equation and the convergence of the chosen approximation techniques on suitable subspaces.”

“The constructive framework produces a fully 4D-covariant action that belongs to the class of generalised extended mimetic gravity models.”

“The paper proves a fully nonlinear, saturable lower bound valid for arbitrary current vectors Δq: D_bath ≥ B(Δq,V,V'), where the bound depends only on the transported-charge signal Δq and the pre/post collision covariance matrices V and V'.”

“The paper derives a Pontryagin maximum principle on the belief space, providing necessary conditions for optimality in this hybrid setting.”

“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.”

“The paper introduces an explicit formulation of object arrangement preferences along four interpretable constructs: spatial practicality, habitual convenience, semantic coherence, and commonsense appropriateness.”

“The paper highlights the importance of coordinated time-power optimization in balancing sensing accuracy and communication performance in wireless powered ISAC systems.”

“The eigenfunctions admit an expansion with universal coefficients so that the dependence on the twist $a$ is hidden only in these ground state eigenfunctions, and we suggest a general formula that allows one to construct these eigenfunctions from non-symmetric Macdonald polynomials.”

“The paper finds that the entanglement entropy of Hawking radiation before the Page time increases with time, with the slope determined by the central charge. After the Page time, the unitarity of black hole evaporation is restored, and the entanglement entropy includes a logarithmic correction related to the central charge.”

“Dream2Flow overcomes the embodiment gap and enables zero-shot guidance from pre-trained video models to manipulate objects of diverse categories-including rigid, articulated, deformable, and granular.”

“ConfigTuner demonstrates up to a 1.36x increase in throughput compared to Megatron-LM.”

“The proposed framework achieves superior performance over conventional sensing methods with reduced sensing power.”

“The paper focuses on modifying the damping and shifting schemes used in the original CFFT formulation to reduce boundary errors and improve accuracy and convergence.”

“The paper obtains mean-field analogues of momentum distribution formulas for electron gas in high density and metallic density limits, and applies to a general class of singular potentials.”

“The paper provides a necessary and sufficient condition for the incenter of a given n-simplex with k-rational vertices to be k-rational.”

“The proposed HOOA achieves significant improvements, which reduces average task completion delay by 2.5% and average energy consumption by 3.1% compared with the best-performing benchmark approach and state-of-the-art DRL algorithm, respectively.”

“The resulting formulation is based on a 4D Hodge-Laplacian operator with a spatiotemporal diffusion tensor and convection field, augmented by a small temporal perturbation to ensure nondegeneracy.”

“Convolution defines a matrix transform that preserves positivity.”

“The paper derives closed-form BF structures and develops an efficient first-order algorithm to achieve high-quality local solutions.”

“Late time levels are enhanced for the coated particles, implying a reduced effective interfacial diffusivity and a broadened release-time distribution.”

“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 shows that there exists a unique minimal strong solution to the given particle system up until a certain maximal stopping time, which is stated explicitly in terms of the dual formulation of a linear programming problem.”

“The paper derives necessary and sufficient conditions for the existence of such residual generators and provides explicit design formulas.”

“The paper shows that the Pontryagin index emerges as an integer infrared winding, such that the resulting holonomy phase is quantized by Q∈Z and reproduces the standard weight e^{iθQ}.”

“The paper identifies an additional contribution originating from a relative rotation in the polarization vectors, formulating this effect as a gravitational holonomy associated to the internal Lorentz group.”

“The paper formulates a unified taxonomy for pre-training paradigms, ranging from single-modality baselines to sophisticated unified frameworks.”

“The paper constructs the solution formula for the initial value problem by analyzing the spatiotemporal pattern and decomposing it into simpler segments.”

“The results showcase the real-world feasibility and superior performance of nonlinear MPC for 3D path-following guidance at ground speeds up to 36 meters per second.”

“The paper discusses the use of VQE as a novel SAT-solver and the importance of qubit efficiency in the Noisy Intermediate Scale Quantum-era.”

“SiLRI effectively exploits human suboptimal interventions, reducing the time required to reach a 90% success rate by at least 50% compared with the state-of-the-art RL method HIL-SERL, and achieving a 100% success rate on long-horizon manipulation tasks where other RL methods struggle to succeed.”

“The paper constructs a general class of unique solutions to certain matrix equations and derives several equivalent properties of W-weighted DMP and MPD inverses.”

“The paper formulates a gauge-invariant expression for the orbital magnetic octupole moment and links it to a higher-rank Hall response induced by spatially nonuniform electric fields.”

“The Zakharov-Shabat equations themselves recover the Lax operators under suitable change of independent variables in the case of the KP hierarchy and the modified KP hierarchy (in the matrix formulation).”

“The paper proves that the unreduced singular instanton homology has 2-torsion for any null-homologous fibered knot (except for a specific case) and provides a formula for calculating it.”

“DiffThinker significantly outperforms leading closed source models including GPT-5 (+314.2%) and Gemini-3-Flash (+111.6%), as well as the fine-tuned Qwen3-VL-32B baseline (+39.0%), highlighting generative multimodal reasoning as a promising approach for vision-centric reasoning.”

“The novelty of this work is two-fold: extending the catalogue of known optimal RMRAs and formulating a sub-optimal RMRA that abides by CFEs.”

“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 paper gives sufficient criteria that guarantee the integrability for the aforementioned generalized structures, formulated in terms of properties of the associated 2-form and connection.”

“The paper presents a class of QSLs formulated in terms of the two-parameter Sharma-Mittal entropy (SME), applicable to finite-dimensional systems evolving under general nonunitary dynamics.”