“Understanding the evaluation metrics is key to unlocking the power of the latest self-driving technology!”

“Each Pokemon is represented by a numerical vector: [HP, Attack, Defense, Special Attack, Special Defense, Speed].”

“MNIST data are used.”

“The article begins by stating the common misconception that LLMs like ChatGPT and Claude can perform highly accurate predictions using Excel files, before noting the fundamental limits of the model.”

“Geminiとのやり取りを元に、構成されています。”

“Softmax takes the raw, unbounded scores produced by a neural network and transforms them into a well-defined probability distribution...”

“The paper presents an online variational inference framework to compute its approximation at each time step.”

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

“The authors' method enables simulations of bosonic quantum mixtures with substantially larger bond dimensions than previous works.”

“The paper shows that the homeomorphism problem for compact topological n-manifolds is Borel equivalent to equality on natural numbers, while the homeomorphism problem for noncompact topological 2-manifolds is of maximal complexity.”

“The paper derives the graphicality of infinite sequences for double power-laws, uncovering a rich phase-diagram and pointing out the existence of five qualitatively distinct ways graphicality can be violated.”

“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 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 constructs solitary waves in Dirac--Klein--Gordon (in one and three spatial dimensions) and studies the dependence of energy and charge on $ω$.”

“The method effectively suppresses spectral pollution and resolves closely spaced spectral components.”

“The method, which is general, numerically exact, and computationally not intensive, can easily be generalised to relativistic systems.”

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

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

“The paper proves that α=-1 is the unique choice achieving optimal energy stability under a specific condition, highlighting its theoretical advantage.”

“The paper provides an analytical expression of the Lyapounov as a function of energy in the presence of both diagonal and off-diagonal disorder.”

“The proposed delay compensation strategy achieves a reduction of over 200,000 infected individuals at the peak.”

“For any Feller's Brownian motion that is not purely driven by jumps at the boundary, we construct a sequence of boundary random walks whose appropriately rescaled processes converge weakly to the given Feller's Brownian motion.”

“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 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.”

“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 Bayesian DP algorithm alternates between posterior updates and value iteration, employing an estimator for the risk-based Bellman operator that combines Monte Carlo sampling with convex optimization.”

“The paper introduces smooth cumulative- and inverse-cumulative-distribution-function ((I)CDF) timesteppers that evolve distributions rather than particles.”

“The discovered accelerator, featuring second differences and cross-product terms, achieved over 75 percent success rate in improving convergence compared to raw sequences.”

“BF-APNN substantially reduces training time compared to RT-APNN while preserving high solution accuracy.”

“The newly proposed mCCAdL thermostat achieves a substantial improvement in the numerical stability over the original CCAdL thermostat, while significantly outperforming popular alternative stochastic gradient methods in terms of the numerical accuracy for large-scale machine learning applications.”

“The paper introduces Energy-Aware Bayesian-CBFs (EB-CBFs) that construct conservative energy-based barriers directly from the Hamiltonian and vector-field posteriors, yielding safety filters that minimally modify a nominal controller while providing probabilistic energy safety guarantees.”

“The paper identifies "smooth branches of extremal amplitudes separated by sharp kinks at $d=5$ and $d=7$, coinciding with a transition in threshold analyticity and the loss of some well-known dispersive positivity constraints."”

“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 paper demonstrates that classical crosstalk effects can significantly alter multi-qubit dynamics, which previous models could not explain.”

“The prosumer community can achieve gains from trade up to 40% relative to the grid-only benchmark.”

“The paper presents the first construction of an NN-FT that encodes the full Virasoro symmetry of a 2d CFT.”

“The problem becomes ill-posed as the system transitions from the ballistic to the diffusive regime, characterized by the Knudsen number converging to zero.”

“The method couples a high-fidelity, asymptotic-preserving VPL solver with inexpensive, strongly correlated surrogates based on the Vlasov--Poisson--Fokker--Planck (VPFP) and Euler--Poisson (EP) equations.”

“The numerical results show that the non-diagonal elements involving the initial and final leptons are main sensitive parameters and LFV sources.”

“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 claims an enhanced convergence rate of order $\mathcal{O}(h)$ in the $L^2$-Wasserstein distance, significantly improving the existing order-half convergence.”

“The lower-porosity medium produces higher local and surface-averaged Nusselt numbers.”

“The best prompt-based LLM generator achieves the state-of-the-art (SOTA) performance with significant improvement (>7%), yet it is still below the human expert performance.”

“The study observes finite-time effects close to the FOIPT, as well as evidence that a dynamic phase transition occurs. The location of this transition is measured very precisely and compared with previous results in the literature.”

“The proposed preconditioners significantly accelerate the convergence of iterative solvers compared to existing methods.”

“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 paper provides clear numerical evidences for anyon excitations with fractional charge and pronounced real-space density modulations, directly supporting the recently proposed anyon density-wave halo picture.”

“The article is a brief announcement, likely a technical report or a description of the software.”

“The algorithm consistently achieves lower error than the fluid-based method, and even one order of magnitude lower in a fusion-relevant test case. Moreover, the algorithm exhibits a significant speedup compared to the reference kinetic MC method.”

“The system combines high numerical aperture remote refocusing with tilt-invariant light-sheet scanning and hardware-timed synchronization of laser excitation, galvo scanning, and camera readout.”