“Approximately 89% of trials converged, supporting the theoretical prediction that transparency auditing acts as a contraction operator within the composite validation mapping.”

“By embedding the Riemannian metric tensor into the automatic differentiation graph, our architecture analytically reconstructs the Laplace-Beltrami operator, decoupling solution complexity from geometric discretization.”

“Since the quality of data-driven ROMs is sensitive to the quality of the limited training data, we seek to identify training parameters for which using the associated training data results in the best possible parametric ROM.”

“Filing: OpenAI President Greg Brockman was the biggest donor to Trump's super PAC in H2 2025, donating $25M; Crypto.com operator Foris DAX donated $20M”

“The paper proposes local approximations to the global Minkowski Hamiltonian in quantum field theory (QFT) motivated by the operator-algebraic property of nuclearity.”

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

“The paper demonstrates conformal multiplet structure together with the hallmark of emergent spacetime supersymmetry through characteristic relations between fermionic and bosonic operators.”

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

“The paper proposes a new interpretation of the algebra of line operators in this theory as a tensor product of vector representations of a quantum toroidal algebra.”

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

“The paper characterizes the general form of bijective linear maps that preserve Lie products and operator products equal to fixed elements.”

“Neural operators are a powerful novel tool for high-performance control when hidden low-dimensional structure can be exploited, yet they remain fundamentally constrained by the intrinsic dimensional complexity in more challenging settings.”

“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 computes operator entanglement in closed form and shows that, for Haar-uniform product inputs, their entangling power is fully determined by the latter.”

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

“Each BPS monopole state is naturally labeled by a weight of the relevant $W$-boson representation of $(H^{\vee})^{s}$.”

“The paper establishes continuity of the operators and the unique strong solvability of the corresponding nonlocal parabolic equations in $L_p$ spaces.”

“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 resulting observable is mapped into a transparent decision functional and evaluated through realized cumulative returns and turnover.”

“For every irrational ω with β(ω) < L, where L > 0 denotes the Lyapunov exponent, and every non-resonant phase θ, we prove Anderson localization, i.e. pure point spectrum with exponentially decaying eigenfunctions.”

“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 argues that in the same-helicity sector the $R^2$ operators have no intrinsic meaning, as they merely remove unwanted terms produced by the linear-in-Riemann operators.”

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“Sub-ensemble correlations are determined by the covariance operator, inducing a natural geometry in which statistical independence corresponds to orthogonality of the measurement functionals.”

“The paper derives a generalized Heisenberg-Robertson uncertainty inequality valid across all spectral regimes.”

“PINNs run 90,000 times slower than finite difference with larger errors.”

“The paper establishes factorization results that clarify the relationship between a minimal isometric dilation and an arbitrary isometric dilation of a contraction.”

“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 introduces a suite of performance optimizations, including interleaved pipeline scheduling, attention-aware data scheduling for long-sequence training, hierarchical and overlapped communication for expert parallelism, and DVM-based operator fusion.”

“The study demonstrates that two-nucleon spatial correlations, specifically the pair-number operator and the square-separation operator, encode important details of the halo structure of 6He.”

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“The article likely discusses the potential benefits of quantum machine learning in this specific context, such as improved computational efficiency or accuracy compared to classical methods.”

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“The paper introduces stationary-reweighted soft FQI, which reweights each regression update using the stationary distribution of the current policy. It proves local linear convergence under function approximation with geometrically damped weight-estimation errors.”

“The survey reviews the technology landscape for hardware acceleration of deep learning, spanning GPUs and tensor-core architectures; domain-specific accelerators (e.g., TPUs/NPUs); FPGA-based designs; ASIC inference engines; and emerging LLM-serving accelerators such as LPUs (language processing units), alongside in-/near-memory computing and neuromorphic/analog approaches.”

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“The paper derives generators and relations of the Coulomb branch operator algebra for specific SU(2) theories and analyzes theories with a specific Coulomb branch structure.”

“The proposed method demonstrates superiority over baseline schemes in terms of average sum rate, robustness to CSI imperfection, user mobility, and scalability.”

“The paper defines squeezed cobosons as eigenstates of a Bogoliubov transformed coboson operator and derives explicit expressions for the associated quadrature variances.”

“The paper proposes Bell-type inequalities as operator-level diagnostics of quantum incompatibility in particle-physics systems.”

“The paper proposes to leverage connections between proximal operators and Hamilton-Jacobi partial differential equations (HJ PDEs) to develop novel deep learning architectures for learning the prior.”

“The authors propose a simple fix: reweight each regression step using an estimate of the stationary density ratio, thereby aligning FQE with the norm in which the Bellman operator contracts.”

“The paper shows that the GHZ and Dicke states of three qubits and the GHZ state of four qubits do not allow a description based on Mermin's instructional sets, while one of the generalized Dicke states of four qubits does allow such a description.”

“Whenever two 1+1d conformal field theories (CFTs) differ in symmetry charge assignments of local operators or twisted sectors, any symmetry-preserving spatial interface between the theories must flow to a non-invertible defect.”

“The authors observe that the charge diffusion constant is well described by a simple functional dependence ~ 1/V^2 universally valid both for small and large V.”

“The consistent orderings are in one-to-one correspondence with the Jacobians associated with all field redefinitions of a set of canonical degrees of freedom. For each admissible operator ordering--or equivalently, each path-integral measure--we identify a definite, positive Hilbert-space inner product. All such prescriptions define the same quantum theory, in the sense that they lead to identical physical observables.”

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