“AI can be multidimensional if we wish.”

“When handling multidimensional arrays of 3 or more dimensions, imagine a 'solid' in your head...”

“The framework creates the image-encoding state using a unitary gate, which can later be transpiled to target quantum backends.”

“Financial incentives increase daily steps, whereas charitable incentives deliver a precisely estimated null.”

“The method achieves improved performance over state-of-the-art reconstruction methods, without task-specific supervised training or fine-tuning.”

“The study focuses on atomic calculations employing noninteger Slater-type orbitals. Analytic derivatives of the energy functional are not readily available for these orbitals.”

“The paper shows that, for arbitrary small ε>0, there exists an algorithm for IPs with m constraints that runs in f(m,ε)⋅poly(|I|) time, and returns a near-feasible solution that violates the constraints by at most εΔ.”

“The paper provides a complete characterization of the weight parameters that yield a finite group in two dimensions.”

“Uniqueness of the solution is established in two cases - the one-dimensional setting and the Gaussian case.”

“The information content of the original single-pass question was a 'point,' but it is amplified to a 'complex multidimensional manifold.'”

“The research focuses on the Global Regular Solutions of the Multidimensional Degenerate Compressible Navier-Stokes Equations with Large Initial Data of Spherical Symmetry.”

“The article's subject matter relates to the Dirac-Hestenes Equation.”

“The study investigates existence, uniqueness, and time-asymptotics of regular solutions.”

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“The paper focuses on recovering missing data in multidimensional time series.”