7189 papers
This paper clarifies the ring-theoretic and homological properties of the tilt of extensions between perfectoid rings, building upon Faltings' almost étale extensions and Scholze's tilting operations to advance the construction of big Cohen-Macaulay algebras.
This paper establishes that the internal graph of an H-rigid graph is an isomorphism invariant for the corresponding graph product of hyperfinite II-factors, enabling the classification of such factors for specific graph types and bounding the radius difference between isomorphic graph products by one, utilizing the resolution of the Peterson-Thom conjecture.
This paper proposes neural network methods, specifically PINNs and RVPINNs, to approximate solutions for Neumann series problems of non-expansive Perron-Frobenius operators, providing theoretical error estimates and demonstrating their effectiveness through numerical examples in 1D, 2D, and a two-cavity system.
This paper establishes a unified framework using concentration inequalities to analyze the statistical convergence and robustness of depth-based estimators, explicitly deriving their maximum bias curves and breakdown points while demonstrating how slight variations in these inequalities reveal distinct robustness behaviors across different depth formulations.
This paper establishes that unital graph C*-algebras frequently decompose into amalgamated free products, a structural insight used to fully characterize their residual finite-dimensionality and operator norm stability.
This paper extends fundamental volume comparison theorems in Riemannian geometry to the comparison of total -curvature with respect to -curvature (where ), specifically proving these results for metrics near strictly stable positive Einstein metrics and for negative Einstein metrics under specific sectional curvature assumptions.
This paper introduces a branch-and-cut algorithm that reformulates mixed-integer Nash equilibrium problems as bilevel optimization tasks to either compute a pure Nash equilibrium or prove its non-existence, with specific adaptations and finite termination guarantees for both standard and generalized settings.
This paper proposes and theoretically validates two stochastic gradient descent-based variational inference methods for infinite-dimensional inverse problems, utilizing constant-rate iterations with randomization to efficiently sample from posterior distributions and demonstrating their effectiveness through preconditioning and numerical applications to linear and non-linear problems.
This paper analyzes the overall net profits of two players in a "first to reach " game governed by an urn model, demonstrating that the statistical properties of the game's outcomes differ drastically across three distinct regimes involving sampling without replacement, sampling with replacement plus reinforcement, and a third unspecified regime.
The paper derives a single integral expression valid for all complex numbers that represents the reciprocal gamma function without requiring analytic continuation and simultaneously satisfies a specific functional identity involving the gamma function and sine.
This paper establishes optimal -th order temporal convergence for POD-based reduced order models of semilinear reaction-diffusion equations by employing BDF-q schemes ($1\le q\le 5$) and utilizing first-order difference quotients of snapshots to derive pointwise-in-time error bounds.
This article explores the potential of Frequency Range 3 (7–24 GHz) for Integrated Sensing and Communication (ISAC) in 6G networks, highlighting its unique propagation characteristics and MIMO capabilities while addressing the challenges of implementing ultra-massive MIMO with extremely large aperture arrays and unified channel models.
This paper develops and analyzes two numerical algorithms based on inverse eigenvalue problems and linear algebra techniques to compute recurrence coefficients for multiple orthogonal polynomials on the step-line, demonstrating their accuracy and stability through experiments on both ill-conditioned and well-conditioned examples.
This paper refines moment comparison inequalities for sums of random vectors uniformly distributed on Euclidean spheres by establishing sharp constants and introducing an optimal deficit term, particularly in high dimensions.
This paper presents a novel Lightning Method-based approach for solving the planar heat equation that combines Laplace transformation, Talbot inversion, and collocation to achieve spectral accuracy and robust performance across diverse geometric domains and time intervals.
This paper investigates the fundamental communication-sensing tradeoffs in bistatic integrated sensing and communications over memoryless relay channels by deriving an upper bound and a hybrid-partial-decode-and-compress-forward lower bound for the capacity-distortion function, demonstrating their optimality in specific cases and the benefits of integrated design.
This paper investigates the regularization and completeness of root functions for operator-differential expressions involving bounded invertible and finite-dimensional operators, demonstrating how such forms can regularize singular differential expressions with negative Sobolev space coefficients and establishing completeness under specific Volterra operator and boundary conditions.
This paper extends the classical Kolmogorov-Riesz compactness theorem to asymptotic spaces on by proving that relative compactness in these nonlocally convex F-spaces is characterized by natural tail and translation conditions alongside a necessary additional almost equiboundedness requirement.
This paper proposes and experimentally validates a robust control strategy for regulating the outlet temperature of a counter-current heat exchanger by modeling it as a structured bilinear system and implementing both an output feedback controller with a state observer and a purely integral control law.
This paper establishes uniform-in-time error bounds for the perturbed observation variant of the ensemble Kalman filter applied to the partially observed Lorenz 96 model by utilizing additive covariance inflation to overcome analytical challenges posed by non-symmetric matrices, with and without projecting the background covariance onto the observation space.