7007 papers
This paper introduces Orthonormal Data Collaboration (ODC), a method that enforces orthonormal bases to transform the alignment challenge into a closed-form Orthogonal Procrustes problem, thereby achieving orthogonal concordance, significantly reducing computational complexity, and improving accuracy without compromising privacy or communication efficiency.
This paper extends Control Lyapunov Value Functions to disturbed nonlinear systems by defining the Robust CLVF (R-CLVF) to identify the smallest robust control invariant set and guarantee exponential stabilization, while addressing computational challenges through warmstart and system decomposition techniques.
This paper introduces a complex of cochains known as -fractional charges to define the exterior product of Hölder differential forms, thereby extending the Young integral to arbitrary dimensions and codimensions.
This paper proposes and analyzes stochastic greedy algorithms (MRG, DRG, and Random-WSSA) to efficiently solve budget- and performance-constrained weak submodular sensor selection problems with robustness guarantees, demonstrating their effectiveness in Earth-observing satellite constellation applications.
This paper proposes a novel multi-task subset selection framework that achieves localized distributional robustness by introducing a relative-entropy regularization term, which is proven equivalent to maximizing a monotone composition of submodular functions and can be efficiently solved via greedy algorithms, as validated by experiments on satellite sensor selection and image summarization.
This paper establishes an analogue of Kaplansky's theorem for models of by introducing -bounded weakly immediate types to prove that every such model possesses a unique --spherical completion, thereby demonstrating that is definably spherically complete.
This paper establishes sharp Fourier restriction estimates for certain degenerate higher codimensional quadratic surfaces by introducing a novel iterative broad-narrow analysis that overcomes the failure of rescaling invariance through a generalized Jacobian defined via algebraic and graph-theoretic tools.
This paper investigates infinite -indexed complexes of spaces equipped with multilinear products to derive hierarchies of differential identities and closed multiple products, ultimately demonstrating how maximal differential orders, powers, and coherence conditions generate families of multi-graded differential algebras.
This paper proposes a graph signal processing framework for reversible Markov chains that defines optimal graph filters—specifically Bernstein, Chebyshev, and Legendre filters—to significantly accelerate the convergence of ergodic averages compared to traditional methods.
This paper characterizes the necessary and sufficient conditions for the least squares estimator to be minimax optimal in a convex constrained Gaussian sequence model by linking optimality to the Lipschitz property of the local Gaussian width, while providing algorithms to compute worst-case risk and demonstrating these results across various geometric sets.
This paper establishes that the value function of infinite-dimensional singular stochastic control problems in Hilbert spaces is a -viscosity solution to a variational inequality and satisfies a second-order smooth-fit principle in the controlled direction under specific spectral conditions, by leveraging connections to optimal stopping and techniques from convex and viscosity theory.
This paper proposes an asymptotically optimal online learning and optimization algorithm for minimizing irreversible facility openings under a coverage target, demonstrating that a policy balancing initial limited exploration with subsequent rapid exploitation achieves sub-linear regret that converges exponentially fast to its infinite-horizon limit.
This paper generalizes the classical Morlet-Burghelea-Lashof-Kirby-Siebenmann smoothing theory delooping of disc diffeomorphism groups to various disc embedding spaces, establishing their equivalence to specific loop spaces of quotient classifying spaces and demonstrating how these deloopings unify Hatcher and Budney group actions into a framed little discs operad action.
This paper employs an information-theoretic approach to establish the equivalence between the curvature-dimension condition and entropy differential inequalities on Riemannian manifolds, while deriving new rigidity theorems for -Einstein and -Einstein manifolds through the monotonicity of -entropy along Wasserstein geodesics.
This paper classifies and constructs differential symmetry breaking operators from a line bundle over to a vector bundle over , while determining their factorization identities, the associated branching laws for generalized Verma modules of , and the resulting -representations.
This paper demonstrates that in the independent cascade model on undirected graphs with symmetric influence probabilities, the local symmetry of the network structure induces a global symmetry in activation dynamics, ensuring that the probability of node being activated within steps starting from node is identical to the reverse scenario, a result established through a novel random matrix approach.
This article provides an overview of the Plancherel theory for Riemannian symmetric spaces by demonstrating how Harish-Chandra's theorem can be derived using recently developed methods originally designed for real spherical spaces.
This paper introduces the class of primitive Enriques varieties, demonstrates their stability under the Minimal Model Program by proving that -MMPs for Enriques manifolds terminate with minimal models having canonical singularities, and investigates their asymptotic theory.
This paper establishes the scaling limits of large uniform random trees with fixed vertex degrees and heights by analyzing root-to-vertex paths via coalescent processes, thereby deriving the scaling limits of Bienaymé-Galton-Watson trees in varying environments.
This paper establishes the global existence and long-time convergence to flat interface solutions for the moving interface problem coupling the Navier-Stokes equations with a linear wave equation, demonstrating that initial data sufficiently close to equilibrium leads to stable fluid-structure interactions even in the presence of gravity.