2113 papers
This paper proposes an ADMM-based Bilevel Descent Aggregation (ADMM-BDA) algorithm for sparse hyperparameter selection that overcomes the limitations of existing methods by achieving global convergence without relying on the restrictive lower-level singleton assumption.
This paper introduces rank-3 generalized Clifford manifolds, demonstrating that they canonically induce generalized hypercomplex structures and possess an integrable twistor space characterized by a natural Spin(3)-action and a generalized Nijenhuis tensor-based integrability condition.
This paper provides explicit formulas for the coproducts of modified Drinfeld-Cartan generating series for the Yangian in type and the quantum affine algebra in type , while also presenting an explicit construction of positive prefundamental representations for the latter.
This paper presents an optimization-driven, adjoint-based framework that utilizes both monolithic and partitioned strategies to simultaneously identify structural damage and reconstruct temperature fields in one-way thermo-mechanically coupled systems, demonstrating superior accuracy over traditional assumptions even with sparse and suboptimally placed sensor networks.
This paper introduces a Unifying Primal-Dual Proximal (UPP) framework that linearizes the augmented Lagrangian to unify various distributed nonconvex optimization methods, proving sublinear convergence to stationary points and linear convergence under the Polyak-Łojasiewicz condition, while demonstrating superior performance through specialized algorithms like UPP-MC and Chebyshev-accelerated UPP-SC-OPT.
The paper proves that every graph with a minimum degree of at least $10^810^8K_{k+1}$, thereby resolving a long-standing problem posed by Kühn and Osthus.
This paper develops a theory of flats and hyperplane arrangements for matroids over tracts (T-matroids), establishing cryptomorphic descriptions via lattices of T-flats, hyperplane and point-line arrangements, and quiver representations, with applications to tropical linear spaces.
This paper establishes quantitative Calderón-Zygmund estimates for 2D viscous Hamilton-Jacobi equations with natural gradient growth and applies them to prove the existence of classical solutions for stationary second-order Mean Field Games systems with defocusing power-law couplings, while also surveying existing regularity results and outlining open problems.
This paper establishes precise formulas for various topological indices and graph polynomials, including diameters, perfect matchings, Tutte polynomials, and Wiener and Szeged indices, for the infinite family of Schreier graphs generated by tree automaton groups.
This paper establishes that for an inaccessible cardinal , the isomorphism relation of any theory with fewer than non-isomorphic models of size is continuously reducible to the isomorphism relation of any unstable or superstable non-classifiable theory within the space of regressive functions on .
This paper establishes conditional stability for the backward problem of degenerate viscous Hamilton-Jacobi equations with general non-quadratic Hamiltonians using Carleman estimates and linearization, and proposes numerical identification algorithms based on the adjoint state method and Van Cittert iteration, validated by numerical tests.
This paper investigates linear-quadratic Dirichlet control problems governed by non-coercive elliptic equations on non-convex polygonal domains using energy regularization, establishing solution regularity in weighted Sobolev spaces and deriving optimal error estimates for finite element discretizations that employ graded meshes and a specialized discrete projection.
This paper determines the homotopy type of the moment-angle complex associated with the complex of injective words by showing it is governed by the complex's -vector and establishes a generalized homotopy fibration for polyhedral products over ordered simplicial complexes.
This paper establishes uniform concentration inequalities for random matrices with -subexponential tails (), extending optimal subgaussian results to heavier-tailed distributions and providing new guarantees for robust high-dimensional inference and dimension reduction.
This paper presents an integer linear programming model to formalize the rules of the Nikoli puzzle Evolomino and introduces an algorithm for generating unique instances, demonstrating that state-of-the-art solvers can efficiently solve grids up to 18x18.
This paper introduces the concept of semi-rigidity for stable sheaves on smooth polarized varieties to characterize the existence of stable deformations of direct sums, providing a criterion based on the Yoneda pairing and applying it to line bundles on projective varieties and Lagrangian subvarieties of hyper-Kähler manifolds.
This paper introduces mollified Christoffel-Darboux kernels on algebraic varieties to achieve a uniform boundedness property on the support and enable consistent, quantitatively controlled density recovery from moment data without prior knowledge of the equilibrium measure.
This paper establishes a pointwise geometric description of nonlinear Lebesgue spaces, including their length structure, curvature bounds, and speed definitions for absolutely continuous curves, by first proving a nonlinear Fubini–Lebesgue theorem that identifies L^p curves with mappings into the space of L^p curves.
This paper establishes that for a compact Lie group and sufficiently large rank , the dynamics of the automorphism group acting on the representation space exhibit algebraic rigidity, where orbit closures and invariant probability measures are algebraic in nature, analogous to Ratner's theorems.
This paper proves and numerically validates that tensor-product -finite element approximations for the Dirichlet integral fractional Laplacian on a 3D cuboid with analytic forcing achieve root exponential convergence in the energy norm, specifically bounded by , by leveraging analytic regularity in weighted Sobolev spaces and geometrically refined meshes.