7189 papers
This paper establishes a comprehensive statistical theory for globally optimal empirical risk minimization decision trees by deriving sharp oracle inequalities and minimax optimal rates over a novel piecewise sparse heterogeneous anisotropic Besov space, thereby providing rigorous theoretical guarantees for their performance in high-dimensional regression and classification under both sub-Gaussian and heavy-tailed noise settings.
This paper establishes a Knebusch-type trace formula for signatures of hermitian forms over Azumaya algebras with involution, extending Knebusch's results on symmetric bilinear forms and yielding an exact sequence for total signatures over semilocal base rings that relates to Pfister's local-global principle and the stability index.
This paper establishes a unified bounded-variation solution framework for prox-regular sweeping processes by proving the equivalence between a new integral formulation with a quadratic correction term and the standard differential-measure formulation, while also deriving a Brézis-Ekeland-Nayroles-type variational characterization that ensures stability under uniform limits.
This paper establishes a new global endpoint Sobolev inequality for measures that extends the Meyers-Ziemer theorem by incorporating a maximal function, thereby unifying and advancing the understanding of weighted bounded variation, isoperimetric inequalities, and fractional operator estimates while identifying sharp conditions for non-endpoint cases.
This paper develops a calculus of space-time controlled fields to establish a unified composition rule and a rough stochastic Itô-Wentzell formula for evaluating random fields along rough semimartingales, motivated by recent advances in Itô-Alekseev-Gröbner and related interpolation identities.
This paper establishes the existence of a mountain pass solution and proves its global integrability and local Hölder continuity for an entire Choquard equation involving the Grushin operator on .
This paper investigates steady incompressible viscous flows in a 3D cylindrical annulus with one stationary cylinder, explicitly determining all spiral-symmetric solutions and proving their stability against finite-energy perturbations for small boundary data, while highlighting a key analytical difference depending on which cylinder is fixed.
This paper resolves the open question regarding the parameterized complexity of the Optimal Morse Matching problem by presenting a $2^{O(k \log k)} n$-time algorithm for bounded-treewidth complexes and proving its optimality under the Exponential Time Hypothesis.
This paper investigates four relations on the set of point-hyperplane anti-flags, demonstrating that they are generally mutually recoverable except in the specific case of a field with two elements, where one relation fails to recover the others due to a bijection with exterior points of a hyperbolic polar space.
This paper proposes a novel reformulation of the structured distance to singularity problem as a nonlinear system of equations in two vector unknowns, enabling a faster multivariate Newton-based algorithm that maintains accuracy while ensuring monotonic convergence and avoiding singularities.
This paper proposes and analytically evaluates a spatially-aware secondary license sharing framework for mmWave networks that leverages the directional nature of signals and blockage conditions to optimize spectrum sharing, demonstrating that these physical characteristics can significantly enhance transmission opportunities for secondary users while maintaining primary network performance.
This paper employs cellular sheaves and their cohomology to analyze the infinitesimal rigidity of graph-of-groups realizations, establishing algebraic conditions for Henneberg moves and proving that the Maxwell-count provides a necessary and sufficient condition for minimal rigidity in problems defined over real algebraic groups with specific subgroup constraints.
This paper proves that any family of subsets of an -element ground set containing no -pairwise crossing members has size , thereby confirming the long-standing Karzanov-Lomonosov conjecture regarding the linear growth rate of such cross-free families.
This paper provides a complete combinatorial classification of all modular compactifications of the universal Jacobian over via -functions, characterizing their geometric properties, isomorphism conditions, and structural relationships within an extended stability poset.
This paper establishes the existence of two distinct equilibrium concepts for non-cooperative games under uncertainty—Nash equilibrium with capacity-based mixed strategies and Dow-Werlang equilibrium with non-additive beliefs—by utilizing max-plus integrals and fixed point theorems within an abstract convexity framework.
This paper establishes a free probability analogue of Obata's rigidity theorem by proving that under a non-commutative curvature-dimension condition, the saturation of Voiculescu's free Poincaré inequality forces the underlying von Neumann algebra to split off a freely complemented semicircular component, thereby extending classical Gaussian splitting phenomena to the non-commutative setting.
This paper establishes that the chromatic number of the random Borsuk graph transitions from being -colourable to requiring more than colours when the average degree is constant for $2 \leq k \leq dk=2$ case via continuum AB percolation.
This paper establishes a unified thermodynamic response framework for singular Bayesian models, demonstrating that posterior tempering induces a hierarchy of observables that naturally interpret complex learning-theoretic quantities like the real log canonical threshold and WAIC as free-energy derivatives, thereby revealing phase-transition-like structural reorganizations in models such as neural networks and Gaussian mixtures.
This paper resolves two major open problems by proving that computing shortest monotone paths on simple polytopes and determining their diameters are NP-hard, while also demonstrating that polynomial-time linear paths can be found on specific small extended formulations of any polytope.
This paper establishes that the chromatic threshold for a homogeneous linear equation over is zero if and only if the equation contains a zero-sum subcollection of at least three coefficients, utilizing equivariant topological methods to resolve a question by Griesmer and extend results on recurrence in infinite abelian groups.