2370 papers
This paper establishes a tropical analogue of Porteous' formula by developing characteristic classes for tropical vector bundles on rational polyhedral spaces with boundary, utilizing a splitting principle and the boundary framework to ensure degeneracy loci achieve their expected codimension.
This paper introduces the dib-chromatic number as an extension of the -chromatic number to directed graphs via acyclic vertex colorings, providing general bounds and specific results for tournaments and regular digraphs.
This paper establishes an explicit formula for the rank of the -walk matrix of the Dynkin graph and proves that its Smith normal form consists of a single 1, followed by twos, and the remaining entries being zero.
This paper investigates permutation classes formed by finite subpermutations of infinite pin sequences, proving that they possess proper growth rates and providing a method to calculate them.
This paper computes the height filtration and successive minima of the height function associated with a relatively ample line bundle on a flag bundle over a smooth projective curve defined over an algebraically closed field of positive characteristic.
This paper revisits the Eckstein-Ferris-Pennanen-Robinson duality framework to demonstrate how paramonotonicity ensures the alignment of saddle points with the solution set, characterizes total Fenchel-Rockafellar duality in the subdifferential setting, and derives projection formulas relevant to the Chambolle-Pock algorithm.
This paper introduces the concept of Lorentzian proper position to characterize elementary quotients of M-convex functions and analyze the incidence geometry of tropical linear spaces, revealing that while certain classical incidence properties fail for general tropical spaces, they hold for those possessing adjoints.
This paper proposes the Alternating Gradient-type algorithm with Inexact Lower-level Solutions (AGILS), which leverages a Moreau envelope-based reformulation to efficiently solve convex composite bilevel optimization problems without requiring exact lower-level solutions, while establishing convergence guarantees and demonstrating effectiveness through numerical experiments.
This paper introduces a canonical framework for jointly lifting Brownian motion and low-regularity stochastic rough paths to model rough volatility via a single rough differential equation, thereby extending existing partial rough path theories, providing a numerical approximation scheme for correlated settings, and demonstrating successful calibration to market data.
This paper introduces DR-FoS, a novel doubly-robust estimator for the Functional Average Treatment Effect (FATE) that ensures consistent estimation and valid simultaneous inference even when either the outcome or treatment assignment model is misspecified, demonstrating its effectiveness through simulations and a real-world application to the SHARE dataset.
This paper presents a formalization of Borel determinacy in the Lean 4 theorem prover, including definitions of Gale-Stewart games and a proof of Martin's theorem that closely follows his original "purely inductive" argument.
This paper introduces an efficient algorithm that rapidly computes a complete curve of post hoc false discovery proportion bounds along a path of increasing selection sets by leveraging the forest structure of the reference family and the incremental nature of adding single hypotheses.
This paper presents explicit formulas for the Alexander polynomial of pretzel knots, characterizes those with trivial polynomials, and utilizes these results to construct a new family of knots that are topologically slice but not smoothly slice.
This paper introduces a new scoring variant of the combinatorial game Nim that generalizes both normal and misère play rules, and analyzes its theoretical properties, including optimal strategies and payoff functions.
This paper establishes the global-in-time existence of strong solutions for a class of fractional parabolic reaction-diffusion systems governed by spectral fractional Laplacians with polynomial growth nonlinearities, while also presenting numerical simulations to address an open theoretical question.
This paper demonstrates that even in a non-additive setting, the existence of a codereliction within a monoidal coalgebra modality inherently induces an additive enrichment via bialgebra convolution, thereby uniquely characterizing differential linear categories and establishing the uniqueness of coderelictions.
Motivated by prior work on post-critically finite cubic polynomials, this paper proposes a Markov model based on critical orbits to describe the factorization of iterated PCF cubic polynomials over and constructs groups that are conjectured to contain the Galois groups of these iterations.
This paper establishes the stability and uniqueness of a stochastic branching algorithm for solving semilinear heat equations by deriving sufficient criteria for the integrability of random functionals to prevent solution explosion.
This paper develops Generalized Method of Moments (GMM) and M estimators for network-dependent data by establishing a novel uniform law of large numbers that ensures their consistency and asymptotic normality, while also providing complete procedures for practical estimation and inference.
This paper introduces a Fourier-type formalism on non-commutative spaces to establish two versions of the Hörmander-Mikhlin -multiplier theorem for locally compact Kac groups and semi-finite von Neumann algebras, which generalize classical results and are applied to evolution equations in non-commutative settings.