7425 papers
This paper establishes that magnitude is continuous on the open and dense subset of skew finite subsets within the space of finite subsets of by deriving explicit weight measure formulas for their cubical thickenings and proving the convergence of their magnitudes.
This paper proves that for sufficiently large integers satisfying specific modular constraints, can be expressed as the sum of four generalized polygonal numbers whose parameters have at most 988 prime factors.
This paper proposes a POMDP-based framework for optimizing maintenance in a two-component system with mixed observability and unidirectional degradation dependence, establishing structural policy properties, developing a Baum-Welch parameter estimation method, and demonstrating through numerical experiments that the approach outperforms classical threshold policies with cost reductions of up to 6%.
This paper proves that symmetric formal Fourier-Jacobi series of Hermitian modular forms over arbitrary imaginary quadratic fields converge to genuine modular forms, thereby establishing the geometric unitary Kudla conjecture in arbitrary codimension and removing the modularity hypothesis from the arithmetic inner product formula of Li-Liu.
This paper investigates the plane geometry of -rationals by constructing deformed Farey triangulations and modular surfaces, interpreting these numbers as Ford-like circles, and introducing Springborn operations as quadratic generalizations of Farey addition that correspond geometrically to the homothety centers of circle pairs.
This paper introduces an algebraic method, based on Eisenbud et al. (1977), for computing the index of completely mixed equilibria in finite games to demonstrate that any integer can be such an index, while showing that for monogenic equilibria the index is restricted to with non-zero values equivalent to payoff-robustness, and further extends these findings to extensive-form and boundary equilibria.
This paper provides an explicit classification of all simple -modules that are torsion-free of rank 1 over the Cartan subalgebra, while also establishing analogous results for the first Weyl algebra and the Lie superalgebra .
This paper demonstrates that in tree networks, all synchrony patterns are strictly induced by graph automorphisms rather than exotic mechanisms, and further analyzes how the combinatorial architecture, particularly leaf configurations, governs the linear and Lyapunov stability of these synchronous states.
This paper proposes a model-free spectral inference method based on eigengap ratios that effectively determines the number of communities in both dense and sparse networks with a diverging number of communities, without requiring explicit model fitting or parameter tuning.
This paper validates the legitimacy and effectiveness of a newly proposed high-frequency fast direct solver for electromagnetic integral equations on non-canonical geometries by leveraging semiclassical microlocal results to analyze its asymptotic spectral properties.
This paper utilizes Clifford algebra to derive a hydrodynamics formulation for a modified Dirac equation featuring a nonlinear mass term that preserves homogeneity and admits a chiral split, while also proving the global existence of solutions for a regularized version of the equation.
This paper establishes the convergence of an age-structured mechanical model for tumor growth, which accounts for cell life-cycles and pressure-driven proliferation, to a Hele-Shaw free boundary problem governed by a nonlinear Darcy's law in the incompressible limit.
This paper demonstrates that for Kautz graphs with sufficiently large diameters, a regular routing scheme achieves a better all-to-all makespan than any shortest-path routing scheme by proving the existence of edges with congestion strictly exceeding the regular routing's step count.
This paper establishes new extremal properties for geometric quantiles under minimal assumptions, deriving moment-free bounds on their norms and revealing a novel connection between their lower bounds and Tukey depth central regions.
This paper introduces Exp-ParaDiag, a novel time-parallel framework that integrates exponential integrators to solve parabolic PDEs and nonlinear problems with rigorous convergence guarantees and temporal accuracy ranging from first to sixth order.
This paper establishes a strengthened comparison theorem for the extreme eigenvalues of sums of independent random symmetric matrices against Gaussian counterparts, leveraging this result to improve eigenvalue bounds across various fields and providing the first complete proof of the injectivity properties for sparse random dimension reduction maps conjectured by Nelson & Nguyen.
This paper provides a general characterization of the class of sine-skewed models on the d-dimensional torus that exhibit a singular Fisher information matrix near symmetry, thereby resolving an open question regarding the conditions under which this inferential issue occurs.
This paper presents a formalization in Lean of the foundational commutative algebra result that projectivity of an -module descends along a faithfully flat ring map, thereby verifying Perry's correction to a subtle gap in the classical work of Raynaud and Gruson.
This paper establishes the existence of superdecomposable pure-injective modules over Jacobian algebras associated with triangulations of closed surfaces (excluding spheres with four or fewer punctures) by demonstrating the presence of independent pairs of dense chains of pointed modules in non-domestic skew-gentle and (skew) Brauer graph algebras, thereby confirming M. Prest's conjecture for these specific cases.
This paper presents a complete classification of complex unital 3-dimensional structurable algebras into seven non-isomorphic classes, detailing their structural properties such as derivation algebras and automorphism groups, and investigates the resulting -graded Lie algebras via the Allison-Kantor construction.