2267 papers
This paper introduces the theory of the Collatz process and the method of dynamical balls to formulate the Collatz conjecture, explore its connection to Sophie Germain primes, and develop tools for analyzing the convergence of sequences generated by iterating on fixed integers.
This paper presents and proves the existence of an efficient algorithm for computing -expansions of classical modular forms of arbitrary weight and level for any congruence subgroup, while also providing the necessary theoretical background and practical implementation details.
This paper provides a comprehensive catalog of Lambert series identities, detailing their formal properties, combinatorial generalizations, and connections to partition functions, while offering a reference compendium of known formulas for various special cases without focusing on rigorous analytic convergence.
This paper proposes a nonparametric two-sample hypothesis test for low-rank random graphs of differing sizes, utilizing maximum mean discrepancy on optimally transported graph embeddings to determine if the networks originate from the same distribution.
This paper establishes that the decomposition theorem components for contraction maps of torus actions of complexity one are intersection cohomology complexes of even codimensional subvarieties, leading to the vanishing of odd-dimensional intersection cohomology for rational complete varieties of this type and providing explicit formulas for the Betti numbers of affine trinomial hypersurfaces based on their defining equations.
This paper constructs spectral triples for one- and two-qubit states to define Connes spectral distances, which are then used to propose new measures for quantum discord and coherence, revealing geometric structures such as the Pythagorean theorem in specific two-qubit cases.
This paper establishes results on distinguishing Siegel cusp forms of degree two, demonstrating that a level-one Hecke eigenform can be uniquely determined by its second Hecke eigenvalue under a specific assumption and that two such eigenforms can be distinguished using -functions.
This paper investigates the iteration of the stationary-logic constructible model by proving distributivity and stationary-set preservation for countable iterations of club-shooting forcings using mutually stationary sets, and introducing mutually fat sets to achieve stronger results for uncountable iterations, thereby demonstrating the ability to force models where and where iterated sequences decrease with arbitrarily large order types.
This paper presents various elementary approaches to elliptical range theorems for the Davis-Wielandt shell, numerical range, and conformal range, focusing on their quadratic representations.
This paper characterizes the amenability of countable Borel equivalence relations via the uniform Liouville property, investigates Kesten's property for return probabilities on topological groups, and constructs an amenable contractible Polish group lacking this property by linking it to anti-concentration inequalities in measurable lamplighter groups.
This paper introduces a bilevel optimization model (TN-DA) for designing large-scale transit networks that integrates latent demand through rider adoption behavior, and proposes five efficient heuristic algorithms that outperform exact methods in computational speed while maintaining high solution quality and key adoption properties in real-world case studies.
This paper demonstrates that by strategically combining sample splitting with specific nuisance function tuning strategies (such as undersmoothing or oversmoothing), both plug-in and first-order bias-corrected estimators can achieve minimax rates of convergence for doubly robust functionals across all Hölder smoothness classes, overcoming limitations of existing literature.
This paper presents a minimal port-Hamiltonian formulation for interacting particle systems to analyze their stability and mean-field limits, while simultaneously issuing an erratum that corrects a previous claim regarding trajectory compactness by providing a counterexample for repulsive interactions and a revised proof for Hamiltonian gradient convergence.
This paper introduces efficient, parameter-free geodesic slice sampling algorithms for generating samples from probability distributions on the sphere, proving their uniform ergodicity and demonstrating superior performance over standard methods like random-walk Metropolis-Hastings and Hamiltonian Monte Carlo in challenging directional data scenarios.
This paper introduces a simplified perspective on Hodge-Newton indecomposability to provide a uniform proof of a combinatorial identity derived from affine Deligne-Lusztig varieties with finite Coxeter parts.
This paper investigates the asymptotic agreement and divergence between geometric and virtual counts of pointed curves with fixed complex structure in blow-ups of projective space, providing explicit formulas for toric cases via Jacobian integrals and computing virtual counts for using quantum cohomology.
This paper establishes the convergence of the expected signature of a generalized physical Brownian motion to a nontrivial tensor in the small mass limit () by analyzing a graded PDE system, revealing that the limit differs from the standard mathematical Brownian motion and exhibits explicit combinatorial patterns when the system's coefficient matrix is diagonalizable.
This paper introduces weighted Grassmann orbifolds via Plücker weight vectors, classifies them up to homeomorphism, establishes conditions for torsion-free integral cohomology, and explicitly computes their integral cohomology rings and equivariant structure constants.
This paper proposes a model predictive control policy for home battery management under tiered peak power charges that, using simple forecasts, achieves electricity costs within 1.7% of the theoretical minimum derived from perfect foresight.
This paper improves upon previous results by Heise et al. by proving that the weak chromatic number of -uniform hypergraphs arising from linearly or PL-embeddable simplicial complexes in is infinite for most dimensions and uniformities, and further extends these findings to show that the weak chromatic number of -dimensional faces in triangulations of any fixed triangulable -manifold is infinite for all $1 \le s \le d$.