173 papers
The paper introduces FMint-SDE, a multimodal foundation model based on decoder-only transformers that leverages in-context learning and error correction to provide a general-purpose, efficient, and accurate solution for simulating stochastic differential equations across diverse scientific domains.
This paper introduces a novel approach using disintegration maps to establish criteria for identifying metric measure foliations based on the geometric arrangement of conditional measure supports in Wasserstein space, while also demonstrating the framework's application to studying perturbations of such foliations.
This paper introduces the concept of (W')-specification to prove that recurrence sets in a broad class of subshifts and piecewise expanding interval maps, which lack the standard specification property, possess full Hausdorff dimension.
This paper provides a complete symplectic-topological classification of periodic orbits in the spatial rotating Kepler problem by introducing a new coordinate system based on the Laplace-Runge-Lenz vector, computing their Conley-Zehnder and Robbin-Salamon indices, and determining their contributions to symplectic homology via the Morse-Bott spectral sequence.
This paper introduces the concept of "zippers" as a novel and streamlined method for constructing universal circles—key dynamical structures associated with hyperbolic 3-manifolds—by deriving them directly from uniform quasimorphisms or uniform left orders.
This paper establishes necessary and sufficient conditions for the input-to-state stability (ISS) of impulsive switched systems with both stable and unstable modes by introducing time-varying ISS-Lyapunov functions under relaxed mode-dependent average dwell and leave time constraints, while also providing methods to construct decreasing Lyapunov functions and guarantee ISS even with unknown switching signals.
This paper establishes a principled dynamical theory for sequential retrieval in input-driven Hopfield networks by deriving explicit mathematical conditions for self-sustained memory transitions within a two-timescale architecture, thereby bridging classical associative memory models with modern reasoning systems.
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 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 establishes a converse Lyapunov theorem for the boundedness of reachability sets in infinite-dimensional systems with Lipschitz continuous flows, demonstrating its applicability to semi-linear evolution equations and deriving a result for forward completeness in ordinary differential equations without restricting input magnitudes.
This paper develops and analyzes mathematical models based on logistic equations and the Linear Quadratic model to demonstrate how optimal control theory can improve radiotherapy strategies by reducing tumor burden while minimizing damage to healthy tissue compared to constant radiation approaches.
This paper establishes the existence, uniqueness, boundedness, and global stability of solutions for a Cauchy problem involving a non-homogeneous first-order differential equation with Krasnoselskii-Pokrovskii hysteresis, specifically analyzing its application to inversion-free feedforward control in magnetic shape memory alloy actuators through theoretical theorems and numerical examples.
This paper proves Lubin's conjecture in new cases by demonstrating that over -tame extensions, the consistent sequences associated with a commuting pair of noninvertible and invertible height-one formal power series form a crystalline character of weight 1.
This paper employs rigorous topological-numerical methods, specifically Morse decomposition and Conley index computations, to analyze the global dynamics of a discrete-time two-gene Andrecut-Kauffman model, revealing complex phenomena such as multistability and chaotic attractors across a wide range of parameters.
This paper presents a Monte Carlo-based computational framework to analyze the steady-state distributions and stability of random differential equations with uncertain, multi-modal parameters, demonstrating its efficacy through a Rosenzweig-MacArthur predator-prey model that reveals complex, multi-modal equilibrium behaviors.
This paper investigates the Equi-Baire one property for families of Möbius transformations, demonstrating that iterates of loxodromic maps form such a family on their attracting basins and establishing that a one-parameter subgroup satisfies this condition on all compact sets if and only if it is relatively compact in .
This paper establishes a variational principle for holomorphic correspondences on the Riemann sphere by defining their measure-theoretic entropy and using it to formulate the pressure of continuous functions, analogous to the theory for continuous maps on compact metric spaces.
This paper proposes an SEIRV epidemic model with relapse and intervention to analyze malware propagation dynamics, establish stability conditions, identify key influencing parameters, and optimize cost-effective control strategies using a hybrid gradient-based framework calibrated with real-world infection data.
This paper generalizes the Duffin–Schaeffer theorem to real residue systems by establishing a zero-one law for inhomogeneous approximation based on the parameter's membership in specific sets, utilizing novel results on the distribution of primes in Bohr sets and the equidistribution of circle rotations.
This paper establishes that for a generic set of finite-dimensional irreducible representations of the fundamental group of a surface's unit tangent bundle, the twisted Ruelle zeta function either vanishes at zero with an order determined by the genus or equals the Reidemeister--Turaev torsion, thereby extending Fried's conjecture to generic acyclic representations and confirming the constancy of the vanishing order for untwisted zeta functions across a dense set of Anosov metrics.