273 papers
This paper proves that alternating gradient descent with small random initialization converges linearly to the unique balanced factorization of a low-rank matrix, which minimizes the nuclear norm, by providing a rigorous analysis that clarifies why certain counterexamples do not apply and distinguishing this behavior from asymmetric or simultaneous gradient descent methods.
This study computationally validates a kinetic PDE derived from a stochastic reinforcement-learning model for market-entry games, demonstrating that while the equation accurately reproduces aggregate behaviors and weakens finite-player dependencies as population size grows, it exhibits specific limitations in capturing full individual distributions and long-term sorting dynamics, thereby establishing a clear map of its reliability as a surrogate for costly particle simulations.
This paper presents a novel delay differential equation model incorporating periodic contact rates, waning vaccine immunity, and temporary cross-immunity to analyze the transmission dynamics of COVID-19, demonstrating that disease eradication is achievable when the basic reproduction number falls below unity under specific parameter regimes.
This paper introduces a non-commutative version of the extended multistep Shanks transformation for sequences in associative non-commutative algebras, expressing it via quasideterminants and implementing it through generalized non-commutative E- and epsilon-algorithms, with applications demonstrated in solving matrix equations, series, and image reconstruction.
This paper develops a dependent portfolio risk model with a constant dividend barrier and extended-exponential premium income to derive Gerber-Shiu functions for mechanism-specific ruin probabilities, demonstrating through theoretical analysis and empirical application to French motor insurance that incorporating inter-claim duration dependence improves claim severity modeling and enhances ruin risk assessment.
This paper establishes a rigorous scaling theory for ordering in high-dimensional stochastic systems by decomposing Fisher information dynamics into exact terms, deriving sharp alignment bounds and fluctuation laws, and providing an exactly solvable multivariate Ornstein–Uhlenbeck benchmark that quantifies the efficiency of random shear contributions relative to isotropic and aligned limits.
This paper demonstrates that the cost convexity exponent fundamentally dictates the architecture of resistance-optimal networks, driving a transition from unique, fully connected dense structures under convex costs to sparse, loopless backbones under concave costs, with a critical collapse threshold that shifts with network size.
This paper demonstrates that while Pontryagin maximum principle-based optimal control yields better nominal performance for population-level depression interventions, a sliding-mode control strategy offers significantly superior robustness against parameter uncertainties and external disturbances, highlighting a critical trade-off between nominal efficiency and resilience in public health modeling.
This paper establishes the existence, uniqueness, and strong convergence rates of Euler-Maruyama approximations for a general class of path-dependent stochastic differential equations driven by weighted running extrema under non-Lipschitz Bihari-Osgood conditions.
This paper evaluates four continuous approximation methods for inverting Kepler's equation across varying eccentricities, demonstrating that while global polynomial methods achieve high accuracy at moderate eccentricities, adaptive quadratic splines outperform other approaches at high eccentricities, indicating that no single method is universally optimal for all accuracy measures and orbital conditions.