Research

The moduli space of curves is a cornerstone object in mathematics and theoretical physics, underpinning theories from Gromov–Witten invariants to string theory.  We identify a striking hidde n  regularity: The distribution of its Betti numbers converges to the Gaussian funct...

The Boussinesq equations describe fluid-buoyancy interactions generated by differences in temperature or density. This study classifies radially homogeneous stationary self-similar solutions of the two-dimensional Boussinesq equations in a half-plane. Depending on the range of the homogene...

Random quantum states have a wide range of applications in quantum information theory and quantum computing, but their exact implementation requiries substantial quantum resources. In this work, we show that state t-designs, a class of approximate random quantum states, can be generated wi...

This research deals with the Dirichlet problem for nonlocal stochastic partial differential equations posed on open domains. We consider substantially large classes of nonlocal operators and generalized noise. Furthermore, we develop a comprehensive framework that establishes not only the ...

A study investigating how sharp declines in international trade propagate and are suppressed has been published in Chaos, Solitons & Fractals. Using a hypergraph representation of international trade, the researchers analyzed collapse dynamics at the level of individual trade relations...

The authors show that the mean curvature flow of generic closed surfaces in R^3 avoids asymptotically conical and non-spherical compact singularities with multiplicitiy one. Also, the mean curvature flow of generic closed low-entropy hypersurfaces in R^4 is smooth until it disappears in a ...

A study extending the approximation theorem of the conventional Fourier Neural Operator to non-Markovian processes and proposing an improved architecture for this purpose has been published in the Journal of Scientific Computing. In this study, the research team demonstrated, based on the ...

To improve the efficiency of Monte Carlo integration, this study proposes a machine learning algorithm for stratified sampling that divides the domain space based on the integrand's value, analogous to Lebesgue integration. By utilizing neural networks to learn complex isocontours and prec...

This research presents a new analytical framework for nonlinear stochastic partial differential equations with nonlocal diffusion and spatially correlated noise. By introducing a new condition on the random noise correlation, it significantly enlarges the range of nonlinear phenomena that ...

This work mathematically characterizes the existence and properties of Magnetohydrostatic (MHS) equilibrium states via the vanishing resistivity limit of resistive magnetic relaxation equations subject to stochastic forcing. The "magnetic relaxation process" proposed by H. K. Moffatt is a ...