Many complex data analysis problems within and beyond the scientific domain involve discovering graphical structures and functional relationships within data. Nonlinear variance decomposition with ...

This study provides a computable, direct, and mathematically rigorous approximation to the differential geometry of class manifolds for high-dimensional data, along with non-linear projections from ...

The Kibble-Zurek mechanism (KZM) captures the essential physics of nonequilibrium quantum phase transitions with symmetry breaking. KZM predicts a universal scaling power law for the defect density ...