The practical difficulties in simulating many-body quantum systems such as molecules on classical computers based on central or graphics processing units, have been widely recognized in the quantum ...

Many ecological systems are subject critical transitions, which are abrupt changes to contrasting states triggered by small changes in some key component of the system. Temporal early warning signals ...

You can think of eigenvalues and their associated eigenvectors as a decomposition of a matrix. Eigenvalues and eigenvectors are needed for PCA. But computing eigenvalues and eigenvectors directly is ...