Time crystalline structures are characterized by regularity that single-particle or many-body systems manifest in the time domain, closely resembling spatial of ordinary space crystals. Here we show and can be combined together even six-dimensional time-space lattices realized. As an example, demonstrate such reveal quantum Hall effect quantified third Chern number.

In recent years, interest has grown in modeling spatio-temporal data generated from monitoring networks, satellite imaging, and climate models. Under Gaussianity, the covariance function is core to modeling, inference, prediction. this article, we review various space-time structures which simplified assumptions, such as separability full symmetry, are made facilitate computation, associated te...