It is known that the superposition of two bound states in continuum (BICs) leads to phenomenon an oscillating state, where excitations mediated by modes oscillate persistently. We perform exact calculations for BICs a one-dimensional photonic lattice coupled ``giant atom'' at multiple points. Our work significantly distinct from previous proposals continuous waveguide systems due presence finit...

The Body Centered Cubic (BCe) and Face Centered Cubic (FCC) lattices along with a set of box splines for sampling and reconstruction of trivariate functions are proposed. The BCC lattice is demonstrated to be the optimal choice of a pattern for generic sampling purposes. While the FCC lattice is the second best choice for this purpose, both FCC and BCC lattices significantly outperform the accu...

Testing membership in lattices is of practical relevance, with applications to integer programming, error detection in lattice-based communication and cryptography. In this work, we initiate a systematic study of local testing for membership in lattices, complementing and building upon the extensive body of work on locally testable codes. In particular, we formally define the notion of local te...