A combinatorial criterion for k-separability of multipartite Dicke states

We derive a combinatorial criterion for detecting k-separability of N-partite Dicke states. The criterion is efficiently computable and implementable without full state tomography. We give examples in which the criterion succeeds, where known criteria fail

Multiferroic and Ferroic Topological Order in Ligand-Functionalized Germanene and Arsenene

Two-dimensional (2D) materials that exhibit ferroelectric, ferromagnetic, or topological order have been a major focal topic of nanomaterials research in recent years. The latest efforts in this field explore 2D quantum materials that host multiferroic or concurrent ferroic and topological order. We present a computational discovery of multiferroic state with coexisting ferroelectric and ferromagnetic order in recently synthesized CH2OCH3-functionalized germanene. We show that an electric-field-induced rotation of the ligand CH2OCH3 molecule can serve as the driving mechanism to switch the electric polarization of the ligand molecule, while unpassivated Ge p(z) orbits generate ferromagnetism. Our study also reveals coexisting ferroelectric and topological order in ligand-functionalized arsenene, which possesses a switchable electric polarization and a Dirac transport channel. These findings offer insights into the fundamental physics underlying these coexisting quantum orders and open avenues for achieving states of matter with multiferroic or ferroic-topological order in 2D-layered materials for innovative memory or logic device implementations

A Composite Likelihood-based Approach for Change-point Detection in Spatio-temporal Process

This paper develops a unified, accurate and computationally efficient method for change-point inference in non-stationary spatio-temporal processes. By modeling a non-stationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameters estimation. Asymptotic theories including consistency and distribution of the estimators are derived under mild conditions. In contrast to classical results in fixed dimensional time series that the asymptotic error of change-point estimator is $O_{p}(1)$, exact recovery of true change-points is guaranteed in the spatio-temporal setting. More surprisingly, the consistency of change-point estimation can be achieved without any penalty term in the criterion function. A computational efficient pruned dynamic programming algorithm is developed for the challenging criterion optimization problem. Simulation studies and an application to U.S. precipitation data are provided to demonstrate the effectiveness and practicality of the proposed method