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Abstract Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high-order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations. 

Here, we synthesized and characterized a novel two-dimensional (2D) conjugated electron donor–acceptor (D-A) copolymer (PBDB-T-Ge), wherein the substituent of triethyl germanium was added to the electron donor unit of the polymer. The Turbo–Grignard reaction was used to implement the group IV element into the polymer, resulting in a yield of 86%. This corresponding polymer, PBDB-T-Ge, exhibited a down-shift in the highest occupied molecular orbital (HOMO) level to −5.45 eV while the lowest unoccupied molecular orbital (LUMO) level was −3.64 eV. The peaks in UV-Vis absorption and the PL emission of PBDB-T-Ge were observed at 484 nm and 615 nm, respectively. 

Abstract PLATO (PLAnetary Transits and Oscillations of stars) is ESA’s M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2R$$_\textrm{Earth}$$ $_{\text{Earth}}^{}$) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5%, 10%, 10% for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO‘s target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile towards the end of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.