We consider here a large-scale social network with a continuous response observed for each node at equally spaced time points. The responses from different nodes constitute an ultra-high dimensional vector, whose time series dynamic is to be investigated. In addition, the network structure is also taken into consideration, for which we propose a network vector autoregressive (NAR) model. The NAR model assumes each node's response at a given time point as a linear combination of (a) its previous value, (b) the average of its connected neighbors, (c) a set of node-specific covariates and (d) an independent noise. The corresponding coefficients are referred to as the momentum effect, the network effect and the nodal effect, respectively. Conditions for strict stationarity of the NAR models are obtained. In order to estimate the NAR model, an ordinary least squares type estimator is developed, and its asymptotic properties are investigated. We further illustrate the usefulness of the NAR model through a number of interesting potential applications. Simulation studies and an empirical example are presented.

which is located in the near-infrared and visible region. [9] Bandgaps in TMDCs are tunable by applying external electric field or mechanical strain. Combined with broad-band optical absorption and mechanical flexibility, TMDCs are one of appealing materials for the application in optoelectronic devices such as field effect transistors, photodetectors, and light-emitting diodes. Photodetectors based on molybdenum disulfide (MoS 2 ), [1,3] tungsten disulfide (WS 2 ), [10,11] molybdenum diselenide (MoSe 2 ), [7,8] and their heterojunctions [12] were constructed and exhibited photoresponsivity ranging from a few mA W −1 to several hundred A W −1 , which is related to the materials selected, layer numbers, and device contacts. Intrinsically, the photoresponsivity is restricted by their absorption cross section and present lower values because of small thickness of TMDCs. [9] Integration of TMDC materials into photonic structures such as photonic crystals and microcavities offers a solution to enhance the photoresponsivity. [13][14][15] For example, Fano-resonant photonic crystals could significantly boost light absorption in monolayer MoS 2 and the absorption can reach up to 90% at the resonant wavelength. [13] Another typical approach to enhancing photoresponsivity is to hybridize TMDCs with plasmonic structures. A MoS 2 photodetector hybridized with Ag nanowire network was demonstrated and presented greatly enhanced photocurrent over the pristine MoS 2 photodetectors because of surface plasmon coupling. [5] However, the photoresponsivity can be only enhanced at designed and selected wavelength in these hybrid photodetectors mentioned above. It is promising that 3D mesostructures could enhance light absorption over wide range due to its circular geometry and thus improve photoelectric performance. [16][17][18][19] Rolled-up inorganic nanomembrane-based 3D architectures, [20][21][22] such as nanoscrolls and nanosprings, have great potential in applications of supercapacitors, [23] optical microcavity, [24][25][26] actuators, [27,28] resistive random access memory, [29] motors, [30] etc., because of their distinct properties arising from 3D geometry. In this work, a 3D tubular photodetector is proposed to increase the photoresponsivity of 2D materials benefiting from the significantly enhanced light absorption. We introduce this tubular microstructure into the MoSe 2based photodetector for improved detection performance. 3D photodetector based on rolled-up MoSe 2 nanomembrane was Transition metal dichalcogenides, as a kind of 2D material, are suitable for near-infrared to visible photodetection owing to the bandgaps ranging from 1.0 to 2.0 eV. However, limited light absorption restricts photoresponsivity due to the ultrathin thickness of 2D materials. 3D tubular structures offer a solution to solve the problem because of the light trapping effect which can enhance optical absorption. In this work, thanks to mechanical flexibility of 2D materials, self-rolled-up technology is applied to build up a 3D tubular structure ...

We consider here a large-scale social network with a continuous response observed for each node at equally spaced time points. The responses from different nodes constitute an ultra-high dimensional vector, whose time series dynamic is to be investigated. In addition, the network structure is also taken into consideration, for which we propose a network vector autoregressive (NAR) model. The NAR model assumes each node's response at a given time point as a linear combination of (a) its previous value, (b) the average of its connected neighbors, (c) a set of node-specific covariates and (d) an independent noise. The corresponding coefficients are referred to as the momentum effect, the network effect and the nodal effect, respectively. Conditions for strict stationarity of the NAR models are obtained. In order to estimate the NAR model, an ordinary least squares type estimator is developed, and its asymptotic properties are investigated. We further illustrate the usefulness of the NAR model through a number of interesting potential applications. Simulation studies and an empirical example are presented.

Memristive devices have been widely employed to emulate biological synaptic behavior. In these cases, the memristive switching generally originates from electrical field induced ion migration or Joule heating induced phase change. In this letter, the Ti/ZnO/Pt structure was found to show memristive switching ascribed to a carrier trapping/detrapping of the trap sites (e.g., oxygen vacancies or zinc interstitials) in ZnO. The carrier trapping/detrapping level can be controllably adjusted by regulating the current compliance level or voltage amplitude. Multi-level conductance states can, therefore, be realized in such memristive device. The spike-timing-dependent plasticity, an important Hebbian learning rule, has been implemented in this type of synaptic device. Compared with filamentary-type memristive devices, purely electronic memristors have potential to reduce their energy consumption and work more stably and reliably, since no structural distortion occurs.