Device-to-Device (D2D) communications make highspeed multicast services possible since the multicast receivers with poor downlink channel conditions can be retransmitted by devices nearby via D2D links. In this paper, we consider how to efficiently use D2D communications to help enhance the quality of wireless multicast services in cellular networks. To achieve this, a dynamic D2D retransmission scheme with maximized utility is proposed, which can adaptively select the retransmission algorithm according to the state of the network load. Through both analysis and simulations, we show that our algorithms achieve a significant gain in terms of utility, and reduce the burden of the base station (BS).
It is one of the fundamental and challenging problems to determine the node numbers of hidden layers in neural networks. Various efforts have been made to study the relations between the approximation ability and the number of hidden nodes of some specific neural networks, such as single-hidden-layer and two-hiddenlayer feedforward neural networks with specific or conditional activation functions. However, for arbitrary feedforward neural networks, there are few theoretical results on such issues. This paper gives an upper bound on the node number of each hidden layer for the most general feedforward neural networks called multilayer perceptrons (MLP), from an algebraic point of view. First, we put forward the method of expansion linear spaces to investigate the algebraic structure and properties of the outputs of MLPs. Then it is proved that given k distinct training samples, for any MLP with k nodes in each hidden layer, if a certain optimization problem has solutions, the approximation error keeps invariant with adding nodes to hidden layers. Furthermore, it is shown that for any MLP whose activation function for the output layer is bounded on R, at most k hidden nodes in each hidden layer are needed to learn k training samples.
The central dogma of genetics, which outlines the flow of genetic information from DNA to RNA to protein, has long been the guiding principle in molecular biology. In fact, more than three-quarters of the RNAs produced by transcription of the plant genome are not translated into proteins, and these RNAs directly serve as non-coding RNAs in the regulation of plant life activities at the molecular level. The breakthroughs in high-throughput transcriptome sequencing technology and the establishment and improvement of non-coding RNA experiments have now led to the discovery and confirmation of the biogenesis, mechanisms, and synergistic effects of non-coding RNAs. These non-coding RNAs are now predicted to play important roles in the regulation of gene expression and responses to stress and evolution. In this review, we focus on the synthesis, and mechanisms of non-coding RNAs, and we discuss their impact on gene regulation in plants.
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