Approximation of smooth functionals using deep ReLU networks.

In recent years, deep neural networks have been employed to approximate nonlinear continuous functionals F defined on Lp([-1,1]s) for 1≤p≤∞. However, the existing theoretical analysis in the literature either is unsatisfactory due to the poor approximation results, or does not apply to the rectified linear unit (ReLU) activation function. This paper aims to investigate the approximation power of functional deep ReLU networks in two settings: F is continuous with restrictions on the modulus of continuity, and F has higher order Fréchet derivatives. A novel functional network structure is proposed to extract features of higher order smoothness harbored by the target functional F. Quantitative rates of approximation in terms of the depth, width and total number of weights of neural networks are derived for both settings. We give logarithmic rates when measuring the approximation error on the unit ball of a Hölder space. In addition, we establish nearly polynomial rates (i.e., rates of the form exp-a(logM)b with a>0,0

Role of the blue light receptor gene Icwc-1 in mycelium growth and fruiting body formation of Isaria cicadae.

The Isaria cicadae, is well known highly prized medicinal mushroom with great demand in food and pharmaceutical industry. Due to its economic value and therapeutic uses, natural sources of wild I. cicadae are over-exploited and reducing continuously. Therefore, commercial cultivation in controlled environment is an utmost requirement to fulfill the consumer's demand. Due to the lack of knowledge on fruiting body (synnemata) development and regulation, commercial cultivation is currently in a difficult situation. In the growth cycle of macrofungi, such as mushrooms, light is the main factor affecting growth and development, but so far, specific effects of light on the growth and development of I. cicadae is unknown. In this study, we identified a blue light receptor white-collar-1 (Icwc-1) gene homologue with well-defined functions in morphological development in I. cicadae based on gene knockout technology and transcriptomic analysis. It was found that the Icwc-1 gene significantly affected hyphal growth and fruiting body development. This study confirms that Icwc-1 acts as an upstream regulatory gene that regulates genes associated with fruiting body formation, pigment-forming genes, and related genes for enzyme synthesis. Transcriptome data analysis also found that Icwc-1 affects many important metabolic pathways of I. cicadae, i.e., amino acid metabolism and fatty acid metabolism. The above findings will not only provide a comprehensive understanding about the molecular mechanism of light regulation in I. cicadae, but also provide new insights for future breeding program and improving this functional food production.