The Hippo pathway controls developmental, homeostatic and regenerative tissue growth, and is frequently dysregulated in various diseases. Although this pathway can be activated by innate immune/inflammatory stimuli, the underlying mechanism is not fully understood. Here, we identify a conserved signaling cascade that leads to Hippo pathway activation by innate immune/inflammatory signals. We show that Tak1, a key kinase in innate immune/inflammatory signaling, activates the Hippo pathway by inducing the lysosomal degradation of Cka, an essential subunit of the STRIPAK PP2A complex that suppresses Hippo signaling. Suppression of STRIPAK results in the activation of Hippo pathway through Tao-Hpo signaling. We further show that Tak1-mediated Hippo signaling is involved in processes ranging from cell death to phagocytosis and innate immune memory. Our findings thus reveal a molecular connection between innate immune/inflammatory signaling and the evolutionally conserved Hippo pathway, thus contributing to our understanding of infectious, inflammatory and malignant diseases.

Biconvex programming (or inequality constrained biconvex optimization) is an important model in solving many engineering optimization problems in areas like machine learning and signal and information processing. In this paper, the partial exactness of the partial optimum for the penalty function of biconvex programming is studied. The penalty function is partially exact if the partial Karush–Kuhn–Tucker (KKT) condition is true. The sufficient and necessary partially local stability condition used to determine whether the penalty function is partially exact for a partial optimum solution is also proven. Based on the penalty function, an algorithm is presented for finding a partial optimum solution to an inequality constrained biconvex optimization, and its convergence is proven under some conditions.

This paper focuses on the role of local governments in the development of tourism in China by examining 30 Chinese provinces from 2000 to 2018. The results of empirical research show that fiscal decentralization in China provides local governments with incentives for the development of high pollution industries and of large state-owned enterprises, which do not help the sustainable development of tourism. In addition, there is an “inverted U-shaped” relationship between pollution level and tourism development. Although the growth of China’s tourism industry is pollution-based currently, tourism revenue is considered to decline once a threshold is reached. The competition from local governments for foreign investment is conducive to the improvement of environmental quality and increase in tourism revenue. Based on this, we have proposed a series of sustainable tourism development measures.