The recent success of organometallic halide perovskites (OHPs) in photovoltaic devices has triggered lots of corresponding research and many perovskite analogues have been developed to look for devices with comparable performance but better stability. Upon the preparation of all inorganic halide perovskite nanocrystals (IHP NCs), research activities have soared due to their better stability, ultrahigh photoluminescence quantum yield (PL QY), and composition dependent luminescence covering the whole visible region with narrow line-width. They are expected to be promising materials for next generation lighting and display, and many other applications. Within two years, a lot of interesting results have been observed. Here, the synthesis of IHPs is reviewed, and their progresses in optoelectronic devices and optical applications, such as light-emitting diodes (LEDs), photodetectors (PDs), solar cells (SCs), and lasing, is presented. Information and recent understanding of their crystal structures and morphology modulations are addressed. Finally, a brief outlook is given, highlighting the presently main problems and their possible solutions and future development directions.

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Networks form the backbone of many complex systems, ranging from the Internet to human societies. Accordingly, not only is the range of our interactions limited and thus best described and modeled by networks, it is also a fact that the networks that are an integral part of such models are often interdependent or even interconnected. Networks of networks or multilayer networks are therefore a more apt description of social systems. This colloquium is devoted to evolutionary games on multilayer networks, and in particular to the evolution of cooperation as one of the main pillars of modern human societies. We first give an overview of the most significant conceptual differences between single-layer and multilayer networks, and we provide basic definitions and a classification of the most commonly used terms. Subsequently, we review fascinating and counterintuitive evolutionary outcomes that emerge due to different types of interdependencies between otherwise independent populations. The focus is on coupling through the utilities of players, through the flow of information, as well as through the popularity of different strategies on different network layers. The colloquium highlights the importance of pattern formation and collective behavior for the promotion of cooperation under adverse conditions, as well as the synergies between network science and evolutionary game theory.

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In this article, we address the problem of safety verification of nonlinear hybrid systems. A hybrid symbolicnumeric method is presented to compute exact inequality invariants of hybrid systems efficiently. Some numerical invariants of a hybrid system can be obtained by solving a bilinear SOS programming via the PENBMI solver or iterative method, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact polynomial invariants with rational coefficients, which exactly satisfy the conditions of invariants. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.