Scientists have made efforts to understand the beauty of painting art in their own languages. As digital image acquisition of painting arts has made rapid progress, researchers have come to a point where it is possible to perform statistical analysis of a large-scale database of artistic paints to make a bridge between art and science. Using digital image processing techniques, we investigate three quantitative measures of images – the usage of individual colors, the variety of colors, and the roughness of the brightness. We found a difference in color usage between classical paintings and photographs, and a significantly low color variety of the medieval period. Interestingly, moreover, the increment of roughness exponent as painting techniques such as chiaroscuro and sfumato have advanced is consistent with historical circumstances.

Social reinforcement and modular structure are two salient features observed in the spreading of behavior through social contacts. In order to investigate the interplay between these two features, we study the generalized epidemic process on modular networks with equal-sized finite communities and adjustable modularity. Using the analytical approach originally applied to clique-based random networks, we show that the system exhibits a bond-percolation type continuous phase transition for weak social reinforcement, whereas a discontinuous phase transition occurs for sufficiently strong social reinforcement. Our findings are numerically verified using the finite-size scaling analysis and the crossings of the bimodality coefficient.

We consider inventions as novel combinations of existing technological capabilities. Patent data allow us to explicitly identify such combinatorial processes in invention activities (Youn et al. in J R Soc Interface 12:20150272, 2015). Unconsidered in the previous research, not every new combination is novel to the same extent. Some combinations are naturally anticipated based on patent activities in the past or mere random choices, and some appear to deviate exceptionally from existing invention pathways. We calculate a relative likelihood that each pair of classification codes is put together at random, and a deviation from the empirical observation so as to assess the overall novelty (or conventionality) that the patent brings forth at each year. An invention is considered as unconventional if a pair of codes therein is unlikely to be used together given the statistics in the past. Temporal evolution of the distribution indicates that the patenting activities become more conventional with occasional cross-over combinations. Our analyses show that patents introducing novelty on top of the conventional units would receive higher citations, and hence have higher impact.