The past few centuries have seen a great surge in our understanding and control of 'simple' physical, chemical, and biological processes through data analysis and mathematical modeling of their underlying dynamics. Encouraged by its success, researchers have recently embarked on extending such approaches to gain a qualitative and quantitative understanding of social and economic systems and the dynamics in and of them. This has become possible due to the massive amounts of data generated by information and communication technologies and the unprecedented fusion of off- and online human activity.

However, due to the presence of adaptability, feedback loops, and strong heterogeneity of the individuals and interactions making up our modern digital society, it is not yet clear if statistical ‘laws’ of socio-technical behavior even exist, akin to those found for natural processes. The continuing search has resulted in the fields of computational social science and social network science, which share the goal of first analyzing social phenomena and then modeling them with enough accuracy to make reliable predictions.

This Special Issue invites contributions to such fields of study, with an emphasis on the temporal evolution and dynamics of complex social systems. As topics of interest, we propose research on more realistic models of social dynamics, the use of statistical inference, machine learning, and other cross-disciplinary techniques to complement the analysis of social dynamics, and the creation of loops between data acquisition and model analysis to increase accuracy in the prediction of social trends. We hope this Special Issue will bring together expertise from a wide range of research communities interested in similar topics, including computational social science, network science, information science, and complexity science. We welcome original research and review articles focused on theoretical research results in the fields of computational mathematics, logic and mathematics of computer science, mathematical image and signal processing, and the application of related theoretical results.

Potential topics include but are not limited to the following:

• Computational mathematics
• Computer science of logic and mathematics
• Mathematical image and signal processing
• Mathematics in science and technology, industrial mathematics
• Numerical analysis and scientific computing
• Partial differential equations and their applications