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We propose a program for a computational analysis, based on large scale datasets, of deep conceptual and formal structures, representing the mechanisms of historical transformations in different domains ranging from biological to social, cultural, and knowledge systems. We conceptualize such systems as consisting of complex multi-layer networks. Structural properties of such networks may explain the spreading of innovations. Temporal relations between the dynamics of interacting networks may help to identify causalities. Complex systems may show path and context dependencies. We illustrate our approach by case studies from all those types of systems.