Abstract
We introduce a conceptual framework and an interventional calculus to steer, manipulate, reconstruct the dynamics and produce generating mechanisms of dynamic systems from observations based on the evolution and contribution of each of the system’s components to their intrinsic algorithmic complexity exploiting universal principles from the theory of computability and algorithmic information. This calculus consists in finding and applying controlled interventions to a system/network to estimate how their algorithmic information content is affected in terms of positive or negative shifts towards and away from randomness. We find that the algorithmic information landscape of a system’s degree of freedom runs in parallel to its dynamic space-time evolution providing a path to move systems on the algorithmic information landscape having effects on the system’s dynamics landscape. Based on this causal algorithmic calculus, we advance methods for reprogramming systems that do not require the full knowledge or access to the system’s actual kinetic equations or probability distributions. This new dimension unmasks a separation between components providing a suite of powerful parameter-free algorithms of wide applicability ranging from causal discovery, dimension reduction, feature selection, model generation, maximal randomness analysis and system’s control in application to molecular biology and genetic regulatory networks. We find that the methods can identify key elements on static and dynamic regulatory networks related to function and cell development and a correspondence between the elements moving the network towards and away from randomness with the capabilities of the represented cell to be reprogrammed conforming with the biological knowledge of cell differentiation demonstrating how this causal calculus can help reshape a system’s dynamics in a controlled manner by manipulating its generating mechanisms by way of its algorithmic content.