Black-boxing and cause-effect power

Reductionism assumes that causation in the physical world occurs at the micro level, excluding the emergence of macro-level causation. We challenge this reductionist assumption by employing a principled, well-defined measure of intrinsic cause-effect power - integrated information ({\Phi}), and showing that, according to this measure, it is possible for a macro level to "beat" the micro level. Simple systems were evaluated for {\Phi} across different spatial and temporal scales by systematically considering all possible black boxes. These are macro elements that consist of one or more micro elements over one or more micro updates. Cause-effect power was evaluated based on the inputs and outputs of the black boxes, ignoring the internal micro elements that support their input-output function. We show how black-box elements can have more common inputs and outputs than the corresponding micro elements, revealing the emergence of high-order mechanisms and joint constraints that are not apparent at the micro level. As a consequence, a macro, black-box system can have higher {\Phi} than its micro constituents by having more mechanisms (higher composition) that are more interconnected (higher integration). We also show that, for a given micro system, one can identify local maxima of {\Phi} across several spatiotemporal scales. The framework is demonstrated on a simple biological system, the Boolean network model of the fission-yeast cell-cycle, for which we identify stable local maxima during the course of its simulated biological function. These local maxima correspond to macro levels of organization at which emergent cause-effect properties of physical systems come into focus, and provide a natural vantage point for scientific inquiries.Comment: 45 pages (32 main text, 13 supplementary), 14 figures (9 main text, 5 supplementary

Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of individual properties. On the other hand, causality can exhibit emergence, meaning that new causal laws may arise as we increase the level of abstraction. Causal emergence theory aims to bridge these two concepts and even employs measures of causality to quantify emergence. This paper provides a comprehensive review of recent advancements in quantitative theories and applications of causal emergence. Two key problems are addressed: quantifying causal emergence and identifying it in data. Addressing the latter requires the use of machine learning techniques, thus establishing a connection between causal emergence and artificial intelligence. We highlighted that the architectures used for identifying causal emergence are shared by causal representation learning, causal model abstraction, and world model-based reinforcement learning. Consequently, progress in any of these areas can benefit the others. Potential applications and future perspectives are also discussed in the final section of the review.Comment: 57 pages, 17 figures, 1 tabl

Stock-Flow Dynamic Projection

Borrowing from our experience in agent-based computational economic research from `bottom-up', this paper considers economic system as multi-level dynamical system that micro-level agents' interaction leads to structural transition in meso-level, which results in macro-level market dynamics with endogenous fluctuation or even market crashes. By the concept of transition matrix, we develop technique to quantify meso-level structural change induced by micro-level interaction. Then we apply this quantification to propose the method of dynamic projection that delivers out-of-sample forecast of macro-level economic variable from micro-level big data. We testify this method with a data set of financial statements for 4599 firms listed in Tokyo Stock Exchange for the year of 1980 to 2012. The Diebold-Mariano test indicates that the dynamic projection has significantly higher accuracy for one-period-ahead out-of-sample forecast than the benchmark of ARIMA models

Reduktion der Evolutionsgleichungen in Banach-Räumen

In this thesis we analyze lumpability of infinite dimensional dynamical systems. Lumping is a method to project a dynamics by a linear reduction operator onto a smaller state space on which a self-contained dynamical description exists. We consider a well-posed dynamical system defined on a Banach space X and generated by an operator F, together with a linear and bounded map M : X → Y, where Y is another Banach space. The operator M is surjective but not an isomorphism and it represents a reduction of the state space. We investigate whether the variable y = M x also satisfies a well-posed and self-contained dynamics on Y . We work in the context of strongly continuous semigroup theory. We first discuss lumpability of linear systems in Banach spaces. We give conditions for a reduced operator to exist on Y and to describe the evolution of the new variable y . We also study lumpability of nonlinear evolution equations, focusing on dissipative operators, for which some interesting results exist, concerning the existence and uniqueness of solutions, both in the classical sense of smooth solutions and in the weaker sense of strong solutions. We also investigate the regularity properties inherited by the reduced operator from the original operator F . Finally, we describe a particular kind of lumping in the context of C*-algebras. This lumping represents a different interpretation of a restriction operator. We apply this lumping to Feller semigroups, which are important because they can be associated in a unique way to Markov processes. We show that the fundamental properties of Feller semigroups are preserved by this lumping. Using these ideas, we give a short proof of the classical Tietze extension theorem based on C*-algebras and Gelfand theory