Emergence and causality are two fundamental concepts for understanding complex
systems. They are interconnected. On one hand, emergence refers to the phenomenon …

Despite the near universal assumption of individuality in biology, there is little agreement
about what individuals are and few rigorous quantitative methods for their identification …

The open-endedness of a system is often defined as a continual production of novelty. Here
we pin down this concept more fully by defining several types of novelty that a system may …

Information processing in neural systems can be described and analyzed at multiple
spatiotemporal scales. Generally, information at lower levels is more fine-grained but can be …

Reductionism assumes that causation in the physical world occurs at the micro level,
excluding the emergence of macro-level causation. We challenge this reductionist …

We introduce a notion of emergence for macroscopic variables associated with highly
multivariate microscopic dynamical processes. Dynamical independence instantiates the …

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 …

This book provides an introduction to and an overview of the most important concepts and
structures of modern mathematics. Therefore, I try to motivate and explain those concepts …

Virtually all questions that one can ask about the behavioral and structural complexity of a
stochastic process reduce to a linear algebraic framing of a time evolution governed by an …

This paper investigates the concept of reproduction in an evolutionary context. It draws a
distinction between objects that are reproduced (reproducees), objects that reproduce …