Formal autopoiesis: Solutions of the classical and extended functional closure equations.

Formalization of autopoiesis is an ongoing effort among theoretical biologists. In this field, Letelier and co-authors proposed that Robert Rosen's (M,R)-systems theory be used as a formalism for autopoiesis. In (M,R)-systems theory, Rosen proposes that one solve a set of functional closure equations (FCEs) which account for all of the components of the system as coming from within the system itself. A key part of the functional closure equations is the repair of the metabolism component of the system. Rosen's theory gives the organizational closure of the components as well as their products, as found in autopoiesis. However, according to Razeto-Barry (M,R)-systems leaves out some of the messiness and approximation that we find in autopoiesis as he reformulates it. A related problem is that though FCEs have a long history, they are difficult in practice to solve due to their mathematical formulation. In this paper we give a novel exact solution for the FCEs for continuous real vector-valued functions which is nevertheless difficult to compute. In addition we propose an extended form of FCEs which both captures more of the messiness of autopoiesis and also helps to make the FCEs more solvable. Finally, we use our solution for the extended FCEs to give an extended repair function for a metabolism taken from a representative class of biological dynamics for gene expression (the repressilator). More generally we show that one can use our solution for the extended FCEs to get an extended repair function for continuous real vector-valued functions.

System Integrated Information.

Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of consciousness (called a complex), which are then used to formulate a mathematical framework for assessing both the quality and quantity of experience. The explanatory identity proposed by IIT is that an experience is identical to the cause-effect structure unfolded from a maximally irreducible substrate (a Φ-structure). In this work we introduce a definition for the integrated information of a system (φs) that is based on the existence, intrinsicality, information, and integration postulates of IIT. We explore how notions of determinism, degeneracy, and fault lines in the connectivity impact system-integrated information. We then demonstrate how the proposed measure identifies complexes as systems, the φs of which is greater than the φs of any overlapping candidate systems.

Information Theory, Developmental Psychology, and the Baldwin Effect.

As part of the extended evolutionary synthesis, there has recently been a new emphasis on the effects of biological development on genetic inheritance and variation. The exciting new directions taken by those in the community have by a pre-history filled with related ideas that were never given a rigorous foundation or combined coherently. Part of the historical background of the extended synthesis is the work of James Mark Baldwin on his so-called "Baldwin Effect." Many variant re-interpretations of his work obscure the original meaning of the Baldwin Effect. This paper emphasizes a new approach to the Baldwin Effect, focusing on his work in developmental psychology and how that would impact evolution. We propose a novel population genetics model of the Baldwin Effect. First, the impact of a kind of learning process motivated by motor babbling, in the developmental psychology literature, on evolution; second, that Information-theoretic phenotype reshaping speeds up evolution compared to populations without this kind of learning. The basic idea behind the model is to allow the organism to apply abstraction to his initial phenotype to situate it within one of a few different classes of phenotypes in the local neighborhood of a fitness maximum. The reshaping of the phenotype space thereby allows the organism to reach a nearby fitness maximum. By so doing, valleys in the fitness landscape are leveled out, making a rugged fitness landscape into a set of mesas and plateaus with increasing height. Using this model we can show the first sizeable speed-up for the Baldwin Effect compared to ordinary population genetics. We also introduce an information-theoretic foundation for the Baldwin Effect, which may be of independent interest.

Process Information and Evolution.

Universal Semantic Communication (USC) is a theory that models communication among agents without the assumption of a fixed protocol. We demonstrate a connection, via a concept we refer to as process information, between a special case of USC and evolutionary processes. In this context, one agent attempts to interpret a potentially arbitrary signal produced within its environment. Sources of this effective signal can be modeled as a single alternative agent. Given a set of common underlying concepts that may be symbolized differently by different sources in the environment, any given entity must be able to correlate intrinsic information with input it receives from the environment in order to accurately interpret the ambient signal and ultimately coordinate its own actions. This scenario encapsulates a class of USC problems that provides insight into the semantic aspect of a model of evolution proposed by Rivoire and Leibler. Through this connection, we show that evolution corresponds to a means of solving a special class of USC problems, can be viewed as a special case of the Multiplicative Weights Updates algorithm, and that infinite population selection with no mutation and no recombination conforms to the Rivoire-Leibler model. Finally, using process information we show that evolving populations implicitly internalize semantic information about their respective environments.

Algorithms, games, and evolution.

Even the most seasoned students of evolution, starting with Darwin himself, have occasionally expressed amazement that the mechanism of natural selection has produced the whole of Life as we see it around us. There is a computational way to articulate the same amazement: "What algorithm could possibly achieve all this in a mere three and a half billion years?" In this paper we propose an answer: We demonstrate that in the regime of weak selection, the standard equations of population genetics describing natural selection in the presence of sex become identical to those of a repeated game between genes played according to multiplicative weight updates (MWUA), an algorithm known in computer science to be surprisingly powerful and versatile. MWUA maximizes a tradeoff between cumulative performance and entropy, which suggests a new view on the maintenance of diversity in evolution.

Nodal dynamics, not degree distributions, determine the structural controllability of complex networks.

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167-173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set, is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.