Complexity and Evolution.

Understanding the underlying structure of evolutionary processes is one the most important issues of scientific enquiry of this century [...].

Modelling Worldviews as Stable Metabolisms.

The emergence and evolution of worldviews is a complex phenomenon that requires strong and rigorous scientific attention in our hyperconnected world. On the one hand, cognitive theories have proposed reasonable frameworks but have not reached general modeling frameworks where predictions can be tested. On the other hand, machine-learning-based applications perform extremely well at predicting outcomes of worldviews, but they rely on a set of optimized weights in a neural network that does not comply to a well-founded cognitive framework. In this article, we propose a formal approach used to investigate the establishment of and change in worldviews by recalling that the realm of ideas, where opinions, perspectives and worldviews are shaped, resemble, in many ways, a metabolic system. We propose a general modelization of worldviews based on reaction networks, and a specific starting model based on species representing belief attitudes and species representing belief change triggers. These two kinds of species combine and modify their structures through the reactions. We show that chemical organization theory combined with dynamical simulations can illustrate various interesting features of how worldviews emerge, are maintained and change. In particular, worldviews correspond to chemical organizations, meaning closed and self-producing structures, which are generally maintained by feedback loops occurring within the beliefs and triggers in the organization. We also show how, by inducing the external input of belief change triggers, it is possible to change from one worldview to another, in an irreversible way. We illustrate our approach with a simple example reflecting the formation of an opinion and a belief attitude about a theme, and, next, show a more complex scenario containing opinions and belief attitudes about two possible themes.

Goals as Emergent Autopoietic Processes.

While the phenomena of reaching a goal is generally represented in the framework of optimization, the phenomena of becoming of a goal is more similar to a "self-organization and emergent" rather than an "optimization and preexisting" process. In this article we provide a modeling framework for the former alternative by representing goals as emergent autopoietic structures. In order to conceptually situate our approach, we first review some of the most remarkable attempts to formally define emergence, and identify that in most cases such definitions rely on a preexisting system to be observed prior and post emergence, being thus inadequate for a formalization of emergent goals corresponding to the becoming of a systems as such (e.g. emergence of life). Next, we review how an implementation of the reaction networks framework, known as Chemical Organization Theory (COT), can be applied to formalize autopoietic structures, providing a basis to operationalize goals as an emergent process. We next revisit the definitions of emergence under the light of our approach, and demonstrate that recent taxonomies developed to classify different forms of emergence can be naturally deduced from recent work aimed to explain the kinds of changes of the organizational structure of a reaction network.

Goal Directedness, Chemical Organizations, and Cybernetic Mechanisms.

In this article, we attempt at developing a scenario for the self-organization of goal-directed systems out of networks of (chemical) reactions. Related scenarios have been proposed to explain the origin of life starting from autocatalytic sets, but these sets tend to be too unstable and dependent on their environment to maintain. We apply instead a framework called Chemical Organization Theory (COT), which shows mathematically under which conditions reaction networks are able to form self-maintaining, autopoietic organizations. We introduce the concepts of perturbation, action, and goal based on an operationalization of the notion of change developed within COT. Next, we incorporate the latter with notions native to the theory of cybernetics aimed to explain goal directedness: reference levels and negative feedback among others. To test and refine these theoretical results, we present some examples that illustrate our approach. We finally discuss how this could result in a realistic, step-by-step scenario for the evolution of goal directedness, thus providing a theoretical solution to the age-old question of the origins of purpose.

Beyond planetary-scale feedback self-regulation: Gaia as an autopoietic system.

The Gaia hypothesis states that the Earth is an instance of life. However, appraisals of it tend to focus on the claim that life is a feedback self-regulator that controls Earth's chemistry and climate dynamics, yet, self-regulation by feedbacks is not a definitive characteristic of living systems. Here, we consider the characterization of biological systems as autopoietic systems (causally organized to self-produce through metabolic efficient closure) and then ask whether the Gaia hypothesis is a tractable question from this standpoint. A proof-of-concept based on Chemical Organization Theory (COT) and the Zero Deficiency Theorem (ZDT) applied on a simple but representative Earth's molecular reaction network supports the thesis of Gaia as an autopoietic system. We identify the formation of self-producing organizations within the reaction network, corresponding to recognizable scenarios of Earth's history. These results provide further opportunities to discuss how the instantiation of autopoiesis at the planetary scale could manifests central features of biological phenomenon, such as autonomy and anticipation, and what this implies for the further development of the Gaia theory, Earth's climate modelling and geoengineering.

Spin and Wind Directions I: Identifying Entanglement in Nature and Cognition.

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell's inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics laboratories. This is the first part of a two-part article. In the second part (Aerts et al. in Found Sci, 2017) we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space.

Spin and Wind Directions II: A Bell State Quantum Model.

In the first half of this two-part article (Aerts et al. in Found Sci. doi:10.1007/s10699-017-9528-9, 2017b), we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell's inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms.

Unitary Transformations in the Quantum Model for Conceptual Conjunctions and Its Application to Data Representation.

Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations.

Quantum structure of negation and conjunction in human thought.

We analyze in this paper the data collected in a set of experiments investigating how people combine natural concepts. We study the mutual influence of conceptual conjunction and negation by measuring the membership weights of a list of exemplars with respect to two concepts, e.g., Fruits and Vegetables, and their conjunction Fruits And Vegetables, but also their conjunction when one or both concepts are negated, namely, Fruits And Not Vegetables, Not Fruits And Vegetables, and Not Fruits And Not Vegetables. Our findings sharpen and advance existing analysis on conceptual combinations, revealing systematic deviations from classical (fuzzy set) logic and probability theory. And, more important, our results give further considerable evidence to the validity of our quantum-theoretic framework for the combination of two concepts. Indeed, the representation of conceptual negation naturally arises from the general assumptions of our two-sector Fock space model, and this representation faithfully agrees with the collected data. In addition, we find a new significant and a priori unexpected deviation from classicality, which can exactly be explained by assuming that human reasoning is the superposition of an "emergent reasoning" and a "logical reasoning," and that these two processes are represented in a Fock space algebraic structure.

Effects of small particle numbers on long-term behaviour in discrete biochemical systems.

MOTIVATION: The functioning of many biological processes depends on the appearance of only a small number of a single molecular species. Additionally, the observation of molecular crowding leads to the insight that even a high number of copies of species do not guarantee their interaction. How single particles contribute to stabilizing biological systems is not well understood yet. Hence, we aim at determining the influence of single molecules on the long-term behaviour of biological systems, i.e. whether they can reach a steady state. RESULTS: We provide theoretical considerations and a tool to analyse Systems Biology Markup Language models for the possibility to stabilize because of the described effects. The theory is an extension of chemical organization theory, which we called discrete chemical organization theory. Furthermore we scanned the BioModels Database for the occurrence of discrete chemical organizations. To exemplify our method, we describe an application to the Template model of the mitotic spindle assembly checkpoint mechanism. AVAILABILITY AND IMPLEMENTATION: http://www.biosys.uni-jena.de/Services.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Reaction networks and evolutionary game theory.

The powerful mathematical tools developed for the study of large scale reaction networks have given rise to applications of this framework beyond the scope of biochemistry. Recently, reaction networks have been suggested as an alternative way to model social phenomena. In this "socio-chemical metaphor" molecular species play the role of agents' decisions and their outcomes, and chemical reactions play the role of interactions among these decisions. From here, it is possible to study the dynamical properties of social systems using standard tools of biochemical modelling. In this work we show how to use reaction networks to model systems that are usually studied via evolutionary game theory. We first illustrate our framework by modeling the repeated prisoners' dilemma. The model is built from the payoff matrix together with assumptions of the agents' memory and recognizability capacities. The model provides consistent results concerning the performance of the agents, and allows for the examination of the steady states of the system in a simple manner. We further develop a model considering the interaction among Tit for Tat and Defector agents. We produce analytical results concerning the performance of the strategies in different situations of agents' memory and recognizability. This approach unites two important theories and may produce new insights in classical problems such as the evolution of cooperation in large scale systems.

Cycles and the qualitative evolution of chemical systems.

Cycles are abundant in most kinds of networks, especially in biological ones. Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on the stability of these compositions. While it is accepted that, from a topological standpoint, they enhance network robustness, the consequence of cycles to the dynamics are not well understood. In a former study, we developed a necessary criterion for the existence of a fixed point, which is purely based on topological properties of the network. The structures of interest we identified were a generalization of closed autocatalytic sets, called chemical organizations. Here, we show that the existence of these chemical organizations and therefore steady states is linked to the existence of cycles. Importantly, we provide a criterion for a qualitative transition, namely a transition from one self-sustaining set of molecular species to another via the introduction of a cycle. Because results purely based on topology do not yield sufficient conditions for dynamic properties, e.g. stability, other tools must be employed, such as analysis via ordinary differential equations. Hence, we study a special case, namely a particular type of reflexive autocatalytic network. Applications for this can be found in nature, and we give a detailed account of the mitotic spindle assembly and spindle position checkpoints. From our analysis, we conclude that the positive feedback provided by these networks' cycles ensures the existence of a stable positive fixed point. Additionally, we use a genome-scale network model of the Escherichia coli sugar metabolism to illustrate our findings. In summary, our results suggest that the qualitative evolution of chemical systems requires the addition and elimination of cycles.