Manuel Miranda, Gissell Estrada-Rodriguez, and Ernesto Estrada

Entropy 2023, 25(12), 1599

Geometric realization of simplicial complexes makes them a unique representation of complex systems. The existence of local continuous spaces at the simplices level with global discrete connectivity between simplices makes the analysis of dynamical systems on simplicial complexes a challenging problem. In this work, we provide some examples of complex systems in which this representation would be a more appropriate model of real-world phenomena. Here, we generalize the concept of metaplexes to embrace that of geometric simplicial complexes, which also includes the definition of dynamical systems on them. A metaplex is formed by regions of a continuous space of any dimension interconnected by sinks and sources that works controlled by discrete (graph) operators. The definition of simplicial metaplexes given here allows the description of the diffusion dynamics of this system in a way that solves the existing problems with previous models. We make a detailed analysis of the generalities and possible extensions of this model beyond simplicial complexes, e.g., from polytopal and cell complexes to manifold complexes, and apply it to a real-world simplicial complex representing the visual cortex of a macaque.

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Ivan Shpurov, Tom Froese, Dante R. Chialvo

It has been repeatedly reported that the collective dynamics of social insects exhibit universal emergent properties similar to other complex systems. In this note, we study a previously published data set in which the positions of thousands of honeybees in a hive are individually tracked over multiple days. The results show that the hive dynamics exhibit long-range spatial and temporal correlations in the occupancy density fluctuations, despite the characteristic short-range bees’ mutual interactions. The variations in the occupancy unveil a non-monotonic function between density and bees’ flow, reminiscent of the car traffic dynamic near a jamming transition at which the system performance is optimized to achieve the highest possible throughput. Overall, these results suggest that the beehive collective dynamics are self-adjusted towards a point near its optimal density.

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Timothy Davey

Entropy 2023, 25(12), 1605

This paper offers a measure of how organised a system is, as defined by self-consistency. Complex dynamics such as tipping points and feedback loops can cause systems with identical initial parameters to vary greatly by their final state. These systems can be called non-ergodic or incoherent. This lack of consistency (or replicability) of a system can be seen to drive an additional form of uncertainty, beyond the variance that is typically considered. However, certain self-organising systems can be shown to have some self-consistency around these tipping points, when compared with systems that find no consistent final states. Here, we propose a measure of this self-consistency that is used to quantify our confidence in the outcomes of agent-based models, simulations or experiments of dynamical systems, which may or may not contain multiple attractors.

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Qing Ke, Alexander J. Gates, and Albert-László Barabási

PNAS 120 (48) e2309378120

Distinct citation practices across time and discipline limit our ability to compare different scientific achievements. For example, raw citation counts suggest that advancements in biomedical research have consistently overshadowed the accomplishments from all other disciplines. Here, we introduce a network-based methodology for normalizing citation counts that mitigates the effects of temporal and disciplinary variations in citations. The method allows us to highlight successful periods of scientific discovery across the disciplines and provides insights into the evolution of science.

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Rainer Feistel

Entropy 2023, 25(12), 1596

Living organisms are active open systems far from thermodynamic equilibrium. The ability to behave actively corresponds to dynamical metastability: minor but supercritical internal or external effects may trigger major substantial actions such as gross mechanical motion, dissipating internally accumulated energy reserves. Gaining a selective advantage from the beneficial use of activity requires a consistent combination of sensual perception, memorised experience, statistical or causal prediction models, and the resulting favourable decisions on actions. This information processing chain originated from mere physical interaction processes prior to life, here denoted as structural information exchange. From there, the self-organised transition to symbolic information processing marks the beginning of life, evolving through the novel purposivity of trial-and-error feedback and the accumulation of symbolic information. The emergence of symbols and prediction models can be described as a ritualisation transition, a symmetry-breaking kinetic phase transition of the second kind previously known from behavioural biology. The related new symmetry is the neutrally stable arbitrariness, conventionality, or code invariance of symbols with respect to their meaning. The meaning of such symbols is given by the structural effect they ultimately unleash, directly or indirectly, by deciding on which actions to take. The early genetic code represents the first symbols. The genetically inherited symbolic information is the first prediction model for activities sufficient for survival under the condition of environmental continuity, sometimes understood as the “final causality” property of the model.

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