Stuart A. Kauffman and Andrea Roli

Interface Focus Volume 13 Issue 3

Since Newton, classical and quantum physics depend upon the ‘Newtonian paradigm’. The relevant variables of the system are identified. For example, we identify the position and momentum of classical particles. Laws of motion in differential form connecting the variables are formulated. An example is Newton’s three laws of motion. The boundary conditions creating the phase space of all possible values of the variables are defined. Then, given any initial condition, the differential equations of motion are integrated to yield an entailed trajectory in the prestated phase space. It is fundamental to the Newtonian paradigm that the set of possibilities that constitute the phase space is always definable and fixed ahead of time. This fails for the diachronic evolution of ever-new adaptations in any biosphere. Living cells achieve constraint closure and construct themselves. Thus, living cells, evolving via heritable variation and natural selection, adaptively construct new-in-the-universe possibilities. We can neither define nor deduce the evolving phase space: we can use no mathematics based on set theory to do so. We cannot write or solve differential equations for the diachronic evolution of ever-new adaptations in a biosphere. Evolving biospheres are outside the Newtonian paradigm. There can be no theory of everything that entails all that comes to exist. We face a third major transition in science beyond the Pythagorean dream that ‘all is number’ echoed by Newtonian physics. However, we begin to understand the emergent creativity of an evolving biosphere: emergence is not engineering.

Read the full article at: royalsocietypublishing.org

Bin Zhou, Petter Holme, Zaiwu Gong, Choujun Zhan, Yao Huang, Xin Lu & Xiangyi Meng 

Nature Communications volume 14, Article number: 7031 (2023)

Although the origin of the fat-tail characteristic of the degree distribution in complex networks has been extensively researched, the underlying cause of the degree distribution characteristic across the complete range of degrees remains obscure. Here, we propose an evolution model that incorporates only two factors: the node’s weight, reflecting its innate attractiveness (nature), and the node’s degree, reflecting the external influences (nurture). The proposed model provides a good fit for degree distributions and degree ratio distributions of numerous real-world networks and reproduces their evolution processes. Our results indicate that the nurture factor plays a dominant role in the evolution of social networks. In contrast, the nature factor plays a dominant role in the evolution of non-social networks, suggesting that whether nodes are people determines the dominant factor influencing the evolution of real-world networks.

Read the full article at: www.nature.com

Ricard Solé

Preserving and restoring biodiversity is becoming a great challenge as we face a world where planetary boundaries will likely be crossed over the following decades. Such challenge needs to consider multiple scales of complexity, both in space and time. A common thread in most cases is the presence of nonlinear phenomena generating shifts among alternative states. These breaking points imply a new perception of risk and different management strategies. A broad range of phenomena affect the preservation of healthy communities and constrain the ways to deal with conservation, from local features associated with habitat loss or facilitation to mesoscale or global network-level ecological complexity and the role played by extreme events. How are these scales connected? How can the emergent properties associated with ecosystem dynamics be exploited? Here a synthesis of ideas is presented, with a complex systems view of the different scales involved, the emergent phenomena separating them, and the universal properties that allow defining simple models on each scale.

Read the full article at: www.preprints.org

Georg Börner, Hauke Haehne, Jose Casadiego, Marc Timme

Chaos 33, 073136 (2023)

The dynamics of a complex system is fundamentally governed by the number of its active dynamical variables, the system’s state space dimension. However, identifying state space dimension constitutes a difficult task, in particular if the dimension is much larger than the number of variables observed. Here, we show that it is mathematically possible in principle to infer the dimension of the state space using time series observations of just one variable, for arbitrarily high state space dimensions. We discuss how in practice the success of this inference depends on numerical constraints of data evaluation and experimental choices, such as the sampling intervals and total duration of observations. We illustrate how the approach may be applied to high-dimensional systems, e.g., with 100 variables, and provide general rules of thumb for performing and evaluating measurements of a given system. Our results provide a novel approach for inferring the dimension of complex and networked dynamical systems from scalar time series data and may help to develop alternative methods, e.g., for the reconstruction of the dimensions of system attractors.

Read the full article at: pubs.aip.org

Didier Le Bail, Mathieu Génois, Alain Barrat

Although many tools have been developed and employed to characterize temporal networks, the issue of how to compare them remains largely open. It depends indeed on what features are considered as relevant, and on the way the differences in these features are quantified. In this paper, we propose to characterize temporal networks through their behaviour under general transformations that are local in time: (i) a local time shuffling, which destroys correlations at time scales smaller than a given scale b, while preserving large time scales, and (ii) a local temporal aggregation on time windows of length n. By varying b and n, we obtain a flow of temporal networks, and flows of observable values, which encode the phenomenology of the temporal network on multiple time scales. We use a symbolic approach to summarize these flows into labels (strings of characters) describing their trends. These labels can then be used to compare temporal networks, validate models, or identify groups of networks with similar labels. Our procedure can be applied to any temporal network and with an arbitrary set of observables, and we illustrate it on an ensemble of data sets describing face-to-face interactions in various contexts, including both empirical and synthetic data.

Read the full article at: arxiv.org