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.

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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

Luís F. Seoane and Ricard Solé

Phys. Rev. E 108, 044407

Why are living systems complex? Why does the biosphere contain living beings with complexity features beyond those of the simplest replicators? What kind of evolutionary pressures result in more complex life forms? These are key questions that pervade the problem of how complexity arises in evolution. One particular way of tackling this is grounded in an algorithmic description of life: living organisms can be seen as systems that extract and process information from their surroundings to reduce uncertainty. Here we take this computational approach using a simple bit string model of coevolving agents and their parasites. While agents try to predict their worlds, parasites do the same with their hosts. The result of this process is that, to escape their parasites, the host agents expand their computational complexity despite the cost of maintaining it. This, in turn, is followed by increasingly complex parasitic counterparts. Such arms races display several qualitative phases, from monotonous to punctuated evolution or even ecological collapse. Our minimal model illustrates the relevance of parasites in providing an active mechanism for expanding living complexity beyond simple replicators, suggesting that parasitic agents are likely to be a major evolutionary driver for biological complexity.

Read the full article at: link.aps.org

Falcón-Cortés A, Boyer D, Aldana M, Ramos-Fernández G (2023) Lévy movements and a slowly decaying memory allow efficient collective learning in groups of interacting foragers. PLoS Comput Biol 19(10): e1011528.

Many animal species benefit from spatial learning to adapt their foraging movements to the distribution of resources. Learning involves the collection, storage and retrieval of information, and depends on both the random search strategies employed and the memory capacities of the individual. For animals living in social groups, spatial learning can be further enhanced by information transfer among group members. However, how individual behavior affects the emergence of collective states of learning is still poorly understood. Here, with the help of a spatially explicit agent-based model where individuals transfer information to their peers, we analyze the effects on the use of resources of varying memory capacities in combination with different exploration strategies, such as ordinary random walks and Lévy flights. We find that individual Lévy displacements associated with a slow memory decay lead to a very rapid collective response, a high group cohesion and to an optimal exploitation of the best resource patches in static but complex environments, even when the interaction rate among individuals is low.

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Freya Behrens, Barbora Hudcová, Lenka Zdeborová

Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we relax the regular connectivity grid of cellular automata to a random graph, which gives the class of graph cellular automata. Using the dynamical cavity method (DCM) and its backtracking version (BDCM), we show that this relaxation allows us to derive asymptotically exact analytical results on the global dynamics of these systems on sparse random graphs. Concretely, we showcase the results on a specific subclass of graph cellular automata with “conforming non-conformist” update rules, which exhibit dynamics akin to opinion formation. Such rules update a node’s state according to the majority within their own neighbourhood. In cases where the majority leads only by a small margin over the minority, nodes may exhibit non-conformist behaviour. Instead of following the majority, they either maintain their own state, switch it, or follow the minority. For configurations with different initial biases towards one state we identify sharp dynamical phase transitions in terms of the convergence speed and attractor types. From the perspective of opinion dynamics this answers when consensus will emerge and when two opinions coexist almost indefinitely.

Read the full article at: arxiv.org