I. Sendiña-Nadal, I. Leyva, J.P. Barbot, C. Letellier

Effective control of nonlinear complex networks needs to identify not only the intervention sites but also the state variables to be monitored and the locations at which control inputs should be applied. Here, we present a network-scale generalization of an observability-guided, flatness-based control framework. The resulting control laws are implemented using sliding-mode control and evaluated in heterogeneous networks of chaotic oscillators driven toward a prescribed periodic regime. We compare two control architectures: in the node-wise method, oscillators are independently sensed and actuated, while in the pairwise method, measurements acquired from a single node within each dyad are used to synthesize control inputs applied to both nodes. Across the parameter regimes considered, node-wise control generally achieves accurate control over a broader operating region, whereas pairwise control remains effective over a more restricted region while using half as many measurement locations for a given number of actuated nodes. Moreover, network interactions can enhance control by propagating the control influence to non-actuated nodes, creating a cooperative effect between the collective dynamics and the control action. Collectively, these findings quantify the trade-offs among measurement-location requirements, control performance, and control effort in nonlinear complex networks.

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Maxime Saxena, Fabio Caccioli, R. Maria del Rio-Chanona

Decision Models (DMs), a new class of AI models, give fast responses and return a probability distribution over a fixed set of options. These properties make them candidate human surrogates in economic simulations and surveys, a role increasingly filled by Large Language Models (LLMs), which are costly at scale and under-represent the variation in human behaviour. We present a first evaluation of DMs as human surrogates in economics, comparing 10 DMs with 8 LLMs in three economic settings: a household spending survey on consumption, several classic economic games and a labour-market field experiment. Frontier DMs, those that score highest on general decision-making benchmarks, reproduce the variation in human responses more closely than LLMs in all three settings. They capture the modal human response as well as LLMs in the spending survey, but less well in the economic games. Frontier DMs are also roughly ten times faster than the fastest LLM and can be over a hundred times cheaper. Together, these results suggest that DMs capture the heterogeneity of human behaviour better than LLMs and make large-scale economic simulations more feasible.

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Alessandro Sarti, Giovanna Citti

The problem of the dynamics of living systems and their mathematical representation essentially unfolds on two levels. Firstly, the principles of autopoiesis and operational closure describe how a living system produces and maintains itself. Secondly, living phenomena are recognised as historical, involving the evolution of dynamics and spaces of possibility that change over time. Currently, no differential model can incorporate both of these aspects. We propose adopting the differential heterogenesis framework, which enables us to define differential operators that change in space and time, producing event-based and historical dynamics. In this construction, heterogeneous operator assemblages will be constrained by the principles of autopoiesis and operational closure, providing a theoretical framework for event-based and historical living systems. Finally, we provide a specific example of assembly with Gray-Scott kinetic equations, along with numerical simulations and results.

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David H. Wolpert, David C. Krakauer

“Emergence” refers to the fact that different mathematical languages and theories seem to be required to describe scientific theories that operate at different spatial and temporal scales. Highly circumscribed, special cases of emergence have been investigated using many different formal tools, including coarse-graining (over space and / or time), renormalization, dimension reduction, broken symmetry, and various formulations of causality. Here we extend the mathematics of model theory to unify and extend these earlier investigations. As a preliminary application of our framework, we investigate canonical examples of emergence, including the emergence of genetics from chemistry, of psychology from neurobiology, and of different forms of collective behavior from the laws governing their constituent parts. By exploiting the power of model theory we also uncover many aspects of emergence that were previously obscured. In particular, we uncover some of the rich hierarchical structure that relates different scientific fields. For example, we show that scientific fields can be related via a collection of multiple partial orders, all defined over the same set. On the other hand, under an alternative relation among scientific fields, one which allows cycles, we show that it is possible that the set of all of scientific fields must collapse into a single scientific field. Going forward, these investigations point to the formal tools that might need to be developed in order to arrive at a deeper understanding of this emergent hierarchy of scientific reality.

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