Circuit building blocks of gene regulatory networks (GRN) have been identified through the fibration symmetries of the underlying biological graph. Here, we analyse analytically six of these circuits that occur as functional and synchronous building blocks in these networks. Of these, the lock-on, toggle switch, Smolen oscillator, feed-forward fibre and Fibonacci fibre circuits occur in living organisms, notably Escherichia coli; the sixth, the repressilator, is a synthetic GRN. We consider synchronous steady states determined by a fibration symmetry (or balanced colouring) and determine analytic conditions for local bifurcation from such states, which can in principle be either steady-state or Hopf bifurcations. We identify conditions that characterize the first bifurcation, the only one that can be stable near the bifurcation point. We model the state of each gene in terms of two variables: mRNA and protein concentration. We consider all possible \'admissible\' models-those compatible with the network structure-and then specialize these general results to simple models based on Hill functions and linear degradation. The results systematically classify using graph symmetries the complexity and dynamics of these circuits, which are relevant to understand the functionality of natural and synthetic cells.

As health and health care systems continue to face massive challenges from local to global well-being, understanding the processes that lead to improvement or deterioration in human health has embraced a broad range of forces from genes to national cultures. Despite the many efforts to deploy a common framework that captures diverse drivers at scale, the common missing element is the absence of a flexible mechanism that can guide research within and across levels. This hinders both the cumulation of knowledge and the development of a scientific foundation for multiplex interventions. However, studies across disciplines using a wide variety of methods and measures have converged on \"connectedness\" as crucial to understanding how factors operate in the health space. More formally, a focus on the critical role of the network structure and content of key elements and how they interact, rather than just on the elements themselves, offers both a generalized theory of active factors within levels and the potential to theorize interactions across levels. One critical contemporary health crisis, suicide, is deployed to illustrate the Network Embedded Symbiome Framework. The wide range of health and health care research where networks have been implicated supports its potential but also cautions against inevitable limits that will require creative theorizing and data harmonization to move forward.

A crop boom is a sudden, nonlinear and intense expansion of a new crop. Despite their large impacts, boom-bust dynamics are not well understood; booms are largely unpredictable and difficult to steer once they unfold. Based on the striking resemblances between land regime shifts and crop booms, we apply complex systems theory, highlighting the potential for regime shifts, to provide new insights about crop boom dynamics. We analyse qualitative and quantitative data of rubber and banana plantation expansion in two forest frontier regions of northern Laos. We show that preconditions, including previous booms, explain the occurrence (why) of booms, and triggers like policy and market changes explain their timing (when). Yet, the most important features of booms, their intensity and nonlinearity (how), strongly depended on internal self-reinforcing feedbacks. We identify built-in feedbacks (neighbourhood effects and imitation) and emergent feedbacks (land rush) and show that they were social in nature, multi-scale from plot to region and subject to thresholds. We suggest that these are regular features of booms and propose a definition and causal-mechanistic explanation of crop booms, examining the overlap between booms and regime shifts and the role of frontiers. We then identify opportunities for management interventions before, during and after booms.

This paper provides a comprehensive review of recent advancements in computational methods for modeling, simulation, and optimization of complex systems in materials engineering, mechanical engineering, and energy systems. We identified key trends and highlighted the integration of artificial intelligence (AI) with traditional computational methods. Some of the cited works were previously published within the topic: \"Computational Methods: Modeling, Simulations, and Optimization of Complex Systems\"; thus, this article compiles the latest reports from this field. The work presents various contemporary applications of advanced computational algorithms, including AI methods. It also introduces proposals for novel strategies in materials production and optimization methods within the energy systems domain. It is essential to optimize the properties of materials used in energy. Our findings demonstrate significant improvements in accuracy and efficiency, offering valuable insights for researchers and practitioners. This review contributes to the field by synthesizing state-of-the-art developments and suggesting directions for future research, underscoring the critical role of these methods in advancing engineering and technological solutions.

In this article, we argue that social systems with fission-fusion (FF) dynamics are best characterized within a complex adaptive systems (CAS) framework. We discuss how different endogenous and exogenous factors drive scale-dependent network properties across temporal, spatial and social domains. Importantly, this view treats the dynamics themselves as objects of study, rather than variously defined notions of static \'social groups\' that have hitherto dominated thinking in behavioural ecology. CAS approaches allow us to interrogate FF dynamics in taxa that do not conform to more traditional conceptualizations of sociality and encourage us to pose new types of questions regarding the sources of stability and change in social systems, distinguishing regular variations from those that would lead to system-level reorganization. This article is part of the theme issue \'Connected interactions: enriching food web research by spatial and social interactions\'.

Causal multivariate time-series analysis, combined with network theory, provide a powerful tool for studying complex ecological interactions. However, these methods have limitations often underestimated when used in graphical modelling of ecological systems. In this opinion article, I examine the relationship between formal logic methods used to describe causal networks and their inherent statistical and epistemological limitations. I argue that while these methods offer valuable insights, they are restricted by axiomatic assumptions, statistical constraints and the incompleteness of our knowledge. To prove that, I first consider causal networks as formal systems, define causality and formalize their axioms in terms of modal logic and use ecological counterexamples to question the axioms. I also highlight the statistical limitations when using multivariate time-series analysis and Granger causality to develop ecological networks, including the potential for spurious correlations among other data characteristics. Finally, I draw upon Gödel\'s incompleteness theorems to highlight the inherent limits of fully understanding complex networks as formal systems and conclude that causal ecological networks are subject to initial rules and data characteristics and, as any formal system, will never fully capture the intricate complexities of the systems they represent. This article is part of the theme issue \'Connected interactions: enriching food web research by spatial and social interactions\'.

OBJECTIVE: To explore how the change-point method can be used to analyze complex longitudinal data and detect when meaningful changes (change points) have occurred during rehabilitation.
METHODS: This design is a prospective single-case observational study of a football player in a professional club who sustained an acute lower-limb muscle injury during high-speed running in training. The rehabilitation program was entirely completed in the football club under the supervision of the club\'s medical team. Four wellness metrics and 5 running-performance metrics were collected before the injury and until the player returned to play.
RESULTS: Data were collected over 130 days. In the univariate analysis, the change points for stress, sleep, mood, and soreness were located on days 30, 47, 50, and 50, respectively. The change points for total distance, acceleration, maximum speed, deceleration, and high-speed running were located on days 32, 34, 37, 41, and 41, respectively. The multivariate analysis resulted in a single change point for the wellness metrics and running-performance metrics, on days 50 and 67, respectively.
CONCLUSIONS: The univariate approach provided information regarding the sequence and time point of the change points. The multivariate approach provided a common change point for multiple metrics, information that would benefit clinicians to have a broad overview of the changes in the rehabilitation process. Clinicians may consider the change-point method to integrate and visualize data from multiple sources to evaluate athletes\' progression along the return-to-sport continuum.

To what extent are naturally evolving systems limited in their potential diversity (i.e. \"bounded\") versus unrestricted (\"open-ended\")? Minerals provide a quantitative model evolving system, with well-documented increases in mineral diversity through multiple stages of planetary evolution over billions of years. A recent framework that unifies behaviors of both biotic and abiotic evolving systems posits that all such systems are characterized by combinatorial richness subject to selection. In the case of minerals, combinatorial richness derives from the possible combinations of chemical elements coupled with permutations of their formulas\' coefficients. Observed mineral species, which are selected for persistence through deep time, represent a miniscule fraction of all possible element configurations. Furthermore, this model predicts that as planetary systems evolve, stable minerals become an ever-smaller fraction of the \"possibility space.\" A postulate is that \"functional information,\" defined as the negative log2 of that fraction, must increase as a system evolves. We have tested this hypothesis for minerals by estimating the fraction of all possible chemical formulas observed from one stage of mineral evolution to the next, based on numbers of different essential elements and the maximum chemical formula complexity at each of nine chronological stages of mineral evolution. We find a monotonic increase in mineral functional information through these nine stages-a result consistent with the hypothesis. Furthermore, analysis of the chemical formulas of minerals demonstrates that the modern Earth may be approaching the maximum limit of functional information for natural mineral systems-a result demonstrating that mineral evolution is not open-ended.

Phytoplankton communities are crucial components of aquatic ecosystems, and since they are highly interactive, they always form complex networks. Yet, our understanding of how interactive phytoplankton networks vary through time under changing environmental conditions is limited. Using a 29-year (339 months) long-term dataset on Lake Taihu, China, we constructed a temporal network comprising monthly sub-networks using \"extended Local Similarity Analysis\" and assessed how eutrophication, climate change, and restoration efforts influenced the temporal dynamics of network complexity and stability. The network architecture of phytoplankton showed strong dynamic changes with varying environments. Our results revealed cascading effects of eutrophication and climate change on phytoplankton network stability via changes in network complexity. The network stability of phytoplankton increased with average degree, modularity, and nestedness and decreased with connectance. Eutrophication (increasing nitrogen) stabilized the phytoplankton network, mainly by increasing its average degree, while climate change, i.e., warming and decreasing wind speed enhanced its stability by increasing the cohesion of phytoplankton communities directly and by decreasing the connectance of network indirectly. A remarkable shift and a major decrease in the temporal dynamics of phytoplankton network complexity (average degree, nestedness) and stability (robustness, persistence) were detected after 2007 when numerous eutrophication mitigation efforts (not all successful) were implemented, leading to simplified phytoplankton networks and reduced stability. Our findings provide new insights into the organization of phytoplankton networks under eutrophication (or re-oligotrophication) and climate change in subtropical shallow lakes.

BACKGROUND: Approaches to prevent and manage diabetes at a community population level are hindered because current strategies are not aligned with the structure and function of a community system. We describe a community-driven process based on local data and rapid prototyping as an alternative approach to create diabetes prevention and care management solutions appropriate for each community. We report on the process and provide baseline data for a 3-year case study initiative to improve diabetes outcomes in two rural Nebraska communities.
METHODS: We developed an iterative design process based on the assumption that decentralized decision-making using local data feedback and monitoring will lead to the innovation of local sustainable solutions. Coalitions act as community innovation hubs and meet monthly to work through a facilitated design process. Six core diabetes measures will be tracked over the course of the project using the electronic health record from community clinics as a proxy for the entire community.
RESULTS: Baseline data indicate two-thirds of the population in both communities are at risk for prediabetes based on age and body mass index. However, only a fraction (35% and 12%) of those at risk have been screened. This information led both coalitions to focus on improving screening rates in their communities.
CONCLUSIONS: In order to move a complex system towards an optimal state (e.g., improved diabetes outcomes), stakeholders must have access to continuous feedback of accurate, pertinent information in order to make informed decisions. Conventional approaches of implementing evidence-based interventions do not facilitate this process.