Ricardo Vega, Cameron Nowzari

Emergence and swarms are widely discussed topics, yet no consensus exists on their formal definitions. This lack of agreement makes it difficult not only for new researchers to grasp these concepts, but also for experts who may use the same terms to mean different things. Many attempts have been made to objectively define ‘swarm’ or ’emergence,’ with recent work highlighting the role of the external observer. Still, several researchers argue that once an observer’s vantage point (e.g., scope, resolution, context) is established, the terms can be made objective or measured quantitatively. In this note, we propose a framework to discuss these ideas rigorously by separating externally observable states from latent, unobservable ones. This allows us to compare and contrast existing definitions of swarms and emergence on common ground. We argue that these concepts are ultimately subjective-shaped less by the system itself than by the perception and tacit knowledge of the observer. Specifically, we suggest that a ‘swarm’ is not defined by its group behavior alone, but by the process generating that behavior. Our broader goal is to support the design and deployment of robotic swarm systems, highlighting the critical distinction between multi-robot systems and true swarms.

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Sean Kelty, Raiyan Abdul Baten, Adiba Mahbub Proma, Ehsan Hoque, Johan Bollen & Gourab Ghoshal
Humanities and Social Sciences Communications volume 12, Article number: 926 (2025)

Academic success is distributed unequally; a few top scientists receive the bulk of attention, citations, and resources. However, do these “superstars” foster leadership in scientific innovation? We employ a series of information-theoretic measures that quantify novelty, innovation, and impact from scholarly citation networks, and compare the academic output of scientists in the American Physical Society corpus with varying levels of connections to superstar scientists. The strength of connection is based on the frequency of citations to superstar papers, which is also related to the frequency of collaboration. We find that while strongly-connected scientists publish more, garner more citations, and produce moderately more diverse content, this comes at a cost of lower innovation, less disruption, and higher redundancy of ideas. Further, once one removes papers co-authored with superstars, the academic output of these strongly connected scientists greatly diminishes. In contrast, authors who publish at the same rate without the benefit of collaborations with scientific superstars produce papers that are more innovative, more disruptive, and have comparable citation rates, once one controls for the transferred prestige of superstars. On balance, our results indicate that academia pays a price by focusing attention and resources on superstars.

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Sean P. Maley, Carlos Gershenson, Stuart A. Kauffman

There has been a long debate on how new levels of organization have evolved. It might seem unlikely, as cooperation must prevail over competition. One well-studied example is the emergence of autocatalytic sets, which seem to be a prerequisite for the evolution of life. Using a simple model, we investigate how varying bias toward cooperation versus antagonism shapes network dynamics, revealing that higher-order organization emerges even amid pervasive antagonistic interactions. In general, we observe that a quantitative increase in the number of elements in a system leads to a qualitative transition.
We present a random threshold-directed network model that integrates node-specific traits with dynamic edge formation and node removal, simulating arbitrary levels of cooperation and competition. In our framework, intrinsic node values determine directed links through various threshold rules. Our model generates a multi-digraph with signed edges (reflecting support/antagonism, labeled “help”/“harm”), which ultimately yields two parallel yet interdependent threshold graphs. Incorporating temporal growth and node turnover in our approach allows exploration of the evolution, adaptation, and potential collapse of communities and reveals phase transitions in both connectivity and resilience.
Our findings extend classical random threshold and Erdős-Rényi models, offering new insights into adaptive systems in biological and economic contexts, with emphasis on the application to Collective Affordance Sets. This framework should also be useful for making predictions that will be tested by ongoing experiments of microbial communities in soil.

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Read the full article at: www.pnas.org