Tootfinder

The Mathematical Theory of Behavioural Swarms: Towards Modelling the Collective Dynamics of Living Systems
Rene Fabregas (University of Granada), Jie Liao (Shanghai University of Finance,Economics), Nisrine Outada (University Cadi Ayyad,UMMISCO, IRD-SU)
https://arxiv.org/abs/2508.12183

The Mathematical Theory of Behavioural Swarms: Towards Modelling the Collective Dynamics of Living Systems
Classical swarm models, exemplified by the Cucker--Smale framework, provide foundational insights into collective alignment but exhibit fundamental limitations in capturing the adaptive, heterogeneous behaviours intrinsic to living systems. This paper formalises the mathematical theory of \textit{Behavioural Swarms}, a comprehensive framework where each particle's state incorporates a dynamic internal variable, the \textit{activity} that co-evolves with position and velocity through nonlocal in…

Collective dynamics of strategic classification
Marta C. Couto, Flavia Barsotti, Fernando P. Santos
https://arxiv.org/abs/2508.09340 https://arxiv.org/pdf/…

Collective dynamics of strategic classification
Classification algorithms based on Artificial Intelligence (AI) are nowadays applied in high-stakes decisions in finance, healthcare, criminal justice, or education. Individuals can strategically adapt to the information gathered about classifiers, which in turn may require algorithms to be re-trained. Which collective dynamics will result from users' adaptation and algorithms' retraining? We apply evolutionary game theory to address this question. Our framework provides a mathematically rigoro…

Cognition in Superposition: Quantum Models in AI, Finance, Defence, Gaming and Collective Behaviour
Ivan S. Maksymov
https://arxiv.org/abs/2508.20098 https://

Cognition in Superposition: Quantum Models in AI, Finance, Defence, Gaming and Collective Behaviour
At first glance, quantum mechanics and behavioural science seem worlds apart -- one rooted in equations and particles, the other in thoughts and choices. Yet, emerging research reveals a profound and unexpected bridge between them. This chapter explores that bridge through quantum models of cognition and decision-making, showing how principles from quantum mechanics can help understand, and even predict, the complexities of human perception, behaviour and societal dynamics. We introduce a compu…