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Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
Effective teams are crucial for organisations, especially in environments that require teams to be constantly created and dismantled, such as software development, scientific experiments, crowd-sourcing, or the classroom. Key factors…
When predictions support decisions they may influence the outcome they aim to predict. We call such predictions performative; the prediction influences the target. Performativity is a well-studied phenomenon in policy-making that has so far…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
We consider a model in which a collective state couples to a large number of background states. The background states can be chosen to have properties which are classically characterized as regular or chaotic. We found that the dynamical…
Real-world information communities exhibit inherent structures that characterize a system that is stable and efficient for content production and consumption. In this paper, we study such structures through mathematical modelling and…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only…
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union…
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…
In studies of social dynamics, cohesion refers to a group's tendency to stay in unity, which -- as argued in sociometry -- arises from the network topology of interpersonal ties between members of the group. We follow this idea and propose…
In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash…
We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…
A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…
Researchers working within knowledge-in-pieces traditions have often employed observational approaches to investigate micro-processes of learning. There is growing evidence from this line of work that students' intuitive thinking about…
Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…
We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
In coalition formation games self-organized coalitions are created as a result of the strategic interactions of independent agents. For each couple of agents $(i,j)$, weight $w_{i,j}=w_{j,i}$ reflects how much agents $i$ and $j$ benefit…
A major limitation of the classical control theory is the assumption that the state space and its dimension do not change with time. This prevents analyzing and even formalizing the stability and control problems for open multi-agent…