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The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
Collective behavior is commonly attributed to direct interactions among system components. Using a minimal stochastic model, we show that higher-order collective structure can instead emerge from shared stochastic environments, even in the…
In nature self-organized systems as flock of birds, school of fishes or herd of sheeps have to deal with the presence of external agents such as predators or leaders which modify their internal dynamic. Such situations take into account a…
In communication networks structure and dynamics are tightly coupled. The structure controls the flow of information and is itself shaped by the dynamical process of information exchanged between nodes. In order to reconcile structure and…
Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models…
Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of…
The quest on how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here…
Interactions govern the flow of information and the formation of correlations in quantum systems, dictating the phases of matter found in nature and the forms of entanglement generated in the laboratory. Typical interactions decay with…
Symmetry invariant local interaction of a many body system leads to global constraints. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry.
The design of distributed autonomous systems often omits consideration of the underlying network dynamics. Recent works in multi-agent systems and swarm robotics alike have highlighted the impact that the interactions between agents have on…
Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of…
Geographic borders are not only essential for the effective functioning of government, the distribution of administrative responsibilities and the allocation of public resources, they also influence the interregional flow of information,…
We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…
Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality…
Deep learning has seen a movement away from representing examples with a monolithic hidden state towards a richly structured state. For example, Transformers segment by position, and object-centric architectures decompose images into…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the…
Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework…