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The concept of hierarchy in complex systems is tightly linked to co-evolutionary processes. We propose here to explore it in the case of the co-evolution between transportation networks and territories. More precisely, we extend a…
Network-theoretic tools contribute to understanding real-world system dynamics, e.g., in wildlife conservation, epidemics, and power outages. Network visualization helps illustrate structural heterogeneity; however, details about…
It has recently become popular to analyze the behavior of excess dislocations in plastic deformation under the assumption that such dislocations are arranged into walls with periodic dislocation spacing along the wall direction. This…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
The main purpose of this paper is to study formal deformations of evolution algebras, determining their existence and classifying them up to equivalence. In addition, we examine degenerations in this setting and provide Hasse diagrams that…
We present novel approaches to the dynamics of an open quantum system coupled linearly to a non-Markovian fermionic or bosonic environment. In the first approach, we obtain a hierarchy of stochastic evolution equations of the diffusion…
Dynamic decisions are pivotal to economic policy making. We show how existing evidence from randomized control trials can be utilized to guide personalized decisions in challenging dynamic environments with budget and capacity constraints.…
This contribution shortly outlines and reviews a theoretical and computational approach for a theory of change concerning systems where it is not possible to apply the laws of motion ab initio. The concept of meta-structure relates to the…
The purpose of physics is to describe nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this spectrum of events is desirable, this would…
Reinforcement learning practitioners often avoid hierarchical policies, especially in image-based observation spaces. Typically, the single-task performance improvement over flat-policy counterparts does not justify the additional…
Often, experiments, observations or simulations generate large numbers of snapshots of the configurations of complex many-particle systems. It is important to find methods of extracting useful information from these ensembles of snapshots…
Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To…
The possibility that evolutionary forces -- together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes -- might constrain the logic of…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
Plasticity modelling has long been based on phenomenological models based on ad-hoc assuption of constitutive relations, which are then fitted to limited data. Other work is based on the consideration of physical mechanisms which seek to…
Many systems in chemistry, biology, finance and social sciences present emerging features which are not easy to guess from the elementary interactions of their microscopic individual components. In the past, the macroscopic behavior of such…
Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the…
We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an associated macroscopic model of…
We present a mathematical framework within which Discrete Dislocation Dynamics in three dimensions is well-posed. By considering smooth distributions of slip, we derive a regularised energy for curved dislocations, and rigorously derive the…