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Behavior trees represent a hierarchical and modular way of combining several low-level control policies into a high-level task-switching policy. Hybrid dynamical systems can also be seen in terms of task switching between different…

Multi-digit addition is a clear probe of the computational power of large language models. To dissect the internal arithmetic processes in LLaMA-3-8B-Instruct, we combine linear probing with logit-lens inspection. Inspired by the…

General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…

Interface theories are powerful frameworks supporting incremental and compositional design of systems through refinements and constructs for conjunction, and parallel composition. In this report we present a first Interface Theor -- |Modal…

Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical…

Vanderweele and Knol define biological interaction as an instance wherein "two exposures physically interact to bring about the outcome." A hallmark of biological interaction is that the total effect, produced when factors act together,…

The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further…

Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…

In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are…

We take a fresh look at analogue-digital systems focussing on their physical behaviour. We model a general analogue-digital system as a physical process controlled by an algorithm by viewing the physical process as physical oracle to the…

Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…

A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…

This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…

We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…

Information theory and the framework of information dynamics have been used to provide tools to characterise complex systems. In particular, we are interested in quantifying information storage, information modification and information…

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…

Understanding of the onset and generic mechanisms of transitions between distinct patterns of activity in realistic models of individual neurons and neural networks presents a fundamental challenge for the theory of applied dynamical…

Particle- and agent-based systems are a ubiquitous modeling tool in many disciplines. We consider the fundamental problem of inferring interaction kernels from observations of agent-based dynamical systems given observations of…