Related papers: Endofunctors modelling higher-order behaviours
We use high girth, high chromatic number hypergraphs to show that there are finite models of the equational theory of the semiring of nonnegative integers whose equational theory has no finite axiomatisation, and show this also holds if…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
Synthetic Biology is an interdisciplinary field that utilizes well-established engineering principles, ranging from electrical, control and computer systems, for analyzing the biological systems, such as biological circuits, enzymes,…
This survey paper discusses behaviour of higher-order correlations for one-parameter dynamical systems and more generally for dynamical systems arising from group actions. In particular, we present a self-contained proof of quantitative…
Axiomatizing covarieties of coalgebras for an endofunctor is less intuitive than axiomatizing varieties of algebras via equations (Dahlqvist and Schmid, 2022). Existing techniques come from coalgebraic modal logic, pattern avoidance…
This paper introduces the notion of referring forms as a new metric for analyzing sequential circuits from a functional perspective. Sequential circuits are modeled as causal stream functions, the outputs of which depend solely on the past…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
Complex robot behaviour typically requires the integration of multiple robotic and Artificial Intelligence (AI) techniques and components. Integrating such disparate components into a coherent system, while also ensuring global properties…
We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…
We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is…
The distributed representations currently used are dense and uninterpretable, leading to interpretations that themselves are relative, overcomplete, and hard to interpret. We propose a method that transforms these word vectors into reduced…
Assessing the synergistic high-order behaviors (HOBs) that emerge from underlying structural mechanisms is crucial to characterize complex systems. This work leverages the combined use of predictability and information measures to detect…
A geometric global formulation of the higher-order Lagrangian formalism for systems with finite number of degrees of freedom is provided. The formalism is applied to the study of systems with groups of Noetherian symmetries.
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…
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
The idea of symbolic controllers tries to bridge the gap between the top-down manual design of the controller architecture, as advocated in Brooks' subsumption architecture, and the bottom-up designer-free approach that is now standard…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Understanding how higher-order interactions affect collective behavior is a central problem in nonlinear dynamics and complex systems. Most works have focused on a single higher-order coupling function, neglecting other viable choices. Here…
In contrast to dyadic interactions, higher-order interactions may contain one another, with subgroups naturally embedded within larger groups. These containment patterns arise empirically in ecology, sociology, computer science and the…