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Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
Hierarchically designed mechanical metamaterials involve nested levels of structural organization, mimicking natural structures (such as bones, wood, and bird feathers) to create advanced functional materials. Compositional hierarchy, a…
We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory. More specifically, we provide mutually compatible tools for hierarchical, sequential, and independent parallel composition.…
We present a method for logical specification of the behavior of a system based on the specification of its components and for representing and specifying the effect of a class of communication "signaling pathways" among them. Variations in…
Model-driven engineering is the automatic production of software artefacts from abstract models of structure and functionality. By targeting a specific class of system, it is possible to automate aspects of the development process, using…
A new category $\mathfrak{dp}$, called of dynamical patterns addressing a primitive, nongeometrical concept of dynamics, is defined and employed to construct a $2-$category $2-\mathfrak{dp}$, where the irreducible plurality of species of…
Designers of autonomous agents, whether in physical or virtual environments, need to express nondeterminisim, failure, and parallelism in behaviors, as well as accounting for synchronous coordination between agents. Behavior Trees are a…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
This paper formalizes a widely used dynamical class--replicator-mutator dynamics and Price-style selection-and-transmission--and makes explicit the modeling choices (scale, atomic unit, interaction topology, transmission kernel) that…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
The design of a complex system warrants a compositional methodology, i.e., composing simple components to obtain a larger system that exhibits their collective behavior in a meaningful way. We propose an automaton-based paradigm for…
The activity framework is a promising model-based design approach for Flexible Manufacturing Systems (FMS). It is used in industry for specification and analysis of FMS. It provides an intuitive specification language with a hierarchical…
We introduce materiomusic as a generative framework linking the hierarchical structures of matter with the compositional logic of music. Across proteins, spider webs and flame dynamics, vibrational and architectural principles recur as…
The design of intelligent materials often draws parallels with the complex adaptive behaviors of biological organisms, where robust functionality stems from sophisticated hierarchical organization and emergent long-distance coordination…
Our aim is to introduce a category-theoretic framework sufficiently general to describe a wide variety of open kinematic systems in classical mechanics while uniquely characterizing systems with specified simplest components. The framework…
Soft robotics is an emerging field of research where the robot body is composed of compliant and soft materials. It allows the body to bend, twist, and deform to move or to adapt its shape to the environment for grasping, all of which are…
Assuring the correct behavior of cyber-physical systems requires significant modeling effort, particularly during early stages of the engineering and design process when a system is not yet available for testing or verification of proper…
Animals learn to predict external contingencies from experience through a process of conditioning. A natural mechanism for conditioning is stimulus substitution, whereby the neuronal response to a stimulus with no prior behavioral…
A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented. We show that event-based systems are machines, with inputs and outputs, and that they can be composed with machines of different types,…
Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…