Related papers: First Steps towards Categorical Algebraic Artifici…
Artificial chemistry simulations produce many intriguing emergent behaviors, but they are often difficult to steer or control. This paper proposes a method for steering the dynamics of a classic artificial chemistry model, known as AlChemy…
We construct a wide subcategory of the category of finite association schemes with a collection of desirable properties. Our subcategory has a first isomorphism theorem analogous to that of groups. Also, standard constructions taking…
We develop the compositional theory of active inference by introducing activity, functorially relating statistical games to the dynamical systems which play them, using the new notion of approximate inference doctrine. In order to exhibit…
We propose the chemlambda artificial chemistry, whose behavior strongly suggests that real molecules which embed Interaction Nets patterns and real chemical reactions which resemble Interaction Nets graph rewrites could be a realistic path…
We present the bond-calculus, a process algebra for modelling biological and chemical systems featuring nonlinear dynamics, multiway interactions, and dynamic bonding of agents. Mathematical models based on differential equations have been…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is…
How do complex adaptive systems, such as life, emerge from simple constituent parts? In the 1990s Walter Fontana and Leo Buss proposed a novel modeling approach to this question, based on a formal model of computation known as $\lambda$…
We extend our earlier work on the compositional structure of cybernetic systems in order to account for the embodiment of such systems. All their interactions proceed through their bodies' boundaries: sensations impinge on their surfaces,…
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…
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…
This monograph is a study of the category of polynomial endofunctors on the category of sets and its applications to modeling interaction protocols and dynamical systems. We assume basic categorical background and build the categorical…
We present chemlambda (or the chemical concrete machine), an artificial chemistry with the following properties: (a) is Turing complete, (b) has a model of decentralized, distributed computing associated to it, (c) works at the level of…
Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as…
We extend the higher-order termination method of dynamic dependency pairs to Algebraic Functional Systems (AFSs). In this setting, simply typed lambda-terms with algebraic reduction and separate {\beta}-steps are considered. For left-linear…
Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive…