Related papers: First Steps towards Categorical Algebraic Artifici…
Artificial Chemistries (ACs) are symbolic chemical metaphors for the exploration of Artificial Life, with specific focus on the problem of biogenesis or the origin of life. This paper presents authors thoughts towards defining a unified…
Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work, ultra-cold fermionic atoms have been proposed for these purposes by showing…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
Fuzzy set theory opens new vistas in computability theory and here I show this by defining a new computational metaphor--the fuzzy chemical metaphor. This metaphor is an extension of the chemical metaphor. In particular, I introduce the…
Quantum Algebras (q-algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and…
This paper proposes to use dialgebras to specify the semantics of interactive systems in a natural way. Dialgebras are a conservative extension of coalgebras. In this categorical model, from the point of view that we provide, the notions of…
Artificial Chemistries (ACs) are symbolic chemical metaphors for the exploration of Artificial Life, with specific focus on the origin of life. In this work we define a P system based artificial graph chemistry to understand the principles…
The objectives of this research work which is intimately related to pattern discovery and management are threefold: (i) handle the problem of pattern manipulation by defining operations on patterns, (ii) study the problem of enriching and…
An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge,…
In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…
We advocate the development of a discipline of interacting with and extracting information from models, both mathematical (e.g. game-theoretic ones) and computational (e.g. agent-based models). We outline some directions for the development…
We develop a functorial approach to the study of $n$-abelian categories by reformulating their axioms in terms of their categories of finitely presented functors. Such an approach allows the use of classical homological algebra and…
The behavior of an atom in a molecule, liquid or solid is governed by the force it experiences. If the dependence of this vectorial force on the atomic chemical environment can be $learned$ efficiently with high-fidelity from benchmark…
In this master's thesis, we rigorously develop two frameworks of relational composition of systems using tools from category theory. The first framework addresses port-Hamiltonian systems, which are dynamical systems whose dynamics are…
We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…
We study fibrations arising from indexed categories of the following form: fix two categories $\mathcal{A},\mathcal{X}$ and a functor $F : \mathcal{A} \times \mathcal{X} \longrightarrow\mathcal{X} $, so that to each $F_A=F(A,-)$ one can…
For a nice-enough category $\mathcal{C}$, we construct both the morphism category ${\rm H}(\mathcal{C})$ of $\mathcal{C}$ and the category ${\rm mod}\mbox{-}\mathcal{C}$ of all finitely presented contravariant additive functors over…
In this paper, we introduce product interactions, an algebraic formalism in which neural network layers are constructed from compositions of a multiplication operator defined over suitable algebras. Product interactions provide a principled…
Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles,…