Related papers: First Steps towards Categorical Algebraic Artifici…
This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently…
All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular…
Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…
We develop a model describing long-range atom-atom interactions in a two-dimensional periodic or a-periodic lattice of optical centers considering spectral and spatial broadening effects. Using both analytical and numerical Green's function…
We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is…
Chemical systems are traditionally described by lists of species, reactions, and externally imposed kinetic laws, a framework that lacks an intrinsic algebraic structure governing how transformations compose. We propose an axiomatic…
Molecular interactions are wired in a fascinating way resulting in complex behavior of biological systems. Theoretical modeling provides a useful framework for understanding the dynamics and the function of such networks. The complexity of…
Active matter, as other types of self-organizing systems, relies on the take-up of energy that can be used for different actions, such as active motion or structure formation. Here we provide an agent-based framework to model these…
Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number $\beta$ of species may be involved in the…
Scientists investigate the dynamics of complex systems with quantitative models, employing them to synthesize knowledge, to explain observations, and to forecast future system behavior. Complete specification of systems is impossible, so…
We have extended the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) to support directional bonds and dynamic bonding. The framework supports stochastic formation of new bonds, breakage of existing bonds, and conversion…
A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…
This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC…
The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such…
Our interest lies in exploring the ability of a coupled nonlocal system of two quasilinear parabolic partial differential equations to produce phase separation patterns. The obtained patterns are referred here as morphologies. Our target…
An operatorial model of a system made by $N$ agents interacting each other with mechanisms that can be thought of as cooperative or competitive is presented. We associate to each agent an annihilation, creation and number fermionic…
The relative cell complexes with respect to a generating set of cofibrations are an important class of morphisms in any model structure. In the particular case of the standard (algebraic) model structure on $\textbf{Top}$, we give a new…
In categorical compositional semantics of natural language one studies functors from a category of grammatical derivations (such as a Lambek pregroup) to a semantic category (such as real vector spaces). We compositionally build…
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…