arXiv subjects

Sebastian Pardo G.

Publications and source records attributed to Sebastian Pardo G..

3 recordsLinked to original sources

arXiv2021

A category theory approach using preradicals to model information flows in networks

Category theory has been recently used as a tool for constructing and modeling an information flow framework. Here, we show that the flow of information can be described using preradicals. We prove that preradicals generalize the notion of persistence in spaces where the underlying structure forms a directed acyclic graph. We show that a particular $α$ preradical describes the persistence of a commutative $G$-module associated with a directed acyclic graph. Furthermore, given how preradicals are defined, they are able to preserve the modeled system's underlying structure. This allows us to generalize the notions of standard persistence, zigzag persistence, and multidirectional persistence.

math.CT↗

arXiv2021

Information entropy re-defined in a category theory context using preradicals

Algebraically, entropy can be defined for abelian groups and their endomorphisms, and was latter extended to consider objects in a Flow category derived from abelian categories, such as $R\textit{-}Mod$ with $R$ a ring. Preradicals are endofunctors which can be realized as compatible choice assignments in the category where they are defined. Here we present a formal definition of entropy for preradicals on $R$-Mod and show that the concept of entropy for preradicals respects their order as a big lattice. Also, due to the connection between modules and complete bounded modular lattices, we provide a definition of entropy for lattice preradicals, and show that this notion is equivalent, from a functorial perspective, to the one defined for module preradicals.

math.CT↗

arXiv2020

Construction of edge-ordered multidirected graphlets for comparing dynamics of spatial temporal neural networks

The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically bounded conditions is the notion of an underlying fundamental structure-function constraint imposed by the geometry of the structural networks and the resultant latencies involved with transfer of information. We recently described the construction and theoretical analysis of a framework that models how local structure-function rules give rise to emergent global dynamics on a neural network. An important part of this research program is the requirement for a set of mathematical methods that allow us to catalog, theoretically analyze, and numerically study the rich dynamical patterns that result. One direction we are exploring is an extension of the theory of graphlets. In this paper we introduce an extension of graphlets and associated metric that maps the topological transition of a network from one moment in time to another at the same time that causal relationships are preserved.

q-bio.NC↗