2 citations · 3 across the 7 of their papers we have counts for
9 papers
A methodology to evaluate the evolution of networks using topological data analysis
Joao Pita Costa, Tihana Galinac Grbac
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several top…
Aspects of an internal logic for persistence
João Pita Costa, Primož Škraba, Mikael Vejdemo-Johansson
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respecti…
Variable sets over an algebra of lifetimes: a contribution of lattice theory to the study of computational topology
João Pita Costa, Mikael Vejdemo Johansson, Primož Škraba
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is…
Flat Coset Decompositions of Skew Lattices
Joao Pita Costa, Karin Cvetko-Vah
Skew lattices are non-commutative generalizations of lattices, and the cosets represent the building blocks that skew lattices are built of. As by Leech's Second Decomposition Theo…
A Lattice for Persistence
Primož Škraba, João Pita Costa
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distr…
On the coset category of a skew lattice
Joao Pita Costa
Skew lattices are non-commutative generalizations of lattices. The coset structure decomposition is an original approach to the study of these algebras describing the relation betw…
On the coset structure of a skew lattice
Joao Pita Costa
The class of skew lattices can be seen as an algebraic category. It models an algebraic theory in the category of Sets where the Green's relation D is a congruence describing an ad…
On the coset structure of distributive skew lattices
Joao Pita Costa
In the latest developments in the theory of skew lattices, distributivity has been one of the main topics of study. The largest classes of examples of such algebras are distributiv…
On ideals of a skew lattice
Joao Pita Costa
Ideals are one of the main topics of interest to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory…