1 citations · 3 across the 9 of their papers we have counts for
12 papers
Homology-based Morphometry of Brain Atrophy: Methods and Applications
Donato Quiccione, Mariam Pirashvili, Nathan Broomhead +1
Understanding the structure of the brain, and how it changes with time and disease, is a core goal of structural neuroimaging. Contemporary approaches to structural brain analysis…
An isometry theorem for persistent homology of circle-valued functions
Nathan Broomhead, Mariam Pirashvili
This paper explores persistence modules for circle-valued functions, presenting a new extension of the interleaving and bottleneck distances in this setting. We propose a natural g…
Symmetric cohomology of groups and Poincaré duality
Mariam Pirashvili, Teimuraz Pirashvili
Let be a finite group of order and let be a -module. We construct groups for which where $M^{…
On the Gottlieb group, Drinfeld centre and the centre of a crossed module
Mariam Pirashvili
This new version includes a connection of the main construction to the Gottlieb group, which was absent in the previous versions. However, the first version included material about…
On the nonabelian cohomology with coefficients in a crossed module
Mariam Pirashvili
This paper is concerned with the nonabelian cohomology of groups with coefficients in crossed modules. These objects were introduced by Dedecker and studied by Breen, Borovoi, Nooh…
On the complexity of zero-dimensional multiparameter persistence
Jacek Brodzki, Matthew Burfitt, Mariam Pirashvili
Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preve…
An outline of obstruction theories of extensions via track categories
Mariam Pirashvili
Abelian track categories can be classified via the third Baues-Wirsching cohomology of small categories. This approach is used in this paper to compare and classify different gener…
Topology and geometry of molecular conformational spaces and energy landscapes
Ingrid Membrillo-Solis, Mariam Pirashvili, Lee Steinberg +2
Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding probl…
Crossed modules and symmetric cohomology of groups
Mariam Pirashvili
This paper links the third symmetric cohomology (introduced by Staic and Zarelua ) to crossed modules with certain properties. The equivalent result in the language of 2-groups sta…
Symmetric cohomology of groups
Mariam Pirashvili
We investigate the relationship between the symmetric, exterior and classical cohomologies of groups. The first two theories were introduced respectively by Staic and Zarelua. We s…
Schreier Theory of Track Categories
Mariam Pirashvili
This paper is a continuation of our study of non-abelian Baues-Wirsching cohomologies. In our previous paper, we defined second non-abelian cohomology H2(C;D) of a small category C…
Endomorphisms in short exact sequences
Mariam Pirashvili
We sudy the behaviour of endomorphisms and automorphisms of groups involved in abelian group extensions. The main result can be stated as follows: Let be a…