14 citations · 19 across the 9 of their papers we have counts for
11 papers
Approximation by interval-decomposables and interval resolutions of persistence modules
Hideto Asashiba, Emerson G. Escolar, Ken Nakashima +1
In topological data analysis, two-parameter persistence can be studied using the representation theory of the 2d commutative grid, the tensor product of two Dynkin quivers of type…
Algebraic stability theorem for derived categories of zigzag persistence modules
Yasuaki Hiraoka, Yuichi Ike, Michio Yoshiwaki
We study distances on zigzag persistence modules from the viewpoint of derived categories and Auslander--Reiten quivers. The derived category of ordinary persistence modules is der…
Interleavings and Matchings as Representations
Emerson G. Escolar, Killian Meehan, Michio Yoshiwaki
In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular,…
Field choice problem in persistent homology
Ippei Obayashi, Michio Yoshiwaki
This paper tackles the problem of coefficient field choice in persistent homology. When we compute a persistence diagram, we need to select a coefficient field before computation.…
On Approximation of D Persistence Modules by Interval-decomposables
Hideto Asashiba, Emerson G. Escolar, Ken Nakashima +1
In this work, we propose a new invariant for D persistence modules called the compressed multiplicity and show that it generalizes the notions of the dimension vector and the ra…
On Interval Decomposability of 2D Persistence Modules
Hideto Asashiba, Mickaël Buchet, Emerson G. Escolar +2
In the persistent homology of filtrations, the indecomposable decompositions provide the persistence diagrams. However, in almost all cases of multidimensional persistence, the cla…
On isomorphisms of generalized multifold extensions of algebras without nonzero oriented cycles
H. Asashiba, M. Kimura, K. Nakashima +1
Assume that a basic algebra over an algebraically closed field with a basic set of primitive idempotents has the property that for all . Le…
Decomposition theory of modules: the case of Kronecker algebra
Hideto Asashiba, Ken Nakashima, Michio Yoshiwaki
Let be a finite-dimensional algebra over an algebraically closed field . For any finite-dimensional -module we give a general formula that computes the indecompos…
Relative derived dimensions for cotilting modules
Michio Yoshiwaki
For a Noetherian ring and a cotilting -module of injective dimension at least , we prove that the derived dimension of with respect to the category $\mathcal{X}_T…
Dimensions of triangulated categories with respect to subcategories
Takuma Aihara, Tokuji Araya, Osamu Iyama +2
This paper introduces the concept of the dimension of a triangulated category with respect to a fixed full subcategory. For the bounded derived category of an abelian category, upp…
On selfinjective algebras of stable dimension zero
Michio Yoshiwaki
Let be a selfinjective algebra over an algebraically closed field. We study the stable dimension of , which is the dimension of the stable module category of in the sens…