5 papers
From Raw Data to Structural Semantics: Trade-offs among Distortion, Rate, and Inference Accuracy
Charmin Asirimath, Chathuranga Weeraddana, Sumudu Samarakoon +2
This work explores the advantages of using persistence diagrams (PDs), topological signatures of raw point cloud data, in a point-to-point communication setting. PD is a structural…
Presenting the Sierpinski Gasket in Various Categories of Metric Spaces
Jayampathy Ratnayake, Annanthakrishna Manokaran, Romaine Jayewardene +2
This paper studies presentations of the Sierpinski gasket as a final coalgebra for functors on several categories of metric spaces with additional designated points. The three cate…
Sierpinski Gasket as a Final Coalgebra Obtained by Cauchy Completing the Initial Algebra
Jayampathy Ratnayake, Annanthakrishna Manokaran, Romaine Jayewardene
This paper presents the Sierpinski Gasket () as a final coalgebra obtained by Cauchy completing the initial algebra for an endofunctor on the category of tri-pointed on…
Critical Points to Determine Persistence Homology
Charmin Asirimath, Jayampathy Ratnayake, Chathuranga Weeraddana
Computation of the simplicial complexes of a large point cloud often relies on extracting a sample, to reduce the associated computational burden. The study considers sampling crit…
On the Initial Algebra and Final Co-algebra of some Endofunctors on Categories of Pointed Metric Spaces
Annanthakrishna Manokaran, Romaine Jayewardene, Jayampathy Ratnayake
We consider two endofunctors of the form , where is a non degenerate module, related to the unit interval and the Sierpinski gasket, and thei…