1 citations · 1 across the 10 of their papers we have counts for
10 papers
On the Hausdorff stability of barcodes over posets
Mujtaba Ali, Tom Needham, Anastasios Stefanou +1
The Isometry Theorem of Chazal et al. and Lesnick is a fundamental result in persistence theory, which states that the interleaving distance between two one-parameter persistence m…
Doughnut or Mickey Mouse? Detecting Toroidal Structure in Data through Persistent Cup-Length
Ekaterina S. Ivshina, Galit Anikeeva, Ling Zhou
Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies bas…
Persistence and Topological Complexity
Facundo Mémoli, Ling Zhou
Topological complexity is a homotopy invariant that measures the minimal number of continuous rules required for motion planning in a space. In this work, we introduce persistent a…
Algebraic Zhou valuations
Shijie Bao, Qi'an Guan, Lin Zhou
In this paper, we generalize Zhou valuations, originally defined on complex domains, to the framework of general schemes. We demonstrate that an algebraic version of the Jonsson--M…
Torsion higher Chow cycles modulo
Theodosis Alexandrou, Lin Zhou
We study the injectivity property of certain actions of higher Chow groups on refined unramified cohomology. As an application for every and for each and $n\ge…
Persistent cohomology operations and Gromov-Hausdorff estimates
Anibal M. Medina-Mardones, Ling Zhou
We establish the foundations of the theory of persistent cohomology operations, derive decomposition formulas for wedge sums and products, and prove their Gromov-Hausdorff stabilit…
Hoeffding's inequality for continuous-time Markov chains
Jinpeng Liu, Yuanyuan Liu, Lin Zhou
Hoeffding's inequality is a fundamental tool widely applied in probability theory, statistics, and machine learning. In this paper, we establish Hoeffding's inequalities specifical…
On the functoriality of refined unramified cohomology
Kees Kok, Lin Zhou
In this paper, we generalise the construction of the functorial pullback of refined unramified cohomology between smooth schemes, by following the ideas of Fulton's intersection th…
Persistent Sullivan Minimal Models of Metric Spaces
Ling Zhou
We extend classical tools from rational homotopy theory to topological data analysis by introducing persistent Sullivan minimal models of persistent topological spaces. Our main re…
Some results about the Tight Span of spheres
Sunhyuk Lim, Facundo Memoli, Zhengchao Wan +2
The smallest hyperconvex metric space containing a given metric space X is called the tight span of X. It is known that tight spans have many nice geometric and topological propert…