# The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation

arXiv: https://arxiv.org/abs/1404.3300 · HTML: https://mlsanity.com/paper/1404.3300/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2014.

## Built on by (most cited first, 2 of 2)

- [Generalised Scale-Space Properties for Probabilistic Diffusion Models](https://mlsanity.com/paper/2303.07900/) (2023)
- [Generalised Diffusion Probabilistic Scale-Spaces](https://mlsanity.com/paper/2309.08511/) (2023)

## Abstract (arXiv)

We generalize the SiZer of Chaudhuri and Marron (J. Amer. Statist. Assoc. 94 (1999) 807-823, Ann. Statist. 28 (2000) 408-428) for the detection of shape parameters of densities on the real line to the case of circular data. It turns out that only the wrapped Gaussian kernel gives a symmetric, strongly Lipschitz semi-group satisfying "circular" causality, that is, not introducing possibly artificial modes with increasing levels of smoothing. Some notable differences between Euclidean and circular scale space theory are highlighted. Based on this, we provide an asymptotic theory to make inference about the persistence of shape features. The resulting circular mode persistence diagram is applied to the analysis of early mechanically-induced differentiation in adult human stem cells from their actin-myosin filament structure. As a consequence, the circular SiZer based on the wrapped Gaussian kernel (WiZer) allows the verification at a controlled error level of the observation reported by Zemel et al. (Nat. Phys. 6 (2010) 468-473): Within early stem cell differentiation, polarizations of stem cells exhibit preferred directions in three different micro-environments.