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

Huckemann, S.; Kim, K. R.; Munk, A.; Rehfeld, F.; Sommerfeld , M.; Weickert, J.; Wollnik, C.

doi:10.3150/15-BEJ722

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

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Munk, A.
Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society;

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Citation

Huckemann, S., Kim, K. R., Munk, A., Rehfeld, F., Sommerfeld, M., Weickert, J., et al. (2016). The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation. Bernoulli, 22(4), 2113-2142. doi:10.3150/15-BEJ722.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-E4BF-2

Abstract

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.