@Frosini:2013], chaotic dynamics verification [@Mischaikow:1999; @kaczynski:mischaikow:mrozek:04], sensor network [@Silva:2005], complex network [@LeeH:2012; @Horak:2009], data analysis [@Carlsson:2009; @Niyogi:2011; @BeiWang:2011; @Rieck:2012; @XuLiu:2012], shape recognition [@DiFabio:2011; @AEHW06] and computational biology [@Kasson:2007; @Gameiro:2014; @Dabaghian:2012; @Perea:2015a; @Perea:2015b].]{} Compared with traditional computational topology [@Krishnamoorthy:2007; @YaoY:2009; @ChangHW:2013] and/or computational homology, persistent homology inherently has an additional dimension, the filtration parameter, which can be utilized to embed some crucial geometric or quantitative information into topological invariants. The importance of retaining geometric information in topological analysis has been recognized [@Biasotti:2008], and topology has been advocated as a new approach for tackling big datasets [@BVP15; @BHPP14; @Fujishiro:2000; @Carlsson:2009; @Ghrist:2008]. Most recently, persistent homology has been developed as a powerful tool for analyzing biomolecular topological fingerprints [@KLXia:2014c; @KLXia:2015d; @KLXia:2015e], quantitative fullerene stability analysis [@KLXia:2015a], topological transition in protein folding [@KLXia:2015c], cryo-EM structure determination [@KLXia:2015b], and in conjugation with machine learning for protein classification [@ZXCang:2015] and protein-ligand/drug binding affinity prediction [@ZXCang:2016b]. Differential geometry based topological persistence [@BaoWang:2016a] and multidimensional persistence [@KLXia:2015c] have also been developed for biomolecules analysis and modeling. It is worthy to mention that persistent topology along is able to outperform all the eminent methods in computational biophysics for the blind binding affinity prediction of protein-ligand complexes from massive data 