<?xml version='1.0' encoding='UTF-8'?><codeBook xmlns="ddi:codebook:2_5" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="ddi:codebook:2_5 https://ddialliance.org/Specification/DDI-Codebook/2.5/XMLSchema/codebook.xsd" version="2.5"><docDscr><citation><titlStmt><titl>Replication Data for: Hodge theory-based biomolecular data analysis</titl><IDNo agency="DOI">doi:10.21979/N9/0TK4YR</IDNo></titlStmt><distStmt><distrbtr source="archive">DR-NTU (Data)</distrbtr><distDate>2023-06-23</distDate></distStmt><verStmt source="archive"><version date="2023-06-23" type="RELEASED">1</version></verStmt><biblCit>Wei, Ronald Koh Joon; Wee, JunJie; Laurent, Valerie Evangelin; Xia, Kelin, 2023, "Replication Data for: Hodge theory-based biomolecular data analysis", https://doi.org/10.21979/N9/0TK4YR, DR-NTU (Data), V1</biblCit></citation></docDscr><stdyDscr><citation><titlStmt><titl>Replication Data for: Hodge theory-based biomolecular data analysis</titl><IDNo agency="DOI">doi:10.21979/N9/0TK4YR</IDNo></titlStmt><rspStmt><AuthEnty affiliation="Nanyang Technological University">Wei, Ronald Koh Joon</AuthEnty><AuthEnty affiliation="Nanyang Technological University">Wee, JunJie</AuthEnty><AuthEnty affiliation="Nanyang Technological University">Laurent, Valerie Evangelin</AuthEnty><AuthEnty affiliation="Nanyang Technological University">Xia, Kelin</AuthEnty></rspStmt><prodStmt><software>Python</software><software>MATLAB</software><grantNo agency="Nanyang Technological University">M4081842</grantNo><grantNo agency="Ministry of Education (MOE)">RG109/19</grantNo><grantNo agency="Ministry of Education (MOE)">MOE-T2EP20120-0013</grantNo><grantNo agency="Ministry of Education (MOE)">MOE-T2EP20220-0010</grantNo></prodStmt><distStmt><distrbtr source="archive">DR-NTU (Data)</distrbtr><contact affiliation="Nanyang Technological University">Xia, Kelin</contact><depositr>Wee, JunJie</depositr><depDate>2023-06-19</depDate></distStmt><holdings URI="https://doi.org/10.21979/N9/0TK4YR"/></citation><stdyInfo><subject><keyword xml:lang="en">Mathematical Sciences</keyword><keyword xml:lang="en">Medicine, Health and Life Sciences</keyword><keyword>Mathematical Sciences</keyword><keyword>Medicine, Health and Life Sciences</keyword><keyword>Hodge theory</keyword><keyword>Topological associated domain</keyword><keyword>Chromosomes</keyword></subject><abstract date="2022-06-11">Hodge theory reveals the deep intrinsic relations of differential forms and provides a bridge between differential geometry, algebraic topology, and functional analysis. Here we use Hodge Laplacian and Hodge decomposition models to analyze biomolecular structures. Different from traditional graph-based methods, biomolecular structures are represented as simplicial complexes, which can be viewed as a generalization of graph models to their higher-dimensional counterparts. Hodge Laplacian matrices at different dimensions can be generated from the simplicial complex. The spectral information of these matrices can be used to study intrinsic topological information of biomolecular structures. Essentially, the number (or multiplicity) of k-th dimensional zero eigenvalues is equivalent to the k-th Betti number, i.e., the number of k-th dimensional homology groups. The associated eigenvectors indicate the homological generators, i.e., circles or holes within the molecular-based simplicial complex. Furthermore, Hodge decomposition-based HodgeRank model is used to characterize the folding or compactness of the molecular structures, in particular, the topological associated domain (TAD) in high-throughput chromosome conformation capture (Hi-C) data. Mathematically, molecular structures are represented in simplicial complexes with certain edge flows. The HodgeRank-based average/total inconsistency (AI/TI) is used for the quantitative measurements of the folding or compactness of TADs. This is the first quantitative measurement for TAD regions, as far as we know.</abstract><sumDscr><dataKind>Raw PDB files and Computational codes</dataKind></sumDscr></stdyInfo><method><dataColl><sources/></dataColl><anlyInfo/></method><dataAccs><setAvail/><useStmt/></dataAccs><othrStdyMat><relPubl><citation><titlStmt><IDNo agency="doi">10.1038/s41598-022-12877-z</IDNo></titlStmt><biblCit>Wei, R. K. J., Wee, J., Laurent, V. E., &amp; Xia, K. (2022). Hodge theory-based biomolecular data analysis. Scientific Reports, 12(1), 9699.</biblCit></citation><ExtLink URI="https://www.nature.com/articles/s41598-022-12877-z"/></relPubl><relPubl><citation><titlStmt><IDNo agency="handle">10356/160448</IDNo></titlStmt><biblCit>Wei, R. K. J., Wee, J., Laurent, V. E., &amp; Xia, K. (2022). Hodge theory-based biomolecular data analysis. Scientific Reports, 12(1), 9699.</biblCit></citation><ExtLink URI="https://hdl.handle.net/10356/160448"/></relPubl></othrStdyMat></stdyDscr><otherMat ID="f114415" URI="https://researchdata.ntu.edu.sg/api/access/datafile/114415" level="datafile"><labl>Hodge-Theory-main.rar</labl><notes level="file" type="DATAVERSE:CONTENTTYPE" subject="Content/MIME Type">application/x-rar-compressed</notes></otherMat></codeBook>