Volume 26 • Issue 4 • PP: 174-183 • 2025
A Simplical Complex-Based Kernel Estimation Method for Cracking Higher-Order Graph Structures in Cell Complex Topology
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© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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The primary goal of the article is to examine the data s shape and crack higher-order graph structures in cell complex topology. Further simplical complex-based kernel estimation methods are explored and discussed.
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References
[1] Munkres, J. Elements of Algebraic Topology. Addison Wesley Publishing Company. (1984).
[2] Edelsbrunner, H., Harer, J. (2010). Computational topology: an introduction. American Mathematical Society.
[3] Bertrand, J. (1858). Note sur la th´eorie des poly`edres r´eguliers, Comptes rendus des s´eances de l’Acad´emie des Sciences, 46: 79–82, 117.
[4] Euler, L. (1758). Elementa doctrinae solidorum [Elements of rubrics for solids]. Novi Commentarii Academiae Scientiarum Petropolitanae: 109–140 – via U. Pacific, Stockton, CA.
[5] Evans, M. W., Harlow, F. H. (1957) The particle-in-cell method for hydrodynamic calculations.
[6] Greene, L. H. (2012). Protein structure networks, Briefings in Functional Genomics, 11, 469–478.
[7] Hatcher, A. (2002). Algebraic topology. Cambridge University Press. ISBN 0-521-79540-0.
[8] Greub, W. (1975). Linear Algebra, Springer-Verlag, Fourth edition.
[9] Bruns, W. and Herzog, J. Cohen-Macaulay Rings, 2nd ed. Cambridge, England: Cambridge University Press, 1998.
[10] Mannige, R. V. (2014). Dynamic New World: Refining Our View of Protein Structure, Function and Evolution, Proteomes, 2: 128–153.
[11] Edelsbrunner, H.; Letscher, D.; Zomorodian, A. (2002). ”Topological Persistence and Simplification”. Discrete & Computational Geometry. 28 (4): 511–533.
[12] Goerss, P.G., Jardin, J.F. (2009). Simplicial Homotopy Theory. Birkh¨auser Basel. ISBN 978-3-0346- 0188-7.
[13] Kamiyama., Y. (2024). The Topology of Subspaces of the Configuration Space of Spatial Hexagons. Contributions to Pure and Applied Mathematics,2(1):108.
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