Information Storage as a Proxy for Persistent Homology of Human Connectome
- 1Technical University of Applied Sciences Würzburg-Schweinfurt (THWS), 97070 Würzburg, Germany
- 2Vysshaya Shkola Ekonomiki V Peterburge, St. Petersburg 194100, Russia
- 3Vysshaya Shkola Ekonomiki V Peterburge, Moscow 101000, Russia
Abstract
Persistent homology allows one to measure the structural complexity of a network, which has been interpreted as a proxy for the amount of active memory, yet it is rarely used because of high computational demands. This paper shows that active information storage (AIS) is strongly associated with persistence diagram-based topological complexity while being far cheaper to compute. We evaluate both quantities on the human connectome of 137 subjects across five cognitive tasks and two resting-state conditions from the WU-Minn HCP dataset. Averaged over subjects, the association between the mean AIS and the persistence diagram distance to the resting-state anchor is high for all four persistence diagram distances considered, with Pearson coefficients between 0.74 and 0.80 and Spearman coefficients between 0.85 and 0.90; all four rank associations are significant at the group level and remain so after Holm–Bonferroni correction across the four distances. On a single consumer-grade workstation, persistence diagrams become intractable beyond a few hundred nodes, whereas AIS is evaluated for n = 15,000 in approximately one minute. We also state explicitly the conditions under which the two quantities are expected to agree and the caveats—anchor choice, hemodynamic autocorrelation and the limited number of experimental conditions—that qualify the interpretation of AIS as a measure of active memory.
Related
- RedZeD: Computing persistent homology by Reduction to Zero Differentials
- Persistent Homology of Biquandle Coloring Quivers
- The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology
- Geometric Realizations of Capability Spaces of Large Models and Zigzag Persistent Homology
- Limit Theorems for Persistent Homology of Multiparameter Complex Processes
BibTeX
@article{yamshchikov2026information,
title = {{Information Storage as a Proxy for Persistent Homology of Human Connectome}},
author = {Ivan Yamshchikov and Maxim Zapolskii and Vladimir Smurygin},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14213991},
url = {https://www.mdpi.com/2227-7390/14/21/3991},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Information Storage as a Proxy for Persistent Homology of Human Connectome
AU - Ivan Yamshchikov
AU - Maxim Zapolskii
AU - Vladimir Smurygin
PY - 2026
DA - 2026/11/02
JO - Mathematics
DO - 10.3390/math14213991
UR - https://www.mdpi.com/2227-7390/14/21/3991
AB - Persistent homology allows one to measure the structural complexity of a network, which has been interpreted as a proxy for the amount of active memory, yet it is rarely used because of high computational demands. This paper shows that active information storage (AIS) is strongly associated with persistence diagram-based topological complexity while being far cheaper to compute. We evaluate both quantities on the human connectome of 137 subjects across five cognitive tasks and two resting-state conditions from the WU-Minn HCP dataset. Averaged over subjects, the association between the mean AIS and the persistence diagram distance to the resting-state anchor is high for all four persistence diagram distances considered, with Pearson coefficients between 0.74 and 0.80 and Spearman coefficients between 0.85 and 0.90; all four rank associations are significant at the group level and remain so after Holm–Bonferroni correction across the four distances. On a single consumer-grade workstation, persistence diagrams become intractable beyond a few hundred nodes, whereas AIS is evaluated for n = 15,000 in approximately one minute. We also state explicitly the conditions under which the two quantities are expected to agree and the caveats—anchor choice, hemodynamic autocorrelation and the limited number of experimental conditions—that qualify the interpretation of AIS as a measure of active memory.
SN - 2227-7390
ER -