Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest
University of Wisconsin, Madison（威斯康星大学麦迪逊分校）；Taiwan（中国台湾）；New York University Grossman School of Medicine（纽约大学格罗斯曼医学院）；Georgia State University（佐治亚州立大学）；Waisman Center, University of Wisconsin-Madison（威斯康星大学麦迪逊分校怀斯曼中心）
Moo K. Chung, Shih-Gu Huang, Ian C. Carroll, Vince D. Calhoun, H. Hill Goldsmith
我们提出一种创新的、数据驱动的拓扑数据分析（topological data analysis, TDA）技术，用于估计静息态下动态变化的人类脑功能网络的状态空间。该方法利用Wasserstein距离衡量拓扑差异，可将脑网络聚类为不同的拓扑状态。在识别脑网络状态空间方面，该技术优于常用的k-means聚类，它能有效整合数据的时间动态特性，且无需明确的模型设定。我们进一步采用双生子研究设计探究这些拓扑特征的遗传基础，检验此类状态变化的遗传度。研究结果表明，脑网络的拓扑结构，尤其是其动态状态变化，可能蕴含重要的潜在遗传信息。该方法的MATLAB代码可在https://github.com/laplcebeltrami/PH-STAT获取。
英文摘要：
We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure topological differences, enabling the clustering of brain networks into distinct topological states. This technique outperforms the commonly used k-means clustering in identifying brain network state spaces by effectively incorporating the temporal dynamics of the data without the need for explicit model specification. We further investigate the genetic underpinnings of these topological features using a twin study design, examining the heritability of such state changes. Our findings suggest that the topology of brain networks, particularly in their dynamic state changes, may hold significant hidden genetic information. MATLAB code for the method is available at https://github.com/laplcebeltrami/PH-STAT.
Geometric Realizations of Capability Spaces of Large Models and Zigzag Persistent Homology
School of Mathematics and Statistics, Guizhou University（贵州大学数学与统计学院）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Computer Science and Technology, Guizhou University（贵州大学计算机科学与技术学院）
The Chordal Distance Transform of Geometric Loops and its Persistent Homology
Cardiff University（卡迪夫大学）；Heilbronn Institute for Mathematical Research（希尔布龙数学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Department of Statistics, University of Oxford（牛津大学统计系）
