arXiv subjects

H. Hill Goldsmith

Publications and source records attributed to H. Hill Goldsmith.

3 recordsLinked to original sources

arXiv2024

Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest

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.

math.AT↗

arXiv2020

Statistical Analysis of Dynamic Functional Brain Networks in Twins

Recent studies have shown that functional brain brainwork is dynamic even during rest. A common approach to modeling the brain network in whole brain resting-state fMRI is to compute the correlation between anatomical regions via sliding windows. However, the direct use of the sample correlation matrices is not reliable due to the image acquisition, processing noises and the use of discrete windows that often introduce spurious high-frequency fluctuations and the zig-zag pattern in the estimated time-varying correlation measures. To address the problem and obtain more robust correlation estimates, we propose the heat kernel based dynamic correlations. We demonstrate that the proposed heat kernel method can smooth out the unwanted high-frequency fluctuations in correlation estimations and achieve higher accuracy in identifying dynamically changing distinct states. The method is further used in determining if such dynamic state change is genetically heritable using a large-scale twin study. Various methodological challenges for analyzing paired twin dynamic networks are addressed.

stat.AP↗

arXiv2018

Exact Combinatorial Inference for Brain Images

The permutation test is known as the exact test procedure in statistics. However, often it is not exact in practice and only an approximate method since only a small fraction of every possible permutation is generated. Even for a small sample size, it often requires to generate tens of thousands permutations, which can be a serious computational bottleneck. In this paper, we propose a novel combinatorial inference procedure that enumerates all possible permutations combinatorially without any resampling. The proposed method is validated against the standard permutation test in simulation studies with the ground truth. The method is further applied in twin DTI study in determining the genetic contribution of the minimum spanning tree of the structural brain connectivity.

stat.CO↗