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This paper proposes a novel topological learning framework that can integrate brain networks of different sizes and topology through persistent homology. This is possible through the introduction of a new topological loss function that enables such challenging task. The use of the proposed loss function bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations with ground truth to assess the effectiveness of the topological loss in discriminating networks with different topology. The method is further applied to a twin brain imaging study in determining if the brain network is genetically heritable. The challenge is in overlaying the topologically different functional brain networks obtained from the resting-state functional MRI (fMRI) onto the template structural brain network obtained through the diffusion MRI (dMRI).
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Recent developments in graph theoretic analysis of complex networks have led to deeper understanding of brain networks. Many complex networks show similar macroscopic behaviors despite differences in the microscopic details. Probably two most often observed characteristics of complex networks are scale-free and small-world properties. In this paper, we will explore whether brain networks follow scale-free and small-worldness among other graph theory properties.
Most humans have the good fortune to live their lives embedded in richly structured social groups. Yet, it remains unclear how humans acquire knowledge about these social structures to successfully navigate social relationships. Here we address this knowledge gap with an interdisciplinary neuroimaging study drawing on recent advances in network science and statistical learning. Specifically, we collected BOLD MRI data while participants learned the community structure of both social and non-social networks, in order to examine whether the learning of these two types of networks was differentially associated with functional brain network topology. From the behavioral data in both tasks, we found that learners were sensitive to the community structure of the networks, as evidenced by a slower reaction time on trials transitioning between clusters than on trials transitioning within a cluster. From the neuroimaging data collected during the social network learning task, we observed that the functional connectivity of the hippocampus and temporoparietal junction was significantly greater when transitioning between clusters than when transitioning within a cluster. Furthermore, temporoparietal regions of the default mode were more strongly connected to hippocampus, somatomotor, and visual regions during the social task than during the non-social task. Collectively, our results identify neurophysiological underpinnings of social versus non-social network learning, extending our knowledge about the impact of social context on learning processes. More broadly, this work offers an empirical approach to study the learning of social network structures, which could be fruitfully extended to other participant populations, various graph architectures, and a diversity of social contexts in future studies.
The human brain is a complex dynamical system that gives rise to cognition through spatiotemporal patterns of coherent and incoherent activity between brain regions. As different regions dynamically interact to perform cognitive tasks, variable patterns of partial synchrony can be observed, forming chimera states. We propose that the emergence of such states plays a fundamental role in the cognitive organization of the brain, and present a novel cognitively-informed, chimera-based framework to explore how large-scale brain architecture affects brain dynamics and function. Using personalized brain network models, we systematically study how regional brain stimulation produces different patterns of synchronization across predefined cognitive systems. We then analyze these emergent patterns within our novel framework to understand the impact of subject-specific and region-specific structural variability on brain dynamics. Our results suggest a classification of cognitive systems into four groups with differing levels of subject and regional variability that reflect their different functional roles.
The structural human connectome (i.e. the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network made available by the Open Connectome Project. We apply statistical model selection to characterize the degree distributions of graphs containing up to $simeq 10^6$ nodes and $simeq 10^8$ edges. A three-parameter generalized Weibull (also known as a stretched exponential) distribution is a good fit to most of the observed degree distributions. For almost all networks, simple power laws cannot fit the data, but in some cases there is statistical support for power laws with an exponential cutoff. We also calculate the topological (graph) dimension $D$ and the small-world coefficient $sigma$ of these networks. While $sigma$ suggests a small-world topology, we found that $D < 4$ showing that long-distance connections provide only a small correction to the topology of the embedding three-dimensional space.
Multimodal brain networks characterize complex connectivities among different brain regions from both structural and functional aspects and provide a new means for mental disease analysis. Recently, Graph Neural Networks (GNNs) have become a de facto model for analyzing graph-structured data. However, how to employ GNNs to extract effective representations from brain networks in multiple modalities remains rarely explored. Moreover, as brain networks provide no initial node features, how to design informative node attributes and leverage edge weights for GNNs to learn is left unsolved. To this end, we develop a novel multiview GNN for multimodal brain networks. In particular, we regard each modality as a view for brain networks and employ contrastive learning for multimodal fusion. Then, we propose a GNN model which takes advantage of the message passing scheme by propagating messages based on degree statistics and brain region connectivities. Extensive experiments on two real-world disease datasets (HIV and Bipolar) demonstrate the effectiveness of our proposed method over state-of-the-art baselines.
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