Related papers: Curvature-based Methods for Brain Network Analysis

Recently, there has been increased interest in fusing multimodal imaging to better understand brain organization. Specifically, accounting for knowledge of anatomical pathways connecting brain regions should lead to desirable outcomes such…

Connectomics and network neuroscience offer quantitative scientific frameworks for modeling and analyzing networks of structurally and functionally interacting neurons, neuronal populations, and macroscopic brain areas. This shift in…

Cellular neural circuit and networks consisting of interconnected neurons and glia are ulti- mately responsible for the information processing associated with information processing in the brain. While there are major efforts aimed at…

This paper presents a new look at the neural network (NN) robustness problem, from the point of view of graph theory analysis, specifically graph curvature. Graph curvature (e.g., Ricci curvature) has been used to analyze system dynamics…

Identifying (a) systemic barriers to quality healthcare access and (b) key indicators of care efficacy in the United States remains a significant challenge. To improve our understanding of regional disparities in care delivery, we introduce…

Human brains exhibit highly organized multiscale neurophysiological dynamics. Understanding those dynamic changes and the neuronal networks involved is critical for understanding how the brain functions in health and disease. Functional…

Functional connections in the brain are frequently represented by weighted networks, with nodes representing locations in the brain, and edges representing the strength of connectivity between these locations. One challenge in analyzing…

Graph Neural Networks (GNN) have been extensively used to extract meaningful representations from graph structured data and to perform predictive tasks such as node classification and link prediction. In recent years, there has been a lot…

In this paper we show the similarities and differences of two deep neural networks by comparing the manifolds composed of activation vectors in each fully connected layer of them. The main contribution of this paper includes 1) a new data…

Graph curvature provides geometric priors for Graph Neural Networks (GNNs), enhancing their ability to model complex graph structures, particularly in terms of structural awareness, robustness, and theoretical interpretability. Among…

A goal in network science is the geometrical characterization of complex networks. In this direction, we have recently introduced Forman's discretization of Ricci curvature to the realm of undirected networks. Investigation of this…

Contemporary neuroscience has embraced network science to study the complex and self-organized structure of the human brain; one of the main outstanding issues is that of inferring from measure data, chiefly functional Magnetic Resonance…

Randomly Wired Neural Networks (RWNNs) serve as a valuable testbed for investigating the impact of network topology in deep learning by capturing how different connectivity patterns impact both learning efficiency and model performance. At…

A goal in network science is the geometrical characterization of complex networks. In this direction, we (arXiv:1603.00386; J. Stat. Mech. (2016) P063206) have recently introduced the Forman's discretization of Ricci curvature to the realm…

Population analyses of functional connectivity have provided a rich understanding of how brain function differs across time, individual, and cognitive task. An important but challenging task in such population analyses is the identification…

In this paper, we investigate the geometric structure of activation spaces of fully connected layers in neural networks and then show applications of this study. We propose an efficient approximation algorithm to characterize the convex…

Vascular networks play a crucial role in understanding brain functionalities. Brain integrity and function, neuronal activity and plasticity, which are crucial for learning, are actively modulated by their local environments, specifically…

Traditionally, network analysis is based on local properties of vertices, like their degree or clustering, and their statistical behavior across the network in question. This paper develops an approach which is different in two respects. We…

With the wide adoption of functional magnetic resonance imaging (fMRI) by cognitive neuroscience researchers, large volumes of brain imaging data have been accumulated in recent years. Aggregating these data to derive scientific insights…

Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…