Related papers: Towards a Quantitative Theory of Digraph-Based Com…
Neuropsychiatric disorders impact functional connectivity of the brain at the network level. The identification and statistical testing of disorder-related networks remains challenging. We propose novel methods to streamline the detection…
Recently emerged Topological Deep Learning (TDL) methods aim to extend current Graph Neural Networks (GNN) by naturally processing higher-order interactions, going beyond the pairwise relations and local neighborhoods defined by graph…
Collective synchronization in complex systems arises from the interplay between topology and dynamics, yet how to design and control such patterns in higher-order networks remains unclear. Here we show that a Dirac spectral programming…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…
Directed graphs have asymmetric connections, yet the current graph clustering methodologies cannot identify the potentially global structure of these asymmetries. We give a spectral algorithm called di-sim that builds on a dual measure of…
Conventional spectral digraph partitioning methods typically symmetrize the adjacency matrix, thereby transforming the directed graph partitioning problem into an undirected one, where bipartitioning is commonly linked to minimizing graph…
A directed hypergraph, which consists of nodes and hyperarcs, is a higher-order data structure that naturally models directional group interactions (e.g., chemical reactions of molecules). Although there have been extensive studies on local…
Graph neural networks (GNNs) have been developed to model the relationship between regions of interest (ROIs) in brains and have shown significant improvement in detecting brain diseases. However, most of these frameworks do not consider…
The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and…
Qualitative causal relationships compactly express the direction, dependency, temporal constraints, and monotonicity constraints of discrete or continuous interactions in the world. In everyday or academic language, we may express…
Brain development during adolescence is marked by substantial changes in brain structure and function, leading to a stable network topology in adulthood. However, most prior work has examined the data through the lens of brain areas…
Dense regions in networks are an indicator of interesting and unusual information. However, most existing methods only consider simple, undirected, unweighted networks. Complex networks in the real-world often have rich information though:…
Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…
Applying network science approaches to investigate the functions and anatomy of the human brain is prevalent in modern medical imaging analysis. Due to the complex network topology, for an individual brain, mining a discriminative network…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
Diffusion Magnetic Resonance Imaging (MRI) exploits the anisotropic diffusion of water molecules in the brain to enable the estimation of the brain's anatomical fiber tracts at a relatively high resolution. In particular, tractographic…
Brain network analysis based on functional Magnetic Resonance Imaging (fMRI) is pivotal for diagnosing brain disorders. Existing approaches typically rely on predefined functional sub-networks to construct sub-network associations. However,…
Hypergraphs provide a powerful framework for modeling complex systems and networks with higher-order interactions beyond simple pairwise relationships. However, graph-based clustering approaches, which focus primarily on pairwise relations,…
Prediction the conversion to early-stage dementia is critical for mitigating its progression but remains challenging due to subtle cognitive impairments and structural brain changes. Traditional T1-weighted magnetic resonance imaging…
Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a…