Abstract Network theory helps us understand, analyze, model, and design various complex systems. Complex networks encode the complex topology and structural interactions of various systems in nature. To mine the multiscale coupling, heterogeneity, and complexity of natural and technological systems, we need expressive and rigorous mathematical tools that can help us understand the growth, topology, dynamics, multiscale structures, and functionalities of complex networks and their interrelationships. Towards this end, we construct the node-based fractal dimension (NFD) and the node-based multifractal analysis (NMFA) framework to reveal the generating rules and quantify the scale-dependent topology and multifractal features of a dynamic complex network. We propose novel indicators for measuring the degree of complexity, heterogeneity, and asymmetry of network structures, as well as the structure distance between networks. This formalism provides new insights on learning the energy and phase transitions in the networked systems and can help us understand the multiple generating mechanisms governing the network evolution.
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Hidden network generating rules from partially observed complex networks
Abstract Complex biological, neuroscience, geoscience and social networks exhibit heterogeneous self-similar higher order topological structures that are usually characterized as being multifractal in nature. However, describing their topological complexity through a compact mathematical description and deciphering their topological governing rules has remained elusive and prevented a comprehensive understanding of networks. To overcome this challenge, we propose a weighted multifractal graph model capable of capturing the underlying generating rules of complex systems and characterizing their node heterogeneity and pairwise interactions. To infer the generating measure with hidden information, we introduce a variational expectation maximization framework. We demonstrate the robustness of the network generator reconstruction as a function of model properties, especially in noisy and partially observed scenarios. The proposed network generator inference framework is able to reproduce network properties, differentiate varying structures in brain networks and chromosomal interactions, and detect topologically associating domain regions in conformation maps of the human genome.
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- NSF-PAR ID:
- 10351663
- Date Published:
- Journal Name:
- Communications Physics
- Volume:
- 4
- Issue:
- 1
- ISSN:
- 2399-3650
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The interaction between T-cell receptors (TCRs) and peptides (epitopes) presented by major histocompatibility complex molecules (MHC) is fundamental to the immune response. Accurate prediction of TCR–epitope interactions is crucial for advancing the understanding of various diseases and their prevention and treatment. Existing methods primarily rely on sequence-based approaches, overlooking the inherent topology structure of TCR–epitope interaction networks. In this study, we present $GTE$, a novel heterogeneous Graph neural network model based on inductive learning to capture the topological structure between TCRs and Epitopes. Furthermore, we address the challenge of constructing negative samples within the graph by proposing a dynamic edge update strategy, enhancing model learning with the nonbinding TCR–epitope pairs. Additionally, to overcome data imbalance, we adapt the Deep AUC Maximization strategy to the graph domain. Extensive experiments are conducted on four public datasets to demonstrate the superiority of exploring underlying topological structures in predicting TCR–epitope interactions, illustrating the benefits of delving into complex molecular networks. The implementation code and data are available at https://github.com/uta-smile/GTE.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s42005-021-00701-5
