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.
more »
« less
Deciphering the generating rules and functionalities of complex networks
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.
more »
« less
- NSF-PAR ID:
- 10351662
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 11
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Real-world networked systems often show dynamic properties with continuously evolving network nodes and topology over time. When learning from dynamic networks, it is beneficial to correlate all temporal networks to fully capture the similarity/relevance between nodes. Recent work for dynamic network representation learning typically trains each single network independently and imposes relevance regularization on the network learning at different time steps. Such a snapshot scheme fails to leverage topology similarity between temporal networks for progressive training. In addition to the static node relationships within each network, nodes could show similar variation patterns (e.g., change of local structures) within the temporal network sequence. Both static node structures and temporal variation patterns can be combined to better characterize node affinities for unified embedding learning. In this paper, we propose Graph Attention Evolving Networks (GAEN) for dynamic network embedding with preserved similarities between nodes derived from their temporal variation patterns. Instead of training graph attention weights for each network independently, we allow model weights to share and evolve across all temporal networks based on their respective topology discrepancies. Experiments and validations, on four real-world dynamic graphs, demonstrate that GAEN outperforms the state-of-the-art in both link prediction and node classification tasks.
-
null (Ed.)Abstract Understanding the mechanisms by which neurons create or suppress connections to enable communication in brain-derived neuronal cultures can inform how learning, cognition and creative behavior emerge. While prior studies have shown that neuronal cultures possess self-organizing criticality properties, we further demonstrate that in vitro brain-derived neuronal cultures exhibit a self-optimization phenomenon. More precisely, we analyze the multiscale neural growth data obtained from label-free quantitative microscopic imaging experiments and reconstruct the in vitro neuronal culture networks (microscale) and neuronal culture cluster networks (mesoscale). We investigate the structure and evolution of neuronal culture networks and neuronal culture cluster networks by estimating the importance of each network node and their information flow. By analyzing the degree-, closeness-, and betweenness-centrality, the node-to-node degree distribution (informing on neuronal interconnection phenomena), the clustering coefficient/transitivity (assessing the “small-world” properties), and the multifractal spectrum, we demonstrate that murine neurons exhibit self-optimizing behavior over time with topological characteristics distinct from existing complex network models. The time-evolving interconnection among murine neurons optimizes the network information flow, network robustness, and self-organization degree. These findings have complex implications for modeling neuronal cultures and potentially on how to design biological inspired artificial intelligence.more » « less
-
more » « less
Abstract Single-cell RNA sequencing (scRNA-seq) enables dissecting cellular heterogeneity in tissues, resulting in numerous biological discoveries. Various computational methods have been devised to delineate cell types by clustering scRNA-seq data, where clusters are often annotated using prior knowledge of marker genes. In addition to identifying pure cell types, several methods have been developed to identify cells undergoing state transitions, which often rely on prior clustering results. The present computational approaches predominantly investigate the local and first-order structures of scRNA-seq data using graph representations, while scRNA-seq data frequently display complex high-dimensional structures. Here, we introduce scGeom, a tool that exploits the multiscale and multidimensional structures in scRNA-seq data by analyzing the geometry and topology through curvature and persistent homology of both cell and gene networks. We demonstrate the utility of these structural features to reflect biological properties and functions in several applications, where we show that curvatures and topological signatures of cell and gene networks can help indicate transition cells and the differentiation potential of cells. We also illustrate that structural characteristics can improve the classification of cell types.
-
Learning network topology from partial knowledge of its connectivity is an important objective in practical scenarios of communication networks and social-media networks. Representing such networks as connected graphs, exploring and recovering connectivity information between network nodes can help visualize the network topology and improve network utility. This work considers the use of simple hop distance measurement obtained from a fraction of anchor/source nodes to reconstruct the node connectivity relationship for large scale networks of unknown connection topology. Our proposed approach consists of two steps. We first develop a tree-based search strategy to determine constraints on unknown network edges based on the hop count measurements. We then derive the logical distance between nodes based on principal component analysis (PCA) of the measurement matrix and propose a binary hypothesis test for each unknown edge. The proposed algorithm can effectively improve both the accuracy of connectivity detection and the successful delivery rate in data routing applications.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s41598-021-02203-4
