Multilayer Network Research Articles

SSR-DTA: Substructure-aware multi-layer graph neural networks for drug–target binding affinity prediction

Accurate prediction of drug–target binding affinity (DTA) is essential in the field of drug discovery. Recently, scientists have been attempting to utilize artificial intelligence prediction to screen out a significant number of ineffective compounds, thereby mitigating labor and financial losses. While graph neural networks (GNNs) have been applied to DTA, existing GNNs have limitations in effectively extracting substructural features across various sizes. Functional groups play a crucial role in modulating molecular properties, but existing GNNs struggle with feature extraction from certain motifs due to scale mismatches. Additionally, sequence-based models for target proteins lack the integration of structural information. To address these limitations, we present SSR-DTA, a multi-layer graph network capable of adapting to diverse structural sizes, which can extract richer biological features, thereby improving the robustness and accuracy of predictions. Multi-layer GNNs enable the capture of molecular motifs across different scales, ranging from atomic to macrocyclic motifs. Furthermore, we introduce BiGNN to simultaneously learn sequence and structural information. Sequence information corresponds to the primary structure of proteins, while graph information represents the tertiary structure. BiGNN assimilates richer information compared to sequence-based methods while mitigating the impact of errors from predicted structures, resulting in more accurate predictions. Through rigorous experimental evaluations conducted on four benchmark datasets, we demonstrate the superiority of SSR-DTA over state-of-the-art models. Particularly, in comparison to state-of-the-art models, SSR-DTA demonstrates an impressive 20% reduction in mean squared error on the Davis dataset and a 5% reduction on the KIBA dataset, underscoring its potential as a valuable tool for advancing DTA prediction.

Copula Approximate Bayesian Computation Using Distribution Random Forests

Ongoing modern computational advancements continue to make it easier to collect increasingly large and complex datasets, which can often only be realistically analyzed using models defined by intractable likelihood functions. This Stats invited feature article introduces and provides an extensive simulation study of a new approximate Bayesian computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the parameters of models defined by intractable likelihoods, that unifies and extends previous ABC methods proposed separately. This framework, copulaABCdrf, aims to accurately estimate and describe the possibly skewed and high-dimensional posterior distribution by a novel multivariate copula-based meta-t distribution based on univariate marginal posterior distributions that can be accurately estimated by distribution random forests (drf), while performing automatic summary statistics (covariates) selection, based on robustly estimated copula dependence parameters. The copulaABCdrf framework also provides a novel multivariate mode estimator to perform MLE and posterior mode estimation and an optional step to perform model selection from a given set of models using posterior probabilities estimated by drf. The posterior distribution estimation accuracy of the ABC framework is illustrated and compared with previous standard ABC methods through several simulation studies involving low- and high-dimensional models with computable posterior distributions, which are either unimodal, skewed, or multimodal; and exponential random graph and mechanistic network models, each defined by an intractable likelihood from which it is costly to simulate large network datasets. This paper also proposes and studies a new solution to the simulation cost problem in ABC involving the posterior estimation of parameters from datasets simulated from the given model that are smaller compared to the potentially large size of the dataset being analyzed. This proposal is motivated by the fact that, for many models defined by intractable likelihoods, such as the network models when they are applied to analyze massive networks, the repeated simulation of large datasets (networks) for posterior-based parameter estimation can be too computationally costly and vastly slow down or prohibit the use of standard ABC methods. The copulaABCdrf framework and standard ABC methods are further illustrated through analyses of large real-life networks of sizes ranging between 28,000 and 65.6 million nodes (between 3 million and 1.8 billion edges), including a large multilayer network with weighted directed edges. The results of the simulation studies show that, in settings where the true posterior distribution is not highly multimodal, copulaABCdrf usually produced similar point estimates from the posterior distribution for low-dimensional parametric models as previous ABC methods, but the copula-based method can produce more accurate estimates from the posterior distribution for high-dimensional models, and, in both dimensionality cases, usually produced more accurate estimates of univariate marginal posterior distributions of parameters. Also, posterior estimation accuracy was usually improved when pre-selecting the important summary statistics using drf compared to ABC employing no pre-selection of the subset of important summaries. For all ABC methods studied, accurate estimation of a highly multimodal posterior distribution was challenging. In light of the results of all the simulation studies, this article concludes by discussing how the copulaABCdrf framework can be improved for future research.

Study of a precise treatment protocol for patients with consciousness disorders based on the brain network analysis of functional magnetic resonance imaging.

How to conduct objective and accurate individualized assessments of patients with disorders of consciousness (DOC) and carry out precision rehabilitation treatment technology is a major rehabilitation problem that needs to be solved urgently. In this study, a multi-layer brain network was constructed based on functional magnetic resonance imaging (fMRI) to analyze the structural and functional brain networks of patients with DOC at different levels and to find regulatory targets (imaging markers) with recovery potential for DOC. Then repeated transcranial magnetic stimulation (rTMS) was performed in DOC patients to clinically validate. The brain network connectivity of DOC patients with different consciousness states is different, and the most obvious brain regions appeared in the olfactory cortex and precuneus. rTMS stimulation could effectively improve the consciousness level of DOC patients and stimulate the occipital lobe (specific regions found in this study) and the dorsolateral prefrontal cortex (DLPFC), and both parts had a good consciousness recovery effect. In clinical work, personalized stimulation regimen treatment combined with the brain network characteristics of DOC patients can improve the treatment effect.

Multilayer network analysis of idiosyncratic volatility connectedness: Evidence from China

This paper proposes multilayer networks, including lagged, contemporaneous, and long-run networks, to examine the idiosyncratic connectedness among Chinese financial institutions. We explore the topology of multilayer networks through static and dynamic analysis to capture the information transmission mechanism of idiosyncratic risks. Moreover, we investigate the drivers influencing idiosyncratic connectedness across financial institutions. We find that idiosyncratic risk contagion among financial institutions is stronger in the long-run network. At the same time, we note that the three networks contain different connection structures, which means that the information transmission mechanism of idiosyncratic risks is heterogeneous in multilayer networks. In addition, when the financial system is under stress, we observe that the contemporaneous effect of idiosyncratic connectedness rises rapidly. Institutional level analysis shows that diversified financial institutions play active roles in the lagged network, securities institutions are transmitters of contemporaneous information spillovers, and banking institutions are the main drivers of the long-run network. Finally, our study shows that size is the main factor driving idiosyncratic risk spillovers among financial institutions.

Identification of important nodes in multi-layer hypergraphs based on fuzzy gravity model and node centrality distribution characteristics

Hyperedge is a common structure that represents high-order interactions between nodes in complex networks, and multi-layer networks provide more diverse node interactions than single-layer networks. Therefore, multi-layer hypergraphs can more clearly represent the relationships between nodes. However, there are few studies on identifying important nodes in this framework. This paper proposes a method called HCT to fill this gap. It consists of three parts, namely: Hypergraph Fuzzy Gravity Model (HFGM), Layer Weight Calculation Method based on Node Centrality Distribution Characteristics (CDLW) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). HCT progressively analyzes the importance of a node from three levels: local (the node itself), semi-local (the hyperedges and community to which the node belongs), and global (the layer to which the node belongs). By combining these three results, the global centrality of a node in the entire network can be calculated. Simulation experiments demonstrate that the important nodes identified by HCT exhibit stronger contagion capabilities in nine networks compared to nine combinatorial methods and removing these nodes will seriously damage the connectivity and robustness of the network. The centrality of each node calculated by HCT is also consistent with its actual importance.

Research on multi-sequence MR image synthesis CT algorithm based on unsupervised method

BackgroundUsing multi-sequence MRI to synthesize CT, combining different MRI sequences, and processing synthetic CT (sCT) based on unsupervised algorithms, to conduct more in-depth and comprehensive research on MR-based radiotherapy planning. MethodsFirst, we compare and analyze the effects of single-sequence MRI synthesis to CT to determine the quality of the synthesis and find a set of optimal sequence combinations. In addition, the study introduces a Staged Multi-Sequence Fusion Network (SMSF-Net) that employs an unsupervised approach to effectively fuse information from multiple MRI sequences. The staged sequence fusion module can efficiently extract information from different sequences and combine complementary information from different sequences. Finally, image encoding is processed using a multi-layer convolutional network to generate synthetic CT images. ResultsIn this study, the mean absolute error (MAE), root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) of the SMSF-Net are 18.85, 84.62, 34.31, and 0.962, which are superior to other single-sequence models and multi-sequence models. Experiments show that the improvement of SMSF-Net is statistically significant. In the qualitative comparison experiment, sCT synthesized by SMSF-Net is superior to other models in detail in the synthesis of complex areas of bones and nasal cavities. ConclusionThis study proposes a Staged SMSF-Net. As a multi-sequence MRI synthesis sCT algorithm based on unsupervised learning, SMSF-Net can use the complementary information between multiple sequences to improve the quality of synthetic sCT. This study has reference value for MRI-only radiotherapy planning.

The effect of interpersonal relationships on epidemic spreading in weighted multilayer networks

During the epidemic outbreak, people's reactions to social contacts of varying degrees of intimacy exhibited significant differences. Historical data further reveal that interactions between groups play a crucial role in the epidemic's transmission chain. In light of this, it is essential for epidemiological models to account for more complex interaction mechanisms. Based on this understanding, we have developed a weighted dual-layer network model. One layer simulates the spread of information through 2-simplexes, while the other simulates the actual transmission paths of the disease based on physical contact. The weight between two nodes represents individual differences in information acceptance and self-protection among neighbors with different relationships. We conducted a theoretical analysis using the Micro-Markov Chain Approach to examine transmission behaviors, and we also implemented numerical simulations using the Monte Carlo Method. The simulation results aligned with the theoretical analysis, indicating that stronger interpersonal relationships can enhance information dissemination, prompting more individuals to adopt protective measures, which in turn helps curb the spread of the disease.

Extreme risk spillovers in international energy markets: New insights from multilayer networks in the frequency domain

This paper constructs multilayer risk spillover networks in the frequency domain, containing short-, medium-, and long-term layers, to explore extreme risk spillovers in international energy markets at different frequency bands. We analyze the topology properties of multilayer networks at the system, region, and country levels. Based on daily data from 20 national energy stock markets spanning 2006–2023, the empirical results show that: (1) The overall topology of multilayer networks, including the edge structure and spillover strength structure, exhibit frequency heterogeneity. With the onset of a major crisis, the frequency heterogeneity of the network topology increases significantly, and international energy risk spillovers tend to concentrate in fewer layers (i.e., over one or two frequency bands). (2) Long-term risk is primarily responsible for the extreme risk spillover behavior between energy markets. (3) Compared to short- and medium-term spillovers, long-term spillovers are more crisis-sensitive. Furthermore, long-term spillovers within different regions vary in their sensitivity to local or global crises. (4) As market conditions fluctuate, the key players driving the short-term layer change, whereas those driving the medium- and long-term layers remain relatively stable. Overall, our findings provide new insights for policymakers and investors to prevent international energy systemic risks and optimize investment strategies.

Modeling and analysis of cascading failures in multilayer higher-order networks

With the increasing application of network science, understanding the behavior of higher-order networks has become particularly important. Especially, the study of multilayer higher-order networks is significant for revealing the interdependence and higher-order interactions in complex systems. This paper proposes a mathematical framework to explore multilayer higher-order networks composed of multiple fully interdependent hypergraphs. Each hypergraph consists of the same number of nodes, and nodes between layers are connected one-to-one. By analyzing the cascading failures of multilayer hypergraphs under different topologies, we found that although the network sizes are the same in the steady state, different topological structures (such as star-like, tree-like, and chain-like) significantly affect the time required to reach a stable state, with the star-like topology reaching stability the fastest. Furthermore, we explored the impact of network parameters on the robustness of networks. We found that in multilayer homogeneous hypergraphs, the robustness of the network becomes stronger with an increase in the average hyperdegree or average hyperedge cardinality; in multilayer heterogeneous hypergraphs, the robustness of the network becomes more fragile as the power exponent increases. Finally, experimental results indicate that with the rise in the number of network layers, the network becomes more fragile.

Local and regional processes drive distance decay in structure in a spatial multilayer plant-pollinator network.

Understanding spatial variation in species distribution and community structure is at the core of community ecology. Nevertheless, the effect of distance on metacommunity structure remains little studied. We examine how plant-pollinator community structure changes across geographical distances at a regional scale and disentangle its underlying local and regional processes. We use a multilayer network to represent linked plant-pollinator communities as a metacommunity in the Canary Islands. We used modularity (i.e. the extent to which the community is partitioned into groups of densely interacting species) to quantify distance decay in structure across space. In multilayer modularity, the same species can belong to different modules in different communities, and modules can span communities. This enabled quantifying how similarity in module composition varied with distance between islands. We developed three null models, each controlling for a separate component of the multilayer network, to disentangle the role of species turnover, interaction rewiring and local factors in driving distance decay in structure. We found a pattern of distance decay in structure, indicating that islands tended to share fewer modules with increasing distance. Species turnover (but not interaction rewiring) was the primary regional process triggering distance decay in structure. Local interaction structure also played an essential role in determining the structure similarity of communities at a regional scale. Therefore, local factors that determine species interactions occurring at a local scale drive distance decay in structure at a regional scale. Our work highlights the interplay between local and regional processes underlying community structure. The methodology, and specifically the null models, we developed provides a general framework for linking communities in space and testing different hypotheses regarding the factors generating spatial structure.

Aging transitions of multimodal oscillators in multilayer networks

When individual oscillators age and become inactive, the collective dynamics of coupled oscillators is often affected as well. Depending on the fraction of inactive oscillators or cascading failures that percolate from crucial information exchange points, the critical shift toward macroscopic inactivity in coupled oscillator networks is known as the aging transition. Here, we study this phenomenon in two overlayed square lattices that together constitute a multilayer network, whereby one layer is populated with slow Poincaré oscillators and the other with fast Rulkov neurons. Moreover, in this multimodal setup, the excitability of fast oscillators is influenced by the phase of slow oscillators that are gradually inactivated toward the aging transition in the fast layer. Through extensive numerical simulations, we find that the progressive inactivation of oscillators in the slow layer nontrivially affects the collective oscillatory activity and the aging transitions in the fast layer. Most counterintuitively, we show that it is possible for the intensity of oscillatory activity in the fast layer to progressively increase to up to 100%, even when up to 60% of units in the slow oscillatory layer are inactivated. We explain our results with a numerical analysis of collective behavior in individual layers, and we discuss their implications for biological systems. Published by the American Physical Society 2024

A New Diffusion Strategy Using an Epidemic Spreading Model for Encryption.

The diffusion phenomenon that exhibits intrinsic similarities is pervasive in cryptography and natural systems, evident in liquid diffusion, epidemic spread, animal migration, and encryption techniques. In cryptography, bytes are systematically diffused in a sequential manner to encrypt the value of each byte in the plaintext in a linear fashion. In contrast, within an epidemic spreading model, the diffusion process can be represented within a complex, multilayered network, encompassing layers such as familial and social transmission dynamics. Transmission links establish connections both within and between individual layers. It has had a more rapid spread than linear approaches due to the particularization of non-linear transmission. In this study, the novelty of a cryptography diffusion strategy based on an epidemic model is first proposed, in which pixels and their dynamic adjacency are considered as vertices and edges, respectively, within a complex network framework. Subsequently, the encryption process is governed by the Susceptible-Vaccinated-Infected-Recovered (SVIR) model integrated with chaotic dynamics. Simulation results demonstrate that the proposed algorithm exhibits faster encryption speed while effectively resisting brute force, statistical, and differential attacks. Furthermore, it demonstrates strong robustness against noise interference and data loss.

Aerial-view geo-localization based on multi-layer local pattern cross-attention network

Aerial-view geo-localization based on multi-layer local pattern cross-attention network

Research on the Migration and Settlement Laws of Backflow Proppants after Fracturing Tight Sandstone

This article studies the migration and settlement laws of backflow proppants after fracturing tight sandstone. This paper proposes a fitting method based on a multi-task learning network to address the issue of interference from multiple physical parameters during the transport and settlement processes of proppants. This method can effectively handle multi-dimensional interference factors and fit the mapping logic of multiple engineering parameters to transport patterns through the continuous correction of multi-layer networks. We first introduce the characteristics of tight sandstone reservoirs and their important value in mining, as well as the status of current research on the migration and settlement laws of proppants at home and abroad. Based on this, we then deeply analyze the sedimentation rate model of proppants in tight sandstone backflow and the equilibrium height of proppants under multiple factors of interference while considering the distribution characteristics of proppants. In order to more accurately simulate the transport and settlement laws of proppants, this paper introduces a multi-task learning network. This network can comprehensively consider multi-dimensional parameters, learn the inherent laws of data through training, and achieve accurate fitting of the transport and settlement laws of proppants. This study trained and tested the model using actual production data, and the results showed that the proposed model can fit the input–output relationship well, thus effectively supporting the study of proppant transport and settlement laws.

MARML: Motif-Aware Deep Representation Learning in Multilayer Networks.

The rapid increase in high-throughput, complex, and heterogeneous data has led to the adoption of network-structured models and analyses for interpretation. However, these data are inherently complex and challenging to understand, prompting researchers to turn to graph embedding methods to facilitate analysis. While general network embedding techniques have shown promise in improving downstream prediction and classification tasks, real-world data are complicated due to cross-domain interactions between different types of entities. Multilayered networks have been successful in integrating biological data to represent biological systems' hierarchy, but embedding nodes based on different types of interactions remains an unsolved problem. To address this challenge, we propose the Motif-aware deep representation learning in multilayer (MARML) networks for learning network representations. Our method considers recurring motif patterns, topological information, and attributive information from other sources as node features. We validated the MARML method using various multilayer network datasets. In addition, by incorporating motif information, MARML considers higher order connections across different hierarchies. The learned features exhibited excellent accuracy in tasks related to link prediction and link differentiation, enabling us to distinguish between existing and disconnected triplets. Through the integration of both intrinsic node attributes and topological network structures, we enhance our understanding of complex biological systems.

Attention-based dynamic multilayer graph neural networks for loan default prediction

Whereas traditional credit scoring tends to employ only individual borrower- or loan-level predictors, it has been acknowledged for some time that connections between borrowers may result in default risk propagating over a network. In this paper, we present a model for credit risk assessment leveraging a dynamic multilayer network built from a Graph Neural Network and a Recurrent Neural Network, each layer reflecting a different source of network connection. We test our methodology in a behavioural credit scoring context using a dataset provided by U.S. mortgage financier Freddie Mac, in which different types of connections arise from the geographical location of the borrower and their choice of mortgage provider. The proposed model considers both types of connections and the evolution of these connections over time. We enhance the model by using a custom attention mechanism that weights the different time snapshots according to their importance. After testing multiple configurations, a model with GAT, LSTM, and the attention mechanism provides the best results. Empirical results demonstrate that, when it comes to predicting probability of default for the borrowers, our proposed model brings both better results and novel insights for the analysis of the importance of connections and timestamps, compared to traditional methods.

Spreading Processes With Layer-Dependent Population Heterogeneity Over Multilayer Networks

Spreading Processes With Layer-Dependent Population Heterogeneity Over Multilayer Networks

Target Controllability of Multi-Layer Networks with High-Dimensional Nodes

Target Controllability of Multi-Layer Networks with High-Dimensional Nodes

Exploring Social Networks: An Analysis of Intra-organizational Networks

This research investigates intra-organizational social networks by employing network science methods, aiming to provide actionable insights for both managers and employees. Using datasets from the Colorado Index of Complex Networks (ICON), this study examines four intra-organizational networks from a consulting firm and a research team, focusing on advice requests and skill awareness. The analysis includes network topology, degree distribution, community detection, correlation between communities and node attributes, maximal clique detection, and multilayer network analysis. The findings reveal that intra-organizational networks are intricate and significantly impact organizational efficiency and individual career development. Key insights include the importance of mid-level employees in network connectivity, the existence of "bad edges" where advice is sought from less competent peers, and the influence of regional and locational factors on communication patterns. The study emphasizes the need to enhance knowledge sharing and inter-region communications. For employees, understanding the structure of these networks can guide them to more effectively leverage their social connections for career advancement. This interdisciplinary effort bridges gaps in the existing literature and showcases the potential of integrating network science methods into social science research.

Effect of perturbation and topological structure on synchronization dynamics in multilayer networks

Effect of perturbation and topological structure on synchronization dynamics in multilayer networks