Higher-order Interactions Research Articles

Finite-size effect in Kuramoto oscillators with higher-order interactions.

Finite-size systems of a Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such a scenario in globally coupled populations of Kuramoto phase oscillators with higher-order interactions and observe that fluctuations inherent to finite-size systems drive the transition to the synchronized state before the critical point in the thermodynamic limit. Using numerical methods, we plot the first exit-time distribution of the magnitude of a complex order parameter and obtain numerical transition probabilities across various system sizes. Furthermore, we extend this study to a two-population oscillator system, and, using the velocity field of the associated order parameters, show the emergence of a new fixed point corresponding to a partially synchronized state arising due to the finite-size effect, which is absent in the thermodynamics limit.

How combined pairwise and higher-order interactions shape transient dynamics.

Understanding how species interactions shape biodiversity is a core challenge in ecology. While much focus has been on long-term stability, there is rising interest in transient dynamics-the short-lived periods when ecosystems respond to disturbances and adjust toward stability. These transitions are crucial for predicting ecosystem reactions and guiding effective conservation. Our study introduces a model that uses convex combinations to blend pairwise and higher-order interactions (HOIs), offering a more realistic view of natural ecosystems. We find that pairwise interactions slow the journey to stability, while HOIs speed it up. Employing global stability analysis and numerical simulations, we establish that as the proportion of HOIs increases, mean transient times exhibit a significant reduction, thereby underscoring the essential role of HOIs in enhancing biodiversity stabilization. Our results reveal a robust correlation between the most negative real part of the eigenvalues of the Jacobian matrix associated with the linearized system at the coexistence equilibrium and the mean transient times. This indicates that a more negative leading eigenvalue correlates with accelerated convergence to stable coexistence abundances. This insight is vital for comprehending ecosystem resilience and recovery, emphasizing the key role of HOIs in promoting stabilization. Amid growing interest in transient dynamics and its implications for biodiversity and ecological stability, our study enhances the understanding of how species interactions affect both transient and long-term ecosystem behavior. By addressing a critical gap in ecological theory and offering a practical framework for ecosystem management, our work advances knowledge of transient dynamics, ultimately informing effective conservation strategies.

Dynamic multi-dose vaccination with initial immunity on higher-order networks

Vaccination remains crucial during pandemics for combating disease spread. We here propose a two-layer model for multi-dose vaccination policy, considering vaccine hesitancy, initial immunity, as well as media-driven information dissemination concerning vaccine strategy selection. Moreover, we consider collective opinions through social networks with higher-order interactions. We perform numerical simulations to analyse variations in vaccination strategies. We further compare obtained outcomes with the exploration of real data on vaccination behaviours. Our research indicates that information dissemination can regulate vaccination, and that models accounting for individual immunity align more closely with real-world scenarios. Furthermore, we find that considering vaccination decisions from neighbouring agents is crucial under multi-dose policies for the facilitation of faster vaccination diffusion.

Robustness of multilayer interdependent higher-order network

In real-world complex systems, most networks are interconnected with other networks through interlayer dependencies, forming multilayer interdependent networks. In each system, the interactions between nodes are not limited to pairwise but also exist in a higher-order interaction composed of three or more individuals, thus inducing a multilayer interdependent higher-order network (MIHN). First, we build four types of artificial MIHN models (i.e., chain-like, tree-like, star-like and ring-like), in which the higher-order interactions are described by the simplicial complexes, and the interlayer dependency is built via a one-to-one matching dependency link. Then, we propose a cascading failure model on MIHN and suggest a corresponding percolation-based theory to study the robustness of MIHN by investigating the giant connected components (GCC) and percolation threshold. We find that the density of the simplicial complexes and the number of layers of the network affect its penetration behavior. When the density of simplicial complexes exceeds a certain threshold, the network has a double transition, and the increase in network layers significantly enhances the vulnerability of MIHN. By comparing the simulation results of MIHNs with four types, we observe that under the same density of simplicial complexes, the size of the GCC is independent of the topological structures of MIHN after removing a certain number of nodes. Although the cascading failure process of MIHNs with different structures is different, the final results tend to be the same. We further analyze in detail the cascading failure process of MIHN with different structures and elucidate the factors influencing the speed of cascading failures. Among these four types of MIHNs, the chain-like MIHN has the slowest cascading failure rate and more stable robustness compared to the other three structures, followed by the tree-like MIHN and star-like MIHN. The ring-like MIHN has the fastest cascading failure rate and weakest robustness due to its ring structure. Finally, we give the time required for the MIHN with different structures to reach the stable state during the cascading failure process and find that the closer to the percolation threshold, the more time the network requires to reach the stable state.

Synchronization on fractional multiplex higher-order networks.

This paper explores the synchronization problem in fractional multiplex higher-order networks. Initially, a fractional multiplex higher-order network model is established, which seamlessly integrates multiplex structures with higher-order interactions. Subsequently, by leveraging a well-crafted Lyapunov function, the Lyapunov direct method, and fractional inequalities, it is demonstrated that the fractional multiplex higher-order network can achieve intra-layer synchronization, inter-layer synchronization, and complete synchronization. Finally, the theoretical findings are validated through two numerical examples featuring a simplicial complex or hypergraph structures within the intra-layer network.

A phenotypic drug discovery approach by latent interaction in deep learning

Contemporary drug discovery paradigms rely heavily on binding assays about the bio-physicochemical processes. However, this dominant approach suffers from overlooked higher-order interactions arising from the intricacies of molecular mechanisms, such as those involving cis -regulatory elements. It introduces potential impairments and restrains the potential development of computational methods. To address this limitation, I developed a deep learning model that leverages an end-to-end approach, relying exclusively on therapeutic information about drugs. By transforming textual representations of drug and virus genetic information into high-dimensional latent representations, this method evades the challenges arising from insufficient information about binding specificities. Its strengths lie in its ability to implicitly consider complexities such as epistasis and chemical–genetic interactions, and to handle the pervasive challenge of data scarcity. Through various modeling skills and data augmentation techniques, the proposed model demonstrates outstanding performance in out-of-sample validations, even in scenarios with unknown complex interactions. Furthermore, the study highlights the importance of chemical diversity for model training. While the method showcases the feasibility of deep learning in data-scarce scenarios, it reveals a promising alternative for drug discovery in situations where knowledge of underlying mechanisms is limited.

Enhancement of persistence in the rock-paper-scissors dynamics through higher-order interactions

Higher-order interactions (HOIs) are ubiquitous in real systems, and HOIs among individuals complicate the exploration of species diversity for populations in ecosystems. Therefore, understanding how higher-order interactions affect biodiversity is essential but poses significant challenges. In this paper, we consider higher-order interactions in the competitive processes of spatial rock-paper-scissors (RPS) dynamics, specifically within spatially embedded hyper-lattices, and investigate what biodiversity can be driven by HOIs. Considering hyperedges, species in hyperedges can be different, and different relationships are considered, which can eventually demonstrate the strength of competition. With the competition intensity modulated by the sensitivity of HOIs, extensive simulations have shown that higher-order competitive processes can promote coexistence. We also found that stratification of species densities occurs when three species coexist due to HOIs, which are closely related to the increase of empty sites and disordered spiral entanglement. From investigating the extinction probability in a broad aspect, it has been found that, even if HOIs are working, the coexistence in the system is eventually broken at high mobility regimes. The intensified sensitivity to HOIs can somewhat alleviate extinction, although no striking change has occurred. Our findings may address that modeling predator-prey interactions incorporating HOIs is important for gaining insights into biodiversity, and we hope our study may provide a broad aspect for exploring complex ecosystems.

Enhancing Gene Expression Predictions Using Deep Learning and Functional Annotations.

Transcriptome-wide association studies (TWAS) aim to uncover genotype-phenotype relationships through a two-stage procedure: predicting gene expression from genotypes using an expression quantitative trait locus (eQTL) data set, then testing the predicted expression for trait associations. Accurate gene expression prediction in stage 1 is crucial, as it directly impacts the power to identify associations in stage 2. Currently, the first stage of such studies is primarily conducted using linear models like elastic net regression, which fail to capture the nonlinear relationships inherent in biological systems. Deep learning methods have the potential to model such nonlinear effects, but have yet to demonstrably outperform linear methods at this task. To address this gap, we propose a new deep learning architecture to predict gene expression from genotypic variation across individuals. Our method utilizes a learnable input scaling layer in conjunction with a convolutional encoder to capture nonlinear effects and higher-order interactions without compromising on interpretability. We further augment this approach to allow for parameter sharing across multiple networks, enabling us to utilize prior information for individual variants in the form of functional annotations. Evaluations on real-world genomic data show that our method consistently outperforms elastic net regression across a large set of heritable genes. Furthermore, our model statistically significantly improved predictive performance by leveraging functional annotations, whereas elastic net regression failed to show equivalent gains when using the same information, suggesting that our method can capture nonlinear functional information beyond the capability of linear models.

Role of Higher-Order Scattering Coefficient and Residual Nonlinearities on Instability Criteria in Three-Body Bose-Einstein Condensates

We examine the instability characteristics in a three-body condensate and the effect of higher-order nonlinear effects caused by shape-dependent imprisonment and higher-order scattering coefficients such as S-wave scattering length and effective range for collisions. Using the linear stability technique, we study the spreading relations and gain profile of the adapted Gross Pitaevski equation with higher-order scattering coefficients and enduring nonlinearity. The role of higher-order interactions S-wave scattering length, residual nonlinearity, and effective range for collisions over the modulational instability in immiscible and miscible three-body Bose-Einstein condensates has been discussed in detail. MI can be excited in miscible condensates and changed in immiscible condensates because of residual nonlinearity, without taking into account higher-order nonlinearity and three-body condensates. However, the results of this work demonstrate that the influence of higher-order residual nonlinearity can cause the MI to change in both immiscible and immiscible condensates. The discovered MI spectrum reveals a new soliton production regime in three-body condensates. The results exhibit that higher-order scattering coefficient and remaining nonlinearity interplay can successfully switch the instability gain profile in miscible and immiscible condensates. This makes it possible to regulate the dynamics by varying the MI in a ternary combination of Bose-Einstein condensates.

Hypergraph contrastive learning for recommendation with side information

PurposeThis paper addresses the limitations of current graph neural network-based recommendation systems, which often neglect the integration of side information and the modeling of complex high-order interactions among nodes. The research motivation stems from the need to enhance recommendation performance by effectively utilizing all available data. We propose a novel method called MSHCN, which leverages hypergraph neural networks to integrate side information and model complex interactions, thereby improving user and item representations.Design/methodology/approachThe MSHCN method employs a hypergraph structure to incorporate various types of side information, including social relationships among users and item attributes, which are essential for enriching user and item representations. The k-means clustering algorithm is utilized to create item-associated hypergraphs, while sentiment analysis on user reviews refines the modeling of user interests. Additionally, hypergraphs are constructed for user-user and item-item interactions based on interaction similarity. MSHCN also incorporates contrastive learning as an auxiliary task to enhance the representation learning process.FindingsExtensive experiments demonstrate that MSHCN significantly outperforms existing recommendation models, particularly in its ability to capture and utilize side information and high-order interactions. This results in superior user and item representations and improved recommendation performance.Originality/valueThe novelty of MSHCN lies in its use of a hypergraph structure to integrate diverse side information and model intricate high-order interactions. The incorporation of contrastive learning as an auxiliary task sets it apart from other hypergraph-based models, providing a significant enhancement in recommendation accuracy.

Research on carotid artery plaque anomaly detection algorithm based on ultrasound images

Carotid artery plaque is a key factor in stroke and other cardiovascular diseases. Accurate detection and localization of carotid artery plaque are essential for early prevention and treatment of diseases. However, current carotid artery ultrasound image anomaly detection algorithms face several challenges, such as scarcity of anomaly data in carotid arteries and traditional convolutional neural networks (CNNs) overlooking long-distance dependencies in image processing. To address these issues, we propose an anomaly detection algorithm for carotid artery plaques based on ultrasound images. The algorithm innovatively introduces an anomaly sample pair generation method to increase dataset diversity. Moreover, it employs an improved adaptive recursive gating pyramid pooling module to extract image features. This module significantly enhances the model’s capacity for high-order spatial interactions and adaptive feature fusion, thereby greatly improving the neural network’s feature extraction ability. The algorithm uses a Sigmoid layer to map each pixel’s feature vector to a probability distribution between 0 and 1, and anomalies are detected through probability threshold binarization. Experimental results show that our algorithm’s AUROC index reached 90.7% on a carotid artery dataset, improving by 2.1% compared to the FPI method. This research is expected to provide robust support for the early prevention and treatment of cardiovascular diseases.

Higher-order epistasis within Pol II trigger loop haplotypes.

RNA polymerase II (Pol II) has a highly conserved domain, the trigger loop (TL), that controls transcription fidelity and speed. We previously probed pairwise genetic interactions between residues within and surrounding the TL for the purpose of understand functional interactions between residues and to understand how individual mutants might alter TL function. We identified widespread incompatibility between TLs of different species when placed in the Saccharomyces cerevisiae Pol II context, indicating species-specific interactions between otherwise highly conserved TLs and its surroundings. These interactions represent epistasis between TL residues and the rest of Pol II. We sought to understand why certain TL sequences are incompatible with S. cerevisiae Pol II and to dissect the nature of genetic interactions within multiply substituted TLs as a window on higher order epistasis in this system. We identified both positive and negative higher-order residue interactions within example TL haplotypes. Intricate higher-order epistasis formed by TL residues was sometimes only apparent from analysis of intermediate genotypes, emphasizing complexity of epistatic interactions. Furthermore, we distinguished TL substitutions with distinct classes of epistatic patterns, suggesting specific TL residues that potentially influence TL evolution. Our examples of complex residue interactions suggest possible pathways for epistasis to facilitate Pol II evolution.

Hypernetwork modeling and topology of high-order interactions for complex systems

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species.

Importance of higher-order epistasis in large protein sequence-function relationships.

Epistasis complicates our understanding of protein sequence-function relationships and impedes our ability to build accurate predictive models for novel genotypes. Although pairwise epistasis has been extensively studied in proteins, the significance of higher-order epistasis for protein sequence-function relationships remains contentious, largely due to challenges in fitting higher-order epistatatic interactions for full-length proteins. Here, we introduce a novel transformer-based approach. The key feature of our method is that we can adjust the order of interactions fit by the model by changing the number of attention layers while also accounting for any global nonlinearity induced by the experimental conditions. This allows us to test if inclusion of higher-order interactions leads to enhanced model performance. Applying our method to 10 large protein sequence-function datasets, we found that the importance of higher-order epistasis differs substantially between proteins, accounting for up to 60% of the total variance attributed to epistasis. We also found that including higher-order epistasis is particularly important for generalizing locally sampled fitness data to distant regions of sequence space and for modeling an additional multipeak fitness landscape derived from combining mutagenesis data from 4 orthologous green fluorescencent proteins. Our findings suggest that higher-order epistasis often does play an important role in protein sequence-function relationships, and thus should be properly incorporated during protein engineering and evolutionary data analysis.

Coexistence of multistable synchronous states in a three-oscillator system with higher-order interaction.

We study a three-oscillator system with pairwise (1-simplex) and triadic (2-simplex) interactions, and focus on how the interplay between these two types of interactions influences synchronous dynamics. Using a minimal model, dynamical phenomena in systems that have been previously studied under the thermodynamic limit (N→∞) are further clarified. Various synchronous states, including in-phase and antiphase synchronous states, as well as partial synchronous states are demonstrated. Meanwhile, significant multistable behaviors are revealed. Our work extends previous research on pairwise and triadic interactions, which can deepen our understanding of the impact of correlation between higher-order interaction and multistability. These dynamic phenomena bear resemblance to the diverse synchronization patterns of the heart, and they also serve as pivotal factors in information storage and memory retention within the brain.

Controllability of higher-order networks

Higher-order networks can comprehensively describe interactions among groups, thus emerging as a novel area of exploration in network science. This paper aims to delve into the controllability of higher-order networks, where the network topology is characterized by higher-order interactions and the nodes are higher-dimensional dynamical systems. The collective effects on the network controllability from the dynamics of higher-order interactions, node dynamics, inner interactions, and external control inputs are extensively explored. By applying matrix theory and control theory, some necessary and/or sufficient conditions are developed to determine the controllability of hypergraph networks and simplicial complex networks. Through simulated examples, it becomes evident that the controllability of higher-order networked system is far more complicated than that of traditional networked systems and the higher-order topological structures facilitate the controllability. Remarkably, the integrated network can achieve controllability even when the corresponding traditional network is uncontrollable by external inputs.

A versatile framework for attributed network clustering via K-nearest neighbor augmentation

AbstractAttributed networks containing entity-specific information in node attributes are ubiquitous in modeling social networks, e-commerce, bioinformatics, etc. Their inherent network topology ranges from simple graphs to hypergraphs with high-order interactions and multiplex graphs with separate layers. An important graph mining task is node clustering, aiming to partition the nodes of an attributed network into k disjoint clusters such that intra-cluster nodes are closely connected and share similar attributes, while inter-cluster nodes are far apart and dissimilar. It is highly challenging to capture multi-hop connections via nodes or attributes for effective clustering on multiple types of attributed networks. In this paper, we first present as an efficient approach to attributed hypergraph clustering (AHC). includes a carefully-crafted K-nearest neighbor augmentation strategy for the optimized exploitation of attribute information on hypergraphs, a joint hypergraph random walk model to devise an effective AHC objective, and an efficient solver with speedup techniques for the objective optimization. The proposed techniques are extensible to various types of attributed networks, and thus, we develop as a versatile attributed network clustering framework, capable of attributed graph clustering, attributed multiplex graph clustering, and AHC. Moreover, we devise with algorithmic designs tailored for GPU acceleration to boost efficiency. We have conducted extensive experiments to compare our methods with 19 competitors on 8 attributed hypergraphs, 16 competitors on 6 attributed graphs, and 16 competitors on 3 attributed multiplex graphs, all demonstrating the superb clustering quality and efficiency of our methods.

ST2SI: Image Style Transfer via Vision Transformer using Spatial Interaction

While retaining the original content structure, image style transfer uses style image to render it to obtain stylized images with artistic features. Because the content image contains different detail units and the style image has various style patterns, it is easy to cause the distortion of the stylized image. We proposes a new Style Transfer based on Vision Transformer using Spatial Interaction (ST2SI), which takes advantage of Spatial Interactive Convolution (SIC) and Spatial Unit Attention (SUA) to further enhance the content and style representation, so that the encoder can not only better learn the features of the content domain and the style domain, but also maintain the structural integrity of the image content and the effective integration of style features. Concretely, the high-order spatial interaction ability of Spatial Interactive Convolution can capture complex style patterns, and Spatial Unit Attention can balance the content information of different detail units through the change of attention weight, thus solving the problem of image distortion. Comprehensive qualitative and quantitative experiments prove the efficacy of our approach.

Research on the Wild Mushroom Recognition Method Based on Transformer and the Multi-Scale Feature Fusion Compact Bilinear Neural Network

Wild mushrooms are popular for their taste and nutritional value; however, non-experts often struggle to distinguish between toxic and non-toxic species when foraging in the wild, potentially leading to poisoning incidents. To address this issue, this study proposes a compact bilinear neural network method based on Transformer and multi-scale feature fusion. The method utilizes a dual-stream structure that integrates multiple feature extractors, enhancing the comprehensiveness of image information capture. Additionally, bottleneck attention and efficient multi-scale attention modules are embedded to effectively capture multi-scale features while maintaining low computational costs. By employing a compact bilinear pooling module, the model achieves high-order feature interactions, reducing the number of parameters without compromising performance. Experimental results demonstrate that the proposed method achieves an accuracy of 98.03%, outperforming existing comparative methods. This proves the superior recognition performance of the model, making it more reliable in distinguishing wild mushrooms while capturing key information from multiple dimensions, enabling it to better handle complex scenarios. Furthermore, the development of public-facing identification tools based on this method could help reduce the risk of poisoning incidents. Building on these findings, the study suggests strengthening the research and development of digital agricultural technologies, promoting the application of intelligent recognition technologies in agriculture, and providing technical support for agricultural production and resource management through digital platforms. This would provide a theoretical foundation for the innovation of digital agriculture and promote its sustainable development.

Robustness of hypergraph under attack with limited information based on percolation theory

Hypergraphs serve as a representative form to display higher-order interactions that persist in the community structure of ecological and social systems. A significant characteristic of these entities is their critical behaviours and robustness in response to aggressive assaults. However, in reality, the network structure may be partially observable, meaning that it is distinct from the assumption of global accessibility under random and deliberate assaults. In this work, we provide a theoretical framework to analyse the changes in the giant component in a hypergraph when subjected to limited information disintegration. Percolation theory is employed to derive the size of the giant component and the critical point. Specifically, we apply the message-passing method based on factor graphs to establish a framework for percolation analysis under limited information attacks. On this basis, the hypergraph structure is accurately described. The advantages lie in avoiding the redundant demands of multiple repetitive experiments. Our study demonstrates the relationship between the diversity of the attacked network and the critical condition. By conducting numerical simulations and theoretical research, we also conclude that controlling the observed size of the network and moderately increasing the average hyperdegree can enhance the robustness of the hypergraph. These findings further indicate the impact of hypergraph topology on the resilience of systems and provide analytical insights for optimizing systems with cost-effectiveness and robustness.