High-order Networks Research Articles

Characterization and kinetics of whey protein isolate amyloid fibril aggregates under moderate electric fields

Food proteins solutions enable the controlled flow of electrical current when subjected to a Moderate electric field (MEF). This application results in internal heat generation, known as ohmic heating, accompanied by electrochemical reactions. These effects play a significant role in influencing the formation of protein amyloid fibril aggregates (AFA), which have broad applications in food and biomedical fields, ranging from improving food texture to biomedical applications such as drug delivery and disease treatment. This study focused on investigating the formation of β-Lactoglobulin (β-lg) AFA under MEF conditions using WPI as protein source and various characterization techniques (e.g., Thioflavin T fluorescence, circular dichroism, and electron microscopy). The results indicated that MEF prolonged the lag phase of AFA formation. Furthermore, nucleation and fibril growth showed higher activation coefficients and cooperativity level (n > 2) compared to conventional heating method. MEF treatment resulted in unique fibril clustering and the presence of unexpected higher-order AFA networks confirmed by electron microscopy. These findings highlight the significant role of MEF in influencing the aggregation kinetics of β-lg AFA. Exploring further into the electrochemical and thermal effects during protein aggregation processes holds the key to unlocking deeper insights fibril formation process.

High-order brain network feature extraction and classification method of first-episode schizophrenia: an EEG study

IntroductionA multimodal persistent topological feature extraction and classification method is proposed to enhance the recognition accuracy of first-episode schizophrenia patients. This approach addresses the limitations of traditional higher-order brain network analyses that rely on single persistent features (e.g., persistent images).MethodsThe study utilized resting-state EEG data from 198 subjects recruited at Huilongguan Hospital in Beijing, comprising 102 males and 96 females, with a mean age of 30 years and mean education of 14 years. Persistent topological features were extracted using adaptive thresholding during persistent homology (PH) filtrations. The distribution of these features was visualized through heatmaps and persistence entropies, while the generation process was elucidated using Betti curves and persistence landscapes.ResultsThe classification performance of the multimodal persistent topological features was assessed using various machine learning classifiers. The classifier yielding the highest performance was selected for comparison with traditional brain network features derived from graph theory and single persistent topological features. The results revealed significant topological changes in first-episode schizophrenia patients throughout the persistent homology filtering compared to healthy subjects. The univariate feature selection algorithm achieved a classification accuracy of 94.6% with a combination of attributes meeting the criterion of AC ≥ 0.6.DiscussionThe proposed method demonstrates clinical significance for the early identification and diagnosis of first-episode schizophrenia patients, offering a new research perspective for constructing higher-order functional connectivity networks and extracting topological structure features.

Macroscale Gradient Dysfunction in Alzheimer's Disease: Patterns With Cognition Terms and Gene Expression Profiles.

Macroscale functional gradient techniques provide a continuous coordinate system that extends from unimodal regions to transmodal higher-order networks. However, the alterations of these functional gradients in AD and their correlations with cognitive terms and gene expression profiles remain to be established. In the present study, we directly studied the functional gradients with functional MRI data from seven scanners. We adopted data-driven meta-analytic techniques to unveil AD-associated changes in the functional gradients. The principal primary-to-transmodal gradient was suppressed in AD. Compared to NCs, AD patients exhibited global connectome gradient alterations, including reduced gradient range and gradient variation, increased gradient scores in the somatomotor, ventral attention, and frontoparietal regions, and decreased in the default mode network. More importantly, the Gene Ontology terms of biological processes were significantly enriched in the potassium ion transport and protein-containing complex remodeling. Our compelling evidence provides a new perspective in understanding the connectome alterations in AD.

Compression-based inference of network motif sets.

Physical and functional constraints on biological networks lead to complex topological patterns across multiple scales in their organization. A particular type of higher-order network feature that has received considerable interest is network motifs, defined as statistically regular subgraphs. These may implement fundamental logical and computational circuits and are referred to as "building blocks of complex networks". Their well-defined structures and small sizes also enable the testing of their functions in synthetic and natural biological experiments. Here, we develop a framework for motif mining based on lossless network compression using subgraph contractions. This provides an alternative definition of motif significance which allows us to compare different motifs and select the collectively most significant set of motifs as well as other prominent network features in terms of their combined compression of the network. Our approach inherently accounts for multiple testing and correlations between subgraphs and does not rely on a priori specification of an appropriate null model. It thus overcomes common problems in hypothesis testing-based motif analysis and guarantees robust statistical inference. We validate our methodology on numerical data and then apply it on synaptic-resolution biological neural networks, as a medium for comparative connectomics, by evaluating their respective compressibility and characterize their inferred circuit motifs.

Higher-order network information propagation model based on social impact theory

User relationships are becoming increasingly diverse in current online social networks. This paper utilizes simplicial complexes in higher-order networks to depict multiple user relationships and characterize the topology of social networks. By employing social impact theory and factors such as user interest and information aging to define state transition rules among users, we establish a UAPR information propagation model based on simplicial complexes to simulate the information propagation process in higher-order social networks. The proposed model is simulated on three types of synthetic networks and four real-world simplicial complexes, demonstrating its ability to accurately describe the dynamics and influences of information propagation. Furthermore, our results indicate that different network structures, user interest values, information aging speeds, and intimacy levels significantly influence the information transmission process.

Equilibrium seeking of higher-order networks under facet cover constraints.

Agent intelligence involves specific requirements for social attributes. Intelligent agents make their decisions based on the groups they are part of, tend to satisfy co-members, and enlarge their own benefits. A fundamental question is whether this form of subgroup decision-making accommodate each individual's preferences. In this paper, we examine the evolution of an anticoordination game on a higher-order network in the form of a simplicial complex in relation to the facet cover problem, which ensures that each subgroup yields a positive benefit. We introduce and apply the facet update rule to regulate nodes' group-based interactions. We identify the payoff parameter condition that a strict Nash equilibrium (SNE) satisfies a facet cover. The proposed facet update rule enables the activated facet to reach a facet equilibrium, and all nodes would converge to an SNE with no more than 2m strategy switches, where m is the number of nodes in the simplicial complex. Additionally, we analyze the convergence of the asynchronous update rule, which can be seen as a special case of the facet update rule. Our simulations and extensive examples reveal that the SNE achieved by the facet update rule, on average, covers fewer nodes compared to the asynchronous update rule.

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.

Modeling and analysis of COVID-19 spreading based on complex network theory

Complex networks can effectively describe interactions within real-world complex systems. In researches of epidemic spreading, scientists constructed various physical contact networks between individuals on the microscopic scale and the metapopulation networks on the macroscopic scale. These different types of network structures significantly impact the propagation dynamics of epidemic in human society. For instance, population flows in global airline networks influence the speed and arrival time of epidemics across large-scale space. In this paper we review the epidemic spreading models on various network structures, including fully mixed networks, three types of lower-order networks, three types of higher-order networks, metapopulation networks, and multiple strains competitive epidemic spreading models. We also provide an overview of the application of complex network theory in the COVID-19 pandemic, covering topics of prediction, prevention, and control of the epidemic. Finally, we discuss the strengths and limitations of these models and propose perspectives for future research.

A research of higher-order network emotional phase transitions

This paper explores the law of emotion transmission on the social Internet. By applying higher-order network theory, ER random networks are reconstructed and higher-order network structures with multiple interaction points are generated. The I-state of the SI model is extended to set up the propagation rules of emotions based on higher-order networks. Concepts such as sentiment recession rate are introduced to make sentiment propagate through different simplexes, so as to obtain the propagation rules of higher-order networks. Qualitative analysis of emotional changes during the propagation process verifies the phase transition phenomenon of emotions in the network. By comparing simulated results with actual data, we demonstrate the accuracy of our higher-order network-based emotion propagation model in reflecting real-world trends and outcomes. The study also explores the effects of factors such as the initial proportion of extreme emotions on emotion propagation. This study provides valuable insights into understanding the operation of complex systems and offers important implications for government predictions of opinion development.

Research on brain functional network property analysis and recognition methods targeting brain fatigue

At present, researches on brain fatigue recognition are still in the stage of single task and simple brain region network features, while researches on high-order brain functional network features and brain region state mechanisms during fatigue in multi-task scenarios are still insufficient, making it difficult to meet the needs of fatigue recognition under complex conditions. Therefore, this study utilized functional near-infrared spectroscopy (fNIRS) technology to explore the correlation and differences in the low-order and high-order brain functional network attributes of three task induced mental fatigue, and to explore the brain regions that have a major impact on mental fatigue. Self-training algorithms were used to identify the three levels of brain fatigue. The results showed that during the fatigue development, the overall connection strength of the endothelial cell metabolic activity and neural activity frequency bands of the low-order brain functional network first decreased and then increased, while the myogenic activity and heart rate activity frequency bands showed the opposite pattern. Network topology analysis indicated that from no fatigue to mild fatigue, the clustering coefficient of endothelial cell metabolic activity and myogenic activity frequency bands significantly decreased, while the characteristic path length of myogenic activity significantly increased; when experiencing severe fatigue, the small-world attribute of the neural frequency band significantly weakened. However, each frequency band maintained its small-world attribute, reflecting the self-optimization and adaptability of the network during the fatigue process. During mild fatigue, neuronal activity bands’ node degree, cluster coefficient, and efficiency rose in high-order brain networks, while low-order networks showed no significant changes. As fatigue progressed, the myogenic activity bands of high-order network properties dominated, but neural bands gained prominence in mild fatigue, approaching the level of myogenic bands in severe fatigue, indicating that brain fatigue orchestrated a shift from myogenic to neural dominance in frequency bands. In addition, during the process of fatigue, the four network attributes of the high-order network cluster composed of low-order nodes related to the prefrontal cortex region, left anterior motor region, motor assist region, and left frontal lobe eye movement region significantly increased, indicating that these brain regions had a significant impact on brain fatigue status. The accuracy of using both high-order and low-order features to identify fatigue levels reached 88.095%, indicating that the combined network features of both high-order and low-order fNIRS signals could effectively detect multi-level mental fatigue, providing innovative ideas for fatigue warning.

Charting the brain networks of impulsivity: Meta-analytic synthesis, functional connectivity modelling, and neurotransmitter associations

Abstract Impulsivity is a multi-dimensional construct that plays a crucial role in human behaviour and is believed to be a transdiagnostic marker of several psychiatric disorders. However, given its multi-faceted nature, investigations of its neural correlates are challenging and systematic comparisons across dimensions are lacking. In this study, we used a comprehensive multi-modal approach to investigate the functional network organisation of two dimensions in which impulsivity manifests: decision-making and response inhibition. Activation likelihood estimation (ALE) meta-analyses of task-based fMRI studies within each dimension identified two distinct and non-overlapping functional systems. One located in the default-mode network, associated with value-based judgements and goal-directed decision-making, and the other distributed across higher-order networks associated with cognitive control. Resting-state functional connectivity revealed the two systems were organised into four specialised communities of default-mode, cingulo-insular, fronto-parietal, and temporal regions. Finally, given the widespread use of neurotransmitter-acting medication to treat conditions with impulsive symptoms, we investigated the association between this organisation and neurochemistry and found that integration across communities was associated with PET-derived serotonin receptor density. Our findings reinforce insights from previous behavioural research and provide substantial evidence for the multi-dimensional nature of impulsivity on the neural level. This highlights the necessity for a comprehensive dimensional ontology on all levels of investigation to address impulsivity in a transdiagnostic manner.

Positivity and semi-global polynomial stability of high-order Cohen–Grossberg BAM neural networks with multiple proportional delays

In this paper, we study positivity and semi-global polynomial stability (PS) of higher-order Cohen-Grossberg BAM neural networks with multiple proportional time delays. The proportional delays considered here are unbounded and time-varying, differing from constant, bounded, and distributional time delays. The system model cannot be represented using vector and matrices, making certain approaches within the vector-matrix framework unsuitable for applying. To address this limitation, a direct method based on the solution of the system is proposed to provide sufficient conditions guaranteeing the positivity and semi-global polynomial stability (PS) of the model under consideration. Furthermore, the direct method is applied to establish global PS conditions for BAM neural networks with multiple proportional delays. The obtained conditions contain only a few simple linear scalar inequalities that are easily solved. The applicability of the obtained PS conditions is verified by two numerical examples, and the solution of a linear programming problem is also obtained based on these theoretical results. Notably, this method can be applied to many system models with proportional delays after minor modifications.

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 computational mechanism of cue-stimulus integration for pain in the brain.

The brain integrates information from pain-predictive cues and noxious inputs to construct the pain experience. Although previous studies have identified neural encodings of individual pain components, how they are integrated remains elusive. Here, using a cue-induced pain task, we examined temporal functional magnetic resonance imaging activities within the state space, where axes represent individual voxel activities. By analyzing the features of these activities at the large-scale network level, we demonstrated that overall brain networks preserve both cue and stimulus information in their respective subspaces within the state space. However, only higher-order brain networks, including limbic and default mode networks, could reconstruct the pattern of participants' reported pain by linear summation of subspace activities, providing evidence for the integration of cue and stimulus information. These results suggest a hierarchical organization of the brain for processing pain components and elucidate the mechanism for their integration underlying our pain perception.

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.

Quantifying the Complexity of Nodes in Higher-Order Networks Using the Infomap Algorithm

Accurately quantifying the complexity of nodes in a network is crucial for revealing their roles and network complexity, as well as predicting network emergent phenomena. In this paper, we propose three novel complexity metrics for nodes to reflect the extent to which they participate in organized, structured interactions in higher-order networks. Our higher-order network is built using the BuildHON+ model, where communities are detected using the Infomap algorithm. Since a physical node may contain one or more higher-order nodes in higher-order networks, it may simultaneously exist in one or more communities. The complexity of a physical node is defined by the number and size of the communities to which it belongs, as well as the number of higher-order nodes it contains within the same community. Empirical flow datasets are used to evaluate the effectiveness of the proposed metrics, and the results demonstrate their efficacy in characterizing node complexity in higher-order networks.

Dynamical Fluctuations of Random Walks in Higher-Order Networks

Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate how fluctuations of a dynamical quantity of a random walk exploring a higher-order network arise over time. In the quenched case, where the hypergraph structure is fixed, through large deviation theory we show that the appearance of rare events is hampered in nodes with many higher-order interactions, and promoted elsewhere. Dynamical fluctuations are further boosted in an annealed scenario, where both the diffusion process and higher-order interactions evolve in time. Here, extreme fluctuations generated by optimal higher-order configurations can be predicted in the limit of a saddle-point approximation. Our study lays the groundwork for a wide and general theory of fluctuations and rare events in higher-order networks. Published by the American Physical Society 2024

Multiplex measures for higher-order networks

A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order interactions among a collection of units. In this work, we introduce a comprehensive set of measures to describe structural connectivity patterns in multiplex hypergraphs, considering scales from node and hyperedge levels to the system’s mesoscale. We validate our measures with three real-world datasets: scientific co-authorship in physics, movie collaborations, and high school interactions. This validation reveals new collaboration patterns, identifies trends within and across movie subfields, and provides insights into daily interaction dynamics. Our framework aims to offer a more nuanced characterization of real-world systems marked by both multiplex and higher-order interactions.

Socioeconomic resources in youth are linked to divergent patterns of network integration/segregation across the brain's transmodal axis.

Socioeconomic resources (SER) calibrate the developing brain to the current context, which can confer or attenuate risk for psychopathology across the lifespan. Recent multivariate work indicates that SER levels powerfully relate to intrinsic functional connectivity patterns across the entire brain. Nevertheless, the neuroscientific meaning of these widespread neural differences remains poorly understood, despite its translational promise for early risk identification, targeted intervention, and policy reform. In the present study, we leverage graph theory to precisely characterize multivariate and univariate associations between SER across household and neighborhood contexts and the intrinsic functional architecture of brain regions in 5,821 youth (9-10 years) from the Adolescent Brain Cognitive Development Study. First, we establish that decomposing the brain into profiles of integration and segregation captures more than half of the multivariate association between SER and functional connectivity with greater parsimony (100-fold reduction in number of features) and interpretability. Second, we show that the topological effects of SER are not uniform across the brain; rather, higher SER levels are associated with greater integration of somatomotor and subcortical systems, but greater segregation of default mode, orbitofrontal, and cerebellar systems. Finally, we demonstrate that topological associations with SER are spatially patterned along the unimodal-transmodal gradient of brain organization. These findings provide critical interpretive context for the established and widespread associations between SER and brain organization. This study highlights both higher-order and somatomotor networks that are differentially implicated in environmental stress, disadvantage, and opportunity in youth.