Understanding the systemic resilience of higher-order networks is critical for securing complex systems governed by multi-body interactions. While previous threshold-driven models explore cascading failures on hypergraphs, they conventionally assume absolute nodal fragility, thereby breaking the intrinsic bipartite symmetry of the underlying topology. In this work, we propose a generalized dual-threshold cascading model wherein both nodes and hyperedges possess fractional tolerance thresholds. To overcome the analytical intractability of reciprocal fractional damage, we pioneer a unified, two-stage cavity method utilizing structural generating functions. This theoretical innovation rigorously decouples the localized survival cascade from the global percolation process, revealing a novel Subcritical Survival Phase—where fragmented components endure locally but fail to percolate globally—and identifying a distinct “staircase” stability boundary dictated by discrete capacity constraints. Furthermore, our exact analytical framework elegantly classifies macroscopic breakdowns into mean-field continuous percolations and hybrid first-order collapses. Extensively validated across both homogeneous (Poisson) and highly heterogeneous (scale-free) hypergraphs, the model mathematically captures how topological super-hubs anchor local survival while amplifying catastrophic collapses, providing a universal foundation for evaluating the “robust-yet-fragile” nature of empirical multi-body architectures.

Collective behaviors such as infrastructure failures and social adoption propagate through groups governed by fixed quorum requirements rather than by pairwise contacts. However, it remains unclear how absolute group- and individual-level thresholds jointly shape cascades in higher-order networks. Here we show that a dual-threshold bootstrap percolation model on random hypergraphs separates a connected active backbone from large-scale endogenous activation. A seed-driven giant component emerges continuously at a structural percolation threshold, whereas macroscopic amplification ignites only at a higher dynamical tipping point, creating a metastable safety margin in which communication is possible without systemic outbreak. This decoupling reflects an asymmetric division of labor: the group quorum M acts as a source-side filter, while the individual barrier K serves as a receiver-side gatekeeper. On homogeneous substrates, the structural onset is protected to leading order against K, but heterogeneous connectivity erodes this protection. Our framework provides a basis for predicting cascade risk and designing targeted node- and group-level interventions in complex systems. A bootstrap percolation framework on random hypergraphs pairs a group quorum with an individual barrier to regulate cascades. The quorum governs the emergence of a seed-driven backbone, while the barrier triggers an explosive outbreak at a higher threshold, producing a metastable safety margin that shrinks under heterogeneous connectivity.

Higher-order networks encode interactions among groups of units, yet their resilience under reciprocal cascading damage remains insufficiently understood. Existing threshold models on hypergraphs often assume absolute nodal fragility: a node fails as soon as it loses any incident hyperedge. This assumption couples local survival to global connectivity and obscures the asymmetric tolerances that nodes and group interactions may possess. Here we introduce a dual-threshold cascading failure model in which nodes and hyperedges tolerate independent fractions of lost incident hyperedges and lost constituent nodes, controlled by ϕv and ϕe, respectively. We derive a two-stage cavity theory based on structural generating functions: the first stage solves the local survival fixed point of the cascade, while the second evaluates global connectivity on the resulting damaged substrate. This separation yields closed self-consistency equations for local survival and the giant connected component, identifies continuous and hybrid discontinuous transitions through marginal stability conditions, and reveals a Subcritical Survival Phase in which a finite locally surviving substrate exists without macroscopic percolation. On Poisson hypergraphs, the theory predicts discrete “staircase” stability boundaries induced by integer capacity constraints. On scale-free hypergraphs, degree heterogeneity suppresses continuous thresholds and promotes robust-yet-fragile collapses driven by hubs. Empirically grounded configuration-model simulations using co-authorship, contact, and protein-complex distributions agree with the analytical predictions and exhibit the same local–global decoupling. The framework provides a tractable basis for analyzing resilience in higher-order systems with asymmetric component tolerances.

Existing cascade models on hypergraphs universally adopt homogeneous node roles and single-stage synchronous activation, failing to capture the hierarchical sequential decision-making in real social groups, where leader consensus must precede follower mobilization. To fill this gap, we propose a novel two-stage threshold cascade model on role-differentiated hypergraphs, which enforces a strict sequential activation rule: a hyperedge can only activate its follower set via the overall execution threshold \(\phi_2\) after its leader subset meets the leader consensus threshold \(\phi_1\). We derive the self-consistent equation for steady-state cascade size via mean-field approximation and cavity method, and validate theoretical predictions through numerical simulations on Poisson and uniform hyperedge size distributions. Our results show that the system exhibits universal discontinuous first-order phase transitions, with the leader threshold \(\phi_1\) dominating cascade initiation. We further find that the "small leader - large follower" configuration significantly reduces the critical initial seed fraction, and uncover a non-monotonic discrete truncation effect under uniform distributions. This work provides a rigorous theoretical framework for hierarchical contagion in higher-order networks.

Current research on social contagion rarely investigates how negative relationships shape diffusion outcomes in higher-order structures. To bridge this gap, we introduce a dual-threshold contagion model on signed hypergraphs, where a parameter α tunes the inhibitory influence of negative hyperedges. By combining mean-field theory with analytical approximations, we characterize the cascade conditions up to the second order. We find that strong negative inhibition leads to rich dynamical behaviors, specifically two discontinuous phase transitions featuring explosive activation and an abrupt collapse. Conversely, the system under positive or weakly negative weights demonstrates an asymmetric sensitivity to the dual thresholds. This framework offers a theoretical basis for understanding how signed higher-order interactions, threshold heterogeneity, and seed size collectively regulate global cascades.

Existing research on complex social contagion frequently neglects the role differentiation inherent in higher-order structures. To address this gap, we introduce a hypergraph-based contagion model that explicitly distinguishes between leader and follower roles within hyper-edges (groups). The model incorporates key parameters: activation threshold, follower influence weight, and symmetric and asymmetric group sizes. We derive a self-consistency equation characterizing the cascade size and identify the critical seed sizes associated with first-order phase transitions. Our results demonstrate that increasing follower influence enhances contagion dynamics through peer reinforcement, facilitating large-scale cascades initiated by smaller initial seeds. Crucially, configurations involving smaller symmetric leader-follower group sizes reduce the critical seed size. Furthermore, distributions of leader and follower group sizes following Poisson distributions generally lower the critical seed size compared to fixed-size configurations, attributable to increased structural heterogeneity. These findings provide a basic understanding of threshold-driven contagion in role-differentiated, higher-order systems and provide an analytical framework for modeling diffusion processes in domains such as education, marketing, and political mobilization.

Cohesion plays a crucial role in achieving collective goals, promoting cooperation and trust, and improving efficiency within social groups. To gain deeper insights into the dynamics of group cohesion, we have extended our previous model of noisy group formation by incorporating asymmetric voting behaviors. Through a combination of theoretical analysis and numerical simulations, we have explored the impact of asymmetric voting noise, the attention decay rate, voter selection methods, and group sizes on group cohesion. For a single voter, we discovered that as the group size approaches infinity, group cohesion converges to $1/(R+1)$, where $R$ represents the ratio of asymmetric voting noise. Remarkably, even in scenarios with extreme voting asymmetry ($R \to \infty$), a significant level of group cohesion can be maintained. Furthermore, when the positive or negative voter's voting noise surpasses or falls below the phase transition point of $R_c=1$, a higher rate of attention decay can lead to increased group cohesion. In the case of multiple voters, a similar phenomenon arises when the attention decay rate reaches a critical point. These insights provide practical implications for fostering effective collaboration and teamwork within growing groups striving to achieve shared objectives.

Traditional manufacturing industry is in the early stages of transition to low-carbon innovative production, and is in urgent need of a low-carbon innovation system to achieve the goal of carbon neutrality. In order to realize the effective supervision of enterprise carbon emissions, this paper constructs a tripartite evolutionary game model among the corporate, government and public from the perspective of dynamic subsidies and taxes. The main results are as follows. First, the increase in government subsidies to a certain extent will help encourage companies to choose low-carbon innovative production strategies, but more subsidies are not always better. Excessive subsidies will increase the cost of government regulation and reduce the probability of government regulation. Second, the tripartite evolutionary game system does not converge under the static subsidies and taxes mechanism. But the system could quickly converges to the stable condition under dynamic subsidies and taxes. The stable point is the situation of corporate low-carbon innovation, government regulation, and public supervision. Third, the public intervention and supervision can effectively prevent the phenomenon of government misconduct and enterprises over-emission production. And the influence of public reward and punishment is more effective for the government than for enterprises.

The Public Goods Game (PGG) encounters hurdles when donations are scarce, resulting in failed game initiations. To investigate such phenomena, we propose a threshold-based spatial PGG model operating on a lattice with periodic boundaries. Players strategically choose between cooperation (C) and defection (D), with PGG initiation determined by a cooperative contribution threshold. Additionally, we introduce an adjustment factor for player reputation, reflecting how individual strategy choices and responses from interacting partners influence reputation changes. We hypothesize that within non-initiated PGG, defectors’ reputations decrease, while within initiated PGG, defectors are evaluated and penalized by cooperators. Our findings reveal that higher initiation thresholds can enhance final cooperation levels. Moreover, the inclusion of the reputation adjustment factor acts as a catalyst for cooperative behavior. Interestingly, greater uncertainty in strategy adoption is associated with increased cooperative levels under higher initiation thresholds. This study adds new insights into the evolution of cooperation in the context of spatial structure.

使用索马里医院提供的脑卒中患者数据集,通过四分位距(interquartile range,IQR)方法和合成少数类过采样技术(synthetic minority oversampling technique,SMOTE)算法进行数据预处理,采用特征工程中的嵌入式方法对数据集进行特征分析,确定脑卒中诱发因素.以随机森林(random forest,RF)、极端梯度提升(extreme gradient boosting,XGB)和自适应提升(adaptive boosting,AdB)算法为第一层,高斯朴素贝叶斯(Gaussian naive bayes,GaNB)和支持向量机(support vector machine,SVM)为第二层,逻辑回归(logistic regression,LR)为元学习器构建超级学习者(super learner,SL)集成学习模型.仿真实验结果表明,相较于6种基础算法,SL模型预测效果最优,可为脑卒中的预测分析提供新的选择.

Opinion cascades, initiated by active opinions, offer a valuable avenue for exploring the dynamics of consensus and disagreement formation. Nevertheless, the impact of biased perceptions on opinion cascade, arising from the balance between global information and locally accessible information within network neighborhoods, whether intentionally or unintentionally, has received limited attention. In this study, we introduce a threshold model to simulate the opinion cascade process within social networks. Our findings reveal that consensus emerges only when the collective stubbornness of the population falls below a critical threshold. Additionally, as stubbornness decreases, we observe a higher prevalence of first-order and second-order phase transitions between consensus and disagreement. The emergence of disagreement can be attributed to the formation of echo chambers, which are tightly knit communities where agents' biased perceptions of active opinions are lower than their stubbornness, thus hindering the erosion of active opinions. This research establishes a valuable framework for investigating the relationship between perception bias and opinion formation, providing insights into addressing disagreement in the presence of biased information.

The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable model of group formation where individuals have multidimensional binary opinions and the group grows through a noisy homophily principle, i.e., like-minded individuals attract each other with exceptions occurring with some small probability. Assuming that the level of disagreement is correlated with the number of different opinions coexisting within the group, we find analytically and numerically that in growing groups disagreement emerges spontaneously regardless of how small the noise in the system is. Moreover, for groups of infinite size, fragmentation is inevitable. We also show that the model outcomes are robust under different group growth mechanisms.

Social networks have provided a platform for the effective exchange of ideas or opinions but also served as a hotbed of polarization. While much research attempts to explore different causes of opinion polarization, the effect of perception bias caused by the network structure itself is largely understudied. To this end, we propose a threshold model that simulates the evolution of opinions by taking into account the perception bias, which is the gap between global information and locally available information from the neighborhood within networks. Our findings suggest that polarization occurs when the collective stubbornness of the population exceeds a critical value which is largely affected by the perception bias. In addition, as the level of stubbornness grows, the occurrence of first-order and second-order phase transitions between consensus and polarization becomes more prevalent, and the types of these phase transitions rely on the initial proportion of active opinions. Notably, for regular network structures, a step-wise pattern emerges that corresponds to various levels of polarization and is strongly associated with the formation of echo chambers. Our research presents a valuable framework for investigating the connection between perception bias and opinion polarization and provides valuable insights for mitigating polarization in the context of biased information.

Agreement is the rare exception while disagreement is the universal. To study how opinion disagreement or even polarization emerges, we proposed an agent-based model to mimic a noisy group formation process by recruiting new members who hold binary opposite opinions on different issues. We examine the long-term effects on the proportions of group members who hold different opinions to see how much disagreement there is. We discover that disagreement always arises regardless of the infinitesimal level of noise. In addition, opinions tend to be polarized as group size grows. More importantly, we find the proportions of group members with different opinions are closely correlated with the eigenvalues and eigenvectors of the transition probability matrix. By constructing social networks, our work can be extended to study social fragmentation and community structure in the future.

本文对浙江省各地区新商品的标准化编码注册数据进行分析,通过构建"地区-商品"二部图网络,采用最小复杂度方法计算了浙江省全省及省内各个地区的适应度.分析发现,相比于人均GDP等传统经济指标,适应度的排序更能有效反映地区间经济发展的差异.通过观察并对比各地区在适应度-人均GDP空间上演化路径的差异,我们观察到浙江省经济在整体趋向多元化的同时,各地区的产业分工也正在趋向加深.该研究有效挖掘了浙江省的经济趋势,进一步证实了基于最小复杂度方法的非线性迭代方法能够在省一级的数据尺度上有效区分各地区经济发展模式的差异.

分析并预测股票市场中板块指数的涨跌是自股票市场创立以来,受到持续关注的研究热点之一.但由于股票市场具有非线性的时序特征,使得这一研究方向进展得颇为坎坷.而神经网络恰好在一定程度上可以捕捉非线性特征,这给研究带来了一种可能的途径.本文基于长短期记忆网络(LSTM)和全连接神经网络(FCNN)设计模型,将大盘行情指数、关联板块指数和金融板块三个方面的历史价格和成交量以及十年期国债收益率的历史价格作为输入,对TDX金融行业指数涨跌的走势进行研究.实证结果表明使用39天的先验数据使得走势预测效果最优,达到了理想的预测效果,且没有出现过拟合.

随着互联网技术的飞速发展, 全球经济正向信息时代全面转型, 主流经济学理论对信息及隐藏在信息背后的认知问题鲜少触及, 难以对新涌现的复杂多变的新经济形态提供理论上的诠释.认知可以促进经济增长和财富的产生, 现在蓬勃发展的平台经济就是提升认知的一种有效手段.认知变现为财富的主要途径是利益释放机制, 具体表现为商家与消费者的互动共同创造了财富.认知存在的差异性体现为, 在经济中同时存在趋稳与非平稳两种机制.本文采用全新的视角, 对上述问题进行深入剖析, 并最终讨论了基于认知的经济增长新观点与主流经济学观点的不同.

评论数据的情感分析一直是自然语言研究的热点之一,特别是评论观点丰富性、情感化、多元化、非结构化等特征方面的研究近年来深受大家关注.本文基于AI Challenger2018细粒度情感分析比赛为研究背景,在分析GCAE和SynATT两种模型基础上,通过研究方面类别情绪分析(ACSA)方法,提出了CNN-GCAE和CNN-SynATT模型,解决了原来模型在数据处理方面的不足,提高了情感分析的精准度和召回率.实验结果表明,改进模型对评论数据情感分析的准确率效果明显.

典型的K-means算法利用手肘法选择合适的K值在实际项目中应用的较多,但是手肘法获取K值自动性低,以及面对海量数据的处理,效率上也有待提高.提出利用手肘法关系图初始点和末尾点连接的关系直线,求K值范围下直线y值与误差平方和的最大差值的方法,最大差值对应的K值为手肘法的最优肘点,由于手肘法需要多次迭代以及数据集稠密度对关系图的影响较小,提出利用数据集预抽样并且将程序部署在spark平台之上的方式自动获取手肘法的肘点K值,这样不仅根据此方法自动获取K-means最优K值而且提高了大数据集的处理效率.