Understanding the evolution of cooperation in multi-player games is of vital significance for natural and social systems. An important challenge is that group interactions often lead to nonlinear synergistic effects. However, previous models mainly focus on deterministic nonlinearity, where synergy or discounting effects occur under specific conditions, not accounting for uncertainty and stochasticity in real-world systems. Here, we develop a probabilistic framework to study the cooperative behavior in stochastic nonlinear public goods games. Through both analytical treatment and Monte Carlo simulations, we provide a comprehensive understanding of social dilemmas with stochastic nonlinearity in both well-mixed and structured populations. We find that increasing the degree of nonlinearity makes synergy more advantageous when competing with discounting, thereby promoting cooperation. Furthermore, we show that network reciprocity loses effectiveness when the probability of synergy is small. Moreover, group size exhibits nonlinear effects on group cooperation regardless of the underlying structure. Our findings thus provide insights into how stochastic nonlinearity influences the emergence of prosocial behavior.

Temporal Knowledge Graph (TKG) reasoning involves predicting future facts based on historical information by learning correlations between entities and relations. Recently, many models have been proposed for the TKG reasoning task. However, most existing models cannot efficiently utilize historical information, which can be summarized in two aspects: 1) Many models only consider the historical information in a fixed time range, resulting in a lack of useful information; 2) some models use all the historical facts, thus some noise or invalid facts are introduced during reasoning. In this regard, we propose a novel TKG reasoning model with dynamic memory enhancement (DyMemR). Inspired by human memory, we introduce memory capacity, memory loss, and repetition stimulation to design a human-like memory pool that could remember potentially useful historical facts. To fully leverage the memory pool, we utilize a two-stage training strategy. The first stage is guided by the memory-based encoding module which learns embeddings from memory-based subgraphs generated through the memory pool. The second stage is the memory-based scoring module that emphasizes the historical facts in the memory pool. Finally, we extensively validate the superiority of DyMemR against various state-of-the-art baselines.

Embedding-based methods currently achieved impressive success in recommender systems. However, such methods are more likely to suffer from bias in data distribution, especially the attribute bias problem. For example, when a certain type of user, like the elderly, occupies the mainstream, the recommendation results of minority users would be seriously affected by the mainstream users’ attributes. To address this problem, most existing methods are proposed from the perspective of fairness, which focuses on eliminating unfairness but deteriorates the recommendation performance. Unlike these methods, in this paper, we focus on improving the recommendation performance for minority users of biased attributes. Along this line, we propose a novel attribute-aware Counterfactual Augmentation framework for Minority Users(CAMUS). Specifically, the CAMUS consists of a counterfactual augmenter, a confidence estimator, and a recommender. The counterfactual augmenter conducts data augmentation for the minority group by utilizing the interactions of mainstream users based on a universal counterfactual assumption. Besides, a tri-training-based confidence estimator is applied to ensure the effectiveness of augmentation. Extensive experiments on three real-world datasets have demonstrated the superior performance of the proposed methods. Further case studies verify the universality of the proposed CAMUS framework on different data sparsity, attributes, and models.

Indirect reciprocity unveils how social cooperation is founded upon moral systems. Within the frame of dyadic games based on individual reputations, the ‘leading-eight’ strategies distinguish themselves in promoting and sustaining cooperation. However, in real-world societies, there are widespread interactions at the group level, where individuals need to make a singular action choice when facing multiple individuals with different reputations. Here, through introducing the assessment of collective reputations, we develop a framework that embeds group-level reputation structure into public goods games to study the evolution of group-level indirect reciprocity. We show that changing the criteria of group assessment destabilizes the reputation dynamics of leading-eight strategies. In a particular range of social assessment criteria, all leading-eight strategies can break the social dilemma in public goods games and sustain cooperation. Specifically, there exists an optimal, moderately set assessment criterion that is most conducive to promoting cooperation. Moreover, in the evolution of assessment criteria, the preference of the leading-eight strategies for social strictness is inversely correlated with the payoff level. Our work reveals the impact of social strictness on prosocial behaviour, highlighting the importance of group-level interactions in the analysis of evolutionary games and complex social dynamics.

Introduction: Major depressive disorder (MDD) is a debilitating disease involving sensory and higher-order cognitive dysfunction. Previous work has shown altered asymmetry in MDD, including abnormal lateralized activation and disrupted hemispheric connectivity. However, it remains unclear whether and how MDD affects functional asymmetries in the context of intrinsic hierarchical organization.Methods: Here, we evaluate intra- and inter-hemispheric asymmetries of the first three functional gradients, characterizing unimodal-transmodal, visual-somatosensory, and somatomotor/default mode-multiple demand hierarchies, to study MDD-related alterations in overarching system-level architecture.Results: We find that, relative to the healthy controls, MDD patients exhibit alterations in both primary sensory regions (e.g., visual areas) and transmodal association regions (e.g., default mode areas). We further find these abnormalities are woven in heterogeneous alterations along multiple functional gradients, associated with cognitive terms involving mind, memory, and visual processing. Moreover, through an elastic net model, we observe that both intra- and inter-asymmetric features are predictive of depressive traits measured by BDI-II scores.Discussion: Altogether, these findings highlight a broad and mixed effect of MDD on functional gradient asymmetry, contributing to a richer understanding of the neurobiological underpinnings in MDD.