Studies to date on the role of social exclusion in public cooperation have mainly focused on the peer or pool sanctioning types of excluding free-riders from the share of common goods. However, the exclusive behaviors are not necessarily performed by individuals or local organizations but may rather be implemented by a centralized enforcement institution at a global scale. Besides, previous modeling methods of either peer or pool exclusion often presuppose some particular forms of feedback between the individual or collective efforts and the efficiency of social exclusion and, therefore, cannot comprehensively evaluate their effects on the evolution of cooperation in the social dilemma situations. Here, we construct a general model of global exclusion by considering the successful construction of the centralized exclusive institution as an arbitrary non-decreasing and smooth function of the collective efforts made by the global excluders and then theoretically analyze its potential impacts in the replicator dynamics of the public goods game. Interestingly, we have shown that, despite the presence of both the first- and second-order free-riding problems, global exclusion can indeed lead to the emergence or even stabilization of public cooperation without the support of any other evolutionary mechanism. In addition, we have also observed rich dynamical behaviors, such as the occurrence of a global or local family of neutrally stable closed orbits revolving around a nonlinear center or the existence of stable heteroclinic cycles between defectors, cooperators as well as global excluders, which give rise to a classification of up to 21 different phases.

The focus of fine-grained image classification tasks is to ignore interference information and grasp local features. This challenge is what the visual attention mechanism excels at. Firstly, we have constructed a two-level attention convolutional network, which characterizes the object-level attention and the pixel-level attention. Then, we combine the two kinds of attention through a second-order response transform algorithm. Furthermore, we propose a clustering-based grouping attention model, which implies the part-level attention. The grouping attention method is to stretch all the semantic features, in a deeper convolution layer of the network, into vectors. These vectors are clustered by a vector dot product, and each category represents a special semantic. The grouping attention algorithm implements the functions of group convolution and feature clustering, which can greatly reduce the network parameters and improve the recognition rate and interpretability of the network. Finally, the low-level visual features and high-level semantic information are merged by a multi-level feature fusion method to accurately classify fine-grained images. We have achieved good results without using pre-training networks and fine-tuning techniques.

Computer vision systems are insensitive to the scale of objects in natural scenes, so it is important to study the multi-scale representation of features. Res2Net implements hierarchical multi-scale convolution in residual blocks, but its random grouping method affects the robustness and intuitive interpretability of the network. We propose a new multi-scale convolution model based on multiple attention. It introduces the attention mechanism into the structure of a Res2-block to better guide feature expression. First, we adopt channel attention to score channels and sort them in descending order of the feature’s importance (Channels-Sort). The sorted residual blocks are grouped and intra-block hierarchically convolved to form a single attention and multi-scale block (AMS-block). Then, we implement channel attention on the residual small blocks to constitute a dual attention and multi-scale block (DAMS-block). Introducing spatial attention before sorting the channels to form multi-attention multi-scale blocks(MAMS-block). A MAMS-convolutional neural network (CNN) is a series of multiple MAMS-blocks. It enables significant information to be expressed at more levels, and can also be easily grafted into different convolutional structures. Limited by hardware conditions, we only prove the validity of the proposed ideas through convolutional networks of the same magnitude. The experimental results show that the convolution model with an attention mechanism and multi-scale features is superior in image classification.

Recent empirical studies have revealed that social interactions among agents in realistic networks merely exist intermittently and occur in a particular sequential order. However, it remains unexplored how to theoretically describe evolutionary dynamics of multiple strategies on temporal networks. Herein, we develop a deterministic theory for studying evolutionary dynamics of any n × n pairwise games in structured populations where individuals are connected and organized by temporally activated edges. In the limit of weak selection, we derive replicator-like equations with a transformed payoff matrix characterizing how the mean frequency of each strategy varies over time, and then obtain critical conditions for any strategy to be evolutionarily stable on temporal networks. Interestingly, the re-scaled payoff matrix is a linear combination of the original payoff matrix with an additional one describing local competitions between any pair of different strategies, whose weights are solely determined by network topology and selection intensity. As a particular example, we apply the deterministic theory to analysing the impacts of temporal networks in the mini-ultimatum game, and find that temporally networked population structures result in the emergence of fairness. Our work offers theoretical insights into the subtle effects of network temporality on evolutionary game dynamics.

Despite significant advancements in object detection technology, most existing detection networks fail to investigate global aspects while extracting features from the inputs and cannot automatically adjust based on the characteristics of the inputs. The present study addresses this problem by proposing a detection network consisting of three stages: preattention, attention, and prediction. In the preattention stage, the network framework is automatically selected based on the features of the images’ objects. In the attention stage, the transformer structure is introduced. Taking into account the global features of the target, this study combines a self-attention module in the transformer model and convolution operation to integrate image features from global to local and for detection, thus improving the ship target accuracy. This model uses mathematical methods to obtain results of predictive testing in the prediction stage. The above improvements are based on the You Only Look Once version 4 (YOLOv4) framework, named “Auto-T-YOLO”. The model achieves the highest accuracy of 96.3% on the SAR Ship Detection dataset (SSDD) compared to the other state-of-the-art (SOTA) model. It achieves 98.33% and 91.78% accuracy in the offshore and inshore scenes, respectively. The experimental results verify the practicality, validity, and robustness of the proposed model.