Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an arbitrary number of strategies on graphs is still missing. Here, we solve this by drawing an analogy with the Balls-and-Boxes problem, based on which we show that the local configuration of multiplayer games on graphs is equivalent to distributing k identical co-players among n distinct strategies. We use this to derive the replicator equation for any n-strategy multiplayer game under weak selection, which can be solved in polynomial time. As an example, we revisit the second-order free-riding problem, where costly punishment cannot truly resolve social dilemmas in a well-mixed population. Yet, in structured populations, we derive an accurate threshold for the punishment strength, beyond which punishment can either lead to the extinction of defection or transform the system into a rock-paper-scissors-like cycle. The analytical solution also qualitatively agrees with the phase diagrams that were previously obtained for non-marginal selection strengths. Our framework thus allows an exploration of any multi-strategy multiplayer game on regular graphs.

The lesion regions of a medical image account for only a small part of the image, and a critical imbalance exists in the distribution of the positive and negative samples, which affects the segmentation performance of the lesion regions. Dice loss is beneficial for the image segmentation involving an extreme imbalance of the positive and negative samples but it ignores the background regions, which also contain a large amount of information. In this work, we propose an improved dice loss that can mine the information in background areas and modify network architecture to improve performance. The improved dice loss called weighted soft dice loss (WSDice loss). Our loss function gives a small weight to the background area of the label, so the background area will be added to the calculation when calculating dice loss. It can also soft the hard label in the lesion area to increase the robustness of the model to noise label. What’s more, we propose to cascade Focal loss and WSDice loss. Focal Loss is a Distribution-based loss function, WSDice Loss is a Regionbased loss function, the optimization directions of them are different. The cascaded loss function can make full use of the advantages of both and greatly improve model performance. In addition, we add a simple but effective channel attention module to the decode module of U-net. We experimented on the ChestX-ray8 datasets. Compared with Dice loss, WSDice loss improves the dice coefficient by 1.59%, cascaded loss function can improve dice coefficient by 7.81%. The improved in model architecture can increase the dice coefficient by 1.36%.

In this paper, the distributed control problem of nonlinear strict-feedback multiagent systems is addressed under directed and time-invariant communication graphs. With the utilization of the prescribed performance control methodology, a control algorithm is proposed to ensure predefined bounds of overshoot, convergence rates, and steady-state values of the neighborhood synchronization errors in the presence of unknown dead-zone inputs. The algorithm is fully distributed in the sense that the control input for each agent is independent of any global information of the communication graph and is solely based on local relative output information from its neighborhood set. The approximating structures, e.g., neural networks or fuzzy systems, and the command filters that are typically incorporated to avoid the need for analytical derivatives in the backstepping design are not employed here, resulting in a low-complexity design. Simulation results are included to verify the algorithm.

This brief addresses the distributed consensus problem of nonlinear multi-agent systems under a general directed communication topology. Each agent is governed by higher-order dynamics with mismatched uncertainties, multiple completely unknown high-frequency gains, and external disturbances. The main contribution of this brief is to present a new distributed consensus algorithm, enabling the control input of each agent to require minimal information from its neighboring agents, that is, only their output information. To this end, a dynamic system is explicitly constructed for each agent to generate a reference output. Theoretical and simulation verifications of the proposed algorithm are rigorously studied to ensure that asymptotic consensus can be achieved and that all closed-loop signals remain bounded.