arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2302.12295physics.soc-phphysics.data-an
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网络上的信息级联与相变

Information cascade on networks and phase transitions

Masato Hisakado, Kazuaki Nakayama, Shintaro Mori

AI总结:

本文研究了随机图、BA模型和格点网络上的信息级联投票模型,发现网络枢纽大小影响信息级联相变和超常相变,枢纽越小投票性能越优。

摘要:

本文研究了在几种网络——随机图、Barabási-Albert(BA)模型和格点网络——上信息级联的投票模型,使用单一参数$ω$;$ω=1,0,-1$分别对应这些网络。$ω$与枢纽的大小有关。我们讨论了网络所依赖的相之间的差异。在$ω\ne -1$时,可以观察到以下两种类型的相变:信息级联相变和超常相变。第一种是大多数投票者做出正确选择的状态与大多数投票者做出错误选择的状态之间的转变。这是一种属于非平衡相变的吸收相变。在对称情况下,相变是连续的,其普适类与非线性Pólya模型相同。相反,在非对称情况下,存在不连续相变,其间隙取决于网络。超常相变是收敛速度的转变,收敛速度转变的临界点取决于$ω$。在$ω=1$时,在BA模型中,这种转变消失。在格点情况下,两种相变在$ω=-1$时均消失。总之,随着性能接近格点情况,$ω\sim-1$在所有网络中表现出最佳的投票性能。随着枢纽尺寸减小,性能得到改善。

英文摘要:

Herein, we consider a voting model for information cascades on several types of networks -- a random graph, the Barabási-Albert(BA) model, and lattice networks -- by using one parameter $ω$; $ω=1,0, -1$ respectively correspond to these networks. $ω$ is related to the size of hubs. We discuss the differences between the phases in which the networks depend. In $ω\ne -1$, without, the following two types of phase transitions can be observed: information cascade transition and super-normal transition. The first is the transition between a state where most voters make correct choices and a state where most of them are wrong. This is an absorption transition that belongs to the non-equilibrium transition. In the symmetric case, the phase transition is continuous and the universality class is the same as nonlinear Pólya model. In contrast, in the asymmetric case, there is a discontinuous phase transition, where the gap depends on the network. The super-normal transition is the transition of the convergence speed, and the critical point of the convergence speed transition depends on $ω$. At $ω=1$, in the BA model, this transition disappears. Both phase transitions disappear at $ω=-1$ in the lattice case. In conclusion, as the performance near the lattice case, $ω\sim-1$ exhibits the best performance of the voting in all networks. As the hub size decreases, the performance improves.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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