发表机构
Chalmers University of Technology（查尔姆斯理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究扩展偏好中心性模型，引入密度惩罚以模拟空间活动，提供开源实现 prefcent，并通过实验验证其收敛性及惩罚对中心分布的影响。
AI 中文摘要
偏好中心性（Hellervik, Nilsson 和 Andersson, 2019）通过活动与吸引力之间的反馈来模拟空间活动。我们对其进行了扩展，引入了一个密度惩罚。局部响应取决于单位容量的活动量，并随容量缩放。一个单位容量均匀的修正保持了总活动量，并且对于选定的响应函数和惩罚强度，守恒决定了该修正。我们提供了 prefcent，一个开源的参考实现，带有收敛性和可行性检查，并记录每次运行的输入和设置。它复现了伴随的 Porto Alegre 研究在所有 65,357 个网络段上的 200 次迭代输出，中位相对差异约为 $10^{-14}$。在一个强反馈示例中，惩罚降低了集中度，并在更少的迭代次数内达到停止容差。其他合成示例展示了惩罚强度如何改变中心的相对显著性，以及中心数量如何随运输成本变化。另一个示例在同一网络和容量景观上，从不同的初始状态达到不同的数值均衡。在三个合成二维景观的多起点扫描中，在参数值范围内出现了不同的收敛状态：在反馈强度和运输成本的网格的 420 个点中的 172 个点处，包括 75 个状态在中心数量上不同的点。本说明提供了一个模型规范，以及一个可复现的计算基础，用于进一步的理论和实证工作。
英文摘要
Preferential centrality (Hellervik, Nilsson and Andersson, 2019) models spatial activity through feedback between activity and attraction. We extend it with a density penalty. The local response depends on activity per unit of capacity and scales with capacity. A correction that is uniform per unit of capacity preserves total activity, and for a chosen response function and penalty strength, conservation determines this correction. We provide prefcent, an open-source reference implementation with convergence and feasibility checks and records of each run's inputs and settings. It reproduces the 200-iteration outputs of a companion Porto Alegre study across all 65,357 network segments, with median relative differences of order $10^{-14}$. In a strong-feedback example, the penalty reduces concentration and reaches the stopping tolerance in fewer iterations. Other synthetic examples show how penalty strength changes the relative prominence of centers and how their number varies with transport costs. A further example reaches different numerical equilibria from different initial states on the same network and capacity landscape. In multi-start sweeps on three synthetic two-dimensional landscapes, distinct converged states occur over a range of parameter values: at 172 of 420 points of a grid in feedback strength and transport cost, including 75 where the states differ in their number of centers. The note provides a model specification and a reproducible computational basis for further theoretical and empirical work.
Comments15 pages, 8 figures. Software: prefcent 0.1.1, doi:10.5281/zenodo.23103539. Reproduction archive: doi:10.5281/zenodo.23158476
