有向偏好依附网络中的空间依赖性
Spatial Dependence in Directed Preferential-Attachment Networks
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中文总结 AI 辅助
研究有向偏好依附网络中的空间依赖性，通过扩展的有向PA模型，结合高斯过程对数正态场等方法，推导相关函数，开发估计器，经模拟和实际航班数据分析，验证依赖性传递，实现体积变化分解，得出共超越转变尺度等成果。
中文摘要 AI 辅助
空间嵌入的有向网络，如航空网络，附近节点常同时呈现高活跃度。偏好依附（PA）解释了枢纽主导地位。本文通过一个有向PA模型将其扩展到空间协同移动，该模型的出节点和入节点权重遵循时间上持久的高斯过程对数正态场。在次线性PA下，出度比例收敛到明确的归一化幂权重，而自环排除产生耦合的入度极限。我们推导了一个严格凹的逆函数，从终端度比例中恢复入权重。对于有序网络历史，我们为PA指数开发了一个最小化-最大化（MM）权重估计器和轮廓似然；时间预白化和空间拟似然估计潜在协方差。模拟验证了距离衰减依赖性的传递，并展示了随机段体积如何在原始度数中创建与距离无关的共模。对美国国内航班（2015 - 2019）的分析将全网络体积变化与短程空间成分分开。观测体积重建再现了原始度数共模，拟合场产生了约150公里的探索性共超越转变尺度。对欧洲空中交通的逐运营商分析也揭示了相同的分解。
英文摘要
Spatially embedded directed networks, such as airline networks, often exhibit simultaneous high activity at nearby nodes. Preferential attachment (PA) explains hub dominance. We extend it to spatial co-movement through a directed PA model whose out- and in-node weights follow temporally persistent Gaussian-process lognormal fields. Under sublinear PA, out-degree proportions converge to explicit normalized powered weights, whereas self-loop exclusion yields a coupled in-degree limit. We derive a strictly concave inverse that recovers the in-weights from terminal degree proportions. For ordered network histories, we develop a minorization-maximization (MM) weight estimator and profile likelihood for the PA exponent; temporal pre-whitening and a spatial quasi-likelihood estimate the latent covariance. Simulations verify transmission of distance-decaying dependence and show how random segment volume creates a distance-independent common mode in raw degrees. An analysis of U.S. domestic flights (2015-2019) separates network-wide volume variation from a short-range spatial component. An observed-volume reconstruction reproduces the raw-degree common mode, and the fitted field yields an exploratory co-exceedance transition scale of roughly 150 km. A per-carrier analysis of European air traffic also reveals the same decomposition.
