Textual geographic information is indispensable and heavily relied upon in
practical applications. The absence of clear distribution poses challenges in
effectively harnessing geographic information, thereby driving our quest for
exploration. We contend that geographic information is influenced by human
behavior, cognition, expression, and thought processes, and given our intuitive
understanding of natural systems, we hypothesize its conformity to the Gamma
distribution. Through rigorous experiments on a diverse range of 24 datasets
encompassing different languages and types, we have substantiated this
hypothesis, unearthing the underlying regularities governing the dimensions of
quantity, length, and distance in geographic information. Furthermore,
theoretical analyses and comparisons with Gaussian distributions and Zipf's law
have refuted the contingency of these laws. Significantly, we have estimated
the upper bounds of human utilization of geographic information, pointing
towards the existence of uncharted territories. Also, we provide guidance in
geographic information extraction. Hope we peer its true countenance uncovering
the veil of geographic information.

地理信息与人类行为、认知、表达和思维过程密切相关，并符合伽马分布。通过实验证实了伽马分布假设，并揭示了地理信息数量、长度和距离的规律。同时，地理信息的利用存在上限，还提供了地理信息提取的指导，揭开地理信息的面纱。

探索文本地理信息规律

Exploring the law of text geographic information

This paper proposes Dirichlet Variational Autoencoder (DirVAE) using a
Dirichlet prior for a continuous latent variable that exhibits the
characteristic of the categorical probabilities. To infer the parameters of
DirVAE, we utilize the stochastic gradient method by approximating the Gamma
distribution, which is a component of the Dirichlet distribution, with the
inverse Gamma CDF approximation. Additionally, we reshape the component
collapsing issue by investigating two problem sources, which are decoder weight
collapsing and latent value collapsing, and we show that DirVAE has no
component collapsing; while Gaussian VAE exhibits the decoder weight collapsing
and Stick-Breaking VAE shows the latent value collapsing. The experimental
results show that 1) DirVAE models the latent representation result with the
best log-likelihood compared to the baselines; and 2) DirVAE produces more
interpretable latent values with no collapsing issues which the baseline models
suffer from. Also, we show that the learned latent representation from the
DirVAE achieves the best classification accuracy in the semi-supervised and the
supervised classification tasks on MNIST, OMNIGLOT, and SVHN compared to the
baseline VAEs. Finally, we demonstrated that the DirVAE augmented topic models
show better performances in most cases.

本文提出了使用 Dirichlet 优先的 DirVAE 模型，利用随机梯度法来推论模型参数，解决了潜变量坍塌问题，并在 MNIST，OMNIGLOT，和 SVHN 等数据集上进行了半监督和监督分类任务的实验，结果表明 DirVAE 模型在生成的潜在表达方面与其它基线模型相比具有最佳的对数似然，并且没有出现基线模型出现的坍塌问题，同时，对比基线模型，利用 DirVAE 模型学到的潜在表达还能够实现更好的半监督和监督分类性能。

狄利克雷变分自编码器

Dirichlet Variational Autoencoder

Cellular systems are becoming more heterogeneous with the introduction of low
power nodes including femtocells, relays, and distributed antennas.
Unfortunately, the resulting interference environment is also becoming more
complicated, making evaluation of different communication strategies
challenging in both analysis and simulation. Leveraging recent applications of
stochastic geometry to analyze cellular systems, this paper proposes to analyze
downlink performance in a fixed-size cell, which is inscribed within a weighted
Voronoi cell in a Poisson field of interferers. A nearest out-of-cell
interferer, out-of-cell interferers outside a guard region, and cross-tier
interference are included in the interference calculations. Bounding the
interference power as a function of distance from the cell center, the total
interference is characterized through its Laplace transform. An equivalent
marked process is proposed for the out-of-cell interference under additional
assumptions. To facilitate simplified calculations, the interference
distribution is approximated using the Gamma distribution with second order
moment matching. The Gamma approximation simplifies calculation of the success
probability and average rate, incorporates small-scale and large-scale fading,
and works with co-tier and cross-tier interference. Simulations show that the
proposed model provides a flexible way to characterize outage probability and
rate as a function of the distance to the cell edge.

本文提出了一种针对蜂窝系统下行信道的分析方法，利用随机几何方法将蜂窝固定在带权 Voronoi 单元格内，考虑包括防护区外部、交叉层干扰等影响因素，并采用 Gamma 分布简化干扰计算，从而有效地评估干扰环境对传输性能的影响。