Phase transition in a stochastic geometry model with applications to statistical mechanics

We study the connected components of the stochastic geometry model on Poisson points which is obtained by connecting points with a probability that depends on their relative position. Equivalently, we investigate the random clusters of the ran- dom connection model defined on the points of a Poisson process in d-dimensional space where the links are added with a particular probability function. We use the thermodynamicrelationsbetweenfreeenergy,entropyandinternalenergytofindthe functions of the cluster size distribution in the statistical mechanics of extensive and non-extensive. By comparing these obtained functions with the probability function predicted by Penrose, we provide a suitable approximate probability function. More- over, we relate this stochastic geometry model to the physics literature by showing how the fluctuations of the thermodynamic quantities of this model correspond to other models when a phase transition (10.1002/mma.6965, 2020) occurs. Also, we obtain the critical point using a new analytical method.

Coverage and Spectral Efficiency of Network Assisted Full Duplex in a Millimeter Wave System

To cope with the growing trend of asymmetric data traffic, we introduce a novel network assisted full duplex (NAFD) for a millimeter wave system. NAFD can dynamically allocate the number of remote radio heads in the uplink mode or in the downlink mode, which can facilitate simultaneous uplink and downlink communications. In this manuscript, we use stochastic geometry to analyze the distribution of the signal-to-interference-plus-noise ratio and the data rate in a NAFD system. The numerical results verify the analysis and show that the NAFD outperforms the dynamic time division duplex system and the traditional flexible duplex system in terms of spectral efficiency.

A short primer on lung stereology

The intention of this short primer is to raise your appetite for proper quantitative assessment of lung micro-structure. The method of choice for obtaining such data is stereology. Rooted in stochastic geometry, stereology provides simple and efficient tools to obtain quantitative three-dimensional information based on measurements on nearly two-dimensional microscopic sections. In this primer, the basic concepts of stereology and its application to the lung are introduced step by step along the workflow of a stereological study. The integration of stereology in your laboratory work will help to improve its quality. In a broader context, stereology may also be seen as a contribution to good scientific practice.