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Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…
Recently, stochastic geometry has been applied to provide tractable performance analysis for low earth orbit (LEO) satellite networks. However, existing works mainly focus on analyzing the ``coverage probability'', which provides limited…
While analyzing mobile systems we often approximate the actual coverage surface and assume an ideal cell shape. In a multi-cellular network, because of its tessellating nature, a hexagon is more preferred than a circular geometry. Despite…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from recently reported…
Results are presented for optimizing device-to-device communications in cellular networks, while maintaining spectral efficiency of the base-station-to-device downlink channel. We build upon established and tested stochastic geometry models…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
A stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes where they receive service according to the Processor-Sharing policy. Once their service requirement is…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
There have been a bulk of analytic results about the performance of cellular networks where base stations are regularly located on a hexagonal or square lattice. This regular model cannot reflect the reality, and tends to overestimate the…
The identification of distribution network topology and parameters is a critical problem that lays the foundation for improving network efficiency, enhancing reliability, and increasing its capacity to host distributed energy resources.…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
Stochastic spreading models defined on complex network topologies are used to mimic the diffusion of diseases, information, and opinions in real-world systems. Existing theoretical approaches to the characterization of the models in terms…
In trying to emulate the spatial position of wireless nodes for purpose of analysis, we rely on stochastic simulation. And, it is customary, for mobile systems, to consider a base-station radiation coverage by an ideal cell shape. For…
The analysis of the dynamics of a large class of excitable systems on locally tree-like networks leads to the conclusion that at $\lambda=1$ a continuous phase transition takes place, where $\lambda$ is the largest eigenvalue of the…
When dedicated positioning systems, such as GPS, are unavailable, a mobile device has no choice but to fall back on its cellular network for localization. Due to random variations in the channel conditions to its surrounding base stations…
This paper proposes exploiting the spatial correlation of wireless channel statistics beyond the conventional received signal strength maps by constructing statistical radio maps to predict any relevant channel statistics to assist…
Given the necessity of connecting the unconnected, covering blind spots has emerged as a critical task in the next-generation wireless communication network. A direct solution involves obtaining a coverage manifold that visually showcases…
In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from experimental data recently…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…