The results indicate that mixtures of M\"obius distributions provide interpretable, parsimonious models for the studied steady state density distributions, that match or outperform the alternatives.
Abstract
We consider the problem of learning models of spatial density functions, representing the steady-state density of mobile nodes moving on a two-dimensional terrain. Deriving such models can assist in network design and optimization problems, e.g., by accelerating the computation of the density function during a parameter sweep. We address the question of applicability of off-the-shelf mixture density network models and of, two varieties of, normalizing flows for the description of mobile node density over a disk. We introduce the use of M\"obius distributions to retain symmetric spatial relations. Our results indicate that mixtures of M\"obius distributions provide interpretable, parsimonious models for the studied steady state density distributions, that match or outperform the alternatives.
This work investigates the influence of the movement patterns (mobility) of network nodes on the overall performance of the network in terms of the area that can be covered by nodes' communications in terms of the area that can be covered by nodes' communications.
In this paper, we consider the connectivity of a random network of N mobile devices in three dimensions (3D), where the location of each device or node has a Gaussian distribution in each dimension. For each pair of nodes, the probability of connectivity is related to the nodes'separation by a Gaussian connectivity fun...
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We introduce a statistical framework for Gaussian fields indexed at arbitrary edge locations on general compact directed metric graphs. The construction is based on a stochastic differential equation with a first-order operator and conditions at the vertices. We characterise well-posedness and identify the covariance r...
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An improved mean-field analysis of cellular automata models of single-lane vehicular traffic is proposed, well suited for models with inhomogeneous stationary states and able to capture the essential properties of phase separation, e.g. in models with slow-to-start rules.
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Moving probability distributions in the context of stochastic processes efficiently is central to modern generative modeling, uncertainty quantification, and control of large engineered systems. Most current methods generate temporal trajectories independently, leaving open whether the trajectories can cooperate throug...
Random spatial tessellations generated by point processes provide fundamental models for proximity relations, space partitioning, and local geometry in stochastic systems. Among them, Poisson–Voronoi and Poisson–Delaunay tessellations induced by homogeneous Poisson point processes form a canonical dual pair widely used...
Learn how Google DeepMind and GovTech Singapore uses lightweight on-device Gemma models to intercept conversational scams in private chats with zero cloud data egress.
