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A navigation on a set of points $S$ is a rule for choosing which point to move to from the present point in order to progress toward a specified target. We study some navigations in the plane where $S$ is a non uniform Poisson point process…

Probability · Mathematics 2011-05-23 Nicolas Bonichon , Jean-François Marckert

We consider a road network represented by a directed graph. We assume to collect many measurements of traffic flows on all the network arcs, or on a subset of them. We assume that the users are divided into different groups. Each group…

Systems and Control · Electrical Eng. & Systems 2025-03-20 Mattia Laurini , Irene Saccani , Stefano Ardizzoni , Luca Consolini , Marco Locatelli

In this paper, we consider the stochastic network with dynamic traffic. The spatial distribution of access points (APs) and users are first modeled as mutually independent Poisson point processes (PPPs). Different from most previous…

Networking and Internet Architecture · Computer Science 2016-12-13 Bin Xia , Yingbin Liu , Chenchen Yang , Zhiyong Chen , Weiliang Xie , Yong Zhao

Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…

Statistical Mechanics · Physics 2008-03-19 J. G. Brankov , N. C. Pesheva , N. Zh. Bunzarova

Diffusion models indirectly estimate the probability density over a data space, which can be used to study its structure. In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the…

Computer Vision and Pattern Recognition · Computer Science 2025-05-08 Qingtao Yu , Jaskirat Singh , Zhaoyuan Yang , Peter Henry Tu , Jing Zhang , Hongdong Li , Richard Hartley , Dylan Campbell

We consider the problem of localization of Poisson source by the observations of inhomogeneous Poisson processes. We suppose that there are $k$ detectors on the plane and each detector provides the observations of Poisson processes whose…

Statistics Theory · Mathematics 2018-06-19 Oleg V. Chernoyarov , Yury A. Kutoyants

In first-passage percolation, one places nonnegative i.i.d. random variables (T(e)) on the edges of Z^d. A geodesic is an optimal path for the passage times T(e). Consider a local property of the time environment. We call it a pattern. We…

Probability · Mathematics 2023-10-09 Antonin Jacquet

Aldous and Pitman (1994) studied asymptotic distributions, as n tends to infinity, of various functionals of a uniform random mapping of a set of n elements, by constructing a mapping-walk and showing these mapping-walks converge weakly to…

Probability · Mathematics 2007-05-23 David Aldous , Jim Pitman

Less than 10 meters deep, shallow landslides are rapidly moving and strongly dangerous slides. In the present work, the probabilistic distribution of the landslide detachment points within a valley is modelled as a spatial Poisson point…

To study the overall connectivity in device-to-device networks in cities, we incorporate a signal-to-interference-plus-noise connectivity model into a Poisson-Voronoi tessellation model representing the streets of a city. Relays are located…

Networking and Internet Architecture · Computer Science 2023-09-07 H. P. Keeler , B. Błaszczyszyn , E. Cali

It is well known that physical interdependencies exist between networked civil infrastructures such as transportation and power system networks. In order to analyze complex nonlinear correlations between such networks, datasets pertaining…

Systems and Control · Electrical Eng. & Systems 2020-11-13 Rounak Meyur , Madhav Marathe , Anil Vullikanti , Henning Mortveit , Virgilio Centeno , Arun Phadke

We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…

Methodology · Statistics 2020-03-31 Shota Gugushvili , Frank van der Meulen , Moritz Schauer , Peter Spreij

In this paper we study the Poisson Hypothesis, which is a device to analyze approximately the behavior of large queueing networks. We prove it in some simple limiting cases. We show in particular that the corresponding dynamical system,…

Probability · Mathematics 2007-05-23 A. Rybko , S. Shlosman

Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…

We investigate a class of growing graphs embedded into the $d$-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on…

Probability · Mathematics 2019-11-13 Peter Gracar , Arne Grauer , Lukas Lüchtrath , Peter Mörters

Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…

Numerical Analysis · Mathematics 2024-05-14 Jaume Anguera Peris , Joakim Jaldén

It is known that the stationary distribution of the random walk process is dependent on the structure of the network. This could provide us a solution of the network reconstruction. However, the stationary distribution of the random walk…

Physics and Society · Physics 2016-03-17 Zhe He , Ming Li , Rui-Jie Xu , Bing-Hong Wang

When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the…

Statistics Theory · Mathematics 2025-01-07 Neil A. Spencer , Cosma Rohilla Shalizi

Density based spatial clustering of points in $\mathbb{R}^n$ has a myriad of applications in a variety of industries. We generalise this problem to the density based clustering of lines in high-dimensional spaces, keeping in mind there…

Machine Learning · Computer Science 2024-10-04 Akanksha Das , Malay Bhattacharyya

We study geometric random graphs defined on the points of a Poisson process in $d$-dimensional space, which additionally carry independent random marks. Edges are established at random using the marks of the endpoints and the distance…

Probability · Mathematics 2022-08-10 Peter Gracar , Arne Grauer , Peter Mörters