Related papers: From Random Lines to Metric Spaces
We study geodesics in the random metric space called the Brownian map, which appears as the scaling limit of large planar maps. In particular, we completely describe geodesics starting from the distinguished point called the root, and we…
This paper focuses on modeling and analysis of the temporal performance variations experienced by a mobile user in a wireless network and its impact on system level design. We consider a simple stochastic geometry model: the infrastructure…
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…
We introduce a new, relatively simple, line-breaking construction of the $\alpha$-stable tree which realises its random finite-dimensional distributions. This is a direct analogue of Aldous' line-breaking construction of the Brownian…
Scale invariance of an algorithm refers to its ability to treat objects equally independently of their size. For neural networks, scale invariance is typically achieved by data augmentation. However, when presented with a scale far outside…
The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at…
In this work, we present a simple and efficient generator of polymeric linear chains, based on a random self-avoiding walk process. The chains are generated using a discrete process of growth, in cubic networks and in a finite time, without…
Empty region graphs are graphs whose vertices are points in $\mathbb{R}^d$ and where two vertices are connected by an edge whenever some associated region does not contain any other vertices. We investigate the asymptotic behaviour of long…
We consider various notions of strains; quantitative measures for the deviation of a linear transformation from an isometry. The main approach, which is motivated by physical applications and follows the work of Patrizio Neff and co-workers…
The nonparametric problem of detecting existence of an anomalous interval over a one dimensional line network is studied. Nodes corresponding to an anomalous interval (if exists) receive samples generated by a distribution q, which is…
Is there a constant $r_0$ such that, in any invariant tree network linking rate-$1$ Poisson points in the plane, the mean within-network distance between points at Euclidean distance $r$ is infinite for $r > r_0$? We prove a slightly weaker…
Nonparametric detection of existence of an anomalous structure over a network is investigated. Nodes corresponding to the anomalous structure (if one exists) receive samples generated by a distribution q, which is different from a…
A central property of a classical geometry is that the geodesic distance between two events is \emph{additive}. When considering quantum fluctuations in the metric or a quantum or statistical superposition of different spacetimes,…
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux-Lie theorem, the phase flow of a Poisson system can be written as the composition of (1) a…
We consider a stationary Poisson hyperplane process with given directional distribution and intensity in $d$-dimensional Euclidean space. Generalizing the zero cell of such a process, we fix a convex body $K$ and consider the intersection…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
Randomized smoothing (RS) has successfully been used to improve the robustness of predictions for deep neural networks (DNNs) by adding random noise to create multiple variations of an input, followed by deciding the consensus. To…
We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability…
This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…
We construct a point set in the Euclidean plane that elucidates the relationship between the fine-scale statistics of the fractional parts of $\sqrt n$ and directional statistics for a shifted lattice. We show that the randomly rotated, and…