Related papers: Modelling gap-size distribution of parked cars usi…
A recent paper [Jokela et al, arxiv:0806.1491 9 June 2008] contains a surmise about an expectation value in a Coulomb gas which interacts with an additional charge xi that sits at a fixed position. Here I demonstrate the validity of the…
Car sharing is expected to reduce traffic congestion and pollution in cities while at the same time improving accessibility to public transport. However, the most popular form of car sharing, one-way car sharing, still suffers from the…
We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution…
We examine a Coulomb gas consisting of $n$ identical repelling point charges at an arbitrary inverse temperature $\beta$, subjected to a suitable external field. We prove that the gas is effectively localized to a small neighbourhood of the…
We analyze the convergence to equilibrium in a family of Kac-like kinetic equations in multiple space dimensions. These equations describe the change of the velocity distribution in a spatially homogeneous gas due to binary collisions…
We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…
We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$.…
We consider the universality of the nearest neighbour eigenvalue spacing distribution in invariant random matrix ensembles. Focussing on orthogonal and symplectic invariant ensembles, we show that the empirical spacing distribution…
The parking-lot model provides a qualitative description of the main features of the phenomenology of granular compaction. We derive here approximate kinetic equations for this model, equations that are based on a $2-$parameter…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
We study systematically stationary solutions to the coupled Vlasov and Poisson equations which have `self-similar' or scaling symmetry in phase space. In particular, we find analytically {\it all} spherically symmetric distribution…
We consider the empirical eigenvalue distribution of an $m\times m$ principle submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. Earlier work of Petz and R\'effy identified the limiting spectral measure…
In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy…
We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…
Long ranged electrostatic interactions are time consuming to calculate in molecular dynamics and Monte-Carlo simulations. We introduce an algorithmic framework for simulating charged particles which modifies the dynamics so as to allow…
All over the world, especially in the university environment, planning managers and traffic engineers are constantly faced with the problem of inadequate allocation of car parking spaces to demanded users. Users could either prefer reserved…
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and give rise to a variety of…
This paper develops a probabilistic anticipation algorithm for dynamic objects observed by an autonomous robot in an urban environment. Predictive Gaussian mixture models are used due to their ability to probabilistically capture continuous…
We perform statistical analysis of the single-vehicle data measured on the Dutch freeway A9 and discussed in Ref. [2]. Using tools originating from the Random Matrix Theory we show that the significant changes in the statistics of the…
We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically.…