Intersections of Randomly Embedded Sparse Graphs are Poisson

Tight planar packings of two trees

When we consider an embedding of graphs into a plane, it would be nice if it does not intersect internally since the embedding simply shows us the structure of graphs. It is easy to embed a tree into a plane with non-self-intersections. If we embed two or more trees into a plane with non-self-intersections, what occurs? In this paper, we consider embeddings of two trees into a plane with using ...

Tree-Based Modeling and Estimation of Gaussian Processes on Graphs with Cycles

We present the embedded trees algorithm, an iterative technique for estimation of Gaussian processes defined on arbitrary graphs. By exactly solving a series of modified problems on embedded spanning trees, it computes the conditional means with an efficiency comparable to or better than other techniques. Unlike other methods, the embedded trees algorithm also computes exact error covariances. ...

Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs

We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit theorems. These conditions can always be expressed in terms of contraction operators or, equivalently, fourth cumulants. Our findings are specifically tailored to d...

On randomly olouring lo ally sparse graphs

Developing an Analytical Model and Simulation of The Contraflow Left-Turn Lane at Signalized Intersections

At some intersections, excessive queue lengths may spill out of the left-turn bay and block the through lanes, jeopardizing level of service for the entire intersection. One of the most effective plans recently presented by the researchers is the "Contraflow left-turn lane" (CLL) In this method, left-turn vehicles will use the nearest lane in the opposite direction in addition to the usual left...