Random embeddings with an almost Gaussian distortion

Autoregressive Gaussian Random Vectors of First Order

From Almost Gaussian to Gaussian

We consider lower and upper bounds on the difference of differential entropies of a Gaussian random vector and an approximately Gaussian random vector after they are “smoothed” by an arbitrarily distributed random vector of finite power. These bounds are important to establish the optimality of the corner points in the capacity region of Gaussian interference channels. A problematic issue in a ...

On Notions of Distortion and an Almost Minimum Spanning Tree with Constant Average Distortion

Minimum Spanning Trees of weighted graphs are fundamental objects in numerous applications. In particular in distributed networks, the minimum spanning tree of the network is often used to route messages between network nodes. Unfortunately, while being most efficient in the total cost of connecting all nodes, minimum spanning trees fail miserably in the desired property of approximately preser...

Low-Distortion Embeddings of Trees

We prove that every tree T = (V,E) on n vertices with edges of unit length can be embedded in the plane with distortion O( √ n); that is, we construct a mapping f :V → R such that ρ(u, v) ≤ ‖f(u) − f(v)‖ ≤ O( √ n) · ρ(u, v) for every u, v ∈ V , where ρ(u, v) denotes the length of the path from u to v in T . The embedding is described by a simple and easily computable formula. This is asymptotic...

Coarse-grained embeddings of time series: random walks, Gaussian random processes, and deterministic chaos

A new method for studying time series is described based on a statistic indicating the degree to which trajectories passing through a small region of an embedding space are parallel. The method is particularly suited to time series with a significant correlation time. Analytic results are presented for Brownian motion and Gaussian random processes. These are generally different from the results...