An optimal endpoint trace embedding

An optimal endpoint trace embedding

We find an optimal Sobolev-type space on R all of whose functions admit a trace on subspaces of R of given dimension. A corresponding trace embedding theorem with sharp range is established.

An Optimal Skorokhod Embedding for Di usionsA

An Optimal Skorokhod Embedding for Diffusions

Given a Brownian motion (Bt)t≥0 and a general target law μ (not necessarily centred or even in L) we show how to construct an embedding of μ in B. This embedding is an extension of an embedding due to Perkins, and is optimal in the sense that it simultaneously minimises the distribution of the maximum and maximises the distribution of the minimum among all embeddings of μ. The embedding is then...

Optimal Probe Scheduling for Network Endpoint Localization

The objective of the network endpoint localization problem is to estimate the endpoints (source and destination) of some message passed through a communication network based upon the set of partially synchronized sensors that intercept the message. The topology of the network is unknown, however some prior information about node degrees in the network be available to the monitor. A preliminary ...

Finding Optimal 1-Endpoint-Crossing Trees

Dependency parsing algorithms capable of producing the types of crossing dependencies seen in natural language sentences have traditionally been orders of magnitude slower than algorithms for projective trees. For 95.899.8% of dependency parses in various natural language treebanks, whenever an edge is crossed, the edges that cross it all have a common vertex. The optimal dependency tree that s...