An evaluation of the Sure Start Widnes Trailblazer pampering group

This project report discusses an evaluation of the pampering group of the Widnes Sure Start Widnes Trailblazer programme. The pampering group is a weekly service of health and beauty tratments to parents and parents-to-be, as well as informal advice from other parents and professionals about childbirth and child rearing in order to support parents during pregnancy and a baby's first year.The report was comissioned by Sure start Widnes Trailblazer and funded by Halton Borough Council

A semidefinite program for unbalanced multisection in the stochastic block model

We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent communities, up to the information-theoretic limits determined by Abbe and Sandon (2015). Our result extends prior SDP approaches by allowing for many communities of different sizes. By virtue of a semidefinite approach, our algorithms succeed against a semirandom variant of the stochastic block model, guaranteeing a form of robustness and generalization. We further explore how semirandom models can lend insight into both the strengths and limitations of SDPs in this setting.Comment: 29 page

All unital qubit channels are 44-noisy operations

We show that any unital qubit channel can be implemented by letting the input system interact unitarily with a $4$-dimensional environment in the maximally mixed state and then tracing out the environment. We also provide an example where the dimension of such an environment has to be at least $3$.Comment: 8 pages, no picture