This week

As a means of continual improvement and innovation, online controlled experiments are widely used by internet and technology companies to test and evaluate product changes, and new features, and to ensure that user feedback drives decisions. However, experiments on networks are complicated by the fact that the stable unit treatment value assumption (SUTVA) no longer holds. Due to the interconnectivity of users in these networks, a user’s outcome may be influenced by their own treatment assignment as well as the treatment assignment of those they are socially connected with. The design and analysis of the experiment must account for this. In this talk we will explore recent work in this area and focus particularly on the general additive network effect (GANE) family of non-linear models that jointly and flexibly model treatment and network effects. We will then consider Bayesian optimal design in the context of such models, proposing the use of the genetic algorithm to optimize for accurate and precise estimation of treatment effects, while accounting for parameter uncertainty. Through numerical studies with various real-life networks and network-outcome models, we demonstrate the robust performance of our methods compared to existing design construction strategies.

Abstract: On subRiemannian manifolds, the de Rham complex is not the ideal candidate to use to carry out geometric analysis. However, special subcomplexes have successfully been applied in very specific settings, such as Heisenberg groups and the Cartan group. I will give an overview of different techniques used to obtain such subcomplexes, as well as point out their limitations when used on arbitrary Carnot groups, and a possible way to overcome them

Title - The Hasse norm principle: degrees of failure

Abstract - For an extension of number fields K/k, we say that the Hasse norm principle (HNP) holds if an element of k is a global norm whenever it is a norm everywhere locally. A result of Bartels states that HNP holds for any extension of prime degree. In light of this, one can ask for which integers d does there exist a degree d extension of number fields failing HNP? I will report on work in progress (joint with Gareth Tracey) answering this question.