The average condition number of most tensor rank decomposition problems is infinite

The tensor rank decomposition, or canonical polyadic decomposition, is the decomposition of a tensor into a sum of rank-1 tensors. The condition number of the tensor rank decomposition measures the sensitivity of the rank-1 summands with respect to structured perturbations. Those are perturbations preserving the rank of the tensor that is decomposed. On the other hand, the angular condition number measures the perturbations of the rank-1 summands up to scaling. We show for random rank-2 tensors with Gaussian density that the expected value of the condition number is infinite. Under some mild additional assumption, we show that the same is true for most higher ranks $r\geq 3$ as well. In fact, as the dimensions of the tensor tend to infinity, asymptotically all ranks are covered by our analysis. On the contrary, we show that rank-2 Gaussian tensors have finite expected angular condition number. Our results underline the high computational complexity of computing tensor rank decompositions. We discuss consequences of our results for algorithm design and for testing algorithms that compute the CPD. Finally, we supply numerical experiments

The Logit-Response Dynamics

We develop a characterization of stochastically stable states for the logit-response learning dynamics in games, with arbitrary specification of revision opportunities. The result allows us to show convergence to the set of Nash equilibria in the class of best-response potential games and the failure of the dynamics to select potential maximizers beyond the class of exact potential games. We also study to which extent equilibrium selection is robust to the specification of revision opportunities. Our techniques can be extended and applied to a wide class of learning dynamics in games.Learning in games, logit-response dynamics, best-response potential games

Robust stochastic stability

A strategy profile of a game is called robustly stochastically stable if it is stochastically stable for a given behavioral model independently of the specification of revision opportunities and tie-breaking assumptions in the dynamics. We provide a simple radius-coradius result for robust stochastic stability and examine several applications. For the logit-response dynamics, the selection of potential maximizers is robust for the subclass of supermodular symmetric binary-action games. For the mistakes model, the weaker property of strategic complementarity suffices for robustness in this class of games. We also investigate the robustness of the selection of risk-dominant strategies in coordination games under best-reply and the selection of Walrasian strategies in aggregative games under imitation.Learning in games, stochastic stability, radius-coradius theorems, logit-response dynamics, mutations, imitation

Diagnosis and Management of COVID-19 Disease

SARS-CoV-2 is a novel coronavirus that was identified in late 2019 as the causative agent of COVID-19 (aka coronavirus disease 2019). On March 11, 2020, the World Health Organization (WHO) declared the world-wide outbreak of COVID-19 a pandemic. This document summarizes the most recent knowledge regarding the biology, epidemiology, diagnosis, and management of COVID-19

How the Liberal Democrats are using Facebook ads to court ‘remainers’

It is evident from their manifesto that the Liberal Democrats want to appeal to “remain” voters. It is by looking at their Facebook ads, however, that we get a clearer idea of how their strategy on Brexit has been unfolding, an analysis by LSE researchers Damian Tambini, Nick Anstead and João Carlos Magalhães suggests. This post is the first in a series that will analyse data collected as part of a joint project recently launched by the LSE Media Policy Project and the “Who Targets Me” initiative. The new project will study political micro-targeting on the social media platform during the 2017 UK general election

Labour’s advertising campaign on Facebook (or “Don’t Mention the War”)

Britain’s decision to leave the European Union is the most important event in the recent political history of the UK. However, days before election day, Labour’s campaign on Facebook seems to be ignoring the Brexit issue, an analysis by LSE researchers Damian Tambini, Nick Anstead and João Carlos Magalhães indicates. This post is the second in a series that is examining data collected as part of a joint project recently launched by the LSE Media Policy Project and the “Who Targets Me” initiative. In the first post, we considered the Liberal Democrat campaign. The project is studying political micro-targeting on the social media platform during the 2017 UK general election

Is the Conservative Party deliberately distributing fake news in attack ads on Facebook?

The Conservative Party made clear that they would run an anti-Corbyn campaign, attempting to contrast the alleged weaknesses of the leader of the Labour Party with Theresa May’s supposedly superior leadership. An analysis of Tories’ Facebook advertising by LSE researchers Damian Tambini, Nick Anstead and João Carlos Magalhães suggests that this negative campaign included specific instances of demonstrably false or misleading information