The proof of the detection lower bound is based on a new bound on the total variation distance between a Wishart matrix and an appropriately normalized GOE matrix and in the sparse regime, a conjecture for the optimal detection boundary is made.Expand

For many classes of trees, including complete trees and spiders, this work provides algorithms that reconstruct the labels using only a polynomial number of traces, a stark contrast to known results on string trace reconstruction, which require exponentially many traces.Expand

A new model of competition on growing networks is introduced, with the key property that node choices evolve simultaneously with the network, and which matches empirical observations in many real-world networks.Expand

An analysis of traffic to websites known for publishing fake news in the months preceding the 2016 US presidential election finds that social media was the primary outlet for the circulation of fake news stories and aggregate voting patterns were strongly correlated with the average daily fraction of users visiting websites serving fake news.Expand

A first step in proving the conjecture that different seeds lead to different distributions of limiting trees from a total variation point of view is taken, showing that seeds with different degree profiles Lead to different limiting distributions for the (appropriately normalized) maximum degree.Expand

Tight bounds are provided on the amount of exact coalescence time data needed to recover the population size history of a single, panmictic population at a certain level of accuracy.Expand

It is shown that as c goes from zero to infinity, the limiting probability that a random profile is manipulable goes fromzero to one in a smooth fashion, i.e., there is a smooth phase transition between the two regimes.Expand

It is shown that different seeds lead to different distributions of limiting trees from a total variation point of view, and statistics are constructed that measure, in a certain well-defined sense, global "balancedness" properties of such trees.Expand

This work considers the relaxed problem of approximate reconstruction, and shows that approximating to within $n^{1/3 - \delta}$ edit distance requires n^{1 + 3\delta/2}/\mathrm{polylog}(n)$ traces for $0< \Delta < 1/3$ in the worst case.Expand

A new model of correlated randomly growing graphs is introduced and it is shown that whenever the seed graph has an influence in the underlying graph growth model, then correlation can be detected in this model, even if the graphs are grown together for just a single time step.Expand