• Publications
  • Influence
Testing for high-dimensional geometry in random graphs
TLDR
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.
Reconstructing Trees from Traces
TLDR
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.
Coexistence in Preferential Attachment Networks
TLDR
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.
Geographic and Temporal Trends in Fake News Consumption During the 2016 US Presidential Election
TLDR
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.
On the Influence of the Seed Graph in the Preferential Attachment Model
TLDR
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.
Can one hear the shape of a population history?
TLDR
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.
A Smooth Transition from Powerlessness to Absolute Power
TLDR
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.
From trees to seeds: on the inference of the seed from large trees in the uniform attachment model
TLDR
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.
Approximate Trace Reconstruction
TLDR
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.
Correlated randomly growing graphs
TLDR
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.
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