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- Yuri Niyazov, Carl Vogel, Richard Price, Ben Lund, David Judd, Adnan Akil +3 others
- PloS one
- 2016

Using matching and regression analyses, we measure the difference in citations between articles posted to Academia.edu and other articles from similar journals, controlling for field, impact factor, and other variables. Based on a sample size of 31,216 papers, we find that a paper in a median impact factor journal uploaded to Academia.edu receives 16% more… (More)

We define the bisector energy E(P) of a set P in R 2 to be the number of quadruples (a, b, c, d) ∈ P 4 such that a, b determine the same perpendicular bisector as c, d. Equivalently, E(P) is the number of isosceles trapezoids determined by P. We prove that if no line or circle contains M (n) points of an n-point set P, then for any ε > 0 we have

We show that, for a finite set A of real numbers, the size of the set A + A A + A = a + b c + d : a, b, c, d ∈ A, c + d = 0 is bounded from below by

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