Papers › On the Structure of Bad Science Matrices
On the Structure of Bad Science Matrices
Alex Albors, Hisham Bhatti, Lukshya Ganjoo, Raymond Guo, Dmitriy Kunisky, Rohan Mukherjee, Alicia Stepin, Tony Zeng
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The bad science matrix problem consists in finding, among all matrices A ∈ℝ^(n ×n) with rows having unit ℓ² norm, one that maximizes β(A) = 1/2ⁿ ∑_(x ∈-1, 1ⁿ) Ax_∞. Our main contribution is an explicit construction of an n ×n matrix A showing that β(A) ≥√(log₂(n+1)), which is only 18% smaller than the asymptotic rate. We prove that every entry of any optimal matrix is a square root of a rational number, and we find provably optimal matrices for n ≤4.
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