All reports by Author Rosie Zhao:

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TR22-079
| 25th May 2022
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Hamed Hatami, Pooya Hatami, William Pires, Ran Tao, Rosie Zhao#### Lower Bound Methods for Sign-rank and their Limitations

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TR22-041
| 23rd March 2022
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TsunMing Cheung, Hamed Hatami, Rosie Zhao, Itai Zilberstein#### Boolean functions with small approximate spectral norm

Hamed Hatami, Pooya Hatami, William Pires, Ran Tao, Rosie Zhao

The sign-rank of a matrix $A$ with $\pm 1$ entries is the smallest rank of a real matrix with the same sign pattern as $A$. To the best of our knowledge, there are only three known methods for proving lower bounds on the sign-rank of explicit matrices: (i) Sign-rank is ... more >>>

TsunMing Cheung, Hamed Hatami, Rosie Zhao, Itai Zilberstein

The sum of the absolute values of the Fourier coefficients of a function $f:\mathbb{F}_2^n \to \mathbb{R}$ is called the spectral norm of $f$. Green and Sanders' quantitative version of Cohen's idempotent theorem states that if the spectral norm of $f:\mathbb{F}_2^n \to \{0,1\}$ is at most $M$, then the support of ... more >>>