In the last few days, a Denial of Service attack was launched on universities in Israel, leading the administrators of the Israel Academic network to block access to it from the global internet. Consequently, websites such as ECCC have been accessible only from within the Israeli and European academic networks.
It seems that this blocking was just removed, and we hope it will not be put back in the future.
Needless to say, deciding on such blocking is not in our control, but we do apologize for this disruption of service.
We give quantitative bounds on the sparsity of a real polynomial with non-negative coefficients vanishing on a slice of the Boolean cube $\{\pm1\}^n$. We obtain similar bounds on the dimension of real orthogonal representations of (the complement of) Johnson-type graphs. The estimates are related to the classical problem about ... more >>>
The quantum analogue of the PCP theorem for QMA remains wide open. A central obstacle is the local indistinguishability of quantum codes: every sufficiently small view of an encoded witness is independent of the witness, seemingly preventing a local verifier from distinguishing YES from NO instances. One approach to this ... more >>>
For a prime $p\geq 3$, a somewhat restricted $3$-AP in $\mathbb{F}_p^n$ is a triplet $(x,x+a,x+2a)$, where $x\in\mathbb{F}_p^n$ and $a\in \{0,1,2\}^n$. We prove a counting lemma for somewhat restricted $3$-APs in dense sets in $\mathbb{F}_p^n$. More precisely, we prove that for all $\alpha>0$, there exists $\beta>0$, such that for sufficiently large ... more >>>
