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 prove a common generalization of two structure theorems: the dimension-free decomposition theorem for idempotent Schur multipliers and the idempotent theorem in harmonic analysis. Roughly speaking, our result shows that an invariant integer-valued kernel with Hilbert-space factorization norm $\gamma$ admits a signed decomposition into at most $2^{O(\gamma^4)}$ elementary pieces. In ... more >>>
We study low-degree testing for group-valued functions over a Boolean slice. Specifically given a degree parameter $d$ and oracle access to a function $f:\{0,1\}^n_{n/2} \to G$ where $\{0,1\}^n_k$ denotes the set of vectors in $\{0,1\}^n$ of Hamming weight $k$ and $G$ is an Abelian group (not necessarily finite), the low-degree ... more >>>
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 >>>
