Oded Regev

Abstract: Phase-separated membraneless bodies play important roles in nucleic acid biology. While current models for the roles of phase separation largely focus on the compartmentalization of constituent proteins, we reason that other properties of phase separation may play functional roles. Specifically, we propose that interfaces of phase-separated membraneless bodies could have functional roles in spatially organizing biochemical reactions. Here we propose such a model for the nuclear speckle, a membraneless body implicated in RNA splicing. In our model, sequence-dependent RNA positioning along the nuclear speckle interface coordinates RNA splicing. Our model asserts that exons are preferentially sequestered into nuclear speckles through binding by SR proteins, while introns are excluded through binding by nucleoplasmic hnRNP proteins. As a result, splice sites at exon-intron boundaries are preferentially positioned at nuclear speckle interfaces. This positioning exposes splice sites to interface-localized spliceosomes, enabling the subsequent splicing reaction. Our model provides a simple mechanism that seamlessly explains much of the complex logic of splicing. This logic includes experimental results such as the antagonistic duality between splicing factors, the position dependence of splicing sequence motifs, and the collective contribution of many motifs to splicing decisions. Similar functional roles for phase-separated interfaces may exist for other membraneless bodies.

TL;DR: In this article, a nonquantum version of the Bonami-Beckner hypercontractive inequality for matrix-valued functions on the Boolean cube has been presented, which is based on a powerful inequality by Ball, Carlen, and Lieb.

TL;DR: A new public key cryptosystem whose security guarantee is considerably stronger than previous results is provided, and a family of collision resistant hash functions with an improved security guarantee in terms of the unique shortest vector problem is proposed.

TL;DR: For arbitrary constraint satisfaction problems, this paper showed that for any odd $k and any instance of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a $\frac{1}{2} + \Omega(1/\sqrt{D})$ fraction of constraints, where D$ is a bound on the number of constraints that each variable occurs in.

TL;DR: In particular, this article showed that strong parallel repetition holds neither with entangled provers nor with non-signaling provers, and provided a tight characterization of the asymptotic behavior of the entangled value under parallel repetition of unique games in terms of a semidefinite program.