לוח שנה משולב

Originating from the works of Bekenstein and Hawking on the entropy of black holes, area laws constitute a central tool for understanding entanglement and locality properties in quantum systems. Essentially, in a system that obeys an area law, the _entanglement_ entropy of a bounded region scales like its boundary
area, rather than its volume.

In 2007, in a seminal paper, Hastings proved that all 1D quantum spin systems with a constant spectral gap obey an area law in their ground state. The proof, however, uses rather involved analytical tools such as the Lieb-Robinson bounds and does not seem to be generalizable to higher dimensions. In this talk I will present a new, purely combinatorial, proof of the 1D area law for frustration-free systems. The proof gives an exponentially better bound on the entanglement entropy, and, in addition, might be generalizable to higher dimensions.

In the center of the proof lies a new tool called ``the detectability lemma'', which proves extremely useful for studying the ground states of frustration-free systems. I will describe this lemma, and also use it to present a very simple proof of another seminal result of Hastings: the exponential decay of correlations in the ground states of gapped spin systems (in any dimension).

The talk connects various works: Aharonov, Arad, Landau and Vazirani, 2008 & 2010 [3,4], as well as Hastings 2003 & 2007 [1,2].

Refs:
[1] http://arxiv.org/abs/cond-mat/0305505
[2] http://arxiv.org/abs/0705.2024
[3] http://arxiv.org/abs/0811.3412
[4] http://arxiv.org/abs/1011.3445

Autism is a neuro-cognitive disorder characterized by a broad spectrum of clinical features including repetitive behaviors, restricted interests, language impairment, and altered social interactions. Although chromosome rearrangements affecting specific genomic intervals have been found in patients with autism, the basis for this syndrome is unknown. Deletion of 16p11.2 has been associated with autism, and patients with this deletion have a wide range of clinical symptoms. Here we used chromosome engineering to generate mice with deletion of the 27 genes corresponding to those affected in autism patients with 16p11.2 deletion, as well as mice harboring duplication of the same region. Mice with decreased dosage of this region have unique phenotypes including neonatal lethality, alterations in the volumes of specific brain regions, as well as behaviors reminiscent of clinical features of autism. In particular, mice with 16p11.2 deletion showed behaviors that were repetitive and restricted to specific locations, in contrast to diploid controls that showed a gradual increase in freedom of movement under similar conditions. These findings provide the first functional evidence that compromised dosage of 16p11.2 is causal in autism.