Knapsack Problems in Groups

We generalize the classical knapsack and subset sum problems to arbitrary groups and study the computational complexity of these new problems. We show that these problems, as well as the bounded submonoid membership problem, are P-time decidable in hyperbolic groups and give various examples of finitely presented groups where the subset sum problem is NP-complete.Comment: 28 pages, 12 figure

Structure of the AAA protein Msp1 reveals mechanism of mislocalized membrane protein extraction.

The AAA protein Msp1 extracts mislocalized tail-anchored membrane proteins and targets them for degradation, thus maintaining proper cell organization. How Msp1 selects its substrates and firmly engages them during the energetically unfavorable extraction process remains a mystery. To address this question, we solved cryo-EM structures of Msp1-substrate complexes at near-atomic resolution. Akin to other AAA proteins, Msp1 forms hexameric spirals that translocate substrates through a central pore. A singular hydrophobic substrate recruitment site is exposed at the spiral's seam, which we propose positions the substrate for entry into the pore. There, a tight web of aromatic amino acids grips the substrate in a sequence-promiscuous, hydrophobic milieu. Elements at the intersubunit interfaces coordinate ATP hydrolysis with the subunits' positions in the spiral. We present a comprehensive model of Msp1's mechanism, which follows general architectural principles established for other AAA proteins yet specializes Msp1 for its unique role in membrane protein extraction

Совокупная факторная производительность в российских регионах в 2000–2014 гг.

The article offers a calculation of total factor productivity (TFP) in Russian regions in 2000–2014. Because of the quality issues with available data, the main conclusions in the article are based on average rather than annual TFP values for each region. It is shown that there is a highly significant positive link between the share of extracting industries in a regional economy and the TFP of the respective region. The author argues that TFP grew faster in regions with the highest shares of mineral resource extractio