Protein structures in nature often exhibit a high degree of regularity (for example, secondary structure and tertiary symmetries) that is absent from random compact conformations. With the use of a simple lattice model of protein folding, it was demonstrated that structural regularities are related to high "designability" and evolutionary stability. The designability of each compact structure is measured by the number of sequences that can design the structure-that is, sequences that possess the structure as their nondegenerate ground state. Compact structures differ markedly in terms of their designability; highly designable structures emerge with a number of associated sequences much larger than the average. These highly designable structures possess "proteinlike" secondary structure and even tertiary symmetries. In addition, they are thermodynamically more stable than other structures. These results suggest that protein structures are selected in nature because they are readily designed and stable against mutations, and that such a selection simultaneously leads to thermodynamic stability.

We prove a special case of a conjecture in asymptotic analysis by Harold Widom. More precisely, we establish the leading and next-to-leading term of a semi-classical expansion of the trace of the square of certain integral operators on the Hilbert space L 2 (R d ). As already observed by Gioev and Klich, this implies that the bi-partite entanglement entropy of the free Fermi gas in its ground state grows at least as fast as the surface area of the spatially bounded part times a logarithmic enhancement.

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A simple algorithm which gives the multipole vectors in terms of the roots of a polynomial is given. We find that the reported alignmet of the low l multipole vectors can be summarised as an anti-alignmet of these with the dipole direction.This anti-alignment is not only present in l = 2 and 3 but also for l = 5 and higher.This alignment is likely due to non-linearity in the data processing. Our results are based on the three year WMAP data, we also list corresponding results for the first year data. * Electronic address: helling@atdotde.de † Electronic address: p.schupp@iu-bremen.de ‡ Electronic address: t.tesileanu@iu-bremen.de

Abstract:We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. For rational θ, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions. UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous N × N symmetry breaking in the Morita dual SU (N ) theory due to electric flux condensation.