Let (M, ω, α) be a compact symplectic manifold with contact type boundary: α is a contact one-form on ∂M which satisfies dα = ω|∂M and makes ∂M convex. Assume in addition that [ω, α] ∈ H(M,∂M ;R) is zero, so that α can be extended to a one-form θ on M satisfying dθ = ω. After fixing such a θ once and for all, one can talk about exact Lagrangian submanifolds in M . The Floer cohomology of two su...

MOTIVATION Specific functions of ribonucleic acid (RNA) molecules are often associated with different motifs in the RNA structure. The key feature that forms such an RNA motif is the combination of sequence and structure properties. In this article, we introduce a new RNA sequence-structure comparison method which maintains exact matching substructures. Existing common substructures are treated...

In recent years we have witnessed a growth in sequencing yield, the number of samples sequenced, and as a result-the growth of publicly maintained sequence databases. The increase of data present all around has put high requirements on protein similarity search algorithms with two ever-opposite goals: how to keep the running times acceptable while maintaining a high-enough level of sensitivity....

We have exactly enumerated all sequences and conformations of HP proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the hydrophobic-polar (HP) model, where only two types of monomers are distinguished, we determined and statistically analyzed designing sequences, i.e., sequences that have a non-degenerate ground state. Furthermore we were interested in ch...

The exact sequence of low degree associated to a first quadrant bicomplex (five terms long in [4, 1.4.5.1] seven terms long in [2, Lemma 7.5]) has been used in a number of situations, for example, in obtaining a cohomological description of the Brauer group of a commutative ring R [2]. In this note we observe that the sequence may be extended to an infinitely long exact sequence. The terms aris...

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the distribution of the LCS in a simpler, yet nontrivial, variant of the original model called the Bernoulli matching (BM) model which reduces to the original model...