The correlation between the primary and secondary structures of proteins was analysed using a large data set from the Protein Data Bank. Clear preferences of amino acids towards certain secondary structures classify amino acids into four groups: alpha-helix preferrers, strand preferrers, turn and bend preferrers, and His and Cys (the latter two amino acids show no clear preference for any secondary structure). Amino acids in the same group have similar structural characteristics at their Cbeta and Cgamma atoms that predicts their preference for a particular secondary structure. All alpha-helix preferrers have neither polar heteroatoms on Cbeta and Cgamma atoms, nor branching or aromatic group on the Cbeta atom. All strand preferrers have aromatic groups or branching groups on the Cbeta atom. All turn and bend preferrers have a polar heteroatom on the Cbeta or Cgamma atoms or do not have a Cbeta atom at all. These new rules could be helpful in making predictions about non-natural amino acids.

An algorithm is given for the reconstruction of the initial state of a key-stream generator (KSG) consisting of a short linear feedback shift register (length ≤ 30), whose clock is controlled by an algebraically simple internal KSG. The algorithm is based on the fact that the expected number of possible LFSR initial states exponentially decreases with the length of the known part of the output sequence. Index Terms-Clock-controlled FSR (feedback shift register), Levenshtein distance.

The distribution of water molecules around aromatic rings in the protein structures and crystal structures of small molecules shows quite a small number of the strongest OH-π interactions, a larger number of parallel interactions, and the largest number of the weakest CH-O interactions.

Using the data from Protein Data Bank the correlations of primary and secondary structures of proteins were analyzed. The correlation values of the amino acids and the eight secondary structure types were calculated, where the position of the amino acid and the position in sequence with the particular secondary structure differ at most 25. The diagrams describing these results indicate that correlations are significant at distances between -9 and 10. The results show that the substituents on Cbeta or Cgamma atoms of amino acid play major role in their preference for particular secondary structure at the same position in the sequence, while the polarity of amino acid has significant influence on alpha-helices and strands at some distance in the sequence. The diagrams corresponding to polar amino acids are noticeably asymmetric. The diagrams point out the exchangeability of residues in the proteins; the amino acids with similar diagrams have similar local folding requirements.

A generalization of Sullivan inequality on the ratio of the probability of a linear code to that of any of its cosets is proved. Starting from this inequality, a sufficient condition for successful decoding of linear codes by a probabilistic method is derived. A probabilistic decoding algorithm for "low-density parity-check codes" is also analyzed. The results obtained allow one to estimate experimentally the probability of successful decoding using these probabilistic algorithms.