2,350 research outputs found
Chirality in a quaternionic representation of the genetic code
A quaternionic representation of the genetic code, previously reported by the
authors, is updated in order to incorporate chirality of nucleotide bases and
amino acids. The original representation assigns to each nucleotide base a
prime integer quaternion of norm 7 and involves a function that associates with
each codon, represented by three of these quaternions, another integer
quaternion (amino acid type quaternion) in such a way that the essentials of
the standard genetic code (particulaty its degeneration) are preserved. To show
the advantages of such a quaternionic representation we have, in turn,
associated with each amino acid of a given protein, besides of the type
quaternion, another real one according to its order along the protein (order
quaternion) and have designed an algorithm to go from the primary to the
tertiary structure of the protein by using type and order quaternions. In this
context, we incorporate chirality in our representation by observing that the
set of eight integer quaternions of norm 7 can be partitioned into a pair of
subsets of cardinality four each with their elements mutually conjugates and by
putting they in correspondence one to one with the two sets of enantiomers (D
and L) of the four nucleotide bases adenine, cytosine, guanine and uracil,
respectively. Thus, guided by two diagrams proposed for the codes evolution, we
define functions that in each case assign a L- (D-) amino acid type integer
quaternion to the triplets of D- (L-) bases. The assignation is such that for a
given D-amino acid, the associated integer quaternion is the conjugate of that
one corresponding to the enantiomer L. The chiral type quaternions obtained for
the amino acids are used, together with a common set of order quaternions, to
describe the folding of the two classes, L and D, of homochiral proteins.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:1505.0465
Representation theory for high-rate multiple-antenna code design
Multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment, but the practical success of using multiple antennas depends crucially on our ability to design high-rate space-time constellations with low encoding and decoding complexity. It has been shown that full transmitter diversity, where the constellation is a set of unitary matrices whose differences have nonzero determinant, is a desirable property for good performance. We use the powerful theory of fixed-point-free groups and their representations to design high-rate constellations with full diversity. Furthermore, we thereby classify all full-diversity constellations that form a group, for all rates and numbers of transmitter antennas. The group structure makes the constellations especially suitable for differential modulation and low-complexity decoding algorithms. The classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd. We, therefore, also consider extensions of the constellation designs to nongroups. We conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels
- …