An all-substrings common subsequence algorithm

Given two strings A and B of lengths n(a) and n(b), n(a) <= n(b), respectively, the all-substrings longest common subsequence (ALCS) problem obtains, for every substring B` of B, the length of the longest string that is a subsequence of both A and B. The ALCS problem has many applications, such as finding approximate tandem repeats in strings, solving the circular alignment of two strings and finding the alignment of one string with several others that have a common substring. We present an algorithm to prepare the basic data structure for ALCS queries that takes O(n(a)n(b)) time and O(n(a) + n(b)) space. After this preparation, it is possible to build that allows any LCS length to be retrieved in constant time. Some trade-offs between the space required and a matrix of size O(n(b)(2)) the querying time are discussed. To our knowledge, this is the first algorithm in the literature for the ALCS problem. (C) 2007 Elsevier B.V. All rights reserved.

A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.

POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

POLYNOMIAL IDENTITIES OF FINITE DIMENSIONAL SIMPLE ALGEBRAS

Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

Pharmacogenetics of Warfarin: Development of a Dosing Algorithm for Brazilian Patients

A dosing algorithm including genetic (VKORC1 and CYP2C9 genotypes) and nongenetic factors (age, weight, therapeutic indication, and cotreatment with amiodarone or simvastatin) explained 51% of the variance in stable weekly warfarin doses in 390 patients attending an anticoagulant clinic in a Brazilian public hospital. The VKORC1 3673G>A genotype was the most important predictor of warfarin dose, with a partial R(2) value of 23.9%. Replacing the VKORC1 3673G>A genotype with VKORC1 diplotype did not increase the algorithm`s predictive power. We suggest that three other single-nucleotide polymorphisms (SNPs) (5808T>G, 6853G>C, and 9041G>A) that are in strong linkage disequilibrium (LD) with 3673G>A would be equally good predictors of the warfarin dose requirement. The algorithm`s predictive power was similar across the self-identified ""race/color"" subsets. ""Race/color"" was not associated with stable warfarin dose in the multiple regression model, although the required warfarin dose was significantly lower (P = 0.006) in white (29 +/- 13 mg/week, n = 196) than in black patients (35 +/- 15 mg/week, n = 76).