We have developed a simple yet powerful approach for disease gene association mapping by linkage disequilibrium (LD). This method is unique because it applies a model with evolutionary theory that incorporates a parameter for the location of the causal polymorphism. The method exploits LD maps, which assign a location in LD units (LDU) for each marker. This approach is based on single marker te...

We give a review of the theory of factorization of block Toeplitz matrices of the type T = (Ti−j)i,j∈Zd , where Ti−j are complex k × k matrices, in the form T = LDU, with L and L−1 lower block triangular, U and U−1 upper block triangular Toeplitz matrices, and D a diagonal matrix function. In particular, it is discussed how decay properties of Ti a ect decay properties of L, L−1, U , and U−1. W...

The numerical solution of the bidomain equations is a fundamental tool in the field of computational cardiac electrophysiology. The multi-scale nature of the processes involved and the increasing complexity of the tissue and ionic models of interest make the use of High Performance Computing techniques mandatory. The solution of the linear system arising from the Finite Element discretisation o...

This work introduces new relative perturbation bounds for the LDU factorization of (row) diagonally dominant matrices under structure-preserving componentwise perturbations. These bounds establish that if (row) diagonally dominant matrices are parameterized via their diagonally dominant parts and off-diagonal entries, then tiny relative componentwise perturbations of these parameters produce ti...

As from 2001, the Southern African Development Community (SADC) has embarked on a course to deepen regional integration through restructuring. Under the new structure SADC has centralised the coordination of its activities to the Secretariat in Gaborone. The former Sector Coordinating Units have been merged into four directorates, one of which is the Food, Agriculture and Natural Resources (FAN...

A linkage disequilibrium map is expressed in linkage disequilibrium (LD) units (LDU) discriminating blocks of conserved LD that have additive distances and locations monotonic with physical (kb) and genetic (cM) maps. There is remarkable agreement between LDU steps and sites of meiotic recombination in the one body of data informative for crossing over, and good agreement with another method th...

Let U/K represent a connected, compact symmetric space, where θ is an involution of U that fixes K, φ : U/K → U is the geodesic Cartan embedding, and G is the complexification of U. We investigate the intersection, studied by Pickrell, of φ(U/K) with the Birkhoff decomposition of G corresponding to a θ-stable triangular, or LDU, factoriztion of Lie(G). When g ∈ φ(U/K) is generic, the factorizat...

This work introduces a new perturbation bound for the L factor of the LDU factorization of (row) diagonally dominant matrices computed via the column diagonal dominance pivoting strategy. This strategy yields L and U factors which are always well-conditioned and, so, the LDU factorization is guaranteed to be a rank-revealing decomposition. The new bound together with those for the D and U facto...