Group classification of the generalized complex Ginzburg-Landau equations is presented. An approach to group classification of systems of reaction-diffusion equations with general diffusion matrix is formulated.

We consider the simultaneous diffusion and homogenization limit of the linear Boltzmann equation in a periodic medium in the regime where the mean free path is much smaller than the lattice constant. The resulting equation is a diffusion equation, with an averaged diffusion matrix that is formally obtained by first performing the diffusion limit and then the homogenization one. The rigorous pro...

Binary codes over two-dimensional arrays are very useful in data storage, where each array column represents a storage device or unit that may suffer failure. In this paper we propose a new framework for probabilistic construction of codes on two-dimensional arrays. Instead of a pure combinatorial erasure model used in traditional array codes, we propose a mixed combinatorial-probabilistic mode...

While algorithms and methodologies to study uncertainty in the Earth Sciences are constantly evolving, there are currently few open-source integrated softwares that allows the general practitioners access to these developments. This paper presents SGEMS-UQ, a plugin for the SGEMS platform, that is used to perform distance-based uncertainty analysis on geostatistical simulations, and the resulti...

A set of vertices of the q-ary n-dimensional Hamming space is called a distance-2 MDS code if it has exactly one element in intersection with every line. By an isotopism we mean an isometric transformation of the Hamming space that independently permutes the symbols in every coordinate but does not change the coordinate order. A set M of vertices is called transitive if its automorphism group (...

The hull H(C) of a linear code C is defined by H(C) = C ∩ C⊥. A linear code with a complementary dual (LCD) is a linear code with H(C) = {0}. The dimension of the hull of a code is an invariant under permutation equivalence. For binary and ternary codes the dimension of the hull is also invariant under monomial equivalence and we show that this invariant is determined by the extended weight enu...

The study of MDS self-dual codes has attracted lots of attention in recent years. There are many papers on determining existence of q−ary MDS self-dual codes for various lengths. There are not existence of q−ary MDS self-dual codes of some lengths, even these lengths < q. We generalize MDS Euclidean self-dual codes to near MDS Euclidean self-dual codes and near MDS isodual codes. And we obtain ...

Minimum-Storage Regenerating (MSR) codes have emerged as a viable alternative to Reed-Solomon (RS) codes as they minimize the repair bandwidth while they are still optimal in terms of reliability and storage overhead. Although several MSR constructions exist, so far they have not been practically implemented mainly due to the big number of I/O operations. In this paper, we analyze high-rate MDS...