Abstract. The global existence of a non-negative weak solution to a multi-dimensional parabolic strongly coupled model for two competing species is proved. The main feature of the model is that the diffusion matrix is non-symmetric and generally not positive definite and that the non-diagonal matrix elements (the cross-diffusion terms) are allowed to be “large”. The ideas of the existence proof...

We study two problems of private matrix multiplication, over a distributed computing system consisting master node, and multiple servers that collectively store family public matrices using Maximum-Distance-Separable (MDS) codes. In the first problem Private Secure Matrix Multiplication (PSMM) from colluding servers, intends to compute product its confidential A with target stored on without re...

Let R be a finite chain ring (e.g. a Galois ring), K its residue field and C a linear code over R. We prove that d(C), the Hamming distance of C, is d((C : α)), where (C : α) is a submodule quotient, α is a certain element of R and denotes the canonical projection to K. These two codes also have the same set of minimal codeword supports. We explicitly construct a generator matrix/polynomial of ...

Let R be a finite chain ring (e.g. a Galois ring), K its residue field and C a linear code over R. We prove that d(C), the Hamming distance of C, is d((C : α)), where (C : α) is a submodule quotient, α is a certain element of R and denotes the canonical projection to K. These two codes also have the same set of minimal codeword supports. We explicitly construct a generator matrix/polynomial of ...

This paper applies fast sparse multidimensional scaling (MDS) to a large graph of music similarity, with 267K vertices that represent artists, albums, and tracks; and 3.22M edges that represent similarity between those entities. Once vertices are assigned locations in a Euclidean space, the locations can be used to browse music and to generate playlists. MDS on very large sparse graphs can be e...

One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized Reed-Solomon codes. We also present some classes of quantum codes from matrix-product codes. It turns out that many of our quantum codes are new in the sense that the ...

A three-dimensional (3D) theoretical morphospace of gomphonemoid and cymbelloid diatoms was skeletonized using concepts from extended Reeb graph analysis and Morse theory. The resultant skeleton tree was matched to a cladogram of the same group of related taxa using adjacency matrices of the trees and ordinated with multidimensional scaling (MDS) of leaf nodes. From this, an unweighted path mat...

This paper applies fast sparse multidimensional scaling (MDS) to a large graph of music similarity, with 267K vertices that represent artists, albums, and tracks; and 3.22M edges that represent similarity between those entities. Once vertices are assigned locations in a Euclidean space, the locations can be used to browse music and to generate playlists. MDS on very large sparse graphs can be e...

Multidimensional Scaling (MDS) is a powerful dimension reduction technique for embedding high-dimensional data into a lowdimensional target space. Thereby, the distance relationships in the source are reconstructed in the target space as best as possible according to a given embedding criterion. Here, a new stress function with intuitive properties and a very good convergence behavior is presen...