Selecting rank-1 lattices with respect to maximized mutual minimum distance has been shown to be very useful for image representation and synthesis in computer graphics. While algorithms using rank-1 lattices are very simple and e cient, the selection of their generator vectors often has to resort to exhaustive computer searches, which is prohibitively slow. For the two-dimensional setting, we ...

Euclidean distance matrix completion problem aims at reconstructing the low dimensional geometry structure of nodes given only a few pairwise distances between nodes [1]. This problem arises in many applications including networks and machine learning where much information of points is laking. For instance, in sensor networks, due to the constraints of energy and communication radius, sensor n...

For each rank metric code C ⊆ K, we associate a translation structure, the kernel of which is showed to be invariant with respect to the equivalence on rank metric codes. When C is K-linear, we also propose and investigate other two invariants called its middle nucleus and right nucleus. When K is a finite field Fq and C is a maximum rank distance code with minimum distance d < min{m,n} or gcd(...

The minimum rank of a sign pattern matrix is defined to be the smallest possible rank over all real matrices having the given sign pattern. The maximum nullity of a sign pattern is the largest possible nullity over the same set of matrices, and is equal to the number of columns minus the minimum rank of the sign pattern. Definitions of various graph parameters that have been used to bound maxim...

This paper investigates error and erasure decoding methods for codes with maximum rank distance. These codes can be used for correcting column and row errors and erasures in an ( ) array. Such errors occur e.g. in magnetic tape recording or in memory chip arrays. For maximum rank distance codes (Rank-Codes), there exists a decoding algorithm similar to the Peterson-Gorenstein-Zierler technique ...

The minimum rank of a sign pattern matrix is defined to be the smallest possible rank over all real matrices having the given sign pattern. The maximum nullity of a sign pattern is the largest possible nullity over the same set of matrices, and is equal to the number of columns minus the minimum rank of the sign pattern. Definitions of various graph parameters that have been used to bound maxim...

Biological genomes can be represented as square, symmetric, orthogonal, 0-1 matrices. It turns out that the rank distance applied to two genome matrices has a biological significance: it is related smallest number of basic rearrangement mutations, such reversals, translocations, transpositions (taken with weight 2), etc. explain differences between genomes. Therefore, closer will produce smalle...