Some new rank methods to select the best prototypes from a training set are proposed in this paper in order to establish its size according to an external parameter, while maintaining the classification accuracy. The traditional methods that filter the training set in a classification task like editing or condensing have some rules that apply to the set in order to remove outliers or keep some ...

It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the weights for these spaces are nonincreasing, the first few variables are in a sense more important than the rest. We thus propose to copy the points of a rank-1 lattice rule a n...

A mere hyperbolic law, like the Zipf's law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon distribution. A modeling is proposed leading to a universal form. A theoretical suggestion for the "best (or optimal) distribution", is provided through an entro...

focus on political, economic, cultural city of kermanshah, the reasons for moving to the city, and consequently, it is natural population growth. this part of the urban hierarchy rule out - as far and despite the high potential for job creation in the province are because of the unbalanced distribution of population, the potential of the whole province is not to be used, so that today we face t...

Say that A is a Hadamard factorization of the identity In of size n if A ◦AT = In, where ◦ denotes the Hadamard or entrywise product, and AT denotes the transpose of A. As n = rk(In) = rk(A ◦ AT ) ≤ rk(A)2, it is clear that the rank of any Hadamard factorization of the identity must be at least √ n. Dietzfelbinger et al. [DHS96] raised the question if this bound can be achieved, and showed a bo...

The upper class of a lattice rule is a convenient e n tity for classiication and other purposes. The rank of a lattice rule is a basic characteristic, also used for classiication. By introducing a rank proportionality factor and obtaining certain recurrence relations, we s h o w h o w m a n y lattice rules of each rank exist in any prime upper class. The Sylow p-decomposition may be used to obt...