A general algorithm for finding a minimal critical set for any latin square is presented. By implementing this algorithm, minimal critical sets for all the latin squares of order six have been found. In addition, this algorithm is used to prove that the size of the minimal critical set for a back circulant latin square of order seven is twelve, and for order nine is twenty. These results provid...

Various methods have been proposed to construct Latin hypercube designs with small correlations. Orthogonal arrays have been used to construct Latin hypercube designs with multidimensional stratification. To integrate these two ideas, we propose a method to construct Latin hypercube designs with both controlled correlations and multi-dimensional stratification. For numerical integration, the co...

This paper discusses distribution of the dative in Modern Icelandic. Similar to Latin, Modern Icelandic exhibits occurrences of the possessive dative, i.e., the dative which marks the possessor of a noun. However, although Latin shows free occurrences of possessive datives, there is a syntactic restriction imposed on the distribution of possessive datives in Modern Icelandic. The possessive dat...

We provide probabilistic lower bounds for the star discrepancy of Latin hypercube samples. These bounds are sharp in the sense that they match the recent probabilistic upper bounds for the star discrepancy of Latin hypercube samples proved in [M. Gnewuch, N. Hebbinghaus. Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples. Preprint 2016.]. Toge...

Abstract. We show there is a natural connection between Latin squares and commutative sets of monomials defining geometric structures in finite phase-space of prime power dimensions. A complete set of such monomials defines a mutually unbiased basis (MUB) and may be associated with a complete set of mutually orthogonal Latin squares (MOLS). We translate some possible operations on the monomial ...

A Latin square L = L(`ij) over the set S = {0, 1, . . . , n − 1} is called totally non-polynomial over Zn iff 1. there are no polynomials Ui(y) ∈ Zn[y] such that Ui(j) = `ij for all i, j ∈ Zn; 2. there are no polynomials Vj(x) ∈ Zn[x] such that Vj(i) = `ij for all i, j ∈ Zn. In the presented paper we describe four possible constructions of such Latin squares which might be of particular interes...

The authors studied whether Latin or French as a foreign curricular language is a better preparation for learning Spanish. Fifty native German speakers who took a university Spanish course concluded their course with a translation test. English was the 1st foreign language for all students, whereas half of them had learned French and the other half had learned Latin as their 2nd foreign languag...

In this paper, we introduce a symmetric-key Latin square image cipher (LSIC) for grayscale and color images. Our contributions to the image encryption community include 1) we develop new Latin square image encryption primitives including Latin Square Whitening, Latin Square S-box and Latin Square P-box ; 2) we provide a new way of integrating probabilistic encryption in image encryption by embe...

BACKGROUND Latin America Treatment and Innovation Network in Mental Health (LATIN-MH) is a research hub located in Brazil and Peru that conducts a research project to help reduce the treatment gap in mental health in Latin America (LA). Besides its research core, LATIN-MH has a Capacity Building (CB) component that aims to help young researchers receive the specific training to contribute to th...

OBJECTIVES To analyze scientific activity in Latin American nursing using bibliometric indicators. MATERIALS AND METHODS This is a quantitative, descriptive study of the universe of Latin American nursing journals (119) and scientific documents (13,208) published according to current library databases including: the Web of Science (WOS), Medline, LILACS, Periodica, Cuiden, and SciELO. A datab...