In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges. 1 Background information In any combinatorial configuration it is possible to identify a subset which uniquely determines the structure of the configuration and in some cases i...

We introduce quantum Latin squares, combinatorial quantum objects which generalize classical Latin squares. We show that quantum Latin squares can be seen as weakened versions of mutually-unbiased bases (MUBs). Our main results use quantum Latin squares to give a new construction of unitary error bases (UEBs), basic structures in quantum information which lie at the heart of procedures such as ...

A latin transversal in a square matrix of order n is a set of entries, no two in the same row or column, which are pairwise distinct. A longstanding conjecture of Ryser states that every Latin square with odd order has a latin transversal. Some results on the existence of a large partial latin transversal can be found in [11,6,16]. Mainly motivated by Ryser’s conjecture, Erdős and Spencer [8] p...

In this paper I will explore the entropy of the Latin language with a particular eye towards the differences in entropy between authors and between times when Latin was a living language. I expect to find that not only are the texts of authors discernible by their entropies, but that there is a gradual change in the entropy of the language from the earliest Latin texts until later ’Church Latin...

"Using published census data, metropolitan area population and employment statistics are constructed for several large Latin American cities in 1950, 1960, and 1970, and compared to similar statistics from selected North American cities. The Latin cities are experiencing decentralization of population and some decentralization of employment. Overall population density patterns of large Latin ci...

The branch group of a strongly controllable group code is a shift group. We show that a shift group can be characterized in a very simple way. In addition it is shown that if a strongly controllable group code is labeled with Latin squares, then the shift group is solvable. Moreover the mathematical structure of a Latin square (as a translation net) and of a shift group are shown to be closely ...

We propose an approach to constructing nested Latin hypercube designs. Such designs are useful for conducting multiple computer experiments with different levels of accuracy. A nested Latin hypercube design with two layers is defined to be a special Latin hypercube design that contains a smaller Latin hypercube design as a subset. Our method is easy to implement and can accommodate any number o...

Scholarly interest in Jews as a subject of Latin American Studies has grown markedly in the last two decades, especially when compared to research on other Latin Americans who trace their ancestry to the Middle East, Asia or Eastern Europe. In this context, we propose the use of the term ‘Jewish-Latin American’, rather than ‘Latin American Jewry’, in order to shift the dominant paradigm about e...

Efficient sampling strategies that scale with the size of the problem, computational budget, and users’ needs are essential for various sampling-based analyses, such as sensitivity and uncertainty analysis. In this study, we propose a new strategy, called Progressive Latin Hypercube Sampling (PLHS), which sequentially generates sample points while progressively preserving the distributional pro...

Despite a centuries-long tradition in lexicography, Latin lacks state-of-the-art computational lexical resources. This situation is strictly related to the still quite limited amount of linguistically annotated textual data for Latin, which can help the building of new lexical resources by supporting them with empirical evidence. However, projects for creating new language resources for Latin h...