Latin orthogonal

Meals were consumed by the subjects following a Latin Square Design. Statistical analysis was performed by a General Linear Models Procedure (20) using split-plot in time analysis with the following non-orthogonal contrasts ... 

Tang B. 1993. Orthogonal array-based Latin hypercubes. J Am Stat Assoc 88 1392-1397. 

CONSTRUCTIONS AND COMBINATORIAL PROBLEMS IN DESIGN OF EXPERIMENTS, Damaraju Raghavarao. In-depth reference work examines orthogonal Latin squares, incomplete block designs, tactical configuration, partial geometry, much more. Abundant explanations, examples. 416pp. 5K x 8X. 

Sample size and treatment choice are key design questions for general multifactor experiments. Authors have proposed the use of standard factorial experiments in completely randomized designs, block designs, or Latin squares (see, for example, Chapter 6 and Churchill, 2003). However, the unusual distribution of gene expression data makes one question the relevance of standard orthogonal factorial experiments in this context. 

Statistical manipulations on the USDA database (cluster analysis, principal component analysis with varimax rotation e.g., Everitt, 1980) revealed subsets of represent ve species, as idealized in Fig 2b, but with dif ent variables (orthogonal principal components) than traditional fractions as measured by USDA. A set cf species from each orthogonal subset appears in Table 1. The Latin names, and where available, the common names of the biomass species are given. The extractives ranges are ash content, 4 to 17% protein content, 5 to 14% polyphenol, 3 to 11% and oil content, 1 to 4%. However no species contains extremes of all 4 variables. Nor can species be found, retaining native compositions, at extremes of just one extractive composition, while the other fractions are present at constant levels. Thus we use orthogonal but non-intuitive compositions in this work, then rank pyrolysis effects in terms of traditional extractives content to get an understanding of their impact on biomass pyrolysis. 

Viji SN, Prasad PA, Gautham N (2009) Protein-ligand docking using mutually orthogonal Latin squares (MOLSDOCK). J Chem Inf Model 49(12) 2687-2694... 

Hereafter the summation is taken from 1 to A/ for Latin indices and from 1 to Af — 1 for the Greek ones. According to Equation (6.9), tia determine the orthogonal transformation to the local frame of reference. One can check that the second condition. Equation (6.10), makes the metric tensor diagonal in the coordinates S and fo,. This condition is not essential but it simplifies the following derivations. The instanton trajectory approaches the potential minima along one of the normal modes, which we numerate as the A/th. We can also choose fa to coincide with the other N — 1 normal coordinates at the potential minimum. Due to Equation (6.10), we have... 

It can be seen that both the Greek and Latin characters form Latin squares. Every Graeco-Latin square consists of two Latin squares that are orthogonal, that is, that every pair occurs exactly once. (Graeco-Latin alphanumeric Sudoku puzzles have appeared, but are not as yet popular.) In general, there are n — 1 solutions above, where = 3, one has the A, B, C and the a, /3, y sets. With = 4, there are three solutions ... 

The more than three-dimensional designs are referred to as hyper-Graeco-Latin squares, or a complete set of mutually orthogonal Latin squares. In Example 2, the use of four factors at three levels adds the prefix hyper. ... 

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