Direct transformations yielding the knight's move pattern in 3x3x3 arrays

Three-way arrays (or tensors) can be regarded as extensions of the traditional two-way data matrices that have a third dimension. Studying algebraic properties of arrays is relevant, for example, for the Tucker three-way PCA method, which generalizes principal component analysis to three-way data. One important algebraic property of arrays is concerned with the possibility of transformations to simplicity. An array is said to be transformed to a simple form when it can be manipulated by a sequence of invertible operations such that a vast majority of its entries become zero. This paper shows how 3 × 3 × 3 arrays, whether symmetric or nonsymmetric, can be transformed to a simple form with 18 out of its 27 entries equal to zero. We call this simple form the “knight's move pattern” due to a loose resemblance to the moves of a knight in a game of chess. The pattern was examined by Kiers, Ten Berge, and Rocci. It will be shown how the knight's move pattern can be found by means of a numeric–algebraic procedure based on the Gröbner basis. This approach seems to work almost surely for randomly generated arrays, whether symmetric or nonsymmetric

Analysis of the association between spawning time QTL markers and the biannual spawning behavior in rainbow trout (Oncorhynchus mykiss)

The rainbow trout is a salmonid fish that occasionally exhibits broodstocks with biannual spawning behavior, a phenomenon known as a double annual reproductive cycle (DARC). Spawning time quantitative trait loci (SPT-QTLs) affect the time of the year that female rainbow trout spawn and may influence expression of the DARC trait. In this study, microsatellite markers linked and unlinked to SPT-QTLs were genotyped to investigate the underlying genetics of this trait. SPT-QTLs influenced the DARC trait since in two case-control comparisons three linked markers (OmyFGT12TUF, One3ASC and One19ASC) had significant levels of allelic frequency differentiation and marker-character association. Furthermore, alleles of One3ASC and One19ASC had significantly higher frequencies in populations that carried the DARC trait

Quantifying the Adaptive Potential of an Antibiotic Resistance Enzyme

For a quantitative understanding of the process of adaptation, we need to understand its “raw material,” that is, the frequency and fitness effects of beneficial mutations. At present, most empirical evidence suggests an exponential distribution of fitness effects of beneficial mutations, as predicted for Gumbel-domain distributions by extreme value theory. Here, we study the distribution of mutation effects on cefotaxime (Ctx) resistance and fitness of 48 unique beneficial mutations in the bacterial enzyme TEM-1 β-lactamase, which were obtained by screening the products of random mutagenesis for increased Ctx resistance. Our contributions are threefold. First, based on the frequency of unique mutations among more than 300 sequenced isolates and correcting for mutation bias, we conservatively estimate that the total number of first-step mutations that increase Ctx resistance in this enzyme is 87 [95% CI 75–189], or 3.4% of all 2,583 possible base-pair substitutions. Of the 48 mutations, 10 are synonymous and the majority of the 38 non-synonymous mutations occur in the pocket surrounding the catalytic site. Second, we estimate the effects of the mutations on Ctx resistance by determining survival at various Ctx concentrations, and we derive their fitness effects by modeling reproduction and survival as a branching process. Third, we find that the distribution of both measures follows a Fréchet-type distribution characterized by a broad tail of a few exceptionally fit mutants. Such distributions have fundamental evolutionary implications, including an increased predictability of evolution, and may provide a partial explanation for recent observations of striking parallel evolution of antibiotic resistance

Taxicab correspondence analysis of abundance data in archaeology: three case studies revisited

This paper compares the method of Correspondence Analysis (CA) for finding patterns in archaeological sites by artifacts abundance data, with a robust variant, named Taxicab Correspondence Analysis (TCA). We show that this comparison is useful, especially for sparse tables with outliers. We identify three kinds of outliers. Three well-known datasets are reanalyzed