Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Transcriptional responses of host peripheral blood cells to tuberculosis infection

Host responses following exposure to Mycobacterium tuberculosis (TB) are complex and can significantly affect clinical outcome. These responses, which are largely mediated by complex immune mechanisms involving peripheral blood cells (PBCs) such as T-lymphocytes, NK cells and monocyte-derived macrophages, have not been fully characterized. We hypothesize that different clinical outcome following TB exposure will be uniquely reflected in host gene expression profiles, and expression profiling of PBCs can be used to discriminate between different TB infectious outcomes. In this study, microarray analysis was performed on PBCs from three TB groups (BCG-vaccinated, latent TB infection, and active TB infection) and a control healthy group. Supervised learning algorithms were used to identify signature genomic responses that differentiate among group samples. Gene Set Enrichment Analysis was used to determine sets of genes that were co-regulated. Multivariate permutation analysis (p < 0.01) gave 645 genes differentially expressed among the four groups, with both distinct and common patterns of gene expression observed for each group. A 127-probeset, representing 77 known genes, capable of accurately classifying samples into their respective groups was identified. In addition, 13 insulin-sensitive genes were found to be differentially regulated in all three TB infected groups, underscoring the functional association between insulin signaling pathway and TB infection. Published by Elsevier Ltd.

Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.