Arrow Plot: a new graphical tool for selecting up and down regulated genes and genes differentially expressed on samples subgroups

Background: A common task in analyzing microarray data is to determine which genes are differentially expressed across two (or more) kind of tissue samples or samples submitted under experimental conditions. Several statistical methods have been proposed to accomplish this goal, generally based on measures of distance between classes. It is well known that biological samples are heterogeneous because of factors such as molecular subtypes or genetic background that are often unknown to the experimenter. For instance, in experiments which involve molecular classification of tumors it is important to identify significant subtypes of cancer. Bimodal or multimodal distributions often reflect the presence of subsamples mixtures. Consequently, there can be genes differentially expressed on sample subgroups which are missed if usual statistical approaches are used. In this paper we propose a new graphical tool which not only identifies genes with up and down regulations, but also genes with differential expression in different subclasses, that are usually missed if current statistical methods are used. This tool is based on two measures of distance between samples, namely the overlapping coefficient (OVL) between two densities and the area under the receiver operating characteristic (ROC) curve. The methodology proposed here was implemented in the open-source R software. Results: This method was applied to a publicly available dataset, as well as to a simulated dataset. We compared our results with the ones obtained using some of the standard methods for detecting differentially expressed genes, namely Welch t-statistic, fold change (FC), rank products (RP), average difference (AD), weighted average difference (WAD), moderated t-statistic (modT), intensity-based moderated t-statistic (ibmT), significance analysis of microarrays (samT) and area under the ROC curve (AUC). On both datasets all differentially expressed genes with bimodal or multimodal distributions were not selected by all standard selection procedures. We also compared our results with (i) area between ROC curve and rising area (ABCR) and (ii) the test for not proper ROC curves (TNRC). We found our methodology more comprehensive, because it detects both bimodal and multimodal distributions and different variances can be considered on both samples. Another advantage of our method is that we can analyze graphically the behavior of different kinds of differentially expressed genes. Conclusion: Our results indicate that the arrow plot represents a new flexible and useful tool for the analysis of gene expression profiles from microarrays.

Arrow plot and CA maps on microarray preprocessing methods

Microarray allow to monitoring simultaneously thousands of genes, where the abundance of the transcripts under a same experimental condition at the same time can be quantified. Among various available array technologies, double channel cDNA microarray experiments have arisen in numerous technical protocols associated to genomic studies, which is the focus of this work. Microarray experiments involve many steps and each one can affect the quality of raw data. Background correction and normalization are preprocessing techniques to clean and correct the raw data when undesirable fluctuations arise from technical factors. Several recent studies showed that there is no preprocessing strategy that outperforms others in all circumstances and thus it seems difficult to provide general recommendations. In this work, it is proposed to use exploratory techniques to visualize the effects of preprocessing methods on statistical analysis of cancer two-channel microarray data sets, where the cancer types (classes) are known. For selecting differential expressed genes the arrow plot was used and the graph of profiles resultant from the correspondence analysis for visualizing the results. It was used 6 background methods and 6 normalization methods, performing 36 pre-processing methods and it was analyzed in a published cDNA microarray database (Liver) available at http://genome-www5.stanford.edu/ which microarrays were already classified by cancer type. All statistical analyses were performed using the R statistical software.

Efeitos agudos do tabagismo sobre a modulação autonômica: análise por meio do plot de poincaré

FUNDAMENTO: O tabagismo altera a função autonômica. OBJETIVO: Investigar os efeitos agudos do tabagismo sobre a modulação autonômica e a recuperação dos índices de variabilidade de frequência cardíaca (VFC) pós-fumo, por meio do plot de Poincaré e índices lineares. MÉTODOS: Foram avaliados 25 fumantes jovens, os quais tiveram a frequência cardíaca analisada, batimento a batimento, na posição sentada, após 8 horas de abstinência, por 30 minutos em repouso, 20 minutos durante o fumo e 30 minutos pós-fumo. Análise de variância para medidas repetidas, seguido do teste de Tukey, ou teste de Friedman seguido do teste de Dunn foram aplicados dependendo da normalidade dos dados, com p < 0,05. RESULTADOS: Durante o fumo, houve redução dos índices SD1 (23,4 ± 9,2 vs 13,8 ± 4,8), razão SD1/SD2 (0,31 ± 0,08 vs 0,2 ± 0,04), RMSSD (32,7 ± 13 vs 19,1 ± 6,8), SDNN (47,6 ± 14,8 vs 35,5 ± 8,4), HFnu (32,5 ± 11,6 vs 19 ± 8,1) e do intervalo RR (816,8 ± 89 vs 696,5 ± 76,3) em relação ao repouso, enquanto que aumentos do índice LFnu (67,5 ± 11,6 vs 81 ± 8,1) e da razão LF/HF (2,6 ± 1,7 vs 5,4 ± 3,1) foram observados. A análise visual do plot mostrou menor dispersão dos intervalos RR durante o fumo. Com exceção da razão SD1/SD2, os demais índices apresentaram recuperação dos valores, 30 minutos após o tabagismo. CONCLUSÃO: O tabagismo produziu agudamente modificações no controle autonômico, caracterizadas por ativação simpática e retirada vagal, com recuperação 30 minutos após o fumo.

Plot Suite

Una Plot Suite és una aplicació web que permet localitzar plots d’una Base de Dades a partir de formularis. S’obtindran taules on apareixeran els plots amb les seves característiques i es podrà obtenir còpies dels plots sol·licitats. Gràcies al seu disseny es podran afegir nous plots a la Base de Dades i fins i tot modificar l’estructura d’una manera molt intuïtiva.

Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certainassumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur inthe proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p.There are many statistical tests being used to check whether empirical marker data obeys theHardy-Weinberg principle. Among these are the classical xi-square test (with or withoutcontinuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combinationwith Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE)are numerical in nature, requiring the computation of a test statistic and a p-value.There is however, ample space for the use of graphics in HWE tests, in particular for the ternaryplot. Nowadays, many genetical studies are using genetical markers known as SingleNucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the countsone typically computes genotype frequencies and allele frequencies. These frequencies satisfythe unit-sum constraint, and their analysis therefore falls within the realm of compositional dataanalysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotypefrequencies can be adequately represented in a ternary plot. Compositions that are in exactHWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected ina statistical test are typically “close" to the parabola, whereas compositions that differsignificantly from HWE are “far". By rewriting the statistics used to test for HWE in terms ofheterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted inthe ternary plot. This way, compositions can be tested for HWE purely on the basis of theirposition in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphicalrepresentations where large numbers of SNPs can be tested for HWE in a single graph. Severalexamples of graphical tests for HWE (implemented in R software), will be shown, using SNPdata from different human populations

Within-plot subsampling of trees for assessment in progeny trials of Scots pine

Summary

Calculation and comparison of different permanent sample plot types

Summary

Hydrological processes obtained on the plot scale under four simulated rainfall tests during the cycle of different crop systems

The cropping system influences the interception of water by plants, water storage in depressions on the soil surface, water infiltration into the soil and runoff. The aim of this study was to quantify some hydrological processes under no tillage cropping systems at the edge of a slope, in 2009 and 2010, in a Humic Dystrudept soil, with the following treatments: corn, soybeans, and common beans alone; and intercropped corn and common bean. Treatments consisted of four simulated rainfall tests at different times, with a planned intensity of 64 mm h-1 and 90 min duration. The first test was applied 18 days after sowing, and the others at 39, 75 and 120 days after the first test. Different times of the simulated rainfall and stages of the crop cycle affected soil water content prior to the rain, and the time runoff began and its peak flow and, thus, the surface hydrological processes. The depth of the runoff and the depth of the water intercepted by the crop + soil infiltration + soil surface storage were affected by the crop systems and the rainfall applied at different times. The corn crop was the most effective treatment for controlling runoff, with a water loss ratio of 0.38, equivalent to 75 % of the water loss ratio exhibited by common bean (0.51), the least effective treatment in relation to the others. Total water loss by runoff decreased linearly with an increase in the time that runoff began, regardless of the treatment; however, soil water content on the gravimetric basis increased linearly from the beginning to the end of the rainfall.

Permanent.Plot.ch - a database for Swiss permanent vegetation plots

The aim of the Permanent.Plot.ch project is the conservation of historical data about permanent plots in Switzerland and the monitoring of vegetation in a context of environmental changes (mainly climate and land use). Permanent plots are currently being recognized as valuable tools to monitor long-term effects of environmental changes on vegetation. Often used in short studies (3 to 5 years), they are generally abandoned at the end of projects. However, their full potential might only be revealed after 10 or more years, once the location is lost. For instance, some of the oldest permanent plots in Switzerland (first half of the 20th century) were nearly lost, although they are now very valuable data. The Permanent.Plot.ch national database (GIVD ID EU-CH-001), by storing historical and recent data, will allow to ensuring future access to data from permanent vegetation plots. As the database contains some private data, it is not directly available on internet but an overview of the data can be downloaded from internet (http://www.unil.ch/ppch) and precise data are available on request.

Cost-plus-loss analyses of forest inventory strategies based on kNN-assigned reference sample plot data

Abstract

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Le projet PERMANENT.PLOT.CH demande votre collaboration

Un nouveau projet, baptisé PERMANENT.PLOT.CH, démarre cette année à l'Université de Lausanne. Le but est de répertorier tous les carrés permanents de végétation en Suisse et de les archiver dans une base de donnée informatique. Un appel est lancé à toute personne connaissant l'existence de carrés permanents de végétation, sur le terrain ou dans la litérature, de nous transmettre cette précieuse information.

Effect of neighborhood and plot size on experiments with multiple-harvest oleraceous crops

The objective of this work was to determine the efficiency of the Papadakis method on the quality evaluation of experiments with multiple-harvest oleraceous crops, and on the estimate of the covariate and the ideal plot size. Data from nine uniformity trials (five with bean pod, two with zucchini, and two with sweet pepper) and from one experiment with treatments (with sweet pepper) were used. Through the uniformity trials, the best way to calculate the covariate was defined and the optimal plot size was calculated. In the experiment with treatments, analyses of variance and covariance were performed, in which the covariate was calculated by the Papadakis method, and experimental precision was evaluated based on four statistics. The use of analysis of covariance with the covariate obtained by the Papadakis method increases the quality of experiments with multiple-harvest oleraceous crops and allows the use of smaller plot sizes. The best covariate is the one that considers a neighboring plot of each side of the reference plot.