On the Schoenberg Transformations in Data Analysis: Theory and Illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A simple distance-based discriminant algorithm illustrates the theory, intimately connected to the Gaussian kernels of Machine Learning

Importance of data structure in comparing two dimension reduction methods for classification of microarray gene expression data

BACKGROUND: With the advance of microarray technology, several methods for gene classification and prognosis have been already designed. However, under various denominations, some of these methods have similar approaches. This study evaluates the influence of gene expression variance structure on the performance of methods that describe the relationship between gene expression levels and a given phenotype through projection of data onto discriminant axes. RESULTS: We compared Between-Group Analysis and Discriminant Analysis (with prior dimension reduction through Partial Least Squares or Principal Components Analysis). A geometric approach showed that these two methods are strongly related, but differ in the way they handle data structure. Yet, data structure helps understanding the predictive efficiency of these methods. Three main structure situations may be identified. When the clusters of points are clearly split, both methods perform equally well. When the clusters superpose, both methods fail to give interesting predictions. In intermediate situations, the configuration of the clusters of points has to be handled by the projection to improve prediction. For this, we recommend Discriminant Analysis. Besides, an innovative way of simulation generated the three main structures by modelling different partitions of the whole variance into within-group and between-group variances. These simulated datasets were used in complement to some well-known public datasets to investigate the methods behaviour in a large diversity of structure situations. To examine the structure of a dataset before analysis and preselect an a priori appropriate method for its analysis, we proposed a two-graph preliminary visualization tool: plotting patients on the Between-Group Analysis discriminant axis (x-axis) and on the first and the second within-group Principal Components Analysis component (y-axis), respectively. CONCLUSION: Discriminant Analysis outperformed Between-Group Analysis because it allows for the dataset structure. An a priori knowledge of that structure may guide the choice of the analysis method. Simulated datasets with known properties are valuable to assess and compare the performance of analysis methods, then implementation on real datasets checks and validates the results. Thus, we warn against the use of unchallenging datasets for method comparison, such as the Golub dataset, because their structure is such that any method would be efficient

Stability of gene contributions and identification of outliers in multivariate analysis of microarray data

BACKGROUND: Multivariate ordination methods are powerful tools for the exploration of complex data structures present in microarray data. These methods have several advantages compared to common gene-by-gene approaches. However, due to their exploratory nature, multivariate ordination methods do not allow direct statistical testing of the stability of genes. RESULTS: In this study, we developed a computationally efficient algorithm for: i) the assessment of the significance of gene contributions and ii) the identification of sample outliers in multivariate analysis of microarray data. The approach is based on the use of resampling methods including bootstrapping and jackknifing. A statistical package of R functions was developed. This package includes tools for both inferring the statistical significance of gene contributions and identifying outliers among samples. CONCLUSION: The methodology was successfully applied to three published data sets with varying levels of signal intensities. Its relevance was compared with alternative methods. Overall, it proved to be particularly effective for the evaluation of the stability of microarray data

Restricted Application of Insecticides: A Promising Tsetse Control Technique, but What Do the Farmers Think of It?

Restricted application of insecticides to cattle is a cheap and safe farmer-based method to control tsetse and the diseases they transmit, i.e. human and animal African trypanosomoses. The efficiency of this new control method has been demonstrated earlier but no data is available on its perception and adoption intensity by farmers. We studied these two features in Burkina Faso, where the method has diffused thanks to two development projects. The study allowed identifying three groups of farmers with various adoption intensities, of which one was modern and two traditional. The economic benefit and the farmers' knowledge of the epidemiological system appeared to have a low impact on the early adoption process whereas some modern practices, as well as social factors appeared critical. The quality of technical support provided to the farmers had also a great influence on the adoption rate. The study highlighted individual variations in risk perceptions and benefits, as well as the prominent role of the socio-technical network of cattle farmers. The results of the study are discussed to highlight the factors that should be taken into consideration, to move discoveries from bench to field for an improved control of trypanosomoses vectors

A divergent role for estrogen receptor-beta in node-positive and node-negative breast cancer classified according to molecular subtypes: an observational prospective study

Introduction: Estrogen receptor-alpha (ER-alpha) and progesterone receptor (PgR) are consolidated predictors of response to hormonal therapy (HT). In contrast, little information regarding the role of estrogen receptor-beta (ER-beta) in various breast cancer risk groups treated with different therapeutic regimens is available. In particular, there are no data concerning ER-beta distribution within the novel molecular breast cancer subtypes luminal A (LA) and luminal B (LB), HER2 (HS), and triple-negative (TN). Methods: We conducted an observational prospective study using immunohistochemistry to evaluate ER-beta expression in 936 breast carcinomas. Associations with conventional biopathological factors and with molecular subtypes were analyzed by multiple correspondence analysis (MCA), while univariate and multivariate Cox regression analysis and classification and regression tree analysis were applied to determine the impact of ER-beta on disease-free survival in the 728 patients with complete follow-up data. Results: ER-beta evenly distributes (55.5%) across the four molecular breast cancer subtypes, confirming the lack of correlation between ER-beta and classical prognosticators. However, the relationships among the biopathological factors, analyzed by MCA, showed that ER-beta positivity is located in the quadrant containing more aggressive phenotypes such as HER2 and TN or ER-alpha/PgR/Bcl2- tumors. Kaplan-Meier curves and Cox regression analysis identified ER-beta as a significant discriminating factor for disease-free survival both in the node-negative LA (P = 0.02) subgroup, where it is predictive of response to HT, and in the node-positive LB (P = 0.04) group, where, in association with PgR negativity, it conveys a higher risk of relapse. Conclusion: Our data indicated that, in contrast to node-negative patients, in node-positive breast cancer patients, ER-beta positivity appears to be a biomarker related to a more aggressive clinical course. In this context, further investigations are necessary to better assess the role of the different ER-beta isoforms

Factors associated with compliance among users of solar water disinfection in rural Bolivia

ABSTRACT: BACKGROUND: Diarrhoea is the second leading cause of childhood mortality, with an estimated 1.3 million deaths per year. Promotion of Solar Water Disinfection (SODIS) has been suggested as a strategy for reducing the global burden of diarrhoea by improving the microbiological quality of drinking water. Despite increasing support for the large-scale dissemination of SODIS, there are few reports describing the effectiveness of its implementation. It is, therefore, important to identify and understand the mechanisms that lead to adoption and regular use of SODIS. METHODS: We investigated the behaviours associated with SODIS adoption among households assigned to receive SODIS promotion during a cluster-randomized trial in rural Bolivia. Distinct groups of SODIS-users were identified on the basis of six compliance indicators using principal components and cluster analysis. The probability of adopting SODIS as a function of campaign exposure and household characteristics was evaluated using ordinal logistic regression models. RESULTS: Standardised, community-level SODIS-implementation in a rural Bolivian setting was associated with a median SODIS use of 32% (IQR: 17-50). Households that were more likely to use SODIS were those that participated more frequently in SODIS promotional events (OR = 1.07, 95%CI: 1.01-1.13), included women (OR = 1.18, 95%CI: 1.07-1.30), owned latrines (OR = 3.38, 95%CI: 1.07-10.70), and had severely wasted children living in the home (OR = 2.17, 95%CI: 1.34-3.49). CONCLUSIONS: Most of the observed household characteristics showed limited potential to predict compliance with a comprehensive, year-long SODIS-promotion campaign; this finding reflects the complexity of behaviour change in the context of household water treatment. However, our findings also suggest that the motivation to adopt new water treatment habits and to acquire new knowledge about drinking water treatment is associated with prior engagements in sanitary hygien and with the experience of contemporary family health concerns.Household-level factors like the ownership of a latrine, a large proportion of females and the presence of a malnourished child living in a home are easily assessable indicators that SODIS-programme managers could use to identify early adopters in SODIS promotion campaigns. TRIAL REGISTRATION: ClinicalTrials.gov: NCT0073149

How environmental managers perceive and approach the issue of invasive species: the case of Japanese knotweed s.l. (Rhône River, France)

We would like to thank Springer for publishing our article. The final publication is available at http://link.springer.com/article/10.1007%2Fs10530-015-0969-1International audienceStudying the perceptions of stakeholders or interested parties is a good way to better understand behaviours and decisions. This is especially true for the management of invasive species such as Japanese knotweed s.l. This plant has spread widely in the Rhône basin, where significant financial resources have been devoted to its management. However, no control technique is recognized as being particularly effective. Many uncertainties remain and many documents have been produced by environmental managers to disseminate current knowledge about the plant and its management. This article aims at characterizing the perceptions that environmental managers have of Japanese knotweed s.l. A discourse analysis was conducted on the printed documentation produced about Japanese knotweed s.l. by environmental managers working along the Rhône River (France). The corpus was both qualitatively and quantitatively analysed. The results indicated a diversity of perceptions depending on the type of environmental managers involved, as well as the geographicalareas and scales on which they acted. Whereas some focused on general knowledge relating to the origins and strategies of colonization, others emphasized the diversity and efficacy of the prospective eradication techniques. There is a real interest in implementing targeted actions to meet local issues. To do so, however, these issues must be better defined. This is a challenging task, as it must involve all types of stakeholders

Statistical indicators useful in real spectrum location

In this paper some new results are described, useful for locating the spectrum of a matrix A through mean, standard deviation and third centered moment of the spectrum distribution which can be expressed in terms of traces

Piezo1 integration of vascular architecture with physiological force

The mechanisms by which physical forces regulate endothelial cells to determine the complexities of vascular structure and function are enigmatic¹⁻⁵. Studies of sensory neurons have suggested Piezo proteins as subunits of Ca²⁺-permeable non-selective cationic channels for detection of noxious mechanical impact⁶⁻⁸. Here we show Piezo1 (Fam38a) channels as sensors of frictional force (shear stress) and determinants of vascular structure in both development and adult physiology. Global or endothelial-specific disruption of mouse Piezo1 profoundly disturbed the developing vasculature and was embryonic lethal within days of the heart beating. Haploinsufficiency was not lethal but endothelial abnormality was detected in mature vessels. The importance of Piezo1 channels as sensors of blood flow was shown by Piezo1 dependence of shear-stress-evoked ionic current and calcium influx in endothelial cells and the ability of exogenous Piezo1 to confer sensitivity to shear stress on otherwise resistant cells. Downstream of this calcium influx there was protease activation and spatial reorganization of endothelial cells to the polarity of the applied force. The data suggest that Piezo1 channels function as pivotal integrators in vascular biology