Robust Principal Component Analysis for Compositional Tables

A data table which is arranged according to two factors can often be considered as a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant information would consist of ratios between different cells of such a table. This is particularly useful when analyzing several compositional tables jointly, where the absolute numbers are in very different ranges, e.g. if unemployment data are considered from different countries. Within the framework of the logratio methodology, compositional tables can be decomposed into independent and interactive parts, and orthonormal coordinates can be assigned to these parts. However, these coordinates usually require some prior knowledge about the data, and they are not easy to handle for exploring the relationships between the given factors. Here we propose a special choice of coordinates with a direct relation to centered logratio (clr) coefficients, which are particularly useful for an interpretation in terms of the original cells of the tables. With these coordinates, robust principal component analysis (PCA) is performed for dimension reduction, allowing to investigate the relationships between the factors. The link between orthonormal coordinates and clr coefficients enables to apply robust PCA, which would otherwise suffer from the singularity of clr coefficients.Comment: 20 pages, 2 figure

In Vitro Mechanical Properties of Mineral Trioxide Aggregate in Moist and Dry Intracanal Environments

Introduction: The purpose of this study was to examine the microhardness and modulus of elasticity (MOE) of White ProRoot MTA (Dentsply Tulsa Dental, Tulsa, OK) after setting in moist or dry intracanal conditions. Methods and Materials: To simulate root canal system, 14 polyethylen molds with internal diameter of 1 mm and height of 12 mm were used. These molds were filled with 9-mm thick layers of White ProRoot Mineral Trioxide Aggregate (MTA; Dentsply Tulsa Dental, Tulsa, OK). The experimental group (n=7) had a damp cotton pellet with 1.5 mm height and a 1.5 mm layer of resin composite placed on it. In control group (n=7) the whole 3 mm above MTA were filled with resin composite. The specimens were kept in 37°C and relative humidity of 80% for 4 days in order to simulate physiological conditions. Specimens were longitudinally sectioned and nanoindentation tests were carried out using Berkovich indenter at loading rate of 2 mN/s at 4×5 matrices of indents which were located in the coronal, middle and apical thirds of the specimen’s cross section, to evaluate the microhardness and modulus of elasticity of the specimen to appraise the progression of the setting process. Differences were assessed using nonparametric generalized Friedman rank sum and Wilcoxon Rank-Sum tests. Results: Statistical analysis showed that there was a significant difference in microhardness and MOE between control and experimental groups at coronal (P<0.001), middle (P<0.001) and apical (P<0.001) thirds of the simulated rod from simulated apical foramen. Kruskal-Wallis test showed no significant effect of depth on microhardness of material in experimental or control groups. Conclusion: Within limitations of this in vitro study, it seems that moist intracanal environment improves setting of MTA in various depths.Keywords: Microhardness; Mineral Trioxide Aggregate; Modulus of Elasticity; Nanoindentatio

General approach to coordinate representation of compositional tables

This is the peer reviewed version which has been published in final form at [https://doi.org/10.1111/sjos.12326]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.Compositional tables can be considered a continuous counterpart to the well-known contingency tables. Their cells, which generally contain positive real numbers rather than just counts, carry relative information about relationships between two factors. Hence, compositional tables can be seen as a generalization of (vector) compositional data. Due to their relative character, compositions are commonly expressed in orthonormal coordinates using a sequential binary partition prior to being further processed by standard statistical tools. Unfortunately, the resulting coordinates do not respect the two-dimensional nature of compositional tables. Information about relationship between factors is thus not well captured. The aim of this paper is to present a general system of orthonormal coordinates with respect to the Aitchison geometry, which allows for an analysis of the interactions between factors in a compositional table. This is achieved using logarithms of odds ratios, which are also widely used in the context of contingency tables

Představení projektu GAČR: Identifikace bariér v procesu komunikace prostorových sociálně-demografických informací

Příspěvek byl podpořen projektem GAČR – 23-06187S – Identifikace bariér v procesu komunikace prostorových sociálně-demografických informac

X-ray fluorescence scanning of soft and wet-sediment cores in terrestrial environments : A robust blind source separation approach

X-ray fluorescence (XRF) scanning of split cores using automated cores scanners is rapid but expensive and semi-quantitative method in sedimentary geochemistry. While searching for a low-cost and quantitative solution in environmental geochemistry, we investigated the application of hand-held XRF device in scanning on two siliciclastic-sediment cores from dam-reservoirs in Slovakia. The core-scan data were compared with XRF data from dry, powdered sample aliquots, grain size, water content, and magnetic susceptibility data, which were used as independent variables. The aim of the manuscript is to investigate the applicability of time-series statistical methods to reveal the physical and chemical signals from hand-held XRF scanning of wet-sediment cores. The geochemical data were processed using the centred log-ratio (clr) technique, and then by the Second-Order Blind Identification (SOBI) method, which is a subtype of robust Blind Source Separation (BSS) techniques commonly used to enhance the signal-to-noise ratio in time series analysis of data in medicine or acoustics. So far, BSS has been rarely applied in geochemistry. Raw element concentrations (ppm/wt%) of core scans and sediment powders are essentially incomparable, but their clr coefficients show statistically significant correlation for Al, P, K, Ca, Mn, Fe, Cu, As, Sr, Zr, and Pb, which reduces the difference between the two measurement methods and justifies previous attempts to calibrate the core-scanning data using log-ratio techniques. Scores of three of eight latent components (IC2, IC4, and IC7) found by SOBI in the core scan- and powder data show significant statistical correlation demonstrating the applicability of the core-scan technique. Their geochemical interpretation is based on the IC loadings by element clr, and the stratigraphic correlation with the sediment grain size and water content. These ICs explain geochemical variability due to grain-size contrast between sandy and silty layers, input of biogenic productivity-sensitive elements (Ca and P), eutrophication, and accumulation of anthropogenic elements. The robust BSS approach represents a promising method of processing of large datasets in environmental geochemistry.peerReviewe

Assessment of Mineral Trioxide Aggregate Setting in Simulated Root Canal with Different Root Canal Wall Thickness: In Vitro Study

Setting of mineral trioxide aggregate (MTA) is affected by various factors. The purpose of this in vitro study was to evaluate the influence of root canal wall thickness on mechanical properties of MTA along the whole apical plug. Bovine bone mold tubes with internal diameter of 2 mm, height of 5 mm, and wall thickness of 0.8 mm, 1.2 mm, and 1.6 mm were filled with 3 mm ProRoot MTA and were kept in 37 °C and relative humidity of 100% for 7 days. The indentation hardness and reduced modulus of elasticity were measured in a large overview matrix and detailed matrix placed 1.5 mm from simulated apical foramen in order to obtain particularized information about gradient of altering mechanical properties. The uppermost layer of material in contact with simulated apical foramen had reduced mechanical properties irrespective of root canal wall thickness. The most distinct decrease of microhardness (32%) and reduced modulus of elasticity (27%) in interfacial layer were present in specimen with thinnest root canal wall. This effect could be observed in detailed measurement up to 190 µm in material. The interfacial layer of MTA, which was in contact during setting with root canal wall thinner than 1.2 mm, had reduced mechanical properties

The Importance of School World Atlases According to Czech Geography Teachers

Over 600 geography teachers answered an online survey containing 30 questions about school world atlases, an integral part of geography education. The study measured the importance and frequency of use of atlases, identified the most frequently used school atlases, and determined the type of tasks solved with atlases and the supplementary teaching aids used. The authors analysed the individual responses of teachers and investigated the relationships between the various responses. To maximise the survey’s information value, many of the questions were open-ended, and teachers responded in the form of plain text. To extract information from these answers, linguistics methods were used. Teachers assessed the importance of atlases as essential. Over 90% of them used atlases in either every lesson or every second lesson. The most important factor in the use of atlases was the experience of the teachers. Those with longer praxis used atlases more often than less experienced teachers. Teachers considered thematic maps as the most problematic part of the atlases. The most frequently solved tasks were the simplest, such as identifying objects on a map. The findings of the survey quantified the importance of atlases in geography education and can assist geography teachers, atlas publishers, and cartographers in general

Multivariate Independent Component Analysis Identifies Patients in Newborn Screening Equally to Adjusted Reference Ranges

Newborn screening (NBS) of inborn errors of metabolism (IEMs) is based on the reference ranges established on a healthy newborn population using quantile statistics of molar concentrations of biomarkers and their ratios. The aim of this paper is to investigate whether multivariate independent component analysis (ICA) is a useful tool for the analysis of NBS data, and also to address the structure of the calculated ICA scores. NBS data were obtained from a routine NBS program performed between 2013 and 2022. ICA was tested on 10,213/150 free-diseased controls and 77/20 patients (9/3 different IEMs) in the discovery/validation phases, respectively. The same model computed during the discovery phase was used in the validation phase to confirm its validity. The plots of ICA scores were constructed, and the results were evaluated based on 5sd levels. Patient samples from 7/3 different diseases were clearly identified as 5sd-outlying from control groups in both phases of the study. Two IEMs containing only one patient each were separated at the 3sd level in the discovery phase. Moreover, in one latent variable, the effect of neonatal birth weight was evident. The results strongly suggest that ICA, together with an interpretation derived from values of the “average member of the score structure”, is generally applicable and has the potential to be included in the decision process in the NBS program.peerReviewe