The Often-Overlooked Power of Summary Statistics in Exploratory Data Analysis: Comparison of Pattern Recognition Entropy (PRE) to Other Summary Statistics and Introduction of Divided Spectrum-PRE (DS-PRE).

Unsupervised exploratory data analysis (EDA) is often the first step in understanding complex data sets. While summary statistics are among the most efficient and convenient tools for exploring and describing sets of data, they are often overlooked in EDA. In this paper, we show multiple case studies that compare the performance, including clustering, of a series of summary statistics in EDA. The summary statistics considered here are pattern recognition entropy (PRE), the mean, standard deviation (STD), 1-norm, range, sum of squares (SSQ), and X4, which are compared with principal component analysis (PCA), multivariate curve resolution (MCR), and/or cluster analysis. PRE and the other summary statistics are direct methods for analyzing data-they are not factor-based approaches. To quantify the performance of summary statistics, we use the concept of the "critical pair," which is employed in chromatography. The data analyzed here come from different analytical methods. Hyperspectral images, including one of a biological material, are also analyzed. In general, PRE outperforms the other summary statistics, especially in image analysis, although a suite of summary statistics is useful in exploring complex data sets. While PRE results were generally comparable to those from PCA and MCR, PRE is easier to apply. For example, there is no need to determine the number of factors that describe a data set. Finally, we introduce the concept of divided spectrum-PRE (DS-PRE) as a new EDA method. DS-PRE increases the discrimination power of PRE. We also show that DS-PRE can be used to provide the inputs for the k-nearest neighbor (kNN) algorithm. We recommend PRE and DS-PRE as rapid new tools for unsupervised EDA.

Cerium oxide nanoparticles with antioxidant capabilities and gadolinium integration for MRI contrast enhancement.

The chelating gadolinium-complex is routinely used as magnetic resonance imaging (MRI) -contrast enhancer. However, several safety issues have recently been reported by FDA and PRAC. There is an urgent need for the next generation of safer MRI-contrast enhancers, with improved local contrast and targeting capabilities. Cerium oxide nanoparticles (CeNPs) are designed with fractions of up to 50% gadolinium to utilize the superior MRI-contrast properties of gadolinium. CeNPs are well-tolerated in vivo and have redox properties making them suitable for biomedical applications, for example scavenging purposes on the tissue- and cellular level and during tumor treatment to reduce in vivo inflammatory processes. Our near edge X-ray absorption fine structure (NEXAFS) studies show that implementation of gadolinium changes the initial co-existence of oxidation states Ce3+ and Ce4+ of cerium, thereby affecting the scavenging properties of the nanoparticles. Based on ab initio electronic structure calculations, we describe the most prominent spectral features for the respective oxidation states. The as-prepared gadolinium-implemented CeNPs are 3-5 nm in size, have r1-relaxivities between 7-13 mM-1 s-1 and show clear antioxidative properties, all of which means they are promising theranostic agents for use in future biomedical applications.