PARAFAC2×N: Coupled decomposition of multi-modal data with drift in N modes.

Analysis of GC×GC-TOFMS data for large numbers of poorly-resolved peaks, and for large numbers of samples remains an enduring problem that hinders the widespread application of the technique. For multiple samples, GC×GC-TOFMS data for specific chromatographic regions manifests as a 4th order tensor of I mass spectral acquisitions, J mass channels, K modulations, and L samples. Chromatographic drift is common along both the first-dimension (modulations), and along the second-dimension (mass spectral acquisitions), while drift along the mass channel is for all practical purposes nonexistent. A number of solutions to handling GC×GC-TOFMS data have been proposed: these involve reshaping the data to make it amenable to either 2nd order decomposition techniques based on Multivariate Curve Resolution (MCR), or 3rd order decomposition techniques such as Parallel Factor Analysis 2 (PARAFAC2). PARAFAC2 has been utilised to model chromatographic drift along one mode, which has enabled its use for robust decomposition of multiple GC-MS experiments. Although extensible, it is not straightforward to implement a PARAFAC2 model that accounts for drift along multiple modes. In this submission, we demonstrate a new approach and a general theory for modelling data with drift along multiple modes, for applications in multidimensional chromatography with multivariate detection. The proposed model captures over 99.9% of variance for a synthetic data set, presenting an extreme example of peak drift and co-elution across two modes of separation.

Multi-Way Analysis Coupled with Near-Infrared Spectroscopy in Food Industry: Models and Applications.

Near-infrared spectroscopy (NIRS) is a fast and powerful analytical tool in the food industry. As an advanced chemometrics tool, multi-way analysis shows great potential for solving a wide range of food problems and analyzing complex spectroscopic data. This paper describes the representative multi-way models which were used for analyzing NIRS data, as well as the advances, advantages and limitations of different multi-way models. The applications of multi-way analysis in NIRS for the food industry in terms of food process control, quality evaluation and fraud, identification and classification, prediction and quantification, and image analysis are also reviewed. It is evident from this report that multi-way analysis is presently an attractive tool for modeling complex NIRS data in the food industry while its full potential is far from reached. The combination of multi-way analysis with NIRS will be a promising practice for turning food data information into operational knowledge, conducting reliable food analyses and improving our understanding about food systems and food processes. To the best of our knowledge, this is the first paper that systematically reports the advances on models and applications of multi-way analysis in NIRS for the food industry.

New and Potent Quinuclidine-Based Antimicrobial Agents.

Developing new antibiotics is currently very important since antibiotic resistance is one of the biggest problems of global health today. In the search for a new class of potential antimicrobial agents, ten new compounds were designed and synthesized based on the quinuclidinium heterocyclic core and the oxime functional group. The antimicrobial activity was assessed against a panel of representative gram-positive and gram-negative bacteria. All compounds demonstrated potent activity against the tested microorganisms, with the minimum inhibitory concentration (MIC) values ranging from 0.25 to 256.00 µg/mL. Among the tested compounds, two quaternary compounds, para-N-chlorobenzyl and meta-N-bromobenzyl quinuclidinium oximes, displayed the most potent and broad-spectrum activity against both gram-positive and gram-negative bacterial strains (MIC values from 0.25 to 4.00 µg/mL), with the lowest value for the important multidrug resistant gram-negative pathogen Pseudomonas aeruginosa. In the case of Klebsiella pneumoniae, activity of those compounds are 256-fold and 16-fold better than gentamicin, respectively. MTT assays showed that compounds are nontoxic for human cell lines. Multi-way analysis was used to separately reduce dimensionality of quantum chemical data and biological activity data to obtain a regression model and the required parameters for the enhancement of biological activity.

Toward automated chromatographic fingerprinting: A non-alignment approach to gas chromatography mass spectrometry data.

In contrast to targeted analysis of volatile compounds, non-targeted approaches take information of known and unknown compounds into account, are inherently more comprehensive and give a more holistic representation of the sample composition. Although several non-targeted approaches have been developed, there's still a demand for automated data processing tools, especially for complex multi-way data such as chromatographic data obtained from multichannel detectors. This work was therefore aimed at developing a data processing procedure for gas chromatography mass spectrometry (GC-MS) data obtained from non-targeted analysis of volatile compounds. The developed approach uses basic matrix manipulation of segmented GC-MS chromatograms and PARAFAC multi-way modelling. The approach takes retention time shifts and peak shape deformations between samples into account and can be done with the freely available N-way toolbox for MATLAB. A demonstration of the new fingerprinting approach is presented using an artificial GC-MS data set and an experimental full-scan GC-MS data set obtained for a set of experimental wines.

On feature extraction and classification in prostate cancer radiotherapy using tensor decompositions.

External beam radiotherapy is commonly prescribed for prostate cancer. Although new radiation techniques allow high doses to be delivered to the target, the surrounding healthy organs (rectum and bladder) may suffer from irradiation, which might produce undesirable side-effects. Hence, the understanding of the complex toxicity dose-volume effect relationships is crucial to adapt the treatment, thereby decreasing the risk of toxicity. In this paper, we introduce a novel method to classify patients at risk of presenting rectal bleeding based on a Deterministic Multi-way Analysis (DMA) of three-dimensional planned dose distributions across a population. After a non-rigid spatial alignment of the anatomies applied to the dose distributions, the proposed method seeks for two bases of vectors representing bleeding and non bleeding patients by using the Canonical Polyadic (CP) decomposition of two fourth order arrays of the planned doses. A patient is then classified according to its distance to the subspaces spanned by both bases. A total of 99 patients treated for prostate cancer were used to analyze and test the performance of the proposed approach, named CP-DMA, in a leave-one-out cross validation scheme. Results were compared with supervised (linear discriminant analysis, support vector machine, K-means, K-nearest neighbor) and unsupervised (recent principal component analysis-based algorithm, and multidimensional classification method) approaches based on the registered dose distribution. Moreover, CP-DMA was also compared with the Normal Tissue Complication Probability (NTCP) model. The CP-DMA method allowed rectal bleeding patients to be classified with good specificity and sensitivity values, outperforming the classical approaches.

Multi-way analysis for decadal pollution trends assessment: the Guadalquivir River estuary as a case study.

Alongside history, human activities have contributed to the deployment of environmental quality. In particular, during the last decades the problem of water preservation has gained increasing attention. Statistical analysis is essential to analyze environmental data and to identify trends of pollutants over space and time. Usually applied techniques for data treatment are based on the organization of data in a two-way array, missing some shades on pollutants distribution. This fact supports the use of multi-way techniques, which allow the analysis of the results through different directions at the same time. For Three Modes Principal Components Analysis (3MPCA) a principal components analysis is conducted using three modes and a "core" matrix that allows assessing their interactions. In the case of environmental studies, it offers information about the spatial-temporal evolution of pollutants in a certain water body. The Guadalquivir River estuary has been used as a model system. It is a representative human influenced system, where different pollution inputs have been characterized. In this study, decadal evolution of pollutants has been discussed, to evaluate among others the effects of EU legislation on river water quality. The aim of this work is the establishment of the evolution, during the last decade, of nutrients and metals ultra-traces distribution in an estuary affected by anthropic activities. As examples, Pb and PO4(3-) show a trend to decrease their weight on water pollution, total suspended solids (TSS) behavior is related with massive rain events, and the rising of new technologies appears as a source of emerging pollutants as Co in urban-industrial areas.

TriClust: A Tool for Cross-Species Analysis of Gene Regulation.

We present a software tool, called TriClust, for multi-way analysis of gene expression data from paired conditions of multiple organisms. The analysis is based on a new concept called triclustering, which is an extension of biclustering over a third dimension that represents the organism where the microarray experiment is performed. TriClust provides a comprehensive analysis of co-regulated genes under a subset of experimental conditions over multiple organisms. The results are visualized using heat-maps and the Gene Ontology (GO) term enrichment statistics. The experimental results indicate that TriClust can successfully identify biologically significant triclusters and promote a useful tool for cross species analysis of gene regulation from microarray expression data. The statistical results suggest that, when available, triclustering on multi-organism data can result in better gene clusters in comparison to biclustering on single-organism data. The TriClust software is publicly available as a standalone program.