Multivariate analysis methods in physics

In this article, a review of multivariate methods based on statistical learning is given. Several popular multivariate methods useful in high-energy physics analysis are discussed. Selected examples from current research in particle physics are discussed, both from online trigger selection and from off-line analysis. In addition, statistical learning methods, not yet applied in particle physics, are presented and some new applications are suggested. The text was submitted by the author in English.     

SR-XRF analysis and assessment in urban ecology studies: The case of Novosibirsk

This paper considers the elemental composition of aerosols which have accumulated in the snow in winter and that of the top soil layer (0–5 cm), birch (Betula pendula Roth.) leaves collected at the end of the vegetative season, and soils in the vicinity of Novosibirsk. The analysis is carried out using the X-ray fluorescence elemental analysis with synchrotron radiation (SR-XRF) method, which helps reveal the existing local aerosol pollution from industrial sources. The main geochemical indicators of aerosol pollution of the Novosibirsk tin smelter (Novosibirskii Olovokombinat) are As, Sn, Tl, Cd, and Pb; those of three Novosibirsk heat power stations TETs-2, -3, and -5 are V, Mn, I, and Ga. It is found that the accumulation of the majority of technogenic elements in the tissues of higher plants depends on the intensity of the pollution, except for the biophilic Cu, Zn, and Mn, the content of which is more regulated by the physiobiological mechanisms of plants. For example, birch leaves are found to have a lower Mn content in the areas of high technogenic pollution, whereas, in ecologically clean areas, the Mn content in plant tissues is observed to increase. Thus, in Siberia, the snow cover and vegetation are the seasonal depositing components of the urban environment that adequately reflect the existing technogenic aerosol pollution. The elemental SR-XRF analysis of snow and plant tissues can be used to carry out a timely and reliable environmental assessment of an urban territory.     

Application of WDXRF in the provenance studies of Persian haft rang tiles: a statistical approach

An outstanding style of Persian tilework, which emerged from the north‐eastern Iran in the 15th century, was extensively used for decorating architectural facades during the Safavid period (from the 16th through the 18th century). This type of tilework, the so‐called haft rang, technically comprises of forming a clay body and firing two glazed layers on top of the body. In the present paper, the first analytical data concerning haft rang tiles is provided. To do so, forty three samples of Safavid haft rang bodies were analysed by wavelength dispersive x‐ray fluorescence (WDXRF) and the obtained data were handled by principal component analysis (PCA). The results showed that the 17th century haft rang tiles wherever found are local products; that is, Safavid tile‐makers have used local clay sources to make the bodies of haft rang tiles. The analytical data also showed that old tileworks, in general sense, can be simply replaced by newly manufactured tiles or, at least, all tilework revetments in an individual edifice might not have been produced in an identical workshop. Moreover, WDXRF was used as an accurate and precise method to determine the chemical composition and to support compositional classification in provenance studies and can be considered as a reliable alternative for studying the provenance of archaeological ceramics. Copyright © 2013 John Wiley & Sons, Ltd.     

Crawling motility through the analysis of model locomotors: Two case studies

We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.     

Multivariate calibration in TXRF analysis of water

The aim of this paper is the application of multivariate linear calibration for quantitative determination of elements (K, Cd, Co, Hg, As, Pb, Ni, and Al) in water by using Total Reflection X‐ray Fluorescence Analysis with partial least squares (PLS) as a regression method to improve a result of common univariate method. In purpose of elimination of matrix effects in X‐ray fluorescence analysis, experimental design was applied. As a set of standard samples for multivariate calibration, a five‐level eight‐factor calibration design of 25 samples was chosen, ensuring mutual orthogonality of factors. For model's validation, the independent test set of 15 samples was examined. The collection of spectra and quantitative measurements was carried out on S2 PICOFOX. The PLS regression was performed by using software package STATISTICA. Quality indicators of multivariate calibration as slope (b) and intercept (a) of calibration, correlation coefficient (r), determination coefficient (R²), root mean square errors of calibration and of prediction, standard errors of calibration and of prediction, biases of calibration, and biases of prediction were calculated. These results were compared with the univariate model, and as a result, the multivariate calibration method exceeds the univariate one. The obtained results could be applied in a laboratory for an analysis of water solutions in the concentration range 0.05–2.00 mg/L. In many real situations, when analytical chemist deals with multi‐element mixtures, multivariate calibration approach combined with orthogonal design for multivariate calibration set could be successfully used to improve a conventional univariate calibration.     

Multivariate analysis of single-molecule spectra: surpassing spectral diffusion

The full exploitation of single-molecule spectroscopy in disordered systems is often hampered by spectral diffusion processes of the optical transitions due to structural fluctuations in the local environment of the probe molecule which leads to temporal averaging of the signal. Multivariate statistical pattern recognition techniques, originally developed for single-molecule cryoelectron microscopy, allow us to retrieve detailed information from optical single-molecule spectra. As an example, we present the phonon side band of the B800 excitations of the light-harvesting 2 (LH2) complex from Rhodospirillum molischianum, revealing the electron-phonon coupling strength for these transitions. The measured Debye-Waller factors, ranging from 0.4 to 0.9, fall in the regime of weak electron-phonon coupling.     

Total reflection X ray fluorescence in environmental and geochemical studies: unveiling solute provenance in streams during a rain episode

Rural population uses water for irrigation, animal watering and for their own consumption, therefore water contamination is a major concern and a priority for its inhabitants. Unveiling the presence and source of contaminants can help to understand the dynamic of pollutants and therefore define management politics to address the issue. One way to elucidate the origin of contaminants in surface water is by studying rain episodes, relating water discharge with changes in solute concentration. Total Reflection x‐ray Fluorescence (TXRF) was used as the main analytical technique. The study was based on the analysis of samples originating from a Pampean stream (Buenos Aires, Argentina). Solutes (As, P, Ca, Fe, K, Zn, Br) were monitored before, during and after a storm event. During the monitoring it was observed that As was diluted at the beginning of the episode and concentration increased slowly after the rain ceased. The pattern of As is consistent with Ca, K and Fe behavior, revealing a groundwater source. Instead, P concentration increased in the early hours, it was diluted later and finally increased. This behavior indicates that the source of this analyte is superficial and sub superficial water, implying a runoff origin. The simultaneous determination of these analytes by TXRF allowed comparing solute behavior under the same episode, allowing reveal their provenance. Copyright © 2016 John Wiley & Sons, Ltd.     

Multivariate analysis for forensic characterization,discrimination, and classification of marker pen inks

The multivariate analysis methods have recently gained high popularity within the field of forensic sciences because of their high accuracy and precision. The accurate and unbiased results are the preliminary need for a forensic investigation. The aim of the present work is to examine the marker pen inks which are widely used in various places like documentation in parcels, for photograph attestation, and also as a study material in the classroom. This research is focused on the three important aspects; first is to characterize the marker inks, second, to discriminate permanent marker and whiteboard marker inks using destructive (extracting of ink samples from paper substrate) and nondestructive (without ink extraction) techniques of ultraviolet–visible absorbance combined with peak identification examination as well as chemometric methods, and the third is to build a classification model for permanent and whiteboard marker inks. It is concluded that the chemometric method, that is, principal component analysis provides better discrimination power as compared to visual examination. However, destructive and nondestructive approaches give almost similar discriminating power. The classification model developed using linear discriminant analysis provides 87.5% of correct classification of marker ink samples. The method can further be used to formulate a statistical model for the determination of class/group of the other forensic exhibits.     

哈尔滨市城区大气重金属沉降特征和来源研究

鉴于大气重金属降尘对城市居民健康存在一定的威胁,针对哈尔滨市从未开展过重金属沉降特征研究的现状,采用被动采样技术共收集大气降尘样品46份,用AFS-230E原子荧光光度计和ICP-AES全谱直读电感耦合等离子发射光谱法测量样品中的重金属元素含量,计算各元素年沉降通量,利用Pearson系数法、主成分分析法、富集因子法进行重金属沉降特征和来源分析。结果表明,Mn和Co元素主要来自于自然源,其余各元素沉降主要由人为源构成,且人为源中占主导地位的是燃煤尘、汽车尘和金属冶金尘。     

Mössbauer,X-ray fluorescence and paleomagnetic studies of deep-sea sediments from the Peru Basin: two million years of sedimentation history

Summary Sediment cores with different sub-bottom depths (I: 45 cm and II: 700 cm) from the Peru Basin have been investigated. From the depth profile of the relative amount of Fe(II) a redox zone is obtained which correlates with the organic carbon flux into the sediment (core I). M?ssbauer parameters suggest that the iron in the sediments is mainly contained in clay minerals and to varying extent also in goethite. Paper presented at ICAME-95, Rimini, 10–16 September 1995.     

Volcanic products of Lipari (Aeolian islands,Italy): Multivariate analysis of petrographic and radiometric data

A petrographic and radiometric study, along with statistical multivariate analysis of volcanic products of the island of Lipari (Aeolian islands, Italy) was carried out. The volcanological history of Lipari was reconstructed defining two stages (pre- and post-erosive stages) further on subdivided in four volcanic phases, each of which characterized by products with a particular chemical composition and separated by stratigraphic unconformities. The correlations between petrographic features, determined by X-ray fluorescence, and volcanological history of the island highlight a gradual differentiation with younger rocks showing a more acid chemical composition than the older ones. Radiometric features, and in particular the content of primordial radionuclides ²³⁸U, ²³²Th and ⁴⁰K, have been measured through gamma-ray spectrometry with hyper-pure germanium detector.The different volcanic lithologies, such as basalts, andesites and rhyolites, have been characterized by petrographic diagrams. The calculated dose rate has also been used as an additional classification parameter.Older products show low alkali content than the younger ones. This is related with the increasing of incompatible elements, such as uranium and thorium, in the younger products.Principal components and hierarchical clustering statistical analyses have provided additional information on sample differentiation and similarities.     

Raman spectroscopy and polarization: Selected case studies

We show, through several selected case studies, the potential benefits that can be obtained by controlling the polarization states of the exciting and scattered radiations in a Raman scattering experiment. When coupled with polarization control, Raman spectroscopy is thus capable of providing extra information on the structural properties of the materials under investigation. The experimental examples presented in this work are taken from the area of both conventional, i.e., far-field, as well as from near-field Raman spectroscopy. They cover topics such as the stress tensor measurement in strained semiconductor structures, the vibration mode assignment in pentacene thin films and the Raman scattering tensor determination from near-field measurements on azobenzene monolayers. The basic theory necessary for modelling the far- and near-field polarized Raman responses is also given and the model efficiency is illustrated on the experimental data.     

光学薄膜参数椭偏测量中的多变量误差分析

本文采用多变量的误差分析方法给出光学薄膜参数对于椭偏角ψ,反射率R,入射角和吸收薄膜厚度的误差因子公式。由此便可确定出光学参数的测量精度。本文还利用误差因子与薄膜折射率,薄膜厚度和入射角的关系曲线,讨论了最佳测量条件和测量结构的选取。并且指出,在同时确定两个或多个未知参数时,不能只由可测量量随某一个参数变化的灵敏来讨论和确定此参数的测量精度。     

Modeling of environmentally significant interfaces: Two case studies

When some parameters cannot be easily measured experimentally, mathematical models can often be used to deconvolute or interpret data collected on complex systems, such as those characteristic of many environmental problems. These models can help quantify the contributions of various physical or chemical phenomena that contribute to the overall behavior, thereby enabling the scientist to control and manipulate these phenomena, and thus to optimize the performance of the material or device. In the first case study presented here, a model is used to test the hypothesis that oxygen interactions with hydrogen on the catalyst particles of solid oxide fuel cell anodes can sometimes occur a finite distance away from the triple phase boundary (TPB), so that such reactions are not restricted to the TPB as normally assumed. The model may help explain a discrepancy between the observed structure of SOFCs and their performance. The second case study develops a simple physical model that allows engineers to design and control the sizes and shapes of mesopores in silica thin films. Such pore design can be useful for enhancing the selectivity and reactivity of environmental sensors and catalysts. This paper demonstrates the mutually beneficial interactions between experiment and modeling in the solution of a wide range of problems.     

Determination of the provenance of medieval silver coins: potential and limitations of x‐ray analysis using photons,electrons or protons

One hundred and fifty seven ‘Tiroler Kreuzer’, a medieval currency from the county of Tyrol/Austria, were analysed in order to determine their place of mintage. The silver coins were produced during the 15th century in the mints of Merano (South Tyrol) and Hall (North Tyrol) but they have no marks or punches which would allow a clear distinction. Energy‐dispersive x‐ray fluorescence analysis (EDXRF) was applied without sampling in order to determine the silver contents and also minor (Cu, Pb, Bi) and trace elements (Fe, Au, Hg, Ni). Owing to corrosion processes, which changed the chemical composition of the surfaces of the coins, investigations of cross‐sections were necessary using energy‐dispersive x‐ray microanalysis in a scanning electron microscope (SEM/EDX) to determine the stage of corrosion and the Ag concentration of the core of the coins. The results showed differences of up to 50% between the composition of the core and the surface. Finally, proton‐induced x‐ray emission (PIXE) at an external proton beam was applied, in order to detect also Ni, an element which could not be measured by either EDXRF or SEM/EDX in the ppm range. The data show a clear difference in the Ni content between the coins from Merano (～0.1% Ni) and Hall (～0.01% Ni). Copyright © 2003 John Wiley & Sons, Ltd.     

Multivariate analysis of fMRI time series: classification and regression of brain responses using machine learning

Machine learning and pattern recognition techniques are being increasingly employed in functional magnetic resonance imaging (fMRI) data analysis. By taking into account the full spatial pattern of brain activity measured simultaneously at many locations, these methods allow detecting subtle, non-strictly localized effects that may remain invisible to the conventional analysis with univariate statistical methods. In typical fMRI applications, pattern recognition algorithms "learn" a functional relationship between brain response patterns and a perceptual, cognitive or behavioral state of a subject expressed in terms of a label, which may assume discrete (classification) or continuous (regression) values. This learned functional relationship is then used to predict the unseen labels from a new data set ("brain reading"). In this article, we describe the mathematical foundations of machine learning applications in fMRI. We focus on two methods, support vector machines and relevance vector machines, which are respectively suited for the classification and regression of fMRI patterns. Furthermore, by means of several examples and applications, we illustrate and discuss the methodological challenges of using machine learning algorithms in the context of fMRI data analysis.     

Multivariate analysis of spatially heterogeneous phase synchronisation in complex systems: application to self-organised control of material flows in networks

Networks of interacting components are a class of complex systems that has attracted considerable interest over the last decades. In particular, if the dynamics of the autonomous components is characterised by an oscillatory behaviour, different types of synchronisation can be observed in dependence on the type and strength of interactions. In this contribution, we study the transition from non-synchronised to synchronised phase dynamics in complex networks. The most common approach to quantify the degree of phase synchronisation in such systems is the consideration of measures of phase coherence which are averaged over all pairs of interacting components. However, this approach implicitly assumes a spatially homogeneous synchronisation process, which is typically not present in complex networks. As a potential alternative, two novel methods of multivariate phase synchronisation analysis are considered: synchronisation cluster analysis (SCA) and the linear variance decay (LVD) dimension method. The strengths and weaknesses of the traditional as well as both new approaches are briefly illustrated for a Kuramoto model with long-range coupling. As a practical application, we study how spatial heterogeneity influences the transition to phase synchronisation in traffic networks where intersecting material flows are subjected to a self-organised decentralised control. We find that the network performance and the degree of phase synchronisation are closely related to each other and decrease significantly in the case of structural heterogeneities. The influences of the different parameters of our control approach on the synchronisation process are systematically studied, yielding a sequence of Arnold tongues which correspond to different locking modes.     

Multivariate data analysis for depth resolved chemical classification and quantification of sulfur in SNMS

The quantification of elements in quadrupole based SNMS is hampered by superpositions of atomic and cluster signals. Moreover, the conventional SNMS data evaluation employs only atomic signals to determine elemental concentrations, which not allows any chemical specifications of the determined elements. Improvements in the elemental quantification and additional chemical information can be obtained from kinetic energy analysis and the inclusion of molecular signals into mass spectra evaluation. With the help of multivariate data analysis techniques, the combined information is used for the first time for a quantitative and chemically distinctive determination of sulfur. The kinetic energy analysis, used to solve the interference of sulfur with O₂ at masses 32-34 D, turned out to be highly important for the new type of evaluation.     

EDXRF analysis of metal artefacts from the grave goods of the Royal Tomb 14 of Sipán,Peru

Several metallic sheets (about 1 mm thick) from the grave goods of the Royal Tomb 14 (Sipán, Peru) were characterised by energy dispersive X‐ray fluorescence analysis, using both a portable instrument and a capillary collimated spectrometer to investigate details, and micro‐Raman spectroscopy. The samples, belonging to the clothing of the warrior priest, resulted composed of thin copper sheets or tumbaga (natural alloy of copper, silver and gold). They were unearthed covered with typical green patina, formed during their long burial and characterised mainly by copper minerals, such as malachite, atacamite and magnetite identified with micro‐Raman spectroscopy. Due to deterioration of the original alloy, the artefacts analyzed in this work were rather fragile and could not resist hard polishing aimed at cleaning off corrosion products. So a non‐destructive qualitative EDXRF analysis was performed to identify the elemental composition of the metal alloy and a quantitative estimation was made applying the fundamental parameter method. The presence of superficial patina layer and the non‐homogeneous composition was also taken into account during calculation. The data obtained, compared to published results from several artefacts found in the nearby tombs, have been treated with a hierarchical statistic analysis. Copyright © 2011 John Wiley & Sons, Ltd.