Classification of Hungarian medieval silver coins using x-ray fluorescent spectroscopy and multivariate data analysis

A set of silver coins from the collection of Déri Museum Debrecen (Hungary) was examined by X-ray fluorescent elemental analysis with the aim to assign the coins to different groups with the best possible precision based on the acquired chemical information and to build models, which arrange the coins according to their historical periods. Results: Principal component analysis, linear discriminant analysis, partial least squares discriminant analysis, classification and regression trees and multivariate curve resolution with alternating least squares were applied to reveal dominant pattern in the data and classify the coins into several groups. We also identified those chemical components, which are present in small percentages, but are useful for the classification of the coins. With the coins divided into two groups according to adequate historical periods, we have obtained a correct classification (76-78%) based on the chemical compositions. Conclusions: X-ray fluorescent elemental analysis together with multivariate data analysis methods is suitable to group medieval coins according to historical periods. Keywords: X-ray fluorescence spectroscopy, Multivariate techniques, Coin, Silver, Middle age

Binary superlattice design by controlling DNA-mediated interactions

Most binary superlattices created using DNA functionalization or other approaches rely on particle size differences to achieve compositional order and structural diversity. Here we study two-dimensional (2D) assembly of DNA-functionalized micron-sized particles (DFPs), and employ a strategy that leverages the tunable disparity in interparticle interactions, and thus enthalpic driving forces, to open new avenues for design of binary superlattices that do not rely on the ability to tune particle size (i.e., entropic driving forces). Our strategy employs tailored blends of complementary strands of ssDNA to control interparticle interactions between micron-sized silica particles in a binary mixture to create compositionally diverse 2D lattices. We show that the particle arrangement can be further controlled by changing the stoichiometry of the binary mixture in certain cases. With this approach, we demonstrate the abil- ity to program the particle assembly into square, pentagonal, and hexagonal lattices. In addition, different particle types can be compositionally ordered in square checkerboard and hexagonal - alternating string, honeycomb, and Kagome arrangements.Comment: 4 figures in the main text. 5 figures in the supplementary informatio

Dictionary-based Tensor Canonical Polyadic Decomposition

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Symmetric Tensor Decomposition by an Iterative Eigendecomposition Algorithm

We present an iterative algorithm, called the symmetric tensor eigen-rank-one iterative decomposition (STEROID), for decomposing a symmetric tensor into a real linear combination of symmetric rank-1 unit-norm outer factors using only eigendecompositions and least-squares fitting. Originally designed for a symmetric tensor with an order being a power of two, STEROID is shown to be applicable to any order through an innovative tensor embedding technique. Numerical examples demonstrate the high efficiency and accuracy of the proposed scheme even for large scale problems. Furthermore, we show how STEROID readily solves a problem in nonlinear block-structured system identification and nonlinear state-space identification

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Application of Terahertz Technology in Biomolecular Analysis and Medical Diagnosis

Terahertz technology is a nondestructive technique, which has progressed significantly in the scientific research and gains highly attention in the analysis of biological molecular, cellular, tissues and organs. In this decade, some studies were reported on the application of terahertz technology in medical testing and diagnosis. Here, we summarize the terahertz characters, terahertz spectroscopy, and terahertz imaging technology combined with chemometrics. This chapter focuses on introducing the research progress on analyzing the tissues of cancers using terahertz spectroscopy and terahertz imaging technology. Furthermore, the problems should be solved, and development directions of terahertz spectroscopy and terahertz imaging technology are discussed