Independent component analysis combined with Laplace inversion of spectrally resolved spin-alignment echo/T 1 3D 7Li NMR of superionic Li10GeP2S12

The use of independent component analysis (ICA) for the analysis of two-dimensional (2D) spin-alignment echo–T 1 7Li NMR correlation data with transient echo detection as a third dimension is demonstrated for the superionic conductor Li10GeP2S12 (LGPS). ICA was combined with Laplace inversion, or discrete inverse Laplace transform (ILT), to obtain spectrally resolved 2D correlation maps. Robust results were obtained with the spectra as well as the vectorized correlation maps as independent components. It was also shown that the order of ICA and ILT steps can be swapped. While performing the ILT step before ICA provided better contrast, a substantial data compression can be achieved if ICA is executed first. Thereby the overall computation time could be reduced by one to two orders of magnitude, since the number of computationally expensive ILT steps is limited to the number of retained independent components. For LGPS, it was demonstrated that physically meaningful independent components and mixing matrices are obtained, which could be correlated with previously investigated material properties yet provided a clearer, better separation of features in the data. LGPS from two different batches was investigated, which showed substantial differences in their spectral and relaxation behavior. While in both cases this could be attributed to ionic mobility, the presented analysis may also clear the way for a more in-depth theoretical analysis based on numerical simulations. The presented method appears to be particularly suitable for samples with at least partially resolved static quadrupolar spectra, such as alkali metal ions in superionic conductors. The good stability of the ICA analysis makes this a prospect algorithm for preprocessing of data for a subsequent automatized analysis using machine learning concepts.

Independent component analysis combined with Laplace inversion of spectrally resolved spin-alignment echo/T1 3D 7Li NMR of superionic Li10GeP2S12

The use of independent component analysis (ICA) for the analysis of two-dimensional (2D) spin-alignment echo--T1 7Li NMR correlation data with transient echo detection as a third dimension is demonstrated for the superionic conductor Li10GeP2S12 (LGPS). ICA was combined with Laplace inversion, or discrete inverse Laplace transform (ILT), to obtain spectrally resolved 2D correlation maps. Robust results were obtained with the spectra as well as the vectorized correlation maps as independent components. It was also shown that the order of ICA and ILT steps can be swapped. While performing the ILT step before ICA provided better contrast, a substantial data compression can be achieved if ICA is executed first. Thereby the overall computation time could be reduced by one to two orders of magnitude, since the number of computationally expensive ILT steps is limited to the number of retained independent components. For LGPS, it was demonstrated that physically meaningful independent components and mixing matrices are obtained, which could be correlated with previously investigated material properties yet provided a clearer, better separation of features in the data. LGPS from two different batches was investigated, which showed substantial differences in their spectral and relaxation behavior. While in both cases this could be attributed to ionic mobility, the presented analysis may also clear the way for a more in-depth theoretical analysis based on numerical simulations. The presented method appears to be particularly suitable for samples with at least partially resolved static quadrupolar spectra, such as alkali metal ions in superionic conductors. The good stability of the ICA analysis makes this a prospect algorithm for preprocessing of data for a subsequent automatized analysis using machine learning concepts.

Risk Analysis of the Copula Dependent Aggregate Discounted Claims with Weibull Inter-Arrival Time

We model the recursive moments of aggregate discounted claims, assuming the inter-claim arrival time follows a Weibull distribution to accommodate overdispersed and underdispersed data set. We use a copula to represent the dependence structure between the inter-claim arrival time and its subsequent claim amount. We then use the Laplace inversion via the Gaver-Stehfest algorithm to solve numerically the first and second moments, which takes the form of a Volterra integral equation (VIE). We compute the average and variance of the aggregate discounted claims under the Farlie-Gumbel-Morgenstern (FGM) copula and conduct a sensitivity analysis under various Weibull inter-claim parameters and claim-size parameters. The comparison between the equidispersed, overdispersed and underdispersed counting processes shows that when claims arrive at times that vary more than is expected, insured lives can expect to pay higher premium, and vice versa for the case of claims arriving at times that vary less than expected. Upon comparing the Weibull risk process with an equivalent Poisson process, we also found that copulas with a wider range of dependency parameter such as the Frank and Heavy Right Tail (HRT), have a greater impact on the value of moments as opposed to modeling under FGM copula with weak dependence structure.

A Squid-Detected NMR Relaxation Study of Banana Fruit Ripening

HighlightsMeasurements of relaxation times in intact banana at micro-Tesla field was achieved.Bulk spin-spin relaxation time highly correlated with best descriptors of banana ripening.A basis for quasi-continuous distribution of spin-spin relaxation in banana was given.Abstract. Achieving fast, low-cost, and non-destructive internal quality testing techniques in the horticultural industry is a challenge. Developing techniques such as ultra-low field nuclear magnetic resonance (NMR) is a promising solution. Banana is a fast ripening fruit, which undergoes many changes in quality characteristics during ripening, and was chosen as a fit choice for extensive fruit quality study by NMR. A commercial NMR system using a superconducting quantum interference device (SQUID) as a sensor and operating at 100µT was used to measure changes that occurred in banana fruit during ripening. The longitudinal and transverse relaxation times (T1 and T2, respectively), were measured on fruit samples progressively drawn from a larger batch under storage. Physico-chemical attributes such as total soluble solids (TSS), titratable acidity (TA), pH, and color parameters were measured and used as reference measurements. Statistical analysis using cross-correlation, linear regression, analysis of variance (ANOVA), and principal components analysis (PCA) were performed to probe the relationships between various quality attributes. T1 showed high correlations with total soluble solids (R = 0.84), sugar:acid ratio (R = 0.84) and color parameters (R from 0.49 to 0.88). T2, on the other hand, was most highly correlated to pH (R = 0.76) but also had a statistically significant but negative correlation with Ri (-0.58 at p <0.05). PCA results separated the first day from the remaining days of the ripening process and the overall variation was mostly explained by color attributes (a* and h), T1, TSS, and TSS/TA. During seven days of ripening in storage, the trend of change in the peel color of banana was best described by L*, a*, h and total color difference (TCD). The index of ripening, Ri, defined based on the apparent change in peel color was highly correlated to TSS, TSS/TA, L*, a*, h, TCD, and T1. The strong similarity between the evolution of T1 and the most commonly approved characteristics of banana ripening suggest that T1 has great potential for characterizing the ripening process of banana. However, an investigation of the full metabolic profile of banana during ripening would provide an understanding of the link between NMR relaxation and ripening characteristics. A distribution of T1 relaxation time of intact banana fruit at the micro-Tesla field was successfully generated using Laplace inversion. A suitable framework of T1-domain based studies on banana ripening also applicable to other fruit was discussed; it would provide a comprehensive understanding of structural changes and water mobility that occur in ripening banana. The SQUID-detected ultra-low field NMR used here shows promise as a tool for probing the quality of intact banana fruit. Keywords: Banana quality, Laplace inversion, Relaxometry, SQUID-NMR.

GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model

In this paper, we consider the Wiener–Poisson risk model, which consists of a Wiener process and a compound Poisson process. Given the discrete record of observations, we use a threshold method and a regularized Laplace inversion technique to estimate the survival probability. In addition, we also construct an estimator for the distribution function of jump size and study its consistency and asymptotic normality. Finally, we give some simulations to verify our results.