Ball: An R package for detecting distribution difference and association in metric spaces

The rapid development of modern technology facilitates the appearance of numerous unprecedented complex data which do not satisfy the axioms of Euclidean geometry, while most of the statistical hypothesis tests are available in Euclidean or Hilbert spaces. To properly analyze the data of more complicated structures, efforts have been made to solve the fundamental test problems in more general spaces. In this paper, a publicly available R package Ball is provided to implement Ball statistical test procedures for K-sample distribution comparison and test of mutual independence in metric spaces, which extend the test procedures for two sample distribution comparison and test of independence. The tailormade algorithms as well as engineering techniques are employed on the Ball package to speed up computation to the best of our ability. Two real data analyses and several numerical studies have been performed and the results certify the powerfulness of Ball package in analyzing complex data, e.g., spherical data and symmetric positive matrix data

Raman piezospectroscopic evaluation of intergrowth ferroelectric polycrystalline ceramic in biaxial bending configuration

The piezospectroscopic (PS) effect was studied in an intergrowth bismuth layer-structure ferroelectricceramicBi₅TiNbWO₁₅ according to a micro-Raman spectroscopic evaluation. By using a ball-on-ring flexure configuration, a biaxial stress was generated in a Bi₅TiNbWO₁₅ plate-like specimen and in situ collected Raman spectra were acquired and analyzed under several loading conditions. As the observed spectral line contained signals arising from the whole illuminated in-depth region, the laser probe information was deconvoluted (by means of an in-depth probe response function obtained according to the defocusing method) in order to deduce biaxial PS coefficients for the three Raman bands of Bi₅TiNbWO₁₅ located at 763, 857, and 886 cm−1, respectively. The biaxial PS coefficients of these bands were derived to be −1.74±0.16, −2.51±0.16, and −2.64±0.31 cm⁻¹/GPa, respectively, and should be referred to the c axis of the Bi5TiNbWO15 crystal

Nonparametric statistical inference via metric distribution function in metric spaces

The distribution function is essential in statistical inference and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces and are no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the concept of the distribution function in a more general space to meet emerging needs. Note that the linearity allows us to use hypercubes to define the distribution function in a Euclidean space. Still, without the linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce a class of metric distribution functions through the metric only. We overcome this challenging step by proving the correspondence theorem and the Glivenko-Cantelli theorem for metric distribution functions in metric spaces, laying the foundation for conducting rational statistical inference for metric space-valued data. Then, we develop a homogeneity test and a mutual independence test for non-Euclidean random objects and present comprehensive empirical evidence to support the performance of our proposed methods. Supplementary materials for this article are available online

MicroRNA Regulation and Tissue-Specific Protein Interaction Network

BACKGROUND: 'Fine-tuning' of protein abundance makes microRNAs (miRNAs) pervasively implicated in human biology. Although targeting many mRNAs endows the power of single miRNA to regulate complex biological processes, its functional roles in a particular tissue will be inevitably restricted because only a subset of its target genes is expressed. METHODS: Here, we analyze the characteristics of miRNA regulation upon target genes according to tissue-specific gene expression by constructing tissue-specific protein interaction networks for ten main types of tissues in the human body. RESULTS: Commonly expressed proteins are under more intensive but lower-cost miRNAs control than proteins with the tissue-specific expression. MiRNAs that target more commonly expressed genes usually regulate more tissue-specific genes. This is consistent with the previous finding that tissue-specific proteins tend to be functionally connected with commonly expressed proteins. But to a particular miRNA such a balance is not invariable among different tissues implying diverse tissue regulation modes executed by miRNAs. CONCLUSION: These results suggest miRNAs that interact with more commonly expressed genes can be expected to play important tissue-specific roles

Ball: An R Package for Detecting Distribution Difference and Association in Metric Spaces

The rapid development of modern technology has created many complex datasets in non-linear spaces, while most of the statistical hypothesis tests are only available in Euclidean or Hilbert spaces. To properly analyze the data with more complicated structures, efforts have been made to solve the fundamental test problems in more general spaces (Lyons 2013; Pan, Tian, Wang, and Zhang 2018; Pan, Wang, Zhang, Zhu, and Zhu 2020). In this paper, we introduce a publicly available R package Ball for the comparison of multiple distributions and the test of mutual independence in metric spaces, which extends the test procedures for the equality of two distributions (Pan et al. 2018) and the independence of two random objects (Pan et al. 2020). The Ball package is computationally efficient since several novel algorithms as well as engineering techniques are employed in speeding up the ball test procedures. Two real data analyses and diverse numerical studies have been performed, and the results certify that the Ball package can detect various distribution differences and complicated dependencies in complex datasets, e.g., directional data and symmetric positive definite matrix data

Polarized Raman analysis of the molecular rearrangement and residual strain on the surface of retrieved polyethylene tibial plates

The response to applied strain of EtO-sterilized and gamma-irradiated polyethylene materials belonging to tibial inserts has been studied by polarized Raman spectroscopy. Initial calibrations on as-received samples from three different makers were employed to clarify the rearrangement of molecular chains under strain, expressed in terms of Euler angular displacements in space and orientation distribution functions. This body of information was then applied to a quantitative analysis of four tibial inserts (from the same three makers of the unused samples) retrieved after in vivo exposures ranging between 7 months and 5 years 8 months. The main results of the Raman analysis can be summarized as follows: (i) gamma-irradiated samples experienced lower texturing on the molecular scale compared to EtO-sterilized samples, likely due to a higher strain recovery capability; and (ii) independent of sterilization method, the amount of plastic strain was mainly developed early after in vivo implantation, whereby out-of-plane molecules rotated under load onto planes parallel to the sample surface until saturation of angular displacements was reached. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

Innovative tribometer for in situ spectroscopic analyses of wear mechanisms and phase transformation in ceramic femoral heads

The literature on tribological assessments of artificial hip joints usually focuses on correlations between joint composition, size, and specific wear rates, but conspicuously ignores the physical aspects behind the occurrence of degradation mechanisms of friction and wear. Surface degradation in artificial joints occurs because of increases in temperature and local exacerbation of contact stresses inside the moving contact as a consequence of physical and chemical modifications of the sliding surfaces. This article reports about the development of a new pin-on-ball spectroscopy-assisted tribometer device that enables investigating also physical rather than merely engineering aspects of wear processes using in situ Raman and fluorescence techniques. This innovative tribometer is designed to bring about, in addition to conventional tribological parameters, also information of temperature, stress and phase transformations in the femoral heads as received from the manufacturer Raman and fluorescence spectra at the point of sliding contact are recorded durilng reciprocating hard-on-hard dry-sliding tests. Preliminary results were collected on two different commercially available ceramic-on-ceramic hip joint bearing couples, made of monolithic alumina and alumina-zirconia composites. Although the composite couple showed direct evidence of tetragonal-to-monoclinic phase transformation, which enhanced the coefficient of friction, the specific wear rate was significantly lower than that of the monolithic one (i.e., by a factor 2.63 and 4.48 on the pin and head side, respectively). In situ collected data compared to ex situ analyses elucidated the surface degradation processes and clarified the origin for the higher wear resistance of the composite as compared to the monolithic couple. (C) 2013 Elsevier Ltd. All rights reserved

Spectrally resolved microprobe cathodoluminescence of intergrowth Bi₅ˍₓLaₓTiNbWO₁₅ ferroelectrics

Spectrally resolved cathodoluminescence measurements of Bi₅ˍₓLaₓTiNbWO₁₅(x=0–1.50) ceramics at room temperature showed three distinct luminescence bands located at about 380, 502, and 660nm, respectively, which were tentatively assigned to F+ center, oxygen vacancy-related defect and octahedron structure-related luminescence center, respectively. These assignments could be made in light of electron irradiation experiments with different exposure times. Bands related to oxygen vacancies were clearly enhanced by lanthanum doping, indicating that charge compensation occurred by the substitution of Bi for La3+ in perovskitelike structured intergrowth ferroelectrics. We observed that, for contents of La³⁺ x>0.75, La³⁺ ions entered the [Bi₂O₂]²⁺ layer according to a doping mechanism which is briefly discussed in this letter.This work was supported by the Ministry of Sciences and Technology of China through 973-project 2002CB613307 and National Natural Science Foundation of China NSFC No. 50572113