Mean square displacement for a discrete centroid model of cell motion

The mean square displacement (MSD) is an important statistical measure on a stochastic process or a trajectory. In this paper we find an approximation to the mean square displacement for a model of cell motion. The model is a discrete-time jump process which approximates a force-based model for cell motion. In cell motion, the mean square displacement not only gives a measure of overall drift, but it is also an indicator of mode of transport. The key to finding the approximation is to find the mean square displacement for a subset of the state space and use it as an approximation for the entire state space. We give some intuition as to why this is an unexpectedly good approximation. A lower bound and upper bound for the mean square displacement are also given. We show that, although the upper bound is far from the computed mean square displacement, in rare cases the large displacements are approached.

Mutual Information-Based Non-Local Total Variation Denoiser for Low-Dose Cone-Beam Computed Tomography

Conventional non-local total variation (NLTV) approaches use the weight of a non-local means (NLM) filter, which degrades performance in low-dose cone-beam computed tomography (CBCT) images generated with a low milliampere-seconds (mAs) parameter value because a local patch used to determine the pixel weights comprises noisy-damaged pixels that reduce the similarity between corresponding patches. In this paper, we propose a novel type of NLTV based on a combination of mutual information (MI): MI-NLTV. It is based on a statistical measure for a similarity calculation between the corresponding bins of non-local patches vs. a reference patch. The weight is determined in terms of a statistical measure comprising the MI value between corresponding non-local patches and the reference-patch entropy. The MI-NLTV denoising process is applied to CBCT images generated by the analytical reconstruction algorithm using a ray-driven backprojector (RDB). The MI-NLTV objective function is minimized based on the steepest gradient descent optimization to augment the difference between a real structure and noise, cleaning noisy pixels without significant loss of the fine structure and details that remain in the reconstructed images. The proposed method was evaluated using patient data and actual phantom measurement data acquired with lower mAs. The results show that integrating the RDB further enhances the MI-NLTV denoising-based analytical reconstruction algorithm to achieve a higher CBCT image quality when compared with those generated by NLTV denoising-based approach, with an average of 15.97% higher contrast-to-noise ratio, 2.67% lower root mean square error, 0.12% lower spatial non-uniformity, 1.14% higher correlation, and an average of 18.11% higher detectability index. These quantitative results indicate that the incorporation of MI makes the NLTV more stable and robust than the conventional NLM filter for low-dose CBCT imaging. In addition, achieving clinically acceptable CBCT image quality despite low-mAs projection acquisition can reduce the burden on common online CBCT imaging, improving patient safety throughout the course of radiotherapy.

Effect of the solvent on the extraction of polyphenols from distillery stillage and on their antioxidant activity

The increase in the costs of storage and disposal of post-production residues has resulted in the search for new directions for their recycling, which is closely related to the necessity of protecting the natural environment and promoting a circular economy. Moreover, the apparent interest shown by the food market in raw materials with high antioxidant activity implies an increasing use of by-products. The objective of the study was to determine the effect of the type and concentration of the solvent on the efficiency of extracting polyphenols from distillery stillage as well as their antioxidant activity by using several solvents: methanol:water (70:30 v/v), methanol:water (100:0 v/v), ethanol:water (70:30 v/v) or ethanol:water (100:0 v/v). The DPPH radical method was used to determine the antioxidant activity of the obtained extracts. The normalised variable (NV) and statistical measure (MS) were determined, based on which the effectiveness of the solvents was evaluated. The highest polyphenolic content and the antioxidant activity were obtained by using ethanol:water (70:30 v/v) as a solvent in the extraction of polyphenolic compounds from distillery stillage.

Sports Diplomacy Research in Poland, Czechia and Slovakia. Emerging Field of Study?

Sport is a complex phenomenon that academics across many social sciences are focusing on. The interest in sports has been observable for a long time by historians, anthropologists and sociologists. Scientists in the field of international relations are no exception. A typical way sport is studied in international relations is by paying attention to sports diplomacy. The study of sports diplomacy has become a pretty popular part of the research since the second decade of the 21st century and it is possible to observe the dominance of the authors from the American and British universities in sports diplomacy research. Based on the Web of Science dataset, at first sight, the study of sports diplomacy is not seen as a popular field of research in the Central European countries. On the other hand, this statistical measure does not describe a complex situation of what the sports diplomacy research looks like, how it is formed or how it reflects the thinking of the politicians on national public/sports diplomacy. Thus, the article aims to map sports diplomacy research in the Central European states, specifically in Poland, Czechia and Slovakia.

Bias in miRNA enrichment analysis related to gene functional annotations

Motivation: miRNA functional enrichment is a type of analysis that is used to predict which biological functions may be affected by a group of miRNAs or validate whether a list of dysreg- ulated miRNAs are linked to a diseased state. The standard method for functional enrichment analysis uses the hypergeometric distribution to produce p-values, depicting the strength of the association between a group of miRNAs and a biological function. However, in 2015, it was shown that this approach suffers from a bias related to miRNA targets produced by target prediction algorithms and a new randomization test was proposed. Results: In this paper, we demonstrate the existence of another underlying bias which affects gene annotation data sets; additionally, we show that the statistical measure used for the estab- lished randomization test is not sensitive enough to account for it. For this reason, we propose the use of an alternative statistical measure, the "two-sided overlap", and we show that it is able to alleviate the aforementioned issue. Finally, we develop BUFET2, a miRNA enrichment analysis tool that leverages this measure (along with the old one); it is based on BUFET, a fast and scalable implementation of the established randomization test. Availability and Implementation: BUFET2 is written in C++ and is packaged with a Python wrapper script that facilitates experiment execution. Moreover, BUFET2 also comes pre-packaged in a Linux Docker image published on Docker Hub, thus eliminating the need for code compilation. Finally, BUFET2 is also publicly available to execute through a REST API. All datasets used in the experiments throught this paper are openly accessible on Zenodo (https://doi.org/10.5281/zenodo.5175819).

A statistical measure for the skewness of X chromosome inactivation for quantitative traits and its application to the MCTFR data

Background X chromosome inactivation (XCI) is that one of two chromosomes in mammalian females is silenced during early development of embryos. There has been a statistical measure for the degree of the skewness of XCI for qualitative traits. However, no method is available for such task at quantitative trait loci. Results In this article, we extend the existing statistical measure for the skewness of XCI for qualitative traits, and the likelihood ratio, Fieller’s and delta methods for constructing the corresponding confidence intervals, and make them accommodate quantitative traits. The proposed measure is a ratio of two linear regression coefficients when association exists. Noting that XCI may cause variance heterogeneity of the traits across different genotypes in females, we obtain the point estimate and confidence intervals of the measure by incorporating such information. The hypothesis testing of the proposed methods is also investigated. We conduct extensive simulation studies to assess the performance of the proposed methods. Simulation results demonstrate that the median of the point estimates of the measure is very close to the pre-specified true value. The likelihood ratio and Fieller’s methods control the size well, and have the similar test power and accurate coverage probability, which perform better than the delta method. So far, we are not aware of any association study for the X-chromosomal loci in the Minnesota Center for Twin and Family Research data. So, we apply our proposed methods to these data for their practical use and find that only the rs792959 locus, which is simultaneously associated with the illicit drug composite score and behavioral disinhibition composite score, may undergo XCI skewing. However, this needs to be confirmed by molecular genetics. Conclusions We recommend the Fieller’s method in practical use because it is a non-iterative procedure and has the similar performance to the likelihood ratio method.

Dynamics of size classes of cities in Poland in 1950–2018

The study aims to present variability in the population of individual size classes of Polish cities in 1950-2018, its determinants and consequences for the formation of the settlement system. The application of quartiles as the basic statistical measure allowed identifying which parts of particular size classes of cities had the greatest impact (progressively or regressively) on changes in the settlement system. In this respect, strong dynamics of the upper quartile of Polish cities, lasting until the end of the 1970s, becomes apparent. In the 1980s, the dynamics of the upper quartile of large cities showed a shift during development waves in comparison to the culmination of these waves for medium-sized cities. However, since the end of the 1980s, there has been an increasing role of the lower quartile in determining the direction of changes in the size structure of cities, especially in medium and small cities.