Injury risk functions for the four primary knee ligaments

The purpose of this study was to develop injury risk functions (IRFs) for the anterior and posterior cruciate ligaments (ACL and PCL, respectively) and the medial and lateral collateral ligaments (MCL and LCL, respectively) in the knee joint. The IRFs were based on post-mortem human subjects (PMHSs). Available specimen-specific failure strains were supplemented with statistically generated failure strains (virtual values) to accommodate for unprovided detailed experimental data in the literature. The virtual values were derived from the reported mean and standard deviation in the experimental studies. All virtual and specimen-specific values were thereafter categorized into groups of static and dynamic rates, respectively, and tested for the best fitting theoretical distribution to derive a ligament-specific IRF. A total of 10 IRFs were derived (three for ACL, two for PCL, two for MCL, and three for LCL). ACL, MCL, and LCL received IRFs in both dynamic and static tensile rates, while a sufficient dataset was achieved only for dynamic rates of the PCL. The log-logistic and Weibull distributions had the best fit (p-values: >0.9, RMSE: 2.3%-4.7%) to the empirical datasets for all the ligaments. These IRFs are, to the best of the authors' knowledge, the first attempt to generate injury prediction tools based on PMHS data for the four knee ligaments. The study has summarized all the relevant literature on PHMS experimental tensile tests on the knee ligaments and utilized the available empirical data to create the IRFs. Future improvements require upcoming experiments to provide comparable testing and strain measurements. Furthermore, emphasis on a clear definition of failure and transparent reporting of each specimen-specific result is necessary.

On the Distribution of the Information Density of Gaussian Random Vectors: Explicit Formulas and Tight Approximations

Based on the canonical correlation analysis, we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as a general formula to calculate the central moments. Using the general results, we give closed-form expressions of the PDF and CDF and explicit formulas of the central moments for important special cases. Furthermore, we derive recurrence formulas and tight approximations of the general series representations, which allow efficient numerical calculations with an arbitrarily high accuracy as demonstrated with an implementation in Python publicly available on GitLab. Finally, we discuss the (in)validity of Gaussian approximations of the information density.

Two-sample t α -test for testing hypotheses in small-sample experiments

It has been reported that about half of biological discoveries are irreproducible. These irreproducible discoveries were partially attributed to poor statistical power. The poor powers are majorly owned to small sample sizes. However, in molecular biology and medicine, due to the limit of biological resources and budget, most molecular biological experiments have been conducted with small samples. Two-sample t-test controls bias by using a degree of freedom. However, this also implicates that t-test has low power in small samples. A discovery found with low statistical power suggests that it has a poor reproducibility. So, promotion of statistical power is not a feasible way to enhance reproducibility in small-sample experiments. An alternative way is to reduce type I error rate. For doing so, a so-called t _α -test was developed. Both theoretical analysis and simulation study demonstrate that t _α -test much outperforms t-test. However, t _α -test is reduced to t-test when sample sizes are over 15. Large-scale simulation studies and real experiment data show that t _α -test significantly reduced type I error rate compared to t-test and Wilcoxon test in small-sample experiments. t _α -test had almost the same empirical power with t-test. Null p-value density distribution explains why t _α -test had so lower type I error rate than t-test. One real experimental dataset provides a typical example to show that t _α -test outperforms t-test and a microarray dataset showed that t _α -test had the best performance among five statistical methods. In addition, the density distribution and probability cumulative function of t _α -statistic were given in mathematics and the theoretical and observed distributions are well matched.

Reparameterization of the Weibull model for practical uses in food science

The reparameterization of the Weibull cumulative distribution function and its survival function was performed to obtain meaningful parameters in food and biological sciences such as the lag phase (λ), the maximum rate ( μ max ${\mu _{{\rm{max}}}}$ ), and the maximum increase/decrease of the function (A). The application of the Lambert function was crucial in order to achieve an explicit mathematical solution. Since the reparameterized model is applicable only when the shape parameter (α) is greater than one, the Weibull model was modified with the introduction of a new parameter ( μ β ${\mu _\beta }$ ) that represents the model rate at time β (scale parameter). All models were applied to literature data on food technology and microbiology topics: Microbial growth, thermal microbial inactivation, thermal degradation kinetics, and particle size distributions. The Weibull model and the reparameterized versions showed identical fitting performance in terms of coefficient of determination, residual mean standard error, values of residuals, and estimated values of the parameters. Some faults in the datasets used in this study permitted to re-mark the criticality of a good experimental plan when data modeling is approached. The parameter μ β ${\mu _\beta }$ resulted in an interesting new rate parameter that is not correlated with the scale parameter ( | r ¯ | $| {\bar{r}} |$ = 0.64 ± 0.37) and highly correlated with the shape parameter ( | r ¯ | $| {\bar{r}} |$ = 0.90 ± 0.11). Also, the reparameterization of the Weibull probability density function was performed by using both the standard and new parameters and applied to experimental data and gave useful information from the distribution curve, such as the value of the mode ( μ max ${\mu _{{\rm{max}}}}$ ) and a measure of the curve skewness (λ).

Multivariate Analysis of Concrete Image Using Thermography and Edge Detection

With the growing demand for structural health monitoring system applications, data imaging is an ideal method for performing regular routine maintenance inspections. Image analysis can provide invaluable information about the health conditions of a structure’s existing infrastructure by recording and analyzing exterior damages. Therefore, it is desirable to have an automated approach that reports defects on images reliably and robustly. This paper presents a multivariate analysis approach for images, specifically for assessing substantial damage (such as cracks). The image analysis provides graph representations that are related to the image, such as the histogram. In addition, image-processing techniques such as grayscale are also implemented, which enhance the object’s information present in the image. In addition, this study uses image segmentation and a neural network, for transforming an image to analyze it more easily and as a classifier, respectively. Initially, each concrete structure image is preprocessed to highlight the crack. A neural network is used to calculate and categorize the visual characteristics of each region, and it shows an accuracy for classification of 98%. Experimental results show that thermal image extraction yields better histogram and cumulative distribution function features. The system can promote the development of various thermal image applications, such as nonphysical visual recognition and fault detection analysis.

An index for measuring functional extension and evenness in trait space

Most existing functional diversity indices focus on a single facet of functional diversity. Although these indices are useful for quantifying specific aspects of functional diversity, they often present some conceptual or practical limitations in estimating functional diversity. Here, we present a new functional extension and evenness (FEE) index that encompasses two important aspects of functional diversity. This new index is based on the straightforward notion that a community has high diversity when its species are distant from each other in trait space. The index quantifies functional diversity by evaluating the overall extension of species traits and the interspecific differences of a species assemblage in trait space. The concept of minimum spanning tree (MST) of points was adopted to obtain the essential distribution properties for a species assembly in trait space. We combined the total length of MST branches (extension) and the variation of branch lengths (evenness) into a raw FEE0 metric and then translated FEE0 to a species richness-independent FEE index using a null model approach. We assessed the properties of FEE and used multiple approaches to evaluate its performance. The results show that the FEE index performs well in quantifying functional diversity and presents the following desired properties: (a) It allows a fair comparison of functional diversity across different species richness levels; (b) it preserves the essence of single-facet indices while overcoming some of their limitations; (c) it standardizes comparisons among communities by taking into consideration the trait space of the shared species pool; and (d) it has the potential to distinguish among different community assembly processes. With these attributes, we suggest that the FEE index is a promising metric to inform biodiversity conservation policy and management, especially in applications at large spatial and/or temporal scales.

Parsimonious discretization for characterizing multi-exponential decay in magnetic resonance

We address the problem of analyzing noise-corrupted magnetic resonance transverse decay signals as a superposition of underlying independently decaying monoexponentials of positive amplitude. First, we indicate the manner in which this is an ill-conditioned inverse problem, rendering the analysis unstable with respect to noise. Second, we define an approach to this analysis, stabilized solely by the nonnegativity constraint without regularization. This is made possible by appropriate discretization, which is coarser than that often used in practice. Thirdly, we indicate further stabilization by inspecting the plateaus of cumulative distributions. We demonstrate our approach through analysis of simulated myelin water fraction measurements, and compare the accuracy with more conventional approaches. Finally, we apply our method to brain imaging data obtained from a human subject, showing that our approach leads to maps of the myelin water fraction which are much more stable with respect to increasing noise than those obtained with conventional approaches.

An extended and unified modeling framework for benchmark dose estimation for both continuous and binary data

Protection and safety authorities recommend the use of model averaging to determine the benchmark dose approach as a scientifically more advanced method compared with the no-observed-adverse-effect-level approach for obtaining a reference point and deriving health-based guidance values. Model averaging however highly depends on the set of candidate dose-response models and such a set should be rich enough to ensure that a well-fitting model is included. The currently applied set of candidate models for continuous endpoints is typically limited to two models, the exponential and Hill model, and differs completely from the richer set of candidate models currently used for binary endpoints. The objective of this article is to propose a general and wide framework of dose response models, which can be applied both to continuous and binary endpoints and covers the current models for both type of endpoints. In combination with the bootstrap, this framework offers a unified approach to benchmark dose estimation. The methodology is illustrated using two data sets, one with a continuous and another with a binary endpoint.

Proposals of models for new formulations of the current complication-free cure (P+) and uncomplicated tumor control probability (UTCP) concepts, and total normal tissue complication probability of late complications

This study proposes phenomenological models for total normal tissue complication probability (TNTCP) and NTCP0. NTCP0 is a new acronym for reformulating the current complication-free cure (P+) and uncomplicated tumor control probability (UTCP) concepts, and TNTCP will reformulate the current NTCP involving multiple organs at risks. The current probabilistic concepts are incoherently formulated with mathematical operations of tumor control probability (TCP) and normal tissue complication probability (NTCP) that are associated with different stochastic processes and random variables. NTCP0 is equal to NTCP₀ (normal tissue non-complication probability) that is calculated as the ratio of a number of patients of a population without late complications and a total of them. As a cumulative distribution function (CDF) of late complications, TNTCP = sum(NTCP_i), where NTCP_i is the NTCP of the i^th late complication. TNTCP is also a new acronym, and the probabilistic complement of NTCP0, then NTCP0 = 100% - TNTCP. The NTCP0/TNTCP (D(d)) proposing models are based on the relationship between the NTCP0/TNTCP and total dose (D = n×d; where d = dose per fraction, and n = number of fractions). TNTCP(D) model will be correlated with LKB model (the normal CDF) that is an increasing function; and NTCP0(D) model with a decreasing function, which additionally will define clear limits of three possible regions for NTCP0: 0 and 100% deterministic, and a stochastic. These models are function D, which is widely used for characterizing radiation therapies.

Blind Compensation of I/Q Impairments in Wireless Transceivers

The majority of techniques that deal with the mitigation of in-phase and quadrature-phase (I/Q) imbalance at the transmitter (pre-compensation) require long training sequences, reducing the throughput of the system. These techniques also require a feedback path, which adds more complexity and cost to the transmitter architecture. Blind estimation techniques are attractive for avoiding the use of long training sequences. In this paper, we propose a blind frequency-independent I/Q imbalance compensation method based on the maximum likelihood (ML) estimation of the imbalance parameters of a transceiver. A closed-form joint probability density function (PDF) for the imbalanced I and Q signals is derived and validated. ML estimation is then used to estimate the imbalance parameters using the derived joint PDF of the output I and Q signals. Various figures of merit have been used to evaluate the efficacy of the proposed approach using extensive computer simulations and measurements. Additionally, the bit error rate curves show the effectiveness of the proposed method in the presence of the wireless channel and Additive White Gaussian Noise. Real-world experimental results show an image rejection of greater than 30 dB as compared to the uncompensated system. This method has also been found to be robust in the presence of practical system impairments, such as time and phase delay mismatches.