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In this article, the investigation into the Lie symmetry algebra of the geodesic equations of the canonical connection on a Lie group was continued. The key ideas of Lie group, Lie algebra, linear connection, and symmetry were quickly reviewed. The focus was on those Lie groups whose Lie algebra was six-dimensional solvable and indecomposable and for which the nilradical was abelian and had a one-dimensional center. Based on the list of Lie algebras compiled by Turkowski, there were eight algebras to consider that were denoted by A6,20-A6,27. For each Lie algebra, a comprehensive symmetry analysis of the system of geodesic equations was carried out. For each symmetry Lie algebra, the nilradical and a complement to the nilradical inside the radical, as well as a semi-simple factor, were identified. [ABSTRACT FROM AUTHOR]

Although guidelines exist for identifying mixtures, these measures often occur at the end-point of analysis and are protracted. To facilitate early mixture detection, we integrated a high-resolution melt (HRM) mixture screening assay into the qPCR step of the forensic workflow, producing the integrated QuantifilerTM Trio-HRM assay. The assay, when coupled with a prediction tool, allowed for 75.0% accurate identification of the contributor status of a sample (single source vs. mixture). To elucidate the limitations of the developed qPCR-HRM assay, developmental validation studies were conducted assessing the reproducibility and samples with varying DNA ratios, contributors, and quality. From this work, it was determined that the integrated QuantifilerTM Trio-HRM assay is capable of accurately identifying mixtures with up to five contributors and mixtures at ratios up to 1:100. Further, the optimal performance concentration range was found to be between 0.025 and 0.5 ng/µL. With these results, evidentiary-like DNA samples were then analyzed, resulting in 100.0% of the mixture samples being accurately identified; furthermore, every time a sample was predicted as a single source, it was true, giving confidence to any single-source calls. Overall, the integrated QuantifilerTM Trio-HRM assay has exhibited an enhanced ability to discern mixture samples from single-source samples at the qPCR stage under commonly observed conditions regardless of the contributor's sex. [ABSTRACT FROM AUTHOR]

In this paper, we consider the symmetry algebra of the geodesic equations of the canonical connection on a Lie group. We mainly consider the solvable indecomposable six-dimensional Lie algebras with co-dimension two abelian nilradical that have an abelian complement. In dimension six, there are nineteen such algebras, namely, A6,1-A6,19 in Turkowski's list. For each algebra, we give the geodesic equations, a basis for the symmetry Lie algebra in terms of vector fields, and finally we identify the symmetry Lie algebra from standard lists. [ABSTRACT FROM AUTHOR]

The COVID-19 outbreak of 2020 has required many governments to develop and adopt mathematical-statistical models of the pandemic for policy and planning purposes. To this end, this work provides a tutorial on building a compartmental model using Susceptible, Exposed, Infected, Recovered, Deaths and Vaccinated (SEIRDV) status through time. The proposed model uses interventions to quantify the impact of various government attempts made to slow the spread of the virus. Furthermore, a vaccination parameter is also incorporated in the model, which is inactive until the time the vaccine is deployed. A Bayesian framework is utilized to perform both parameter estimation and prediction. Predictions are made to determine when the peak Active Infections occur. We provide inferential frameworks for assessing the effects of government interventions on the dynamic progression of the pandemic, including the impact of vaccination. The proposed model also allows for quantification of number of excess deaths averted over the study period due to vaccination. [ABSTRACT FROM AUTHOR]

As the mathematical properties of Fractional Partial Differential Equations are rapidly being developed, there is an increasing desire by researchers to employ these models in real world data oriented contexts. The main barrier to employing these models is the choice of the fractional order a. Recently, [6] show how to both estimate and make inferences about a from a Bayesian perspective. However, for experimental settings one needs to be able to design experiments that will provide optimal information about a. This work demonstrates how to use information based criteria, namely A, D and E optimality, to choose sampling locations in follow-up designs. Specifically, the simultaneous addition of one, two and three measurement locations is considered for a simple example. The simultaneous addition of four and five measurement locations is also considered across a variety of values of a. The results show that each of the criteria provide different optimal measurement locations as the number of additional measurement locations is increased. Indicating that the choice of optimality criteria should not be decided arbitrarily. [ABSTRACT FROM AUTHOR]

Legal professionals and others have suggested that vaping electronic cigarettes (e-cigs) prior to or during ethanol breath testing may produce false positives. Preliminary breath tests (PBTs) and evidentiary breath tests (EBTs) measure ethanol in exhaled breath and standardized field sobriety tests (SFSTs) are used to assess impairment. Ethanol has been identified in e-cig liquids (e-liquids). Presented are a series of experiments designed to determine the mechanics of vaping ethanol using an e-cig and the effects of vaping ethanol on the SFSTs and breath tests used by law enforcement officers (LEO). Twelve participants (five females, age: 21–32 and seven males, age: 21–55), vaped either one or ten puffs of an e-liquid (0% or 20% ethanol). LEOs assessed impairment using SFSTs (12 and 42 min), PBTs (<1, 27, 32, 37 and 57 min) and EBTs (2, 29, 34, 39 and 59 min) post-vaping. A self-assessment test was administered post-vaping (22 and 52 min). Baseline responses for all measures were collected prior to vaping. Results demonstrated that ethanol in the e-liquids was aerosolized by e-cigs and produced particles that could reach the deep lung tissue based on mean-mass diameter. Ethanol was detected by PBT <3 min after participants vaped one (0.007–0.030 g/210 L) or ten puffs (013–0.074 g/210 L) of a 20% ethanol e-liquid. Ethanol was not detected by PBT at any subsequent time point. Ethanol was not detected by the EBT under any condition. Impairment was not indicated by the SFST. Some subjective effects were reported, but few statistically significant differences between conditions were indicated. A wait period prior to ethanol breath testing is not always mandated, depending on jurisdiction, or observed in all applications, such as workplace testing. The results demonstrate that a wait period must be employed to prevent vaping-related false-positive breath ethanol results. [ABSTRACT FROM AUTHOR]

During the current COVID-19 pandemic, decision-makers are tasked with implementing and evaluating strategies for both treatment and disease prevention. In order to make effective decisions, they need to simultaneously monitor various attributes of the pandemic such as transmission rate and infection rate for disease prevention, recovery rate which indicates treatment effectiveness as well as the mortality rate and others. This work presents a technique for monitoring the pandemic by employing an Susceptible, Exposed, Infected, Recovered, Death model regularly estimated by an augmented particle Markov chain Monte Carlo scheme in which the posterior distribution samples are monitored via Multivariate Exponentially Weighted Average process monitoring. This is illustrated on the COVID-19 data for the State of Qatar. [ABSTRACT FROM AUTHOR]

Historically, two primary criticisms statisticians have of machine learning and deep neural models is their lack of uncertainty quantification and the inability to do inference (i.e., to explain what inputs are important). Explainable AI has developed in the last few years as a sub‐discipline of computer science and machine learning to mitigate these concerns (as well as concerns of fairness and transparency in deep modeling). In this article, our focus is on explaining which inputs are important in models for predicting environmental data. In particular, we focus on three general methods for explainability that are model agnostic and thus applicable across a breadth of models without internal explainability: "feature shuffling", "interpretable local surrogates", and "occlusion analysis". We describe particular implementations of each of these and illustrate their use with a variety of models, all applied to the problem of long‐lead forecasting monthly soil moisture in the North American corn belt given sea surface temperature anomalies in the Pacific Ocean. [ABSTRACT FROM AUTHOR]

Predator-prey models are often used in ecology to represent realistic encounters between species. Lotka-Volterra differential equations are famously used by ecologists to model the relationship between a predator and prey. Given ecological data collection is known to be time consuming and difficult, the purpose of this paper is to optimize the process and improve sampling efficiency. The method of sequential optimality is applied to a more complex population model with multiple basins of attraction, the Lotka-Volterra differential equations. In this application, various theoretical scenarios are simulated using varying sample sizes and timeframes to determine optimal designs. The first scenario uses a standard sample size and design window to represent a realistic budget for ecological data collection. The second scenario decreases the budget and extends the design window as a representation of a limited budget. The third scenario represents ample resources available for sampling. The three scenarios are used to then compare the optimal designs and help ecologists evaluate the method of sequential optimality. I, A and D optimal designs are compared in the simulation results. The I-optimality criterion tends to outperform the A and D criteria and is recommended as a primary selection when using the sequential optimality algorithm. This simulation study has further developed sequential optimality by predicting optimal sampling regimes according to the dynamics associated with the Lotka-Volterra differential equations. [ABSTRACT FROM AUTHOR]

As an expatriate-majority state with a diverse multicultural and multilingual environment, Kuwait offers a distinctive opportunity for examining intercultural communication competence (ICC). This study examines the extent to which cognitive, affective, and behavioral predispositions toward ICC are present within the context of higher education by examining multilingual student populations at three local universities. Using survey data from over 800 respondents, the study explores ICC correlates such as linguistic abilities, formal educational experiences, and other sociodemographic factors. Analyses of variance demonstrate that some expected factors, such as multilingualism or expatriate status, contributed positively to ICC measures, while others did not--including attending English-language universities. Years of university experience positively correlated with both affective and behavioral aspects of ICC, while the cognitive component was least affected. Practical implications include the opportunity for universities to incorporate more cognitive-oriented intercultural lessons into their curricular objectives, which can add both educational and social value. [ABSTRACT FROM AUTHOR]

Strength is a critical factor in the health and job performance of police officers. Using a retrospective longitudinal design, the purpose of this study was to identify differences in strength scores from initial recruitment to in-service tests and to compare gender differences. Strength changes were also compared in low- to high-strength groups. Strength scores included bench press, bench press/lean weight, and bench press/weight. Body weight, percent body fat, and bench press scores were retrieved for the 1990-1995 recruit classes and were paired to most recent scores on 2006 in-service fitness record. Sample included 327 police officers: 30 females and 297 males. Mean age at initial recruitment was 24.6 years and for in-service was 37.1 years. Average time between tests was 12.5 years. Over this period bench press and bench press/lean weight significantly increased for both gender groups (p [less than or equal to] 0.05). Bench press/weight remained relatively consistent. When dividing the men's strength scores into five low- to high-strength groups, there tended to be an averaging effect over time with the strongest group changing least and the weakest group changing most. In conclusion, the results of this study did not follow expected strength trends, which reported annual declines in muscular strength in men and women. Overall, officers increased in strength well into their late 30s. The practical applications of this study include documented benefits gained from maintaining ongoing fitness training and testing, as well as the potentially positive role of weight gain on strength. Also, low- to high-strength groups did not change relative positions over time even with improvements in strength scores, demonstrating the importance of minimum selection criteria for police. KEY WORDS bench press, police, longitudinal study, body weight, sex differences

Toxicologists are often concerned with determining the dosage to which an individual can be exposed with an acceptable risk of adverse effect. These types of studies have been conducted widely in the past, and many novel approaches have been developed. Parametric techniques utilizing ANOVA and non-linear regression models are well represented in the literature. The biggest drawback of parametric approaches is the need to specify the adequate model. Recently, there has been an interest in nonparametric approaches to tolerable dosage estimation. In this work, we focus on the monotonically decreasing dose-response model where the response is a percent to control. This imposes two constraints on the nonparametric approach: the dose-response function must be monotonic and always positive. Here, we propose a Bayesian solution to this problem using a novel class of non-parametric models. A set of basis functions developed in this research is Alamri Monotonic spline (AM-spline). Our approach is illustrated using two simulated datasets and two experimental datasets from pesticide related research at the US Environmental Protection Agency. [ABSTRACT FROM AUTHOR]

Past investigations utilizing diffusion tensor imaging (DTI) have demonstrated that cocaine use disorder (CUD) yields white matter changes, primarily in the corpus callosum. By applying Bayesian model averaging using multiple linear regression in DTI, we demonstrate there may exist relationships between the impaired white matter and glutamic acid decarboxylase (GAD) polymorphisms. This work explored the two-way and three-way interactions between GAD1a (SNP: rs1978340) and GAD1b (SNP: rs769390) polymorphisms and years of cocaine use (YCU). GAD1a was associated with more frontal white matter changes on its own but GAD1b was associated with more midbrain and cerebellar changes as well as a greater increase in white matter changes in the context of chronic cocaine use. The three-way interaction GAD1a|GAD1b|YCU appeared to be roughly an average of the polymorphism two-way interactions GAD1a|YCU and GAD1b|YCU. The three-way interaction demonstrated multiple regions including corpus callosum which featured fewer significant voxel changes, perhaps suggesting a small protective effect of having both polymorphisms on corpus callosum and cerebellar peduncle. [ABSTRACT FROM AUTHOR]

Bayesian Nonparametric (BNP) modelling can be used to obtain more detailed information in test equating studies and to increase the accuracy of equating by accounting for covariates. In this study, two covariates are included in the equating under the Bayes nonparametric model, one is continuous, and the other is discrete. Scores equated with this model were obtained for a single group design for a small group in the study. The equated scores obtained with the model were compared with the mean and linear equating methods in the Classical Test Theory. Considering the equated scores obtained from three different methods, it was found that the equated scores obtained with the BNP model produced a distribution closer to the target test. Even the classical methods will give a good result with the smallest error when using a small sample, making equating studies valuable. The inclusion of the covariates in the model in the classical test equating process is based on some assumptions and cannot be achieved especially using small groups. The BNP model will be more beneficial than using frequentist methods, regardless of this limitation. Information about booklets and variables can be obtained from the distributors and equated scores that obtained with the BNP model. In this case, it makes it possible to compare sub-categories. This can be expressed as indicating the presence of differential item functioning (DIF). Therefore, the BNP model can be used actively in test equating studies, and it provides an opportunity to examine the characteristics of the individual participants at the same time. Thus, it allows test equating even in a small sample and offers the opportunity to reach a value closer to the scores in the target test. [ABSTRACT FROM AUTHOR]

Profile monitoring is defined as the act of utilizing regression and quality control techniques to monitor the functional relationship between a response variable and one or more regressors. Most of the previous studies focused either on parametric modeling of profiles or assumed the response variable followed a normal distribution, but that is an unrealistic scenario in most cases. In this study, a Haar wavelet approach is applied for profile monitoring of Poisson data. We showed via simulation that, Haar wavelet can outperform parametric models when there is a sudden jump in the profile and concluded with a case study. [ABSTRACT FROM AUTHOR]

The COVID-19 outbreak of 2020 has required many governments to develop mathematical-statistical models of the outbreak for policy and planning purposes. This work provides a tutorial on building a compartmental model using Susceptibles, Exposed, Infected, Recovered and Deaths (SEIRD) status through time. A Bayesian Framework is utilized to perform both parameter estimation and predictions. This model uses interventions to quantify the impact of various government attempts to slow the spread of the virus. Predictions are also made to determine when the peak Active Infections will occur. [ABSTRACT FROM AUTHOR]

The increase of exposure to toxic materials and hazardous chemicals is a major concern due to the adverse effect on human health. Among the major concerns of toxicologists is to determine acceptable levels of exposure to hazardous substances. Current approaches often evaluate each endpoint and stressor individually. We propose a novel method to simultaneously determine the Benchmark Dose Tolerable Region (BMDTR) for multiple endpoint and multiple stressor studies by adopting a Bayesian approach. A main concern while assessing the combined toxicological effect of a chemical mixture is the anticipated type of the combined action (i.e. synergistic or antagonistic); thus it was essential to account for interaction effects to handle this situation, imposing more challenges due to the non-linearity of the tolerable region. The proposed method will be evaluated using two approaches, the first one using the estimated value of the posterior median and the second approach using all MCMC samples from the posterior distribution. Furthermore, we propose a new method to determine the endpoint probabilities for each endpoint, which reflects the importance of each endpoint in helping determining the boundaries of the benchmark dose tolerable region (BMDTR). [ABSTRACT FROM AUTHOR]

The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the ‘classical’ approach and the ‘inverse’ regression approach. Both of these models are static models and are used to estimate exact measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe it. The Bayesian time series analysis method of Dynamic Linear Models can be used to monitor the evolution of the measures, thus introducing adynamicapproach to statistical calibration. The research presented employs a new approach to performing statistical calibration. A simulation study in the context of microwave radiometry is conducted that compares the dynamic model to traditional static frequentist and Bayesian approaches. The focus of the study is to understand how well thedynamic statistical calibrationmethod performs under various signal-to-noise ratios,r. [ABSTRACT FROM PUBLISHER]

Bayesian analysis often requires the researcher to employ Markov Chain Monte Carlo (MCMC) techniques to draw samples from a posterior distribution which in turn is used to make inferences. Currently, several approaches to determine convergence of the chain as well as sensitivities of the resulting inferences have been developed. This work develops a Hellinger distance approach to MCMC diagnostics. An approximation to the Hellinger distance between two distributionsfandgbased on sampling is introduced. This approximation is studied via simulation to determine the accuracy. A criterion for using this Hellinger distance for determining chain convergence is proposed as well as a criterion for sensitivity studies. These criteria are illustrated using a dataset concerning theAnguilla australis, an eel native to New Zealand. [ABSTRACT FROM PUBLISHER]

Strength, when considering gender and race, provides a basis for training, hiring, and retention for police officers. The purpose of this study is to identify muscular strength differences among racial groups from initial-recruit to in-service tests. Strength variables included bench press, bench press/lean mass and bench press/body mass. Scores were retrieved for the 1990 to 1995 recruit classes and were paired to the 2006 in-service fitness log. Sample included 309 officers: 30 females (13 black, 17 white) and 279 males (41 black, 238 white). Mean age of recruit was 24.6 ± 3.4 years and for in-service was 37.1 ± 3.7 years. Time between tests was 12.5 ± 2.0 years. Bench press strength significantly increased for all gender and racial groups. Black males were significantly stronger in bench press at initial-recruit and at in-service than white males. All racial and gender groups increased in bench press/lean mass, however, the increase in white females was not significant. No differences were found between black and white females in all strength variables at both testing periods. Black males were significantly stronger than white males in bench press/body mass only at the initial-recruit test. White males showed a significant increase in bench press/body mass over time, but they did not reach the strength level of the black males at in-service. Police departments, with a properly designed physical fitness program, can expect to see increases in strength of personnel over the first half of their careers; however, there are gender and racial differences. [ABSTRACT FROM AUTHOR]

This paper introduces a framework for incorporating uncertainty in water supply system models that uses Bayesian statistics and mixed-integer programming. The output of the framework includes the most probable least cost solution, the probability of feasibility for a given solution, component probabilities for each decision, and a distribution of the optimal objective function value. The method is applied to the problem of developing a water supply system design for Israel, Jordan, and the Palestinian territories. The method allows decision makers to evaluate various alternatives for a water supply plan that incorporates uncertainties in future demand and costs. The design of a water supply plan is a concern with properties that are distinct from traditional approaches to the design of water distribution systems; namely, local engineering decisions concerning pipe diameters and water pressure are not explicitly modeled, but large-scale decisions concerning the construction of water conveyances (pipes, canals, and tunnels) and sources (desalination plants) are the focus in the model. [ABSTRACT FROM AUTHOR]

This paper presents new biostatistical methods for the analysis of microbiome data based on a fully parametric approach using all the data. The Dirichlet-multinomial distribution allows the analyst to calculate power and sample sizes for experimental design, perform tests of hypotheses (e.g., compare microbiomes across groups), and to estimate parameters describing microbiome properties. The use of a fully parametric model for these data has the benefit over alternative nonparametric approaches such as bootstrapping and permutation testing, in that this model is able to retain more information contained in the data. This paper details the statistical approaches for several tests of hypothesis and power/sample size calculations, and applies them for illustration to taxonomic abundance distribution and rank abundance distribution data using HMP Jumpstart data on 24 subjects for saliva, subgingival, and supragingival samples. Software for running these analyses is available. [ABSTRACT FROM AUTHOR]

Bayesian inclusion probabilities have become a popular tool for variable assessment. From a frequentist perspective, it is often difficult to evaluate these probabilities as typically no Type I error rates are considered, neither are any explorations of power of the methods given. This paper considers how a frequentist may evaluate Bayesian inclusion probabilities for screening predictors. This evaluation looks at both unrestricted and restricted model spaces and develops a framework which a frequentist can utilize inclusion probabilities that preserve Type I error rates. Furthermore, this framework is applied to an analysis of the Arabidopsis thaliana with respect to determining quantitative trait loci associated with cotelydon opening angle. [ABSTRACT FROM AUTHOR]

Lack of success in restoring the native Eastern oyster, Crassostrea virginica, to Chesapeake Bay has been linked to the low occurrence of oyster larval setting in tributaries to the Bay. Among the many potential factors that could affect efforts to produce oysters through aquaculture or supplementation of shell beds is substratum condition. The present study examined larval setting on field-produced biofilms from Little Wicomico River (Virginia, USA) to assess whether bacterial community structure (examined by terminal restriction fragment length polymorphism, T-RFLP) or other characteristics of contemporary biofilms in this tributary (biofilm age and mass, algal abundance, and percentage organic matter) inhibited setting of larval oysters. The structure of the natural and heterogenous bacterial community in the biofilms and the success of oyster set were correlated, suggesting that specific microbial species may play a role in oyster setting. Larval set increased with biofilm age and mass, suggesting that established field-produced biofilms have no inhibitory effect. In contrast, the percentage of organic matter was negatively correlated with oyster set, whereas chlorophyll a concentration had no observed effect. The study expands prior knowledge by providing a more realistic timeframe for biofilm development (weeks as opposed to days), recounting effects of biofilms that are more representative of the natural dynamic and disturbance processes that would be expected to occur on submerged structures, and by incorporating seasonal and spatial variation. An important negative effect observed during the study period was heavy predation by Stylochus ellipticus on newly set oysters. Overall, the results of this study, which is the first assessment of the effects of biofilms produced naturally within a Chesapeake Bay tributary, suggest that the absence of large numbers of oysters in Little Wicomico River is not related to microbes or other specific characteristics of biofilms that develop on suitable setting substrata, but rather to heavy predation of newly set larvae. [ABSTRACT FROM AUTHOR]