Controlling composition factors of a finite group by its character degree ratio

For a finite nonabelian group $G$ let \rat(G) be the largest ratio of degrees of two nonlinear irreducible characters of $G$. We show that nonabelian composition factors of $G$ are controlled by \rat(G) in some sense. Specifically, if $S$ different from the simple linear groups \PSL_2(q) is a nonabelian composition factor of $G$, then the order of $S$ and the number of composition factors of $G$ isomorphic to $S$ are both bounded in terms of \rat(G). Furthermore, when the groups \PSL_2(q) are not composition factors of $G$, we prove that |G:\Oinfty(G)|\leq \rat(G)^{21} where \Oinfty(G) denotes the solvable radical of $G$.Comment: 16 pages, 1 tabl

Relationship Between Obesity and Periodontal Status in Vietnamese Patients

This study aims to investigate periodontal status, and the relationship between obesity and periodontal status in patients who first visited the Institute of Traditional Medicine, Ho Chi Minh City, Vietnam. 118 patients aged 18 or older, including 56 obese subjects (BMI≥27.5, mean age: 33.8, males: 11, females: 45) and 62 non-obese subjects (BMI<27.5, mean age: 34.3, males: 4, females: 58) were enrolled for a period of 5 months from February 2014 to June 2014. The information on socio-demographic characteristics and dental habits were collected by questionnaire. Periodontal status (PLI, GI, BOP, PD, CAL) was examined and the anthropometric index was measured. There was significantly higher prevalence of periodontitis (39.3%) in the obese group than the non-obese group (16.4%). Means of GI, BOP, PD, and CAL in obese subjects were significantly higher than those in non-obese subjects. Significantly higher percentages of subjects who had lower education, visited dental offices, scaled and polished their teeth regularly were in the non-obese group than in the obese group. Multiple logistic regression analysis revealed that age (OR=3.10), routine of dental visit (OR=3.34) and obesity (OR=2.79) were risk factors significantly related to periodontitis. Periodontal status in obese subjects was poorer than non-obese subjects. Obesity might be the risk factor for periodontitis in Vietnamese patients

On a conjecture of Gluck

Let $F(G)$ and $b(G)$ respectively denote the Fitting subgroup and the largest degree of an irreducible complex character of a finite group $G$. A well-known conjecture of D. Gluck claims that if $G$ is solvable then $|G:F(G)|\leq b(G)^{2}$. We confirm this conjecture in the case where $|F(G)|$ is coprime to 6. We also extend the problem to arbitrary finite groups and prove several results showing that the largest irreducible character degree of a finite group strongly controls the group structure.Comment: 16 page

The welfare of small livestock producers in Vietnam under trade liberalisation-- Integration of trade and household models

Vietnam has negotiated a series of bilateral and multilateral trade agreements and has made significant steps in integrating into the world economy. This integration is likely to have both positive and negative effects on different stakeholders in the economy. This paper seeks to measure the effects on the welfare of Vietnam’s small livestock producers' by linking a household model and the GTAP trade model. A GTAP utility SplitCom is used to separate out pig and poultry prior to several trade liberalisation scenarios being run. A recursive household model with a two-stage LES-AIDS model on consumption side and Cobb-Douglas functions on production side are used. Impacts of likely changes in the prices of inputs and outputs arising from different trade scenarios on behavior and welfare of the farm household are presented.International Relations/Trade, Livestock Production/Industries,

Explainable AI (XAI): Improving At-Risk Student Prediction with Theory-Guided Data Science, K-means Classification, and Genetic Programming

This research explores the use of eXplainable Artificial Intelligence (XAI) in Educational Data Mining (EDM) to improve the performance and explainability of artificial intelligence (AI) and machine learning (ML) models predicting at-risk students. Explainable predictions provide students and educators with more insight into at-risk indicators and causes, which facilitates instructional intervention guidance. Historically, low student retention has been prevalent across the globe as nations have implemented a wide range of interventions (e.g., policies, funding, and academic strategies) with only minimal improvements in recent years. In the US, recent attrition rates indicate two out of five first-time freshman students will not graduate from the same four-year institution within six years. In response, emerging AI research leveraging recent advancements in Deep Learning has demonstrated high predictive accuracy for identifying at-risk students, which is useful for planning instructional interventions. However, research suggested a general trade-off between performance and explainability of predictive models. Those that outperform, such as deep neural networks (DNN), are highly complex and considered black boxes (i.e., systems that are difficult to explain, interpret, and understand). The lack of model transparency/explainability results in shallow predictions with limited feedback prohibiting useful intervention guidance. Furthermore, concerns for trust and ethical use are raised for decision-making applications that involve humans, such as health, safety, and education. To address low student retention and the lack of interpretable models, this research explored the use of eXplainable Artificial Intelligence (XAI) in Educational Data Mining (EDM) to improve instruction and learning. More specifically, XAI has the potential to enhance the performance and explainability of AI/ML models predicting at-risk students. The scope of this study includes a hybrid research design comprising: (1) a systematic literature review of XAI and EDM applications in education; (2) the development of a theory-guided feature selection (TGFS) conceptual learning model; and (3) an EDM study exploring the efficacy of a TGFS XAI model. The EDM study implemented K-Means Classification for explorative (unsupervised) and predictive (supervised) analysis in addition to assessing Genetic Programming (GP), a type of XAI model, predictive performance, and explainability against common AI/ML models. Online student activity and performance data were collected from a learning management system (LMS) from a four-year higher education institution. Student data was anonymized and protected to ensure data privacy and security. Data was aggregated at weekly intervals to compute and assess the predictive performance (sensitivity, recall, and f-1 score) over time. Mean differences and effect sizes are reported at the .05 significance level. Reliability and validity are improved by implementing research best practices

Complex group algebras of the double covers of the symmetric and alternating groups

We prove that the double covers of the alternating and symmetric groups are determined by their complex group algebras. To be more precise, let $n\geq 5$ be an integer, $G$ a finite group, and let \AAA and \SSS^\pm denote the double covers of \Al_n and \Sy_n, respectively. We prove that \CC G\cong \CC \AAA if and only if G\cong \AAA, and \CC G\cong \CC \SSS^+\cong\CC\SSS^- if and only if G\cong \SSS^+ or \SSS^-. This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasi-simple group is determined uniquely up to isomorphism by the structure of its complex group algebra. The known results on prime power degrees and relatively small degrees of irreducible (linear and projective) representations of the symmetric and alternating groups together with the classification of finite simple groups play an essential role in the proofs.Comment: 27 pages, the previous version is revised slightly, to appear in Algebra & Number Theor