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Full-Text Articles in Mathematics
Work In Progress: The Rica Project: Rich, Immediate Critique Of Antipatterns In Student Code, Leo C. Ureel Ii, Laura Brown, Jon Sticklen, Michelle E. Jarvie-Eggart, Mary Benjamin
Work In Progress: The Rica Project: Rich, Immediate Critique Of Antipatterns In Student Code, Leo C. Ureel Ii, Laura Brown, Jon Sticklen, Michelle E. Jarvie-Eggart, Mary Benjamin
Michigan Tech Publications
Rich, relevant, and immediate student feedback is a core ingredient supporting effective student learning. Feedback is particularly important for introductory computing courses where novice programmers are still learning the basic syntax and semantics of a programming language. Our project is aimed at detecting poor solutions to common problems, termed antipatterns, in student code and providing feedback that guides the student to better solutions. This paper discusses the first year of the project, specifically, the development of a Code Critiquer to detect antipatterns in student code and generate appropriate feedback. This important first step sets-up the project to advance knowledge about …
Gene-Based Association Tests Using New Polygenic Risk Scores And Incorporating Gene Expression Data, Shijia Yan, Qiuying Sha, Shuanglin Zhang
Gene-Based Association Tests Using New Polygenic Risk Scores And Incorporating Gene Expression Data, Shijia Yan, Qiuying Sha, Shuanglin Zhang
Michigan Tech Publications
Recently, gene-based association studies have shown that integrating genome-wide association studies (GWAS) with expression quantitative trait locus (eQTL) data can boost statistical power and that the genetic liability of traits can be captured by polygenic risk scores (PRSs). In this paper, we propose a new gene-based statistical method that leverages gene-expression measure-ments and new PRSs to identify genes that are associated with phenotypes of interest. We used a generalized linear model to associate phenotypes with gene expression and PRSs and used a score-test statistic to test the association between phenotypes and genes. Our simulation studies show that the newly developed …
A Priori And A Posteriori Error Estimates For The Quad-Curl Eigenvalue Problem, Lixiu Wang, Qian Zhang, Jiguang Sun, Zhimin Zhang
A Priori And A Posteriori Error Estimates For The Quad-Curl Eigenvalue Problem, Lixiu Wang, Qian Zhang, Jiguang Sun, Zhimin Zhang
Michigan Tech Publications
In this paper, we consider a priori and a posteriori error estimates of the H(curl2)-conforming finite element when solving the quad-curl eigenvalue problem. An a priori estimate of eigenvalues with convergence order 2(s − 1) is obtained if the corresponding eigenvector u ∈ Hs − 1(Ω) and ∇ × u ∈ Hs(Ω). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the errors of eigenvectors in the energy norm and upper bounds for the errors of eigenvalues. Numerical examples are presented for validation.
A Priori And A Posteriori Error Estimates For The Quad-Curl Eigenvalue Problem, Lixiu Wang, Qian Zhang, Jiguang Sun, Zhimin Zhang
A Priori And A Posteriori Error Estimates For The Quad-Curl Eigenvalue Problem, Lixiu Wang, Qian Zhang, Jiguang Sun, Zhimin Zhang
Michigan Tech Publications
In this paper, we consider a priori and a posteriori error estimates of the H(curl2)-conforming finite element when solving the quad-curl eigenvalue problem. An a priori estimate of eigenvalues with convergence order 2(s 1) is obtained if the corresponding eigenvector u a Hs 1(Ω) and-u a Hs(Ω). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the errors of eigenvectors in the energy norm and upper bounds for the errors of eigenvalues. Numerical examples are presented for validation.
A Computationally Efficient Clustering Linear Combination Approach To Jointly Analyze Multiple Phenotypes For Gwas, Meida Wang, Shuanglin Zhang, Qiuying Sha
A Computationally Efficient Clustering Linear Combination Approach To Jointly Analyze Multiple Phenotypes For Gwas, Meida Wang, Shuanglin Zhang, Qiuying Sha
Michigan Tech Publications
There has been an increasing interest in joint analysis of multiple phenotypes in genome-wide association studies (GWAS) because jointly analyzing multiple phenotypes may increase statistical power to detect genetic variants associated with complex diseases or traits. Recently, many statistical methods have been developed for joint analysis of multiple phenotypes in genetic association studies, including the Clustering Linear Combination (CLC) method. The CLC method works particularly well with phenotypes that have natural groupings, but due to the unknown number of clusters for a given data, the final test statistic of CLC method is the minimum p-value among all p-values of the …
Gene-Based Association Tests Using Gwas Summary Statistics And Incorporating Eqtl, Xuewei Cao, Xuexia Wang, Shuanglin Zhang, Qiuying Sha
Gene-Based Association Tests Using Gwas Summary Statistics And Incorporating Eqtl, Xuewei Cao, Xuexia Wang, Shuanglin Zhang, Qiuying Sha
Michigan Tech Publications
Although genome-wide association studies (GWAS) have been successfully applied to a variety of complex diseases and identified many genetic variants underlying complex diseases via single marker tests, there is still a considerable heritability of complex diseases that could not be explained by GWAS. One alternative approach to overcome the missing heritability caused by genetic heterogeneity is gene-based analysis, which considers the aggregate effects of multiple genetic variants in a single test. Another alternative approach is transcriptome-wide association study (TWAS). TWAS aggregates genomic information into functionally relevant units that map to genes and their expression. TWAS is not only powerful, but …
Simian Immunodeficiency Virus Infection Mediated Changes In Jejunum And Peripheral Sars-Cov-2 Receptor Ace2 And Associated Proteins Or Genes In Rhesus Macaques, Nongthombam Boby, Xuewei Cao, Kelsey Williams, Shiva Kumar Goud Gadila, Monica N. Shroyer, Peter J. Didier, Sudesh K. Srivastav, Arpita Das, Kate Baker, Qiuying Sha, Bapi Pahar
Simian Immunodeficiency Virus Infection Mediated Changes In Jejunum And Peripheral Sars-Cov-2 Receptor Ace2 And Associated Proteins Or Genes In Rhesus Macaques, Nongthombam Boby, Xuewei Cao, Kelsey Williams, Shiva Kumar Goud Gadila, Monica N. Shroyer, Peter J. Didier, Sudesh K. Srivastav, Arpita Das, Kate Baker, Qiuying Sha, Bapi Pahar
Michigan Tech Publications
Angiotensin converting enzyme-2 (ACE2) and associated proteins play a pivotal role in various physiological and pathological events, such as immune activation, inflammation, gut barrier maintenance, intestinal stem cell proliferation, and apoptosis. Although many of these clinical events are quite significant in SIV/HIV infection, expression profiling of these proteins has not been well reported. Considering the different pathological consequences in the gut after HIV infection, we hypothesized that the expression of ACE2 and associated proteins of the Renin-angiotensin system (RAS) could be compromised after SIV/HIV infection. We quantified the gene expression of ACE2 as well as AGTR1/2, ADAM17, and TMPRSS2, and …
Differentially Private Fractional Frequency Moments Estimation With Polylogarithmic Space, Lun Wang, Iosif Pinelis, Dawn Song
Differentially Private Fractional Frequency Moments Estimation With Polylogarithmic Space, Lun Wang, Iosif Pinelis, Dawn Song
Michigan Tech Publications
We prove that Fp sketch, a well-celebrated streaming algorithm for frequency moments estimation, is differentially private as is when p ∈ (0, 1]. Fp sketch uses only polylogarithmic space, exponentially better than existing DP baselines and only worse than the optimal non-private baseline by a logarithmic factor. The evaluation shows that Fp sketch can achieve reasonable accuracy with differential privacy guarantee. The evaluation code is included in the supplementary material.