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Articles 31 - 60 of 66
Full-Text Articles in Mathematics
The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel
The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel
CURE Proceedings
The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …
Joint Semiparametric Kernel Network Regression, Byung Jun Kim, Inyoung Kim
Joint Semiparametric Kernel Network Regression, Byung Jun Kim, Inyoung Kim
Michigan Tech Publications
Variable selection and graphical modeling play essential roles in highly correlated and high-dimensional (HCHD) data analysis. Variable selection methods have been developed under both parametric and nonparametric model settings. However, variable selection for nonadditive, nonparametric regression with high-dimensional variables is challenging due to complications in modeling unknown dependence structures among HCHD variables. Gaussian graphical models are a popular and useful tool for investigating the conditional dependence between variables via estimating sparse precision matrices. For a given class of interest, the estimated precision matrices can be mapped onto networks for visualization. However, the limitation of Gaussian graphical models is that they …
A Clustering Linear Combination Method For Multiple Phenotype Association Studies Based On Gwas Summary Statistics, Meida Wang, Xuewei Cao, Shuanglin Zhang, Qiuying Sha
A Clustering Linear Combination Method For Multiple Phenotype Association Studies Based On Gwas Summary Statistics, Meida Wang, Xuewei Cao, Shuanglin Zhang, Qiuying Sha
Michigan Tech Publications, Part 1
There is strong evidence showing that joint analysis of multiple phenotypes in genome-wide association studies (GWAS) can increase statistical power when detecting the association between genetic variants and human complex diseases. We previously developed the Clustering Linear Combination (CLC) method and a computationally efficient CLC (ceCLC) method to test the association between multiple phenotypes and a genetic variant, which perform very well. However, both of these methods require individual-level genotypes and phenotypes that are often not easily accessible. In this research, we develop a novel method called sCLC for association studies of multiple phenotypes and a genetic variant based on …
Bifurcation Levels Of The Integral Manifolds Of The Newtonian N-Body Problem, Hannah G. Havel
Bifurcation Levels Of The Integral Manifolds Of The Newtonian N-Body Problem, Hannah G. Havel
CURE Proceedings
The N-body problem, first proposed by Isaac Newton, is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It has significance to many areas of science, including physics and computer science, and is crucial in understanding how the universe works. In fact, it was a primary motivation for Newton's development of calculus. An important application of the N-body problem is within celestial mechanics and involves how planets and other celestial bodies move with mutual gravitational attraction. It is important in developing how satellites behave in space using complicated …
An Intertwined Cauchy––Schwarz–Type Inequality Based On A Lagrange–Type Identity, Iosif Pinelis
An Intertwined Cauchy––Schwarz–Type Inequality Based On A Lagrange–Type Identity, Iosif Pinelis
Michigan Tech Publications
Based on an apparently new Lagrange-type identity, a Cauchy–Schwarz-type inequality is proved. The mentioned identity is obtained by using certain “macro” variables; it is hoped that such a method can be used to prove or produce other identities and inequalities.
On Regular D-Handicap Tournaments, Bryan Freyberg, Melissa S. Keranen
On Regular D-Handicap Tournaments, Bryan Freyberg, Melissa S. Keranen
Michigan Tech Publications, Part 1
k-regular d-handicap tournament is an incomplete tournament in which n teams, ranked according to the natural numbers, play exactly k < n − 1 different teams exactly once and the strength of schedule of the ith ranked team is d more than the (i − 1)st ranked team for some d ≥ 1. That is, strength of schedules increase arithmetically by d with strength of team. A d-handicap distance antimagic labeling of a graph (Formula Presented)forms an arithmetic sequence with difference d ≥ 1. A graph G which admits such a labeling is called a d-handicap graph. Constructing a k-regular d-handicap tournament on n teams is equivalent to finding a k-regular d-handicap graph of order n. For d = 1 and n even, the existence has recently been completely settled for all pairs (n, k), and some results are known for d = 2. For d > 2, the only known result is restricted to the case where n is divisible by 2d+2. In this paper, we construct infinite families of d-handicap graphs where the order is not restricted to a power of 2.
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, Part 1
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, Part 1
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, Part 1
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, Part 1
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, Part 1
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, Part 1
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, Part 1
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, Part 1
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.
Hb-Pls: A Statistical Method For Identifying Biological Process Or Pathway Regulators By Integrating Huber Loss And Berhu Penalty With Partial Least Squares Regression, Wenping Deng, Kui Zhang, Cheng He, Sanzhen Liu, Hairong Wei
Hb-Pls: A Statistical Method For Identifying Biological Process Or Pathway Regulators By Integrating Huber Loss And Berhu Penalty With Partial Least Squares Regression, Wenping Deng, Kui Zhang, Cheng He, Sanzhen Liu, Hairong Wei
Michigan Tech Publications, Part 1
Gene expression data features high dimensionality, multicollinearity, and non-Gaussian distribution noise, posing hurdles for identification of true regulatory genes controlling a biological process or pathway. In this study, we integrated the Huber loss function and the Berhu penalty (HB) into partial least squares (PLS) framework to deal with the high dimension and multicollinearity property of gene expression data, and developed a new method called HB-PLS regression to model the relationships between regulatory genes and pathway genes. To solve the Huber-Berhu optimization problem, an accelerated proximal gradient descent algorithm with at least 10 times faster than the general convex optimization solver …
Crash Risk-Based Prioritization Of Basic Safety Message In Dsrc, Seungmo Kim, Byung Jun Kim
Crash Risk-Based Prioritization Of Basic Safety Message In Dsrc, Seungmo Kim, Byung Jun Kim
Michigan Tech Publications, Part 1
Dedicated short-range communications (DSRC) is one of the key technologies enabling safety-critical applications for intelligent transportation system (ITS). Considering the significance of such safety-of-life applications, it is of utmost importance to guarantee reliable delivery of basic safety messages (BSMs). However, in accordance with a V2X network being inherently dynamic in key aspects such as vehicle density and velocity, the networking behavior of a DSRC system is usually highly complicated to analyze. In addition, the United States Federal Communications Commission (US FCC) recently proposed the so-called “5.9 GHz band innovation”, which includes a plan to reduce bandwidth for DSRC to 10 …
Article The Singular Value Expansion For Arbitrary Bounded Linear Operators, Daniel K. Crane, Mark S. Gockenbach
Article The Singular Value Expansion For Arbitrary Bounded Linear Operators, Daniel K. Crane, Mark S. Gockenbach
Michigan Tech Publications, Part 1
The singular value decomposition (SVD) is a basic tool for analyzing matrices. Regarding a general matrix as defining a linear operator and choosing appropriate orthonormal bases for the domain and co-domain allows the operator to be represented as multiplication by a diagonal matrix. It is well known that the SVD extends naturally to a compact linear operator mapping one Hilbert space to another; the resulting representation is known as the singular value expansion (SVE). It is less well known that a general bounded linear operator defined on Hilbert spaces also has a singular value expansion. This SVE allows a simple …
Identities And Inequalities For The Cosine And Sine Functions, Iosif Pinelis
Identities And Inequalities For The Cosine And Sine Functions, Iosif Pinelis
Michigan Tech Publications, Part 1
Identities and inequalities for the cosine and sine functions are obtained.
Testing Gene-Environment Interactions For Rare And/Or Common Variants In Sequencing Association Studies., Zihan Zhao, Jianjun Zhang, Qiuying Sha, Han Hao
Testing Gene-Environment Interactions For Rare And/Or Common Variants In Sequencing Association Studies., Zihan Zhao, Jianjun Zhang, Qiuying Sha, Han Hao
Michigan Tech Publications, Part 1
The risk of many complex diseases is determined by a complex interplay of genetic and environmental factors. Advanced next generation sequencing technology makes identification of gene-environment (GE) interactions for both common and rare variants possible. However, most existing methods focus on testing the main effects of common and/or rare genetic variants. There are limited methods developed to test the effects of GE interactions for rare variants only or rare and common variants simultaneously. In this study, we develop novel approaches to test the effects of GE interactions of rare and/or common risk, and/or protective variants in sequencing association studies. We …
Uniformly Resolvable Decompositions Of Kv In 1-Factors And 4-Stars, Melissa S. Keranen, Donald L. Kreher, Salvatore Milici, Antoinette Tripodi
Uniformly Resolvable Decompositions Of Kv In 1-Factors And 4-Stars, Melissa S. Keranen, Donald L. Kreher, Salvatore Milici, Antoinette Tripodi
Michigan Tech Publications, Part 1
If X is a connected graph, then an X-factor of a larger graph is a spanning subgraph in which all of its components are isomorphic to X. A uniformly resolvable {X, Y }-decomposition of the complete graph Kv is an edge decomposition of Kv into exactly r X-factors and s Y -factors. In this article we determine necessary and sufficient conditions for when the complete graph Kv has a uniformly resolvable decompositions into 1-factors and K1,4-factors.
Perfect 2-Colorings Of The Grassmann Graph Of Planes, Stefaan Dewinter, Klaus Metsch
Perfect 2-Colorings Of The Grassmann Graph Of Planes, Stefaan Dewinter, Klaus Metsch
Michigan Tech Publications, Part 1
We construct an infinite family of intriguing sets, or equivalently perfect 2-colorings, that are not tight in the Grassmann graph of planes of PG(n, q), n ≥ 5 odd, and show that the members of the family are the smallest possible examples if n ≥ 9 or q ≥ 25.
On The Hamilton-Waterloo Problem: The Case Of Two Cycles Sizes Of Different Parity, Melissa S. Keranen, Adrian Pastine
On The Hamilton-Waterloo Problem: The Case Of Two Cycles Sizes Of Different Parity, Melissa S. Keranen, Adrian Pastine
Michigan Tech Publications, Part 1
The Hamilton-Waterloo problem asks for a decomposition of the complete graph of order v into r copies of a 2-factor F1 and s copies of a 2-factor F2 such that r+s = v−1 2 . If F1 consists of m-cycles and F2 consists of n cycles, we say that a solution to (m, n)- HWP(v; r, s) exists. The goal is to find a decomposition for every possible pair (r, s). In this paper, we show that for odd x and y, there is a solution to (2kx, y)-HWP(vm; r, s) if gcd(x, y) ≥ 3, m ≥ 3, and …
Families Of Major Index Distributions: Closed Forms And Unimodality, William Keith
Families Of Major Index Distributions: Closed Forms And Unimodality, William Keith
Michigan Tech Publications, Part 1
Closed forms for fλ,i(q):=∑τ∈SYT(λ):des(τ)=iqmaj(τ)fλ,i(q):=∑τ∈SYT(λ):des(τ)=iqmaj(τ), the distribution of the major index over standard Young tableaux of given shapes and specified number of descents, are established for a large collection of λλ and ii. Of particular interest is the family that gives a positive answer to a question of Sagan and collaborators. All formulas established in the paper are unimodal, most by a result of Kirillov and Reshetikhin. Many can be identified as specializations of Schur functions via the Jacobi-Trudi identities. If the number of arguments is sufficiently large, it is shown that any finite principal specialization of any Schur function sλ(1,q,q2,…,qn−1)sλ(1,q,q2,…,qn−1) …
Universal Rank-Order Transform To Extract Signals From Noisy Data, Glenn Ierley, Alexander Kostinski
Universal Rank-Order Transform To Extract Signals From Noisy Data, Glenn Ierley, Alexander Kostinski
Michigan Tech Publications, Part 1
We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric and objective, and the required data processing is parsimonious. The main ingredients include a rank-order data matrix and its transform to a stable form, which provide linear trends in excellent agreement with least squares regression, despite the loss of magnitude information. A group symmetry orthogonal decomposition of the 2D rank-order transform for iid (white) noise is further ordered by principal component analysis. This two-step procedure provides a noise “etalon” used to characterize arbitrary stationary stochastic processes. The …
Cyclotomic Trace Codes, Dean Crnkovic, Andrea Svob, Vladimir Tonchev
Cyclotomic Trace Codes, Dean Crnkovic, Andrea Svob, Vladimir Tonchev
Michigan Tech Publications, Part 1
A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers (s ≥ 2) of all nonzero elements in GF(pm), where p ≥ 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over GF(4) that give rise to optimal or near optimal quantum codes. In addition, the codes yield interesting combinatorial structures, such as strongly regular graphs and block designs.
Block-Avoiding Sequencings Of Points In Steiner Triple Systems, Donald L. Kreher, Douglas R. Stnson
Block-Avoiding Sequencings Of Points In Steiner Triple Systems, Donald L. Kreher, Douglas R. Stnson
Michigan Tech Publications, Part 1
Given an STS(v), we ask if there is a permutation of the points of the design such that no L consecutive points in this permutation contain a block of the design. Such a permutation is called an L-good sequencing. We prove that 3-good sequencings exist for any STS(v) with v>3and 4-good sequencings exist for any STS(v) with v>71. Similar results also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v=7,9,13 and 15.
Assessing The Likelihood Of Having False Positives Caused By Population Stratification, Renfang Jiang, Jianping Dong
Assessing The Likelihood Of Having False Positives Caused By Population Stratification, Renfang Jiang, Jianping Dong
Michigan Tech Publications, Part 1
Population stratification is always a concern in association analysis. There is a debate on the extent of the problem in less extreme situations (Thomas and Witte [1], Wacholder et al. [2]). Wacholder et al.[3] and Ardlie et al. [4] showed that hidden population structure is not a serious threat to case-control designs. We propose a method of assessing the seriousness of the population stratification before designing association studies. If population stratification is not a serious problem, one may consider using case-control study instead of family-based design to get more power. In a case-control design, we compare chi-square …
Assessment Of Post-Wildfire Debris Flow Occurrence Using Classifier Tree, Priscilla Addison, Thomas Oommen, Qiuying Sha
Assessment Of Post-Wildfire Debris Flow Occurrence Using Classifier Tree, Priscilla Addison, Thomas Oommen, Qiuying Sha
Michigan Tech Publications, Part 1
Besides the dangers of an actively burning wildfire, a plethora of other hazardous consequences can occur afterwards. Debris flows are among the most hazardous of these, being known to cause fatalities and extensive damage to infrastructure. Although debris flows are not exclusive to fire affected areas, a wildfire can increase a location’s susceptibility by stripping its protective covers like vegetation and introducing destabilizing factors such as ash filling soil pores to increase runoff potential. Due to the associated dangers, researchers are developing statistical models to isolate susceptible locations. Existing models predominantly employ the logistic regression algorithm; however, previous studies have …
A Gene Based Approach To Test Genetic Association Based On An Optimally Weighted Combination Of Multiple Traits., Jianjun Zhang, Qiuying Sha, Guanfu Liu, Xuexia Wang
A Gene Based Approach To Test Genetic Association Based On An Optimally Weighted Combination Of Multiple Traits., Jianjun Zhang, Qiuying Sha, Guanfu Liu, Xuexia Wang
Michigan Tech Publications, Part 1
There is increasing evidence showing that pleiotropy is a widespread phenomenon in complex diseases for which multiple correlated traits are often measured. Joint analysis of multiple traits could increase statistical power by aggregating multiple weak effects. Existing methods for multiple trait association tests usually study each of the multiple traits separately and then combine the univariate test statistics or combine p-values of the univariate tests for identifying disease associated genetic variants. However, ignoring correlation between phenotypes may cause power loss. Additionally, the genetic variants in one gene (including common and rare variants) are often viewed as a whole that affects …
Block-Avoiding Sequencings Of Points In Steiner Triple Systems, Donald L. Kreher, Douglas R. Stinson
Block-Avoiding Sequencings Of Points In Steiner Triple Systems, Donald L. Kreher, Douglas R. Stinson
Michigan Tech Publications, Part 1
Given an STS(v), we ask if there is a permutation of the points of the design such that no l consecutive points in this permutation contain a block of the design. Such a permutation is called an l-good sequenc-ing. We prove that 3-good sequencings exist for any STS(v) with v>3 and 4-good sequencings exist for any STS(v) with v>71. Similar re-sults also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v =7, 9, 13 and 15.