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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
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
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
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
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
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
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
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 …
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
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.
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
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 …