Mathematics Commons^™

Decompositions Of Signed-Graphic Matroids, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We give a decomposition theorem for signed graphs whose frame matroids are binary and a decomposition theorem for signed graphs whose frame matroids are quaternary.

Step-Up Simultaneous Tests For Identifying Active Effects In Orthogonal Saturated Designs, Samuel S. Wu, Weizhen Wang

Mathematics and Statistics Faculty Publications

A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given alpha level in the strong sense.

Degradation Models And Implied Lifetime Distributions, Suk Joo Bae, Way Kuo, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In experiments where failure times are sparse, degradation analysis is useful for the analysis of failure time distributions in reliability studies. This research investigates the link between a practitioner's selected degradation model and the resulting lifetime model. Simple additive and multiplicative models with single random effects are featured. Results show that seemingly innocuous assumptions of the degradation path create surprising restrictions on the lifetime distribution. These constraints are described in terms of failure rate and distribution classes.

Statistical Models For Hot Electron Degradation In Nano-Scaled Mosfet Devices, Suk Joo Bae, Seong-Joon Kim, Way Kuo, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In a MOS structure, the generation of hot carrier interface states is a critical feature of the item's reliability. On the nano-scale, there are problems with degradation in transconductance, shift in threshold voltage, and decrease in drain current capability. Quantum mechanics has been used to relate this decrease to degradation, and device failure. Although the lifetime, and degradation of a device are typically used to characterize its reliability, in this paper we model the distribution of hot-electron activation energies, which has appeal because it exhibits a two-point discrete mixture of logistic distributions. The logistic mixture presents computational problems that are …

On The Direction Of Pitchfork Bifurcation, Xiaojie Hou, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result.

On The Exact Multiplicity Of Solutions For Boundary-Value Problems Via Computing The Direction Of Bifurcations, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

A Comparison Of Graphical Methods For Assessing The Proportional Hazards Assumptions In The Cox Model, Inger Persson, Harry J. Khamis

Mathematics and Statistics Faculty Publications

Six graphical procedures to check the assumption of proportional hazards for the Cox model are described and compared. A new way of comparing the graphical procedures using a Kolmogorov-Smirnov like maximum deviation criterion for rejection is derived for each procedure. The procedures are evaluated in a simulation study under proportional hazards and five different forms of nonproportional hazards: (1) increasing hazards, (2) decreasing hazards, (3) crossing hazards, (4) diverging hazards, and (5) nonmonotonic hazards. The procedures are compared in the two-sample case corresponding to two groups with different hazard functions. None of the procedures under consideration require partitioning of the …

Projective-Planar Signed Graphs And Tangled Signed Graphs, Dan Slilaty

Mathematics and Statistics Faculty Publications

A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained by taking a projective-planar signed graph or a copy of −K5" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">−K5 and then taking 1-, 2-, and 3-sums with balanced signed grap

A Robust Measure Of Correlation Between Two Genes On A Microarray, Johanna S. Hardin, Aya Mitani '06, Leanne Hicks, Brian Vankoten

Pomona Faculty Publications and Research

Background

The underlying goal of microarray experiments is to identify gene expression patterns across different experimental conditions. Genes that are contained in a particular pathway or that respond similarly to experimental conditions could be co-expressed and show similar patterns of expression on a microarray. Using any of a variety of clustering methods or gene network analyses we can partition genes of interest into groups, clusters, or modules based on measures of similarity. Typically, Pearson correlation is used to measure distance (or similarity) before implementing a clustering algorithm. Pearson correlation is quite susceptible to outliers, however, an unfortunate characteristic when dealing …