Statistics and Probability Commons^™

Simplified Models Of Vector Control Impact Upon Malaria Transmission By Zoophagic Mosquitoes, Samson S. Kiware, Nakul Chitnis, Sarah J. Moore, Gregor J. Devine, Silas Majambere, Stephen Merrill, Gerry F. Killeen

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

High coverage of personal protection measures that kill mosquitoes dramatically reduce malaria transmission where vector populations depend upon human blood. However, most primary malaria vectors outside of sub-Saharan Africa can be classified as “very zoophagic,” meaning they feed occasionally (

Methods and Findings

We extended a published malaria transmission model to examine the relationship between transmission, control, and the baseline proportion of bloodmeals obtained from humans (human blood index). The lower limit of the human blood index enables derivation of simplified models for zoophagic vectors that (1) Rely on only three field-measurable parameters. (2) Predict immediate and delayed (with …

Human Gene Copy Number Spectra Analysis In Congenital Heart Malformations, Aoy Tomita-Mitchell, Donna K. Mahnke, Craig Struble, Maureen E. Tuffnell, Karl D. Stamm, Mats Hidestrand, Susan Harris, Mary A. Goetsch, Pippa Simpson, David P. Bick, Ulrich Broeckel, Andrew N. Pelech, James S. Tweddell, Michael Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

The clinical significance of copy number variants (CNVs) in congenital heart disease (CHD) continues to be a challenge. Although CNVs including genes can confer disease risk, relationships between gene dosage and phenotype are still being defined. Our goal was to perform a quantitative analysis of CNVs involving 100 well-defined CHD risk genes identified through previously published human association studies in subjects with anatomically defined cardiac malformations. A novel analytical approach permitting CNV gene frequency “spectra” to be computed over prespecified regions to determine phenotype-gene dosage relationships was employed. CNVs in subjects with CHD (n = 945), subphenotyped into 40 …

Genomic Analysis Of Immune Response Against Vibrio Cholerae Hemolysin In Caenorhabditis Elegans, Surasri N. Sahu, Jada Lewis, Isha Patel, Serdar Bozdag, Jeong H. Lee, Joseph E. Leclerc, Hediye Nese Cinar

Mathematics, Statistics and Computer Science Faculty Research and Publications

Vibrio cholerae cytolysin (VCC) is among the accessory V. cholerae virulence factors that may contribute to disease pathogenesis in humans. VCC, encoded by hlyA gene, belongs to the most common class of bacterial toxins, known as poreforming toxins (PFTs). V. cholerae infects and kills Caenorhabditis elegans via cholerae toxin independent manner. VCC is required for the lethality, growth retardation and intestinal cell vacuolation during the infection. However, little is known about the host gene expression responses against VCC. To address this question we performed a microarray study in C. elegans exposed to V. cholerae strains with intact and deleted hlyA …

H-Colouring Bipartite Graphs, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, an H-colouring of G (or homomorphism from G to H) is a function from the vertices of G to the vertices of H that preserves adjacency. H-colourings generalize such graph theory notions as proper colourings and independent sets. For a given H, k∈V(H) and G we consider the proportion of vertices of G that get mapped to k in a uniformly chosen H-colouring of G. Our main result concerns this quantity when G is regular and bipartite. We find numbers 0⩽a−(k)⩽a+(k)⩽1 with the property that for all such G, with high probability the proportion is …

K-8 Preservice Teachers’ Inductive Reasoning In The Problem-Solving Contexts, Marta Magiera

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper reports the results from an exploratory study of K-8 pre-service teachers’ inductive reasoning. The analysis of 130 written solutions to seven tasks and 77 reflective journals completed by 20 pre-service teachers lead to descriptions of inductive reasoning processes, i.e. specializing, conjecturing, generalizing, and justifying, in the problem-solving contexts. The uncovered characterizations of the four inductive reasoning processes were further used to describe pathways of successful generalizations. The results highlight the importance of specializing and justifying in constructing powerful generalizations. Implications for teacher education are discussed.

Mathematical Dispositions And Student Learning: A Metaphorical Analysis, Jinfa Cai, Victoria Robison, John Moyer, Ning Wang, Bikai Nie

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

A Common Framework For Restriction Semigroups And Regular *-Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

Left restriction semigroups have appeared at the convergence of several flows of research, including the theories of abstract semigroups, of partial mappings, of closure operations and even in logic. For instance, they model unary semigroups of partial mappings on a set, where the unary operation takes a map to the identity map on its domain. This perspective leads naturally to dual and two-sided versions of the restriction property. From a varietal perspective, these classes of semigroups–more generally, the corresponding classes of Ehresmann semigroups–derive from reducts of inverse semigroups, now taking a to a⁺=aa⁻¹ (or, dually, …

A Cautionary Note On Generalized Linear Models For Covariance Of Unbalanced Longitudinal Data, Jianhua Z. Huang, Min Chen, Mehdi Maadooliat, Mohsen Pourahmadi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Missing data in longitudinal studies can create enormous challenges in data analysis when coupled with the positive-definiteness constraint on a covariance matrix. For complete balanced data, the Cholesky decomposition of a covariance matrix makes it possible to remove the positive-definiteness constraint and use a generalized linear model setup to jointly model the mean and covariance using covariates (Pourahmadi, 2000). However, this approach may not be directly applicable when the longitudinal data are unbalanced, as coherent regression models for the dependence across all times and subjects may not exist. Within the existing generalized linear model framework, we show how to overcome …

Physiologic Noise Regression, Motion Regression, And Toast Dynamic Field Correction In Complex-Valued Fmri Time Series, Andrew D. Hahn, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

As more evidence is presented suggesting that the phase, as well as the magnitude, of functional MRI (fMRI) time series may contain important information and that there are theoretical drawbacks to modeling functional response in the magnitude alone, removing noise in the phase is becoming more important. Previous studies have shown that retrospective correction of noise from physiologic sources can remove significant phase variance and that dynamic main magnetic field correction and regression of estimated motion parameters also remove significant phase fluctuations. In this work, we investigate the performance of physiologic noise regression in a framework along with correction for …

Various Characterizations Of Modified Weibull And Log Modified Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the well-known modified Weibull and log-modified Weibull distributions are presented. These characterizations are based on a simple relationship between two truncated moments; on the hazard function and on functions of the order statistics.

Generalizing Amdahl’S Law For Power And Energy, Rong Ge, Kirk W. Cameron

Mathematics, Statistics and Computer Science Faculty Research and Publications

Extending Amdahl's law to identify optimal power-performance configurations requires considering the interactive effects of power, performance, and parallel overhead.

Categoricity And Topological Graphs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let X be a topological graph, with arcs joined only at end points. If Y is any locally connected metrizable compactum that is co-elementarily equivalent to X, then Y is homeomorphic to X. In particular, X and Y are homeomorphic if some lattice base for one is elementarily equivalent to some lattice base for the other.

Protection By 20-5,14-Hedge Against Surgically-Induced Ischemia Reperfusion Lung Injury In Rats, Irshad Ali, Stephanie Gruenloh, Ying Gao, Anne V. Clough, John R. Falck, Meetha Medhora, Elizabeth R. Jacobs

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

We previously reported that the cytochrome P450 product 20-hydroxyeicosatetraenoic acid has prosurvival effects in pulmonary artery endothelial cells and ex vivo pulmonary arteries. We tested the potential of a 20-hydroxyeicosatetraenoic acid analog N-[20-hydroxyeicosa-5(Z),14(Z)-dienoyl]glycine (20-5,14-HEDGE) to protect against lung ischemic reperfusion injury in rats. Furthermore, we examined activation of innate immune system components, high mobility group box 1 (HMGB1) and toll-like receptor 4 (TLR4), in this model as well as the effect of 20-5,14-HEDGE on this signaling pathway.

Methods

Sprague-Dawley rats treated with 20-5,14-HEDGE or vehicle were subjected to surgically induced, unilateral lung ischemia for 60 minutes followed by reperfusion …

A Direct D-Bar Reconstruction Algorithm For Recovering A Complex Conductivity In 2d, Sarah J. Hamilton, C. N. L. Herrera, J. L. Mueller, A. Von Herrmann

Mathematics, Statistics and Computer Science Faculty Research and Publications

A direct reconstruction algorithm for complex conductivities in W^{2, ∞}(Ω), where Ω is a bounded, simply connected Lipschitz domain in R² , is presented. The framework is based on the uniqueness proof by Francini (2000 Inverse Problems 6 107–19), but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

Modeling Temporal Pattern And Event Detection Using Hidden Markov Model With Application To A Sludge Bulking Data, Naveen K. Bansal, Xin Feng, Wenjing Zhang, Wutao Wi, Yuanhao Zhao

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper discusses a method of modeling temporal pattern and event detection based on Hidden Markov Model (HMM) for a continuous time series data. We also provide methods for checking model adequacy and predicting future events. These methods are applied to a real example of sludge bulking data for detecting sludge bulking for a water plant in Chicago.

Characterizations Of Certain Continuous Univariate Distributions Based On The Conditional Distribution Of Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

The problem of characterizing probability distributions is an interesting problem which has recently attracted the attention of many researchers. Various characterization results have been established in different directions as reported in the literature. We present here, various characterizations of certain univariate continuous distributions based on the conditional distribution of generalized order statistics.

Design And Implementation Of An Open Framework For Ubiquitous Carbon Footprint Calculator Applications, Farzana Rahman, Casey O'Brien, Sheikh Iqbal Ahamed, He Zhang, Lin Liu

Mathematics, Statistics and Computer Science Faculty Research and Publications

As climate change is becoming an important global issue, more and more people are beginning to pay attention to reducing greenhouse gas emissions. To measure personal or household carbon dioxide emission, there are already plenty of carbon footprint calculators available on the web. Most of these calculators use quantitative models to estimate carbon emission caused by a user's activities. Although these calculators can promote public awareness regarding carbon emission due to an individual's behavior, there are concerns about the consistency and transparency of these existing CO₂ calculators. Apart from a small group of smart phone based carbon footprint calculator …

Interactive Real-Time Embedded Systems Education Infused With Applied Internet Telephony, Kyle Persohn, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

The transition from traditional circuit-switched phone systems to modern packet-based Internet telephony networks demands tools to support Voice over Internet Protocol (VoIP) development. In this paper, we introduce the XinuPhone, an integrated hardware/software approach for educating users about VoIP technology on a real-time embedded platform. We propose modular course topics for design-oriented, hands-on laboratory exercises: filter design, timing, serial communications, interrupts and resource budgeting, network transmission, and system benchmarking. Our open-source software platform encourages development and testing of new CODECs alongside existing standards, unlike similar commercial solutions. Furthermore, the supporting hardware features inexpensive, readily available components designed specifically for educational …

An Experimental Nexos Laboratory Using Virtual Xinu, Paul Ruth, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

The Nexos Project is a joint effort between Marquette University, the University of Buffalo, and the University of Mississippi to build curriculum materials and a supporting experimental laboratory for hands-on projects in computer systems courses. The approach focuses on inexpensive, flexible, commodity embedded hardware, freely available development and debugging tools, and a fresh implementation of a classic operating system, Embedded Xinu, that is ideal for student exploration. This paper describes an extension to the Nexos laboratory that includes a new target platform composed of Qemu virtual machines. Virtual Xinu addresses two challenges that limit the effectiveness of Nexos. First, potential …

Utilizing Induced Voxel Correlation In Fmri Analysis, Daniel B. Rowe, Andrew S. Nencka

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

The Utility Of Transient Sensitivity For Wildlife Management And Conservation: Bison As A Case Study, Michael Buhnerkempe, Nathanial Burch, Sarah J. Hamilton, Kerry M. Byrne, Eddie Childers, Kirstin A. Holfelder, Lindsay Mcmanus, Matthew I. Pyne, Greg Schroeder, Paul F. Doherty

Mathematics, Statistics and Computer Science Faculty Research and Publications

Developing effective management strategies is essential to conservation biology. Population models and sensitivity analyses on model parameters have provided a means to quantitatively compare different management strategies, allowing managers to objectively assess the resulting impacts. Inference from traditional sensitivity analyses (i.e., eigenvalue sensitivity methods) is only valid for a population at its stable age distribution, while more recent methods have relaxed this assumption and instead focused on transient population dynamics. However, very few case studies, especially in long-lived vertebrates where transient dynamics are potentially most relevant, have applied these transient sensitivity methods and compared them to eigenvalue sensitivity methods. We …

Prospective K-8 Teachers’ Knowledge Of Relational Thinking, Marta Magiera, Leigh A. Van Den Kieboom, John Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

The goal of this study was to examine two issues: First, pre-service teachers’ ability and inclination to think relationally prior to instruction about the role relational thinking plays in the K-8 mathematics curriculum. Second, to examine task specific variables possibly associated with pre-service teachers’ inclination to engage in relational thinking. The results revealed that preservice teachers engage in relational thinking about equality, however, their inclination to do so is rather limited. Furthermore, they tend to engage in relational thinking more frequently in the context of arithmetic than algebra-related tasks. Pre-service teachers’ inclination to engage in relational thinking appeared to also …

Characterization Of The Threshold For Nad(P)H:Quinone Oxidoreductase Activity In Intact Sulforaphane-Treated Pulmonary Arterial Endothelial Cells, Robert D. Bongard, Gary S. Krenz, Adam J. Gastonguay, Carol L. Williams, Brian J. Lindemer, Marilyn P. Merker

Mathematics, Statistics and Computer Science Faculty Research and Publications

Treatment of bovine pulmonary arterial endothelial cells in culture with the phase II enzyme inducer sulforaphane (5 μM, 24 h; sulf-treated) increased cell-lysate NAD(P)H:quinone oxidoreductase (NQO1) activity by 5.7 ± 0.6 (mean ± SEM)-fold, but intact-cell NQO1 activity by only 2.8 ± 0.1-fold compared to control cells. To evaluate the hypothesis that the threshold for sulforaphane-induced intact-cell NQO1 activity reflects a limitation in the capacity to supply NADPH at a sufficient rate to drive all the induced NQO1 to its maximum activity, total KOH-extractable pyridine nucleotides were measured in cells treated with duroquinone to stimulate maximal NQO1 activity. NQO1 activation …

Characterizing The Arc, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We offer a mathematical logic framework for talking about when a given topological space is characterizable relative to a “class of its peers.” The framework involves a relational alphabet for which there is a natural way of assigning relational structures to spaces in the peer class; and a putative characterization of the given space consists of a set of first-order sentences over that alphabet, all true for the space. The attempted characterization is a success if any peer space satisfying all the sentences is inevitably homeomorphic to the given space.

For example, it has long been known that the arc …

Common Hypercyclic Vectors For The Conjugate Class Of A Hypercyclic Operator, Kit C. Chan, Rebecca Sanders

Mathematics, Statistics and Computer Science Faculty Research and Publications

Given a separable, infinite dimensional Hilbert space, it was recently shown by the authors that there is a path of chaotic operators, which is dense in the operator algebra with the strong operator topology, and along which every operator has the exact same dense G_δ set of hypercyclic vectors. In the present work, we show that the conjugate set of any hypercyclic operator on a separable, infinite dimensional Banach space always contains a path of operators which is dense with the strong operator topology, and yet the set of common hypercyclic vectors for the entire path is a dense …

Signal And Noise In Complex-Valued Sense Mr Image Reconstruction, Daniel B. Rowe, Iain P. Bruce

Mathematics, Statistics and Computer Science Faculty Research and Publications

In fMRI, brain images are not measured instantaneously and a volume of images can take two seconds to acquire at a low 64x64 resolution. Significant effort has been put forth on many fronts to decrease image acquisition time including parallel imaging. In parallel imaging, sub-sampled spatial frequency points are measured in parallel and combined to form a single image. Measurement time is decreased at the expense of increased image reconstruction difficulty and time. One significant parallel imaging technique known as SENSE utilizes a complex-valued regression coefficient estimation process with transposes replaced by conjugate transposes. However, in SENSE the noise structure …

Semidistributive Inverse Semigroups, Ii, Kyeong Hee Cheong, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The description by Johnston-Thom and the second author of the inverse semigroups S for which the lattice LJ(S) of full inverse subsemigroups of S is join semidistributive is used to describe those for which (a) the lattice L(S) of all inverse subsemigroups or (b) the lattice lo(S) of convex inverse subsemigroups have that property. In contrast with the methods used by the authors to investigate lower semimodularity, the methods are based on decompositions via G_S, the union of the subgroups of the semigroup (which is necessarily cryptic).

The (1,2)-Step Competition Graph Of A Tournament, Kim A. S. Factor, Sarah Merz

Mathematics, Statistics and Computer Science Faculty Research and Publications

The competition graph of a digraph, introduced by Cohen in 1968, has been extensively studied. More recently, in 2000, Cho, Kim, and Nam defined the m-step competition graph. In this paper, we offer another generalization of the competition graph. We define the (1,2)-step competition graph of a digraph D, denoted C_1,2(D), as the graph on V(D) where {x,y}∈E(C_1,2(D)) if and only if there exists a vertex z≠x,y, such that either d_D−y( …

Longitudinal Investigation Of The Curricular Effect: An Analysis Of Student Learning Outcomes From The Liecal Project In The United States, Jinfa Cai, Ning Wang, John Moyer, Chuang Wang, Bikai Nie

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including …

Detecting Temporal Patterns Using Reconstructed Phase Space And Support Vector Machine In The Dynamic Data System, Wenjing Zhang, Xin Feng

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper we present a method for detecting dynamic temporal patterns that are characteristic and predictive of significant events in a dynamic data system. We employ the Gaussian Mixture Model (GMM) to cluster the data sequence into three categories of signals, e.g. normal, patterns and events. The data sequence is then embedded into a Reconstructed Phase Space (RPS) which is topologically equivalent to the dynamics of the original system. We apply a hybrid method using Support Vector Machines (SVM) and Maximum a Posterior (MAP) to classify temporal pattern signals based on the event function. We performed two experimental applications …