Physical Sciences and Mathematics Commons^™

Exploding Haystacks, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Exploding Haystacks: Solutions For Fermi Questions, March 2023, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Numerical Modeling Of Submicron Particles For Acoustic Concentration In Gaseous Flow, Jizhou Liu, Xiaodong Li, Fang Q. Hu

Mathematics & Statistics Faculty Publications

This paper intends to explore the rationality and feasibility of modeling dispersed submicron particles in air by a kinetic-based method called the unified gas-kinetic scheme (UGKS) and apply it to the simulation of particle concentration under a transverse standing wave. A gas-particle coupling scheme is proposed where the gas phase is modeled by the two-dimensional linearized Euler equations (LEE) and, through the analogous behavior between the rarefied gas molecules and the air-suspended particles, a modified UGKS is adopted to estimate the particle dynamics. The Stokes' drag force and the acoustic radiation force applied on particles are accounted for by introducing …

What's Your Sphericity Index? Rationalizing Surface Area And Volume, John A. Adam

Mathematics & Statistics Faculty Publications

Virginia Standards of Learning include mathematical content related to the surface area and the volume of various geometric objects. In the seventh grade, “Students... solve problems involving volume and surface area” In the eighth grade, “Proportional reasoning is expounded upon as students solve a variety of problems. Students find the volume and surface area of more complex three dimensional figures”. In high school geometry, “The student... use[s] surface area and volume of three-dimensional objects to solve practical problems” (Virginia Department of Education, 2016). The challenge is to find scenarios that are engaging to students and keep them interested in the …

Acute Systemic Inflammatory Response To Lipopolysaccharide Stimulation In Pigs Divergently Selected For Residual Feed Intake, Haibo Liu, Kristina M. Feye, Yet T. Nguyen, Anoosh Rakhshandeh, Crystal L. Loving, Jack C. M. Sekkers, Nicholas K. Gabler, Christopher K. Tuggle

Mathematics & Statistics Faculty Publications

Background: It is unclear whether improving feed efficiency by selection for low residual feed intake (RFI) compromises pigs’ immunocompetence. Here, we aimed at investigating whether pig lines divergently selected for RFI had different inflammatory responses to lipopolysaccharide (LPS) exposure, regarding to clinical presentations and transcriptomic changes in peripheral blood cells.

Results: LPS injection induced acute systemic inflammation in both the low-RFI and high-RFI line (n = 8 per line). At 4 h post injection (hpi), the low-RFI line had a significantly lower (p= 0.0075) mean rectal temperature compared to the high-RFI line. However, no significant differences in complete blood count …

Modelling Cholera In Periodic Environments, Drew Posny, Jin Wang

Mathematics & Statistics Faculty Publications

We propose a deterministic compartmental model for cholera dynamics in periodic environments. The model incorporates seasonal variation into a general formulation for the incidence (or, force of infection) and the pathogen concentration. The basic reproduction number of the periodic model is derived, based on which a careful analysis is conducted on the epidemic and endemic dynamics of cholera. Several specific examples are presented to demonstrate this general model, and numerical simulation results are used to validate the analytical prediction.

Next-Peak: A Normal-Exponential Two-Peak Model For Peak-Calling In Chip-Seq Data, Nak-Kyeong Kim, Rasika V. Jayatillake, John L. Spouge

Mathematics & Statistics Faculty Publications

Background: Chromatin immunoprecipitation followed by high-throughput sequencing (ChIP-seq) can locate transcription factor binding sites on genomic scale. Although many models and programs are available to call peaks, none has dominated its competition in comparison studies.

Results: We propose a rigorous statistical model, the normal-exponential two-peak (NEXT-peak) model, which parallels the physical processes generating the empirical data, and which can naturally incorporate mappability information. The model therefore estimates total strength of binding (even if some binding locations do not map uniquely into a reference genome, effectively censoring them); it also assigns an error to an estimated binding location. The comparison study …

Probability Of Identification: A Statistical Model For The Validation Of Qualitative Botanical Identification Methods, Robert A. Labudde, James M. Harnly

Mathematics & Statistics Faculty Publications

A qualitative botanical identification method (BIM) is an analytical procedure that returns a binary result (1 = Identified, 0 = Not Identified). A BIM may be used by a buyer, manufacturer, or regulator to determine whether a botanical material being tested is the same as the target (desired) material, or whether it contains excessive nontarget (undesirable) material. The report describes the development and validation of studies for a BIM based on the proportion of replicates identified, or probability of identification (POI), as the basic observed statistic. The statistical procedures proposed for data analysis follow closely those of the probability of …

A Generalized Cholera Model And Epidemic-Endemic Analysis, Jin Wang, Shu Liao

Mathematics & Statistics Faculty Publications

The transmission of cholera involves both human-to-human and environment-to-human pathways that complicate its dynamics. In this paper, we present a new and unified deterministic model that incorporates a general incidence rate and a general formulation of the pathogen concentration to analyse the dynamics of cholera. Particularly, this work unifies many existing cholera models proposed by different authors. We conduct equilibrium analysis to carefully study the complex epidemic and endemic behaviour of the disease. Our results show that despite the incorporation of the environmental component, there exists a forward transcritical bifurcation at R₀ = 1 for the combined human-environment epidemiological …

On The Global Stability Of A Generalized Cholera Epidemiological Model, Yuanji Cheng, Jin Wang, Xiuxiang Yang

Mathematics & Statistics Faculty Publications

In this paper, we conduct a careful global stability analysis for a generalized cholera epidemiological model originally proposed in [J. Wang and S. Liao, A generalized cholera model and epidemic/endemic analysis, J. Biol. Dyn. 6 (2012), pp. 568-589]. Cholera is a water-and food-borne infectious disease whose dynamics are complicated by the multiple interactions between the human host, the pathogen, and the environment. Using the geometric approach, we rigorously prove the endemic global stability for the cholera model in three-dimensional (when the pathogen component is a scalar) and four-dimensional (when the pathogen component is a vector) systems. This work unifies the …

Stability Analysis And Application Of A Mathematical Cholera Model, Shu Liao, Jim Wang

Mathematics & Statistics Faculty Publications

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

Analysis Of Biological Features Associated With Meiotic Recombination Hot And Cold Spots In Saccharomyces Cerevisiae, Loren Hansen, Nak-Kyeong Kim, Leonardo Mariño-Ramírez, David Landsman

Mathematics & Statistics Faculty Publications

Meiotic recombination is not distributed uniformly throughout the genome. There are regions of high and low recombination rates called hot and cold spots, respectively. The recombination rate parallels the frequency of DNA double-strand breaks (DSBs) that initiate meiotic recombination. The aim is to identify biological features associated with DSB frequency. We constructed vectors representing various chromatin and sequence-based features for 1179 DSB hot spots and 1028 DSB cold spots. Using a feature selection approach, we have identified five features that distinguish hot from cold spots in Saccharomyces cerevisiae with high accuracy, namely the histone marks H3K4me3, H3K14ac, H3K36me3, and H3K79me3; …

Putting The X In Biology: A Review Of The Mathematics Of Life, John Adam

Mathematics & Statistics Faculty Publications

(First Paragraph) Charles Darwin's 1859 work On the Origin of the Species contained no equations. But that does not mean mathematics has no role to play in the science of life; in fact, the field of biomathematics is burgeoning and has been for several decades. Ian Stewart's new book does an admirable job of unfolding the mathematics undergirding so much of the research being carried out today in the many fields that comprise the subject of biology. Stewart sets the context by noting five great revolutions that have changed the way scientists think about life. These five revolutions are: (i) …

Weighted Scores Method For Regression Models With Dependent Data, Aristidis K. Nikoloulopoulos, Harry Joe, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

There are copula-based statistical models in the literature for regression with dependent data such as clustered and longitudinal overdispersed counts, for which parameter estimation and inference are straightforward. For situations where the main interest is in the regression and other univariate parameters and not the dependence, we propose a "weighted scores method", which is based on weighting score functions of the univariate margins. The weight matrices are obtained initially fitting a discretized multivariate normal distribution, which admits a wide range of dependence. The general methodology is applied to negative binomial regression models. Asymptotic and small-sample efficiency calculations show that our …

Computational Protein Biomarker Prediction: A Case Study For Prostate Cancer, Michael Wagner, Dayanand N. Naik, Alex Pothen, Srinivas Kasukurti, Raghu Ram Devineni, Bao-Ling Adam, O. John Semmes, George L. Wright Jr.

Mathematics & Statistics Faculty Publications

Background: Recent technological advances in mass spectrometry pose challenges in computational mathematics and statistics to process the mass spectral data into predictive models with clinical and biological significance. We discuss several classification-based approaches to finding protein biomarker candidates using protein profiles obtained via mass spectrometry, and we assess their statistical significance. Our overall goal is to implicate peaks that have a high likelihood of being biologically linked to a given disease state, and thus to narrow the search for biomarker candidates.

Results: Thorough cross-validation studies and randomization tests are performed on a prostate cancer dataset with over 300 patients, obtained …

Protocols For Disease Classification From Mass Spectrometry Data, Michael Wagner, Dayanand Naik, Alex Pothen

Mathematics & Statistics Faculty Publications

We report our results in classifying protein matrix-assisted laser desorption/ionizationtime of flight mass spectra obtained from serum samples into diseased and healthy groups. We discuss in detail five of the steps in preprocessing the mass spectral data for biomarker discovery, as well as our criterion for choosing a small set of peaks for classifying the samples. Cross-validation studies with four selected proteins yielded misclassification rates in the 10-15% range for all the classification methods. Three of these proteins or protein fragments are down-regulated and one up-regulated in lung cancer, the disease under consideration in this data set. When cross-validation studies …

Activator-Inhibitor Control Of Tissue Growth, John A. Adam

Mathematics & Statistics Faculty Publications

This note develops a simple model for the competition between activator and inhibitor control mechanisms in one-dimensional tissue growth. The pedagogic usefulness of such a model is that it is easily accessible to undergraduate applied mathematicians and is suggestive of behavior known to occur in more realistic biological systems (e.g., some types of cancer). The limitations of the model are obvious and can provide a basis for discussion of the applicability of complementary levels of description in mathematical modeling.