Mathematics Commons^™

Disrupted Superior Collicular Activity May Reveal Cervical Dystonia Disease Pathomechanisms, Eavan M. Mcgovern, Owen Killian, Shruti Narashimham, Brendan Quinlivan, John Butler, Rebecca Beck, Ines Beiser, Laura W. Williams, Ronan P. Killeen, Michael Farrell, Sean O'Riordan, Richard B. Reilly, Michael Hutchinson

Articles

Cervical dystonia is a common neurological movement disorder characterised by muscle contractions causing abnormal movements and postures affecting the head and neck. The neural networks underpinning this condition are incompletely understood. While animal models suggest a role for the superior colliculus in its pathophysiology, this link has yet to be established in humans. The present experiment was designed to test the hypothesis that disrupted superior collicular processing is evident in affected patients and in relatives harbouring a disease-specific endophenotype (abnormal temporal discrimination). The study participants were 16 cervical dystonia patients, 16 unaffected first-degree relatives with abnormal temporal discrimination, 16 unaffected …

Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri

Theses and Dissertations

miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …

Interaction Graphs Derived From Activation Functions And Their Application To Gene Regulation, Simon Joyce

Graduate Dissertations and Theses

Interaction graphs are graphic representations of complex networks of mutually interacting components. Their main application is in the field of gene regulatory networks, where they are used to visualize how the expression levels of genes activate or inhibit the expression levels of other genes.

First we develop a natural transformation of activation functions and their derived interaction graphs, called conjugation, that is related to a natural transformation of signed digraphs called switching isomorphism. This is a useful tool for the analysis of interaction graphs used throughout the rest of the dissertation.

We then discuss the question of what restrictions, if …

Dynamics Of Gene Networks In Cancer Research, Paul Scott

College of Graduate Studies: Theses & Dissertations

Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …

Introducing A Theory Of Neutrosophic Evolution: Degrees Of Evolution, Indeterminacy, And Involution, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

During the process of adaptation of a being (plant, animal, or human), to a new environment or conditions, the being partially evolves, partially devolves (degenerates), and partially is indeterminate i.e. neither evolving nor devolving, therefore unchanged (neutral), or the change is unclear, ambiguous, vague, as in neutrosophic logic. Thank to adaptation, one therefore has: evolution, involution, and indeterminacy (or neutrality), each one of these three neutrosophic components in some degree. The degrees of evolution/indeterminacy/involution are referred to both: the structure of the being (its body parts), and functionality of the being (functionality of each part, or inter-functionality of the parts …

Computational Methods For Prediction And Classification Of G Protein-Coupled Receptors, Khodeza Begum

Open Access Theses & Dissertations

G protein-coupled receptors (GPCRs) constitute the largest group of membrane receptor proteins in eukaryotes. Due to their significant roles in many physiological processes such as vision, smell, and inflammation, GPCRs are the targets of many prescribed drugs. However, the functional and structural diversity of GPCRs has kept their prediction and classification based on amino acid sequence data as a challenging bioinformatics problem. As existing computational methods to predict and classify GPCRs are focused on mammalian (mostly human) data, the ultimate goal of our project is to establish an ensemble approach and implement a web-based software that can be used reliably …

Birth Mass Is The Key To Understanding The Negative Correlation Between Lifespan And Body Size In Dogs, Rong Fan, Gayla R. Olbricht, Xavior Baker, Chen Hou

Mathematics and Statistics Faculty Research & Creative Works

Larger dog breeds live shorter than the smaller ones, opposite of the mass-lifespan relationship observed across mammalian species. Here we use data from 90 dog breeds and a theoretical model based on the first principles of energy conservation and life history tradeoffs to explain the negative correlation between longevity and body size in dogs. We found that the birth/adult mass ratio of dogs scales negatively with adult size, which is different than the weak interspecific scaling in mammals. Using the model, we show that this ratio, as an index of energy required for growth, is the key to understanding why …

Effects Of Cell Cycle Noise On Excitable Gene Circuits, Alan Veliz-Cuba, Chinmaya Gupta, Matthew R. Bennett, Krešimir Josić, William Ott

Mathematics Faculty Publications

We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this concentration effect intensifies in the presence of transcriptional delay. We explain this concentration effect with a three-states stochastic model. For genetic oscillators, we quantify the temporal correlations between daughter cells induced by cell division. Temporal correlations must be captured properly in order to accurately quantify noise sources within gene networks.

Csp And “Omics” Technology Applied On Versatile And Intelligent Portable Platform For Modeling Complex Bio-Medical Data, Florentin Smarandache, Luige Vladareanu, Mihaiela Iliescu, Hongbo Wang, Feng Yongfei, Victor Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents relevant aspects of the idea of using the digital medicine in cancer, so that to shape a viable strategy for creating and implementing an interactive digital platform, NEO-VIP, that should be the basic support to design the strategy for integration of basic, clinical and environmental research on neoplasia progression to cancer. The two main components of the VIPRO Platform are represented by the workstation “Engineering Station” for CPS (Cyber Physical System) and “omics” technology and by the “Graphical Station” for the development of a virtual mechatronic system environment and virtual reality for system components' motion. The NEO-VIP …

Anti-Nogo-A Immunotherapy Does Not Alter Hippocampal Neurogenesis After Stroke In Adult Rats, Timothy O'Brien, Daniel Shepherd, Gwendolyn Kartje-Tillotson, Shih-Yen Tsai, Robert G. Farrer

Mathematics and Statistics: Faculty Publications and Other Works

Ischemic stroke is a leading cause of adult disability, including cognitive impairment. Our laboratory has previously shown that treatment with function-blocking antibodies against the neurite growth inhibitory protein Nogo-A promotes functional recovery after stroke in adult and aged rats, including enhancing spatial memory performance, for which the hippocampus is critically important. Since spatial memory has been linked to hippocampal neurogenesis, we investigated whether anti-Nogo-A treatment increases hippocampal neurogenesis after stroke. Adult rats were subject to permanent middle cerebral artery occlusion followed 1 week later by 2 weeks of antibody treatment. Cellular proliferation in the dentate gyrus was quantified at the …

Fractal Analysis Of Dna Sequences, Christian G. Arias, Pedro Antonio Moreno Phd, Carlos Tellez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Bounds On The Expected Size Of The Maximum Agreement Subtree, Colby Long, Daniel Irving Bernstein, Lam Si Tung Ho, Mike Steel, Katherine St. John, Seth Sullivant

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

General Equations For Natural Selection Under Complete Dominance, Kasthuri Kannan, Adriana Heguy

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Exploring The Space Of Rna Secondary Structures, Heather C. Smith

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Framework For The Teaching Of Modeling For Biologists, M. Drew Lamar, Carrie Diaz Eaton

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Territorial Movement Game, Jan Rychtar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Designing And Mentoring In A Research Experience For Undergraduates, Alex Capaldi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Predator-Prey Dynamics With Intraspecific Competition And An Allee Effect In The Predator Population, Anne E. Yust, Erin N. Bodine

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Extracting Biochemical Parameters From Protein Distributions Of Vascular Cells, Partha Srinivasan

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Identification Of Control Targets In Boolean Molecular Network Models Via Computational Algebra, David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, Reinhard Laubenbacher

Mathematics Faculty Publications

Background: Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type …

Grnsight: A Web Application And Service For Visualizing Models Of Small- To Medium-Scale Gene Regulatory Networks, Kam D. Dahlquist, John David N. Dionisio, Ben G. Fitzpatrick, Nicole A. Anguiano, Anindita Varshneya, Britain J. Southwick, Mihir Samdarshi

Biology Faculty Works

GRNsight is a web application and service for visualizing models of gene regulatory networks (GRNs). A gene regulatory network (GRN) consists of genes, transcription factors, and the regulatory connections between them which govern the level of expression of mRNA and protein from genes. The original motivation came from our efforts to perform parameter estimation and forward simulation of the dynamics of a differential equations model of a small GRN with 21 nodes and 31 edges. We wanted a quick and easy way to visualize the weight parameters from the model which represent the direction and magnitude of the influence of …

Expert Elicitation On The Uncertainties Associated With Chronic Wasting Disease, Michael G. Tyshenko, Tamer Oraby, Shalu Darshan, Margit Westphal, Maxine C. Croteau, Willy Aspinall, Susie Elsaadany, Daniel Krewski, Neil Cashman

School of Mathematical & Statistical Sciences Faculty Publications

A high degree of uncertainty exists for chronic wasting disease (CWD) transmission factors in farmed and wild cervids. Evaluating the factors is important as it helps to inform future risk management strategies. Expert opinion is often used to assist decision making in a number of health, science, and technology domains where data may be sparse or missing. Using the "Classical Model" of elicitation, a group of experts was asked to estimate the most likely values for several risk factors affecting CWD transmission. The formalized expert elicitation helped structure the issues and hence provide a rational basis for estimating some transmission …

Mutation Selection On The Metabolic Pathway And The Effects On Protein Co-Evolution And The Rate Limiting Steps On The Tree Of Life, Katherine S. Porter

Mathematics Summer Fellows

Metabolic pathways are made of a series of reactions by enzymes at different speeds. These pathways include the rate limiting step, which is the slowest step that determines the rate of the overall reaction. To date, one study has examined the pathway of glycolysis and found no evidence of evolutionary stability of its rate limiting step. In addition, phylogenetic evidence has shown evolution in the pathway over time including gene duplication and positive selection within the pathway. This evidence suggests that there is coevolutionary selection on glycolysis. The evidence from this previous study is simulation-based. The Michaelis-Menten kinetics that describe …

Ciliate Codon Translator Program Manual, Quentin D. Altemose

Mathematics Summer Fellows

Understanding the evolutionary history of organisms allows us to better comprehend selective pressures and their effects on larger populations. In our study, we focused on analyzing the DNA of ciliate groups, which are single celled protozoans characterized by the presence of cilia on their outer membrane. We utilized the DNA of the organisms to analyze the changes in population genotype over time. We tested existing evolutionary models (designed to represent natural genetic variation over time in populations) against our data to identify the model with the best fit and likelihood. From the DNA and the evolutionary model with the highest …

Hill's Diagrammatic Method And Reduced Graph Powers, Gregory D. Smith, Richard Hammack

Biology and Medicine Through Mathematics Conference

No abstract provided.

Growth Dynamics For Pomacea Maculata, Lihong Zhao, Karyn L. Sutton, Jacoby Carter

Biology and Medicine Through Mathematics Conference

No abstract provided.

Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Evaluating Infection Prevention Strategies In Out-Patient Dialysis Units Using Agent-Based Modeling, Joanna R. Wares, Barry Lawson, Douglas Shemin, Erika D'Agata

Department of Math & Statistics Faculty Publications

Patients receiving chronic hemodialysis (CHD) are among the most vulnerable to infections caused by multidrug-resistant organisms (MDRO), which are associated with high rates of morbidity and mortality. Current guidelines to reduce transmission of MDRO in the out-patient dialysis unit are targeted at patients considered to be high-risk for transmitting these organisms: those with infected skin wounds not contained by a dressing, or those with fecal incontinence or uncontrolled diarrhea. Here, we hypothesize that targeting patients receiving antimicrobial treatment would more effectively reduce transmission and acquisition of MDRO. We also hypothesize that environmental contamination plays a role in the dissemination of …

Population Projection And Habitat Preference Modeling Of The Endangered James Spinymussel (Pleurobema Collina), Marisa Draper

Senior Honors Projects, 2010-2019

The James Spinymussel (Pleurobema collina) is an endangered mussel species at the top of Virginia’s conservation list. The James Spinymussel plays a critical role in the environment by filtering and cleaning stream water while providing shelter and food for macroinvertebrates; however, conservation efforts are complicated by the mussels’ burrowing behavior, camouflage, and complex life cycle. The goals of the research conducted were to estimate detection probabilities that could be used to predict species presence and facilitate field work, and to track individually marked mussels to test for habitat preferences. Using existing literature and mark-recapture field data, these goals were accomplished …

A Spatiotemporal Mountain Pine Beetle Outbreak Model Predicting Severity, Cycle Period, And Invasion Speed, Jacob P. Duncan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The mountain pine beetle (MPB, Dendroctonus ponderosae), a tree-killing bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years, warm winters and summers have allowed MPB populations to achieve synchronous emergence and successful attacks, resulting in widespread population outbreaks and resultant tree mortality across western North America. We develop an age-structured forest demographic model that incorporates temperature-dependent MPB infestations: the Susceptible-Infested-Juvenile (SIJ) model. Stability of equilibria is analyzed as a function of population growth rates, and indicates the existence of periodic outbreaks that intensify as growth rates …