Applied Mathematics Commons^™

Hpcnmf: A High-Performance Toolbox For Non-Negative Matrix Factorization, Karthik Devarajan, Guoli Wang

COBRA Preprint Series

Non-negative matrix factorization (NMF) is a widely used machine learning algorithm for dimension reduction of large-scale data. It has found successful applications in a variety of fields such as computational biology, neuroscience, natural language processing, information retrieval, image processing and speech recognition. In bioinformatics, for example, it has been used to extract patterns and profiles from genomic and text-mining data as well as in protein sequence and structure analysis. While the scientific performance of NMF is very promising in dealing with high dimensional data sets and complex data structures, its computational cost is high and sometimes could be critical for …

Parts Of The Whole: Teaching Quantitative Reasoning In The Predator-Prey Model, Dorothy Wallace

Numeracy

The classical predator-prey equations are in nearly every differential equations text and mathematical biology text. Usually they are presented fait accompli, leaving the student to analyze them or play with a computer program. Here we show that the process of fully understanding where these equations come from and how they are derived provides numerous opportunities to teach or reinforce quantitative reasoning skills necessary to future scientists. This example is used to invoke logic, systems thinking, causal reasoning, understanding functions of one or more variables, quantities versus rates of change, proportional reasoning, unit analysis, and comparison to data.

1-65-S-Algal Blooms: Algal Blooms Threatening Lake Chapala, R. Corban Harwood

Faculty Publications - Department of Mathematics

This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994. After reading a summary of articles written on the incidents, students are guided through the process of creating a first order differential equation from a verbal model of the factors and analyze the nonautonomous ODE using direction field, parameter evaluation, and exact solution computation to fully describe the population behavior. Students are expected to be familiar with the separable method and direction fields. Students will learn building and improving a model from qualitative descriptions, nondimensionalization, evaluating parameters, and how to use DFIELD software to …

Image Harvest: An Open-Source Platform For High-Throughput Plant Image Processing And Analysis, Avi C. Knecht, Malachy T. Campbell, Adam Caprez, David R. Swanson, Harkamal Walia

Holland Computing Center: Faculty Publications

High-throughput plant phenotyping is an effective approach to bridge the genotype-to-phenotype gap in crops. Phenomics experiments typically result in large-scale image datasets, which are not amenable for processing on desktop computers, thus creating a bottleneck in the image-analysis pipeline. Here, we present an open-source, flexible image-analysis framework, called Image Harvest (IH), for processing images originating from high-throughput plant phenotyping platforms. Image Harvest is developed to perform parallel processing on computing grids and provides an integrated feature for metadata extraction from large-scale file organization. Moreover, the integration of IH with the Open Science Grid provides academic researchers with the computational resources …

A Model For Spheroid Versus Monolayer Response Of Sk-N-Sh Neuroblastoma Cells To Treatment With 15-Deoxy-Pgj2, Dorothy I. Wallace, Ann Dunham, Paula X. Chen, Michelle Chen, Milan Huynh, Evan Rheingold, Olivia F. Prosper

Mathematics Faculty Publications

Researchers have observed that response of tumor cells to treatment varies depending on whether the cells are grown in monolayer, as in vitro spheroids or in vivo. This study uses data from the literature on monolayer treatment of SK-N-SH neuroblastoma cells with 15-deoxy-PGJ₂ and couples it with data on growth rates for untreated SK-N-SH neuroblastoma cells grown as multicellular spheroids. A linear model is constructed for untreated and treated monolayer data sets, which is tuned to growth, death, and cell cycle data for the monolayer case for both control and treatment with 15-deoxy-PGJ₂. The monolayer …

Project Oasis: Optimizing Aquaponic Systems To Improve Sustainability, Siddharth Nigam, Paige Balcom

Honors Theses and Capstones

Started in Fall 2015, Project OASIS (Optimizing Aquaponic Systems to Improve Sustainability) is an interdisciplinary capstone project with the goal of designing a sustainable and affordable small-scale aquaponic system for use in developing nations to tackle the problems of malnutrition and food insecurity. Aquaponics is a symbiotic relationship between fish and vegetables growing together in a recirculating system. The project’s goals were to minimize energy consumption and construction costs while using universally available materials. The computational fluid dynamics (CFD) software OpenFOAM was used to create transient and steady-state models of fish tanks to visualize velocity profiles, streamlines, and particle movement. …

The Neural Dynamics Of Somatosensory Processing And Adaptation Across Childhood: A High-Density Electrical Mapping Study, Neha Uppal, John J. Foxe, John Butler, Frantzy Acluche, Sophie Molholm

Articles

Young children are often hyperreactive to somatosensory inputs hardly noticed by adults, as exemplified by irritation to seams or labels in clothing. The neurodevelopmental mechanisms underlying changes in sensory reactivity are not well understood. Based on the idea that neurodevelopmental changes in somatosensory processing and/or changes in sensory adaptation might underlie developmental differences in somatosensory reactivity, high-density electroencephalography was used to examine how the nervous system responds and adapts to repeated vibrotactile stimulation over childhood. Participants aged 6–18 yr old were presented with 50-ms vibrotactile stimuli to the right wrist over the median nerve at 5 blocked interstimulus intervals (ranging …

Effects Of Invasion Timing In A One-Dimensional Model Of Competing Species With An Infectious Disease, Eliza Jacops

Williams Honors College, Honors Research Projects

In combining two classes of models, we are able to analyze the dynamics of two species that compete for the same resources while fighting a disease. The native species is the disease host and the invasive species enters their habitat and encounters the disease for the first time. Their natural response is to evolve resistance to the disease, and this can assist in their invasion of the natives' habitat. We find conditions for coexistence of the two species, conditions under which an invasion would succeed and wipe out all native individuals, and conditions under which the invasion fails. We explore …

Synthesis Of Satellite Microwave Observations For Monitoring Global Land-Atmosphere Co2 Exchange, Lucas Alan Jones

Graduate Student Theses, Dissertations, & Professional Papers

This dissertation describes the estimation, error quantification, and incorporation of land surface information from microwave satellite remote sensing for modeling global ecosystem land-atmosphere net CO₂ exchange. Retrieval algorithms were developed for estimating soil moisture, surface water, surface temperature, and vegetation phenology from microwave imagery timeseries. Soil moisture retrievals were merged with model-based soil moisture estimates and incorporated into a light-use efficiency model for vegetation productivity coupled to a soil decomposition model. Results, including state and uncertainty estimates, were evaluated with a global eddy covariance flux tower network and other independent global model- and remote-sensing based products.

Dynamics Of An Sir Model With Nonlinear Incidence And Treatment Rate, Balram Dubey, Preeti Dubey, Uma S. Dubey

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, global dynamics of an SIR model are investigated in which the incidence rate is being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). Analytical study of the model shows that the model has two equilibrium points (diseasefree equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is locally asymptotically stable when reproduction number is less than one. Some conditions on the model parameters are obtained to show the existence as well as nonexistence of limit cycle. Some sufficient conditions for global stability of the endemic equilibrium using Lyapunov function are obtained. …

Analysis Of Neuronal Sequences Using Pairwise Biases, Zachary Roth

Department of Mathematics: Dissertations, Theses, and Student Research

Sequences of neuronal activation have long been implicated in a variety of brain functions. In particular, these sequences have been tied to memory formation and spatial navigation in the hippocampus, a region of mammalian brains. Traditionally, neuronal sequences have been interpreted as noisy manifestations of neuronal templates (i.e., orderings), ignoring much richer structure contained in the sequences. This paper introduces a new tool for understanding neuronal sequences: the bias matrix. The bias matrix captures the probabilistic tendency of each neuron to fire before or after each other neuron. Despite considering only pairs of neurons, the bias matrix captures the best …

Stochastic Models For Plant Microtubule Self-Organization And Structure, Ezgi Can Eren, Ram Dixit, Natarajan Gautam

Biology Faculty Research

One of the key enablers of shape and growth in plant cells is the cortical microtubule (CMT) system, which is a polymer array that forms an appropriately-structured scaffolding in each cell. Plant biologists have shown that stochastic dynamics and simple rules of interactions between CMTs can lead to a coaligned CMT array structure. However, the mechanisms and conditions that cause CMT arrays to become organized are not well understood. It is prohibitively time-consuming to use actual plants to study the effect of various genetic mutations and environmental conditions on CMT self-organization. In fact, even computer simulations with multiple replications are …

Partial Covariance Based Functional Connectivity Computation Using Ledoit-Wolf Covariance Regularization, Matthew R. Brier, Anish Mitra, John E. Mccarthy, Beau M. Ances, Abraham Z. Snyder

Mathematics Faculty Research

Highlights •We use the well characterized matrix regularization technique described by Ledoit and Wolf to calculate high dimensional partial correlations in fMRI data. •Using this approach we demonstrate that partial correlations reveal RSN structure suggesting that RSNs are defined by widely and uniquely shared variance. •Partial correlation functional connectivity is sensitive to changes in brain state indicating that they contain functional information. Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a …

Using An Agent-Based Model To Study The Effect Of Reproductive Skew On Mongoose Populations, Stacy Lee Mowry

Theses and Dissertations

Reproductive skew is the name given to the unequal partitioning of breeding

within social groups. Within these groups a mating hierarchy emerges wherein one dominant mating pair holds an unproportional majority of the group's reproductive benefit, while other members mate infrequently, yet allocate energy and resources toward the offspring of the dominant group members. In this paper, we use an agent-based model, which mimics dwarf and banded mongoose populations, to investigate how reproductive skew aftects the speed natural selection, and thus how reproductive skew affects fitness. The results of the model show that due to the geometric structure of skewed …

A Machine Learning Approach To Post-Market Surveillance Of Medical Devices, Jonathan Bates, Shu-Xia Li, Craig Parzynski, Ronald Coifman, Harlan Krumholz, Joseph Ross

Yale Day of Data

Post-market surveillance is a collection of processes and activities used by product manufacturers and regulators, such as the U.S. Food and Drug Administration (FDA) to monitor the safety and effectiveness of medical devices once they are available for use “on the market”. These activities are designed to generate information to identify poorly performing devices and other safety problems, accurately characterize real-world device performance and clinical outcomes, and facilitate the development of new devices, or new uses for existing devices. Typically, a device is monitored by comparing adverse events in the exposed population to a matched unexposed population. This research considers …

Modeling Radiation Effectiveness For Inactivation Of Bacillus Spores, Emily A. Knight

Theses and Dissertations

This research models and analyzes the inactivation of Bacillus spores following a radiation exposure and the process enacted by the Bacillus spore to repair the resulting damage. Irradiation of a spore and the medium surrounding the spore induces chemical reactions that produce reactive oxygen species (ROS). This research will consider the reaction- diffusion of these ROS throughout the spore. These ROS can react with the spore's DNA and enzymes to degrade them to such an extent that the DNA cannot be repaired or replicated, thus causing spore death. In order to survive a dose of radiation, a spore must repair …

Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes

Rose-Hulman Undergraduate Research Publications

From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …

Interdisciplinary Modeling For Water-Related Issues Graduate Course, Laurel Saito, Alexander Fernald, Timothy Link

All ECSTATIC Materials

The science and management of aquatic ecosystems is inherently interdisciplinary, with issues associated with hydrology, atmospheric science, water quality, geochemistry, sociology, economics, environmental science, and ecology. Addressing water resources issues in any one discipline invariably involves effects that concern other disciplines, and attempts to address one issue often have consequences that exacerbate existing issues or concerns, or create new ones (Jørgensen et al. 1992; Lackey et al. 1975; Straskraba 1994) due to the strongly interactive nature of key processes (Christensen et al. 1996). Thus, research and management of aquatic ecosystems must be interdisciplinary to be most effective, but such truly …

Rooted In Hell: Predicting Invasion Rates Of Phragmites Australis, Rachel Nydegger, Jacob P. Duncan, James A. Powell

Browse All Undergraduate research

Across the estuaries of the east coast and wetlands of the Great Lakes, the invasive grass Phragmites australis outcompetes other vegetation and destroys local ecosystems. Because its roots are tolerant to salinity that other plants find hellish, Phragmites invasions begin with vegetative spread of genetic clones in brackish marshlands. This plant can grow over three meters tall at densities of 50 stems/m2, provides poor wildlife habitat, and is very difficult to eradicate.

A discrete life stage model on a yearly time step captures seed survivorship in a seed bank, sexual and asexual recruitment into a juvenile age class, and differential …

Zernike Moments And Genetic Algorithm: Tutorial And Application, Oluleye Babatunde, Leisa Armstrong, Jinsong Leng, Dean Diepeveen

Grain and Other Field Crops Research Articles

Aims/ objectives: To demontrate effectiveness of Zernike Moments for Image Classification. Zernike moment(ZM) is an excellent region-based moment which has attracted the attentions of many image processing researchers since its first application to image analysis. Many papers have been published on several works done on ZM but no single paper ever give a detailed information of how the computation of ZM is done from the time the image is captured to the computation of ZM. This work showed how to effectively apply ZM on RGB images. We have demonstrated the effectiveness of Zernike moment in image classification system. A neuro-genetic …

Mathematical Modeling And Analysis Of Leukemia: Effect Of External Engineered T Cells Infusion, Manju Agarwal, Archana S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a nonlinear model is proposed and analyzed to study the spread of Leukemia by considering the effect of genetically engineered patients T cells to attack cancer cells. The model is governed by four dependent variables namely; naive or susceptible blood cells, infected or dysfunctional blood cells, cancer cells and immune cells. The model is analyzed by using the stability theory of differential equations and numerical simulation. We have observed that the system is stable in the local and global sense if antigenicity rate or rate of stimulation of immune cells is greater than a threshold value dependent …

Controllability Of An Eco-Epidemiological System With Disease Transmission Delay: A Theoretical Study, Samadyuti Haldar, Kunal Chakraborty, T. K. Kar

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the qualitative analysis of a disease transmission delay induced prey preda-tor system in which disease spreads among the predator species only. The growth of the preda-tors’ susceptible and infected subpopulations is assumed as modified Leslie–Gower type. Suffi-cient conditions for the persistence, permanence, existence and stability of equilibrium points are obtained. Global asymptotic stability of the system is investigated around the coexisting equilib-rium using a geometric approach. The existence of Hopf bifurcation phenomenon is also exam-ined with respect to some important parameters of the system. The criterion for disease a trans-mission delay the induced Hopf bifurcation phenomenon …

Multiphysics Modeling To Enhance Understanding Of Microwave Heating Of Food In Domestic Ovens, Jiajia Chen

Department of Agricultural and Biological Systems Engineering: Dissertations, Theses, and Student Research

Nonuniform heating is the biggest issue in the microwave heating of prepared meals. Multiphysics based models are promising tools to improve microwave heating uniformity by properly designing the food product. However, limited availability of accurate temperature-dependent material properties, inadequate model prediction accuracy, and high computational power and complexity in model development are three gaps that greatly limited the application of these models in the food industry.

To fill in the gaps, firstly, we developed a multitemperature calibration protocol to measure temperature-dependent dielectric properties (dielectric constant and loss factor). The temperature-dependent dielectric and thermal (thermal conductivity and specific heat capacity) properties …

Applications Of Latin Hypercube Sampling Scheme And Partial Rank Correlation Coefficient Analysis To Mathematical Models On Wound Healing, Hannah M. Pennington

Mahurin Honors College Capstone Experience/Thesis Projects

Latin hypercube sampling and Partial Rank Correlation Coefficient procedure (LHS/PRCC) can be used in combination to perform a sensitivity analysis that assesses a model over a global parameter space. Through this analysis, the uncertainty of the parameters and therefore the variability of the model output in response to this uncertainty can be observed. Latin hypercube sampling divides the parameter space into equiprobable regions and sample without replacement, producing a global, unbiased selection of parameter values. For montonic, non-linear relationships, the correlation between the outputs and parameters can be understood by performing a Partial Rank Correlation Coefficient procedure. This sensitivity analysis …

Bioinformatic Game Theory And Its Application To Cluster Multi-Domain Proteins, Brittney Keel

Department of Mathematics: Dissertations, Theses, and Student Research

The exact evolutionary history of any set of biological sequences is unknown, and all phylogenetic reconstructions are approximations. The problem becomes harder when one must consider a mix of vertical and lateral phylogenetic signals. In this dissertation we propose a game-theoretic approach to clustering biological sequences and analyzing their evolutionary histories. In this context we use the term evolution as a broad descriptor for the entire set of mechanisms driving the inherited characteristics of a population. The key assumption in our development is that evolution tries to accommodate the competing forces of selection, of which the conservation force seeks to …

A Hierarchical Graph For Nucleotide Binding Domain 2, Samuel Kakraba

Electronic Theses and Dissertations

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2. …

An Individual-Based Model Of Chaparral Vegetation Response To Frequent Wildfire, Timothy Lucas, Dayna Mann, Reanna Dona

Seaver College Research And Scholarly Achievement Symposium

In recent years, the Santa Monica Mountains (SMM) have been plagued by frequent wildfires which threaten the native chaparral species. Nonsprouting chaparral species are completely killed by a fire, but their seeds germinate in response to fire cues. Facultative sprouters both resprout after a wildfire and release seeds that germinate post-fire. This project is based on data collected since 1986 at a biological preserve adjacent to the Malibu campus of Pepperdine University with an average fire return interval of 7.5 years. We present a spatial model that simulates the growth, seed dispersal and resprouting behavior of individual shrubs that compete …

Predicting Invasion Rates For Phragmites Australis, Rachel Nydegger, Jacob Duncan, James A. Powell

Browse All Undergraduate research

In wetlands of Utah and southern Idaho as well as estuaries of the east coast, the ten-foot tall invasive grass Phragmites australis can be found near waterways, where it outcompetes native plants and degrades wildlife habitat. Phragmites australis is an obligate out-crossing plant that can spread sexually through seed disper- sal, or asexually via stolons and rhi- zomes (Kettenring and Mock 2012). Small patches are usually a single genetic individual, spreading vegetatively (and slowly) via runners; when patches become genetically diverse viable seeds are produced and invasion rates can be increase by an order of magnitude (Kettenring et al. 2011)

Modeling Neurovascular Coupling From Clustered Parameter Sets For Multimodal Eeg-Nirs, M. Tanveer Talukdar, H. Robert Frost, Solomon G. G. Diamond

Dartmouth Scholarship

Despite significant improvements in neuroimaging technologies and analysis methods, the fundamental relationship between local changes in cerebral hemodynamics and the underlying neural activity remains largely unknown. In this study, a data driven approach is proposed for modeling this neurovascular coupling relationship from simultaneously acquired electroencephalographic (EEG) and near-infrared spectroscopic (NIRS) data. The approach uses gamma transfer functions to map EEG spectral envelopes that reflect time-varying power variations in neural rhythms to hemodynamics measured with NIRS during median nerve stimulation. The approach is evaluated first with simulated EEG-NIRS data and then by applying the method to experimental EEG-NIRS data measured from …

Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly

Statistical Sciences and Operations Research Publications

Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model, …