Applied Mathematics Commons^™

Lower Bounds On Betti Numbers, Adam Boocher, Eloisa Grifo

Department of Mathematics: Faculty Publications

We survey recent results on bounds for Betti numbers of modules over polynomial rings, with an emphasis on lower bounds. Along the way, we give a gentle introduction to free resolutions and Betti numbers, and discuss some of the reasons why one would study these.

Report: Spatial Facilitation-Inhibition Effects On Vegetation Distribution And Their Associated Patterns, Daniel D'Alessio

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Changes in the spatial distribution of vegetation respond to variations in the production and transportation mechanisms of seeds at different locations subject to heterogeneities, often because of soil characteristics. In semi-arid environments, the competition for water and nutrients pushes the superficial plant’s roots to obtain scarce resources at long ranges. In this report, we assume that vegetation biomass interacts with itself in two different ways, facilitation and inhibition, depending on the relative distances. We present a 1-dimensional Integro-difference model to represent and study the emergence of patterns in the distribution of vegetation.

Computational Analysis To Study The Efficiency Of Shear Activated Nano-Therapeutics In The Treatment Of Atherosclerosis, Nicholas Jefopoulos

Theses, Dissertations and Culminating Projects

Strokes are the fifth leading cause of death in the United States and can cause long-term disabilities in patients who survive a stroke. The vast majority of these strokes are ischemic, primarily caused by intracranial atherosclerosis. Most therapies to combat intracranial atherosclerosis simply manage it and do not remove the buildup of plaque. Targeted shear-activated nanotherapeutics are currently being developed to remove these plaques. We discuss the roles that aggregate particle density, aggregate particle diameter, vessel geometry, stenosis shape and breakup threshold play in the efficiency of this new technology. Computational studies were performed to test these parameters in three …

Applying Deep Learning To The Ice Cream Vendor Problem: An Extension Of The Newsvendor Problem, Gaffar Solihu

Electronic Theses and Dissertations

The Newsvendor problem is a classical supply chain problem used to develop strategies for inventory optimization. The goal of the newsvendor problem is to predict the optimal order quantity of a product to meet an uncertain demand in the future, given that the demand distribution itself is known. The Ice Cream Vendor Problem extends the classical newsvendor problem to an uncertain demand with unknown distribution, albeit a distribution that is known to depend on exogenous features. The goal is thus to estimate the order quantity that minimizes the total cost when demand does not follow any known statistical distribution. The …

Data Science And The Ice-Cream Vendor Problem, Makafui Azasoo

Electronic Theses and Dissertations

Newsvendor problems in Operations Research predict the optimal inventory levels necessary to meet uncertain demands. This thesis examines an extended version of a single period multi-product newsvendor problem known as the ice cream vendor problem. In the ice cream vendor problem, there are two products – ice cream and hot chocolate – which may be substituted for one another if the outside temperature is no too hot or not too cold. In particular, the ice cream vendor problem is a data-driven extension of the conventional newsvendor problem which does not require the assumption of a specific demand distribution, thus allowing …

Manifold Learning With Tensorial Network Laplacians, Scott Sanders

Electronic Theses and Dissertations

The interdisciplinary field of machine learning studies algorithms in which functionality is dependent on data sets. This data is often treated as a matrix, and a variety of mathematical methods have been developed to glean information from this data structure such as matrix decomposition. The Laplacian matrix, for example, is commonly used to reconstruct networks, and the eigenpairs of this matrix are used in matrix decomposition. Moreover, concepts such as SVD matrix factorization are closely connected to manifold learning, a subfield of machine learning that assumes the observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. Since …

The Food Truck Problem, Supply Chains And Extensions Of The Newsvendor Problem, Dennis Quayesam

Electronic Theses and Dissertations

Inventory control is important to ensuring sufficient quantities of items are available tomeet demands of customers. The Newsvendor problem is a model used in Operations Research to determine optimal inventory levels for fulfilling future demands. Our study extends the newsvendor problem to a food truck problem. We used simulation to show that the food truck does not reduce to a newsvendor problem if demand depends on exogenous factors such temperature, time etc. We formulate the food truck problem as a multi-product multi-period linear program and found the dual for a single item. We use Discrete Event Simulation to solve the …

On A Stochastic Model Of Epidemics, Rachel Prather

Master's Theses

This thesis examines a stochastic model of epidemics initially proposed and studied by Norman T.J. Bailey [1]. We discuss some issues with Bailey's stochastic model and argue that it may not be a viable theoretical platform for a more general epidemic model. A possible alternative approach to the solution of Bailey's stochastic model and stochastic modeling is proposed as well. Regrettably, any further study on those proposals will have to be discussed elsewhere due to a time constraint.

A Modified Preconditioned Conjugate Gradient Method For Approximating The Scattering Amplitude, Samson Ayo

Master's Theses

In this thesis, we look at an iterative method for approximating the scattering amplitude that involves solving two linear systems: a forward system Ax=b and an adjoint system A^Ty=g. Once these two systems are solved, the scattering amplitude, defined by g^Tx=y^Tb is easily obtained.

We derive a conjugate gradient-like iteration for a nonsymmetric saddle point matrix that is constructed to have a real positive spectrum. We investigate the use of Schur Complement preconditioners with block-diagonal factorization to speed up the convergence of our method and compare …

Particle Trajectories In Shallow Water Models, Diana Torres

Theses and Dissertations

In this paper we will study particle trajectories under shallow water waves. We will examine equations such as the Korteweg-de Vries and systems dealing with Boussinesq and Euler's Equations to find relationships between particles irrotational velocities. Their solutions and behavior when modeling interacting surface waves will be explored. An attempt to find approximate solutions with different parameters, such as small amplitude and long-crested waves, that will lead to new information and study will be discussed.

Multilateration Index., Chip Lynch

Electronic Theses and Dissertations

We present an alternative method for pre-processing and storing point data, particularly for Geospatial points, by storing multilateration distances to fixed points rather than coordinates such as Latitude and Longitude. We explore the use of this data to improve query performance for some distance related queries such as nearest neighbor and query-within-radius (i.e. “find all points in a set P within distance d of query point q”). Further, we discuss the problem of “Network Adequacy” common to medical and communications businesses, to analyze questions such as “are at least 90% of patients living within 50 miles of a covered emergency …

A Deep Ensemble Method For Multi-Agent Reinforcement Learning: A Case Study On Air Traffic Control, Supriyo Ghosh, Sean Laguna, Laura Wynter, Laura Wynter, Hasan Poonawala

Research Collection School Of Computing and Information Systems

Reinforcement learning (RL), a promising framework for data-driven decision making in an uncertain environment, has successfully been applied in many real-world operation and control problems. However, the application of RL in a large-scale decentralized multi-agent environment remains a challenging problem due to the partial observability and limited communications between agents. In this paper, we develop a model-based kernel RL approach and a model-free deep RL approach for learning a decentralized, shared policy among homogeneous agents. By leveraging the strengths of both these methods, we further propose a novel deep ensemble multi-agent reinforcement learning (MARL) method that efficiently learns to arbitrate …

Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions.

As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …

Socio-Technical Perspective For Electronic Tax Information System In Tanzania, Lucas Ngowi, Ellen Kalinga

Tanzania Journal of Engineering and Technology (TJET)

Socio-technical systems theory has rarely been used by system architects in setting up computing systems. However, the role of socio-technical concepts in computing, which is becoming social in nature, has made the concepts more relevant and commercial. Tax information systems are examples of such systems because they are influenced by external variables such as the political environment, technological trends, and social environment, introducing complexity in their deployment and determining the type of e-services and their delivery to a diverse group of people. It was observed that in Tanzania there is resistance, reluctance and minimal use of electronic tax system because …

Crocheting Mathematics Through Covid-19, Beyza C. Aslan

Journal of Humanistic Mathematics

As it is often said, something good often comes out of most bad situations. The time I spent during COVID-19, at home and isolated with my two children, brought out one secret passion in me: crocheting. Not only did it help me pass the time in a sane and productive way, but also it gave me a new goal in life. It connected my math side with my artistic side. It gave me a new perspective to look at math, and helped me help others see math in a positive way.

Fully Coupled Internal Radiative Heat Transfer For The 3d Material Response Of Heat Shield, Raghava S. C. Davuluri, Rui Fu, Kaveh A. Tagavi, Alexandre Martin

Mechanical Engineering Faculty Publications

The radiative transfer equation (RTE) is strongly coupled to the material response code KATS. A P-1 approximation model of RTE is used to account for radiation heat transfer within the material. First, the verification of the RTE model is performed by comparing the numerical and analytical solutions. Next, the coupling scheme is validated by comparing the temperature profiles of pure conduction and conduction coupled with radiative emission. The validation study is conducted on Marschall et al. cases (radiant heating, arc-jet heating, and space shuttle entry), 3D Block, 2D IsoQ sample, and Stardust Return Capsule. The validation results agree well for …

Near-Optimal Learning Of Tree-Structured Distributions By Chow-Liu, Arnab Bhattacharyya, Sutanu Gayen, Eric Price, N. V. Vinodchandran

Department of Mathematics: Faculty Publications

We provide finite sample guarantees for the classical Chow-Liu algorithm (IEEE Trans. Inform. Theory, 1968) to learn a tree-structured graphical model of a distribution. For a distribution P on Σⁿ and a tree T on n nodes, we say T is an ε-approximate tree for P if there is a T-structured distribution Q such that D(P || Q) is at most ε more than the best possible tree-structured distribution for P. We show that if P itself is tree-structured, then the Chow-Liu algorithm with the plug-in estimator for mutual information with eO (|Σ| …

From Reaction Kinetics To Dementia: A Simple Dimer Model Of Alzheimer’S Disease Etiology, Michael R. Lindstrom, Manuel B. Chavez, Elijah A. Gross-Sable, Eric Y. Hayden, David B. Teplow

School of Mathematical & Statistical Sciences Faculty Publications

Oligomers of the amyloid β-protein (Aβ) have been implicated in the pathogenesis of Alzheimer’s disease (AD) through their toxicity towards neurons. Understanding the process of oligomerization may contribute to the development of therapeutic agents, but this has been difficult due to the complexity of oligomerization and the metastability of the oligomers thus formed. To understand the kinetics of oligomer formation, and how that relates to the progression of AD, we developed models of the oligomerization process. Here, we use experimental data from cell viability assays and proxies for rate constants involved in monomerdimer-trimer kinetics to develop a simple mathematical model …

Multiple Baseline Interrupted Time Series: Describing Changes In New Mexico Medicaid Behavioral Health Home Patients’ Care, Jessica Reno

Mathematics & Statistics ETDs

In 2016, the CareLink New Mexico behavioral health homes program began enrolling Medicaid recipients with the goal of increasing care coordination, improving access to services, and decreasing long-term costs of care for adults with serious mental illness (SMI) and children with severe emotional disturbance (SED). To evaluate these aims, a retrospective interrupted time series study using Medicaid claims data was designed. First, a comparable subset of non-enrolled individuals was selected from the pool of Medicaid recipients with SMI or SED using propensity score matching. Then, segmented regression was applied to three outcomes: total Medicaid charges, number of outpatient behavioral health …

Understanding Covid-19 Dynamics And The Effects Of Interventions In The Philippines: A Mathematical Modelling Study, Jamie M. Caldwell, Elvira P. De Lara-Tuprio, Timothy Robin Y. Teng, Ma. Regina Justina E. Estuar, Raymond Francis R. Sarmiento, Milinda Abayawardana B. Eng, Robert Neil F. Leong, Richard T. Gray, James G. Wood, Linh-Vi Le, Emma S. Mcbryde, Romain Ragonnet, James M. Trauer

Mathematics Faculty Publications

Background

COVID-19 initially caused less severe outbreaks in many low- and middle-income countries (LMIC) compared with many high-income countries; possibly because of differing demographics; socioeconomics; surveillance; and policy responses. Here; we investigate the role of multiple factors on COVID-19 dynamics in the Philippines; a LMIC that has had a relatively severe COVID-19 outbreak.

Methods

We applied an age-structured compartmental model that incorporated time-varying mobility; testing; and personal protective behaviors (through a “Minimum Health Standards” policy; MHS) to represent the first wave of the Philippines COVID-19 epidemic nationally and for three highly affected regions (Calabarzon; Central Visayas; and the National Capital …