Applied Mathematics Commons^™

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 …

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 …

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.

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 …

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 …

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 …

Optimal Transport Driven Bayesian Inversion With Application To Signal Processing, Elijah F. Perez

Mathematics & Statistics ETDs

This paper will outline a Debiased Sinkhorn Divergence driven Bayesian inversion framework. Conventionally, a Gaussian Driven Bayesian framework is used when performing Bayesian inversion. A major issue with this Gaussian framework is that the Gaussian likelihood, driven by the L2 norm, is not affected by phase shift in a given signal. This issue has been addressed in [1] using a Wasserstein framework. However, the Wasserstein framework still has an issue because it assumes statistical independence when multidimensional signals are analyzed. This assumption of statistical independence cannot always be made when analyzing signals where multiple detectors are recording one event, say …

Representation Of Nonlinear Pseudo-Random Generators Using State-Space Equations, Raghad K. Salih

Emirates Journal for Engineering Research

The idea of research is a representation of the nonlinear pseudo-random generators using state-space equations that is not based on the usual description as shift register synthesis but in terms of matrices. Different types of nonlinear pseudo-random generators with their algorithms have been applied in order to investigate the output pseudo-random sequences. Moreover, two examples are given for conciliated the results of this representation.

Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

Due to the rise of COVID-19 cases, many mathematical models have been developed to study the disease dynamics of the virus. However, despite its role in the spread of COVID-19, many SEIR models neglect to account for human behavior. In this project, we develop a novel mathematical modeling framework for studying the impact of mixing patterns and social behavior on the spread of COVID-19. Specifically, we consider two groups, one exhibiting normal behavior who do not reduce their contacts and another exhibiting altered behavior who reduce their contacts by practicing non-pharmaceutical interventions such as social distancing and self-isolation. The dynamics …

Traveling Wave Solutions For Two Species Competitive Chemotaxis Systems, T. B. Issa, Richadi B. Salako, W. Shen

Mathematical Sciences Faculty Research

In this paper, we consider two species chemotaxis systems with Lotka–Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number c∗. We also show the non-existence of such traveling waves with speed less than some critical number c0∗, which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring c∗=c0∗, which implies that the minimum …

Traveling Wave Solutions For Two Species Competitive Chemotaxis Systems, T. B. Issa, R. B. Salako, W. Shen

Faculty Research, Scholarly, and Creative Activity

In this paper, we consider two species chemotaxis systems with Lotka–Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number c∗. We also show the non-existence of such traveling waves with speed less than some critical number c∗0 , which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring c∗ = c∗0 , which …