Applied Mathematics Commons^™

(Si13-07) Optimal Range For Value Of Two-Person Zero-Sum Game Models With Uncertain Payoffs, Sana Afreen, Ajay Kumar Bhurjee

Applications and Applied Mathematics: An International Journal (AAM)

Game theory deals with the decision-making of individuals in conflicting situations with known payoffs. However, these payoffs are imprecisely known, which means they have uncertainty due to vagueness in the data set of most real-world problems. Therefore, we consider a two-person zero-sum game model on a larger scale where the payoffs are imprecise and lie within a closed interval. We define the pure and mixed strategy as well as value for the game models. The proposed method computes the optimal range for the value of the game model using interval analysis. To derive some important results, we establish some lemmas …

(Si13-09) Numerical Methods For Solving Nonlinear Fisher Equation Using Backward Differentiation Formula, Vikash Vimal, Rajesh Kumar Sinha, Liju Pannikkal

Applications and Applied Mathematics: An International Journal (AAM)

This paper examines the numerical solution of the nonlinear Fisher equation that is used to find the growth of tumour cells in the brain. By employing new methods that transform nonlinear partial differential equations (PDE) into nonlinear ordinary differential equations (ODE) through spatial discretization. The stability of the resulting nonlinear system is evaluated using Lyapunov’s criteria. Implicit stiff solvers, including various orders of backward differentiation formulas, are used to address the ODE system. The efficiency of these numerical methods is demonstrated through two examples, and a comparison with existing methods from the literature is conducted. Compared to traditional methods, the …

(Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, Rahul Sharma, Vinod Gill, Naresh Kumar, Kanak Modi, Yudhveer Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we examine various effective methods for addressing the problem of solving Fredholm-type integral equations. Our investigation commences by applying the principles of fractional calculus theory. We employ series representations and products of multivariable incomplete H-functions and multivariable incomplete I-functions to solve these integrals. The outcomes derived from our analysis possess a general nature and hold the potential to yield numerous results.

(Si13-04) System Of Variational Inclusions Involving Cayley Operator And Yosida Approximation Operator With Xor Operations, Mohd Iqbal, Tirth Ram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider and study a new class of system of variational inclusions called a system of variational inclusions involving Cayley operator and Yosida approximation operator with XOR operation. We have shown that our problem is equivalent to a fixed point equation. Based on fixed point formulation, an iterative algorithm is designed to obtain existence and convergence result for our problem.

An Efficient Fourier Caching Algorithm For Walk On Spheres, Zihong Zhou

Dartmouth College Master’s Theses

Walk on Spheres (WoS) is a grid-free Monte Carlo method for solving elliptic partial differential equations (PDEs).
Rather than discretizing the domain, WoS leverages the mean-value principle to obtain Monte Carlo estimates by recursively averaging the solution over the largest contained sphere, terminating upon reaching the boundary.
Unfortunately, WoS requires many independent estimates to achieve noise-free results.

We propose an acceleration technique for WoS, inspired by irradiance caching methods, that computes the solution at a sparse set of locations, and extrapolates these cached values to local neighborhoods. A key insight is that WoS can be extended to compute not only …

Human Capital At Home: Evidence From A Randomized Evaluation In The Philippines, Noam Angrist, Sarah Kabay, Dean S. Karlan, Lincoln Lau, Kevin M. Wong

Education Division Scholarship

Children spend most of their time at home in their early years, yet efforts to promote human capital at home in many low- and middle-income settings remain limited. We conduct a randomized controlled trial to evaluate an intervention which encourages parents and caregivers to foster human capital accumulation among their children between ages 3 and 5, with a focus on math and phonics skills. Children gain 0.52 and 0.51 standard deviations relative to the control group on math and phonics tests, respectively (p<0.001). A year later effects persist, but math gains dissipate to 0.15 (p=0.06) and phonics to 0.13 (p=0.12). Effects appear to be mediated largely through instructional support by parents and not other parent investment mechanisms, such as more positive parent-child interactions or additional time spent on education at home beyond the intervention. Our results show that parents can be effective conduits of educational instruction even in low-resource settings.

Data-Driven Mathematical Modeling And Simulation Of Migration Dynamics During The Russian-Ukrainian War, Danielle Sitalo, Alonso Ogueda-Oliva, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

In this work, we employ a governing system of ordinary differential equations (ODEs) to create a mathematical model for getting insights into the dynamics of migration of Ukrainians evacuating due to war. A suitable assumption on coefficients of this model results in the well-known logistic growth. Additionally, stability analyses of equilibrium solutions for these ODEs are performed, and we employ parameter estimation techniques to identify coefficients using online datasets via both a least-squares approach as well as a physics informed neural network approach. Our findings indicate that over time, the daily influx of Ukrainian refugees to Poland stabilizes at a …

Malware Classification Through Abstract Syntax Trees And L-Moments, Anthony J. Rose, Christine M. Schubert Kabban, Scott R. Graham, Wayne C. Henry, Christopher M. Rondeau

Faculty Publications

The ongoing evolution of malware presents a formidable challenge to cybersecurity: identifying unknown threats. Traditional detection methods, such as signatures and various forms of static analysis, inherently lag behind these evolving threats. This research introduces a novel approach to malware detection by leveraging the robust statistical capabilities of L-moments and the structural insights provided by Abstract Syntax Trees (ASTs) and applying them to PowerShell. L-moments, recognized for their resilience to outliers and adaptability to diverse distributional shapes, are extracted from network analysis measures like degree centrality, betweenness centrality, and closeness centrality of ASTs. These measures provide a detailed structural representation …

Optimization And Machine Learning Techniques For Analyzing Spatiotemporal Dynamics, Dipak Prasad Dulal

All ETDs from UAB

In a numerical context, the tensor CP decomposition challenge can be reformulated into a series of least squares subproblems, which can be addressed using the renowned Alternating Least Square algorithm (ALS). The ALS algorithm is often characterized by a 'swamp phenomenon' that slows down its convergence, especially when dealing with extensive data structures. One of the goals of our research is to find ways to speed up the convergence of the ALS algorithm. This thesis discusses the use of Canonical Polyadic decomposition techniques and machine learning models in various data-driven domains, such as COVID-19, higher-order images and videos (e.g. RGB …

Performance Studies Of An Axial Flow Waterjet Pump Using An Unsteady Reynolds-Averaged Navier-Stokes Model, Stephen E. Monroe, Junfeng Wang, Chunlei Liang

Northeast Journal of Complex Systems (NEJCS)

In this study, an Unsteady Reynolds-Averaged Navier-Stokes (URANS) model is demonstrated its suitability for studying the flow and performance of open marine propellers and waterjet pumps. First, the accuracy of the URANS model is validated by studying turbulent flow past counter-rotating propellers (CRPs). Specifically, experimental data from Miller (1976) is employed for comparison against the URANS results. Subsequently, URANS is used to study the flow and performance of an Office of Naval Research (ONR) axial flow waterjet pump (AxWJ-2). Due to the large number of degrees of freedom for both simulations, parallel computations over 80 cores are performed. For the …

Representation Theory Arising From Groups In Physics, Jaxon Green

Master's Theses

A representation is a group homomorphism whose image is a group of invertible matrices. Representations and their associated matrices are analyzed through well-established techniques from linear algebra. We characterize representations by a unique decomposition into irreducible representations just as we characterize the decomposition of matrices into their eigenspaces. Through the study of these representations, we uncover mathematical relationships that underlie groups with physical applications. Due to physical symmetries, we study how the irreducible representations of groups that embody the actions of even the most basic rotations are utilized in the computation of irreducible representations groups that reflect more complicated mechanics, …

Solving Fractional Differential Equations On A Quantum Computer: A Variational Approach, Fong Yew Leong, Dax Enshan Koh, Jian Feng Kong, Siong Thye Goh, Jun Yong Khoo, Wei Bin Ewe, Hongying Li, Jayne Thompson, Dario Poletti

Research Collection School Of Computing and Information Systems

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap history states. The proposed algorithm is not only efficient in terms of time complexity but also has lower memory costs compared to classical methods. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation costs scale economically with the number of time steps. As a proof of concept, we apply our algorithm to solve a range of fractional partial differential equations commonly encountered in engineering …

A Micromagnetic Study Of Skyrmions In Thin-Film Multilayered Ferromagnetic Materials, Nicholas J. Dubicki

Dissertations

Magnetic skyrmions are topologically protected, localized, nanoscale spin textures in non-centrosymmetric thin ferromagnetic materials and heterostructures. At present they are of great interest to physicists for potential applications in information technology due to their particle-like properties and stability. In a system of multiple thin ferromagnetic layers, the stray field interaction was typically treated with various simplifications and approximations. It is shown that extensive analysis of the micromagnetic equations leads to an exact representation of the stray field interaction energy in the form of layer interaction kernels, a so-called 'finite thickness' representation. This formulation reveals the competition between perpendicular magnetic anisotropy …

Certifying Stability In Runge-Kutta Schemes: Algebraic Conditions And Semidefinite Programming, Austin Juhl

Dissertations

Numerical stability is a critical property for a time-integration scheme. In the context of Runge-Kutta methods applied to stiff differential equations, A-stability is one of the most basic and practically important notions of stability. Dating back to the work of Dahlquist, it has been known that A-stability is equivalent to the Runge-Kutta stability function satisfying a particular convex feasibility problem. Specifically, up to a transformation, the stability function lies in the convex cone of positive functions. In recent years, sum-of-squares optimization and semidefinite programming have become valuable tools in developing rigorous certificates of stability in dynamical systems. Therefore, it is …

Large Deviation Theory In Stochastic Processes: Applications To Biological Modeling, Moshe C. Silverstein

Dissertations

This dissertation delves into developing and applying stochastic models to analyze complex biological systems. It leverages Large Deviation Theory (LDT) to gain insights into these systems, focusing on two key examples: neural networks and calcium signaling dynamics. Traditional deterministic methods frequently fail to capture biological processes' randomness and inherent variability. Meanwhile, many stochastic approaches struggle to be mathematically tractable or provide accessible insights. The approach introduced in this study provides rigorous mathematical frameworks to enhance understanding of these stochastic behaviors while remaining tractable and insightful.

A stochastic model for a random biological neural network is constructed that addresses the dependencies …

Efficient Numerical Methods For Monge-Ampere Type Equations, Jake S. Brusca

Dissertations

Current numerical methods for Monge-Ampere-type equations and Optimal Transport problems face challenges when handling higher dimensions and large-scale data. This dissertation aims to develop and analyze efficient, highly parallelizable numerical algorithms for solving the Monge-Ampere equation to address these issues. Two approaches are employed:

(1) The discretization method is enhanced by introducing an integral repre-sentation of the Monge-Ampere operator. This integral can be discretized using higher-order quadrature, yielding a more efficient, higher-order monotone scheme that allows for narrower stencils. An additional advantage of this discretization is its natural extension to arbitrary dimensions.

(2) The nonlinear solvers for this scheme are …

Diagrams In Involutive Residuated Lattices, Isis A. Gallardo

Electronic Theses and Dissertations

First, we show that every distributive lattice-ordered pregroup can be embedded into a functional algebra over an integral chain, thereby improving the existing Cayley/Holland style embedding theorem. Using this result, we demonstrate that the variety of all dis tributive lattice-ordered pregroups is generated by the functional algebra on the integers. Additionally, we prove that the equational theory of this variety is decidable.

Next, we establish that DLP is equal to the join of its subvarieties LP_n, where 𝑛 ∈ ℤ⁺, consisting of 𝑛-periodic ℓ-pregroups. We also prove that every algebra in LP_n can be embedded …

Development And Testing Of Small-Scale Flash Dryer For Maize Bran, Eden Ngowi

Tanzania Journal of Engineering and Technology (TJET)

Sun drying is the most common technique used to dry various food products due to its economic convenience. However, it is not effective owing to its unreliable nature leading to microbial deterioration and aflatoxin contamination of food. In Tanzania, about 1.3 million tonnes of maize bran are at risk of deterioration annually due to improper drying. The aim of this study was to design, fabricate and test an efficient small-scale flash dryer for maize bran. Using principles of material and energy balance, a small-scale flash dryer with a throughput of 500 kg of dry product per hour was designed resulting …

Exploring The Transformation Of Sustainable Collective Spaces: A Study From Mlalakuwa Informal Settlement, Jacob Lutta

Tanzania Journal of Engineering and Technology (TJET)

A major challenge in collective space transformation is addressing the complexity of informal urbanisation in developing countries. Using a case study approach, this paper examines the concerns related to a particular informal settlement's sustainable collective space transformation. One of the key findings is that the absence of formal rules and regulations in the development of informal settlements in combination with land-grabbing leads to the absence of open spaces that could be used collectively. It is observed that sustainability in urban development is another body of critical thought that integrates several streams of current urban elements and embodies various conceptions of …

Evaluation Of Business-Driven Reference Architecture For Big Data Analytics Implementation By Public Sector Organizations In Resource-Constrained Setting: A Case Study Of Uganda, Matendo Didas

Tanzania Journal of Engineering and Technology (TJET)

Big Data Analytics (BDA) is a new area at the nexus of agenda, public sector organizations, and government business. It may satisfy the growing need for trustworthy, cost-effective services in the public sector for better, more informed decision-making processes. BDA has been proposed on the planning schedules of several public sector organizations and the government. Therefore, from the previous work, using Uganda as a case study, specifically the Uganda Bureau of Statistics (UBOS), Ministry of Health (MoH), and Ministry of Education and Sports (MoES), this study aims to evaluate a designed Business-Driven Reference Architecture for Big Data Analytics Implementation (BRABDAI) …

Investigation Of Heavy Metal Composition And Associated Health Risks From Selected Groundwater Wells In Temeke, Dar-Es-Salaam, Justin M. Jeremiah

Tanzania Journal of Engineering and Technology (TJET)

Water quality continues to be the challenge to residents in Dar es Salaam due to various anthropogenic activities in the city. This study was conducted to assess groundwater quality by determining concentrations of heavy metals. Both probability and Nonprobability sampling techniques were used to collect samples from 40 groundwater wells in 24 wards of Temeke municipal and analysed using Microwave Plasma Atomic Emission Spectrometer (Agilent 4210 MP-AES) at the Geochemistry Laboratory of the University of Dar es Salaam. Results indicated varying heavy metal concentrations ranging from 0.71 ± 0.08 to 6.64 ± 0.21 mg/l for As, 0.02 ± 0.01 to …

Assessing The Importance Of Air-Decking Blasting In Controlling Bigv At An Open Pit Gold Mine In Tanzania Using Ann Model, Karim R. Baruti

Tanzania Journal of Engineering and Technology (TJET)

Air-decking blasting technique is used to control blast induced ground vibration (BIGV) in several mines including open-pit gold mines located in Tanzania. While the importance of air-deck to control BIGV is practically evident, theoretical models such as BIGV prediction models cannot be used to assess the importance of air-decking. The main objective of this study was to assess the importance of the air-decking blasting technique to control BIGV using the artificial neural network (ANN)Model. To achieve this objective, ANNs were modeled and trained to learn the pattern of data using Multilayer Perception with Back Propagation to predict BIGV. The main …

Perona-Malik Diffusion-Driven Regularization For Image Resolution Enhancement In Electrical Capacitance Tomography, Nassor Ally

Tanzania Journal of Engineering and Technology (TJET)

Electrical Capacitance Tomography (ECT) is a non-invasive promising method for monitoring industrial processes, such as oil-gas flow in pipelines and solid-gas flow in pneumatic systems. Despite its potential benefits, ECT generates poor-quality images, often used only for qualitative analysis. A non-linear relationship between measured capacitances and permittivity distribution and the ill-posedness of the sensitivity matrix elements causes this limitation. This hinders the applicability of ECT in monitoring online industrial process applications. This work proposes a reconstruction method based on a nonlinear diffusion function to generate high-quality images from the measured capacitance data from the ECT system. The diffusion regularization functional …

Macro–Micro-Coupled Simulations Of Bead–Spring Breaking-Reforming Networks, Andrei Medved

Theses and Dissertations

In this work we investigate the dynamic behavior of bead-spring polymer solutions in viscoelastic fluids, which are essential in industries like materials science, biotechnology, and pharmaceuticals. The study leverages GPU-accelerated simulations and detailed modeling of polymer chain dynamics at the mesoscale, which enables efficient analysis of intricate fluid behaviors and the microscale dynamics of polymer chains. Additionally, the research examines the breaking-reforming dynamics of polymer chains, crucial for understanding phenomena such as shear thinning and thickening. The findings have broad applications, from improving inkjet printing and 3D printing technologies to developing new drug delivery systems and biocompatible materials. This work …

Analysis Of The Effect Of Vaccination, Efficient Surveillance And Treatment On The Transmission Dynamics Of Cholera, Loyinmi Adedapo Chris, Ajala Adebisi Shukurat, Alani L. Ijaola

Al-Bahir

In this study, we presented a modified SIR-SI model to investigate the dynamics and potential controls for cholera transmission, with an incident rate equipped with a saturation factor to investigate the combined impact of three vital measures which include effective surveillance, vaccination campaign and proper treatment in case severity. We established among other things, the qualitative analysis of the model to validate the results. Furthermore, the reproduction number (R0) was found to be less than unity (1), through the stability analysis. Additionally, finite different scheme was utilized in solving the differential equations of the model. MATLAB software was used for …

Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer

CODEE Journal

This paper aims to develop a mathematical model to study the dynamics of addiction as individuals go through their detox journey. The motivation for this work is three fold. First, there has been a significant increase in drug overdose and drug addiction following the COVID-19 pandemic, and addiction may be interpreted as a infectious disease. Secondly, the dynamics of infectious disease could be modeled via compartmental models described by differential equations and one can therefore leverage the existing analytical and numerical methods to model addiction as a disease. Finally, the work helps to inform how mathematical models governed by differential …

The Bioremediation Effect Of Microalgae On Wastewater: A Green Technology Approach, Mohamed Ahmed Reda Hamed Dr, Marwa Abdelfattah Abdallah Dr

Journal of Engineering Research

The present study lays an emphasis on the microalgae-based for simultaneous wastewater bioremediation using Chlorella vulgaris and Micrococcus luteus mixed algal cultures to remove its constituent pollutants, amazing green technology guarantees benefits with the decrease in the formation of dangerous solid sludge. Ten days of fully monitoring laboratory experimental program were performed in batch cultures to investigate the effect of various dominant mixing ratios for attaining wastewater concentrations and different governing temperature ranges on the performance of microalgae treatment. The results revealed that there is a significant impact of both wastewater concentrations and temperature treatment conditions on the capability of …

Unlocking The Potential Of Rooftop Sustainable Systems: Understanding Barriers And Facilitators, Mahmoud Desouki, Taghreed A. El-Haddad

Journal of Engineering Research

Urbanization is reducing green spaces in old cities globally, including Egypt, adversely impacting air quality, climate, and psychological well-being. The rooftop has the potential to offer viable alternatives that provide multiple benefits. They can host sustainable systems, and foster social activities. Despite these advantages, their adoption in cities like Tanta the Egyptian city, one of the world's most densely populated cities with a shrinking per capita green space, remains limited. Most rooftops are often serving as dumping grounds for trash and unused items. This study aims to explore the reasons behind this underutilization to find ways to encourage the use …

Indicators And Evidence Of Environmental Sustainability For Pedestrian In Public Parks (Towards An Approach For Formulating A Guideline Evaluation Model), Nashwa Youssif

Journal of Engineering Research

يتناول البحث أحد المجالات التي فرضت تواجدها في الأونة الأخيرة علي الساحة العلمية والبحثية التي تتعلق بالعلاقة التبادلية التأثير بين الإنسان والفراغ العمراني حيث يتنامي الإهتمام بالخصائص الإنسانيه و مدي توافقها مع هذا الفراغ العمراني.

وتعد مسارات المشاة من أهم الحيزات العمرانية التى تشكل النسيج العمراني وأحد أهم وسائل التواصل الإجتماعي والثقافي والوظيفي نظرآ لإرتباطها بالغالبية العظمي من أفراد المجتمع، ومساعدتها على جذب العديـد من الأنشطة داخل الحدائق العامة. مما يشير إلي ضرورة الإهتمام بتحسين بيئة حركة المشاه كمدخل للتواصل والإستدامة.

ومن هنا تتمثل مشكلة البحث في نقص الدراسات حول تقييم العلاقة بين معايير الاستدامة التصميمية والنظم البيئية لمسارات المشاة …

The Feasibility Of Utilizing The Open Dynamic Interaction Network (Odin) App To Assess Rema Data Across 30 Days Among Those Recovering From Alcoholism, Dennis E. Mcchargue, Bilal Khan, Jesscia Phelps, Patrick Duryea, Kimberly A. Tyler, Arthur Andrews, Ellie Reznicek, Lucy Napper, Mohamed Saad, Hsuan-Wee Lee

Department of Psychology: Faculty Publications

About ~4 million people with an alcohol use disorder receive treatment annually, and frequent relapse has produced a rapid revolving door between recovery and use. This paper presents preliminary data from a prospective micro-longitudinal study (30 days) that examines co-evolution of relapse risk processes of people with alcohol use disorders who entered a short-term residential substance use treatment. The primary goal of the current data was to assess the feasibility of using the open dynamic interaction network (ODIN) responsive ecological momentary assessment (rEMA). rEMA collected daily estimates on affect, urges, sober-support engagement, and use. The ODIN app administered twelve questions …