Applied Mathematics Commons^™

Contributions To Nonparametric Testing In Clustered Data, Hasika Kalani Wickrama Senevirathne

Mathematics & Statistics Theses & Dissertations

Clustered data refers to a specific kind of correlated data where units within the same cluster are correlated while units from different clusters are independent. The number of units in each cluster, known as the cluster size, can be associated with the cluster’s outcome. This is known as the informative cluster size (ICS) and affects the inference drawn from clustered data. Recently, a hypothesis testing method has been developed to detect the presence of ICS. However, considering ICS alone may not be sufficient when comparing outcomes across multiple groups of units within clustered data. The size of a group within …

Water Body Satellite Images Segmentation Using Maxwell Boltzmann Distribution, Lama Affara, Ali El-Zaart, Rabih Damaj

BAU Journal - Science and Technology

Images can exhibit diverse attributes and characteristics, because of variations in both the quantity of each intensity level and their respective positions, histograms display varying distributions. Some images feature symmetric histograms, while others exhibit asymmetry. In image segmentation tasks, traditional mean-based thresholding methods work well with symmetric histograms, relying on Gaussian distribution definitions. However, situations arise where asymmetric distributions must be considered. Threshold-based segmentation entails the partitioning of intensity levels into separate regions determined by the threshold value. Within this category of thresholding methods, Minimum Cross Entropy Thresholding (MCET) stands out as a mean-based thresholding technique with a unique self-contained …

3d Organ-Scale Models Of Tumor Growth And Treatment, Rafael Ramon Bravo

USF Tampa Graduate Theses and Dissertations

To understand the dynamics of cancer, mathematical oncologists have developed models of tumor growth and treatment response. Some models are mechanistic and approach tumor growth at the cell-scale, focusing on the evolution of cancerous cells within the ecology of normal tissue, and are often simulated with agent-based modeling. Other models are more clinically motivated and model tumor growth operating at the organ-scale, using patient data to predict treatment response, and are often simulated with partial differential equations. We developed the Hybrid Automata Library which includes both agent-based modeling and partial differential equations for modeling at either of these scales. We …

Black Holes In Time: The Effect Of Grid Radiation On The Tumor Immune Microenvironment, Rebecca A. Bekker

USF Tampa Graduate Theses and Dissertations

Tumor-immune interactions shape a developing tumor and its tumor immune microenvironment (TIME) resulting in either well-infiltrated, immunologically inflamed ‘hot’ tumor beds, or ‘cold’ immune deserts with low levels of infiltration. The pre-treatment immune state of the TIME is associated with treatment outcome; immunologically hot tumors generally exhibit better responses to radio- and immunotherapy than cold tumors. However, radiotherapy is known to induce opposing immunological consequences, resulting in both immunostimulatory and inhibitory responses. In fact, it is thought that the radiation induced tumoricidal immune response is curtailed by subsequent applications of radiation. Thus, I hypothesize that spatially fractionated radiotherapy (SFRT), administered …

An Empirical Study On Detecting And Explaining Global Structural Change In Evolving Graph Using Martingale, Tarun Teja Kairamkonda

Theses and Dissertations

There is a growing interest in practical applications involving networks of interacting entities such as sensor networks, social networks, urban traffic networks, and power grids, all of which can be represented using evolving graphs. Changes in these evolving graphs can signify shifts in the behavior of interacting entities or alterations in the patterns of their interactions. Identifying and detecting these changes is crucial for addressing potential challenges or opportunities in various domains. In this study, we propose an approach for detecting structure change in evolving graphs based on the martingale change detection framework on multiple graph features extracted over time. …

Numerical Issues For A Non-Autonomous Logistic Model, Marina Mancuso, Kaitlyn M. Martinez, Carrie Manore, Fabio Milner

CODEE Journal

The user-friendly aspects of standardized, built-in numerical solvers in
computational software aid in the simulations of many problems solved using
differential equations. The tendency to trust output from built-in numerical
solvers may stem from their ease-of-use or the user’s unfamiliarity with the
inner workings of the numerical methods. Here, we show a case where the
most frequently used and trusted built-in numerical methods in Python’s
SciPy library produce incorrect, inconsistent, and even unstable approxima-
tions for a the non-autonomous logistic equation, which is used to model
biological phenomena across a variety of disciplines. Some of the most com-
monly used …

Impact Of Covid-19 On Disaggregate Consumption And Online Retail Sales: Evidence From The Usa, Gulzar Ahmed, Olcay Akman

Spora: A Journal of Biomathematics

This study applies the difference-in-difference technique to analyze the consumption pattern during COVID-19 against pre-COVID-19 years. We analyze the online retail sales before and after COVID-19 using time series and linear regression models. Time series intervention analysis results suggest that COVID-19 has caused a statistically significant change in the mean level of online retail sales share in e-commerce. Using a difference-in-difference approach, we find a 4% decrease in aggregate consumption from March to December 2020 compared to the benchmark period although statistically insignificant. Further, using a fixed effects model with time dummies, we find a nearly 8% significant decrease in …

Hardware Acceleration Of Numerical Methods For Solving Ordinary Differential Equations, Soham Bhattacharya

Theses and Dissertations

Along with the advancement in technology, the role of hardware accelerators is increasing consistently, delivering advancements in scientific simulations and data analysis in scientific computing, signal processing tasks in communication systems, matrix operations, and neural network computations in artificial intelligence and machine learning models. On the other hand, several high-speed computer applications in this era of high-performance computing often depend on ordinary differential equations (ODEs); however, their nonlinear nature can present a challenge to obtaining analytic solutions. Consequently, numerical approaches prove effective in delivering only approximate solutions to these equations. This research discusses the implementation of a customized hardware accelerator …

Capturing Latent Abilities And Latent Capacities Of Professional Golfers Using Nonlinear Mixed Effects Growth Modeling, Mac Wetherbee

Electronic Theses and Dissertations

This study demonstrates an effective and innovative approach to measuring the latent athletic abilities and capacities of professional golfers. I used nonlinear mixed effects growth modeling (e.g., Dynamic Measurement Modeling) to measure professional golfers’ ability levels and capacities for improvement. I accomplished this using a two-stage modeling approach. First, a crossed linear mixed effects model estimated each player’s ability level in each year. In the second stage, I used the results from the first stage to estimate several candidate nonlinear growth trajectories for players’ abilities over time. The quadratic growth trajectory was the best-fitting of these trajectories and was used …

Circling The Square: Computing Radical Two, Isaiah Mellace, Joshua Kroeker

NEXUS: The Liberty Journal of Interdisciplinary Studies

Discoveries of equations for irrational numbers are not new. From Newton’s Method to Taylor Series,there are many ways to calculate the square root of two to arbitrary precision. The following method is similar in this way, but it is also a fascinating derivation from geometry that has applications to other irrationals. Additionally, the equation derived has some properties that may lead to fast computation. The first part of this paper is dedicated to deriving the equation, and the second is focused on computer science implementations and optimizations.

The Polyaneuploid Cancer Cell State And Therapeutic Resistance: Eco-Evolutionary Dynamics In Structured Populations, Anuraag Bukkuri

USF Tampa Graduate Theses and Dissertations

In this dissertation, I develop and apply eco-evolutionary modeling techniques to understand how the polyaneuploid cancer cell (PACC) state, entered when aneuploid cells exit the cell cycle after S phase and undergo a whole genome duplication, contributes to therapeutic resistance. Since resistance remains one of the primary causes of treatment failure in cancer patients, it is critical to understand how such demographic state transitions allow for acclimatization of cancer cells to therapeutic stressors and how they interact with evolutionary processes to promote irreversible resistance.

In Chapters Two and Three, I lay the foundation for this work. In Chapter Two, I …

Nidus Idearum. Scilogs, Xiv: Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this fourteenth book of scilogs – one may find topics on examples where neutrosophics works and others don’t, law of included infinitely-many-middles, decision making in games and real life through neutrosophic lens, sociology by neutrosophic methods, Smarandache multispace, algebraic structures using natural class of intervals, continuous linguistic set, cyclic neutrosophic graph, graph of neutrosophic triplet group , how to convert the crisp data to neutrosophic data, n-refined neutrosophic set ranking, adjoint of a square neutrosophic matrix, neutrosophic optimization, de-neutrosophication, the n-ary soft set relationship, hypersoft set, extending the hypergroupoid to the superhypergroupoid, alternative ranking, Dezert-Smarandache Theory (DSmT), reconciliation between …

A Meta-Ensemble Predictive Model For The Risk Of Lung Cancer, Sideeqoh Oluwaseun Olawale-Shosanya, Olayinka Olufunmilayo Olusanya, Adeyemi Omotayo Joseph, Kabir Oluwatobi Idowu, Oyelade Babatunde Eriwa, Adedeji Oladimeji Adebare, Morufat Adebola Usman

Al-Bahir

The lungs play a vital role in supplying oxygen to every cell, filtering air to prevent harmful substances, and supporting defense mechanisms. However, they remain susceptible to the risk of diseases such as infections, inflammation, and cancer that affect the lungs. Meta-ensemble techniques are prominent methods used in machine learning to enhance the accuracy of classifier learning systems in making predictions. This work proposes a robust predictive model using a meta-ensemble method to identify high-risk individuals with lung cancer, thereby taking early action to prevent long-term problems benchmarked upon the Kaggle Machine Learning practitioners' Lung Cancer Dataset. Three machine learning …

(R2083) A Multiobjective Optimization Model For Selecting Portfolios In Emerging Financial Markets Under Uncertainty, Milad Saleki, Mohammad Saber Fallahnezhad, Davood Shishebori, Hasan Khademi Zare

Applications and Applied Mathematics: An International Journal (AAM)

In the issue of financial portfolio selection, especially in emerging financial markets, the investor usually intends to make the best possible choice based on several conflicting objectives, such as return, risk, and liquidity. To obtain a suitable portfolio using ideal values and the maximum possible deviations, we suggest fuzzy goal programming and its combination with satisfaction functions and expert opinions. The model can determine the best portfolio based on the opinions of financial market experts, taking into account uncertainties. This model formulates a multiobjective financial portfolio selection approach by considering fuzzy parameters obtained from emerging financial markets. In addition, the …

Modeling Redistribution Of Nanozeolites In Holographic Recording, Dana Mackey, Jack Lyons Dr, Izabela Naydenova

Articles

Zeolite doped photopolymers have been studied experimentally due to their potential application in the develop- ment of optical sensors. It has been shown that dopant redistribution can be achieved by holographic recording and has a direct influence on the sensitivity of the recorded grating. To achieve better theoretical understanding of these processes, this paper proposes an extended photopolymerization-diffusion mathematical model for describing the dynamics of nanozeolite redistribution during recording in an acrylamide-based photopolymer. Using numerical simulations of this model, we investigate how recording conditions, dopant transport parameters, and initial load affect the refractive index modulation of the resulting photonic structure.

Matrix Approximation And Image Compression, Isabella R. Padavana

Master's Theses

This thesis concerns the mathematics and application of various methods for approximating matrices, with a particular eye towards the role that such methods play in image compression. An image is stored as a matrix of values with each entry containing a value recording the intensity of a corresponding pixel, so image compression is essentially equivalent to matrix approximation. First, we look at the singular value decomposition, one of the central tools for analyzing a matrix. We show that, in a sense, the singular value decomposition is the best low-rank approximation of any matrix. However, the singular value decomposition has some …

(R2076) New Exact Solution Of Gilson–Pickering Equation In Plasma, Bingnuo Yang, Weinan Wu, Hongfeng Yu, Peng Guo

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we use Paul-Painlev´e approach method, extended rational sine-cosine method and extended rational sinh-cosh method to construct the exact solution of the nonlinear Gilson-Pickering (GP) equation in plasma. The exact solution of GP equation obtained by the above three methods is new, and we use mathematical software to draw the two-dimensional and three-dimensional graphs of the new exact solutions. Through the study of nonlinear equations in plasma, this study will enrich the research and connotation of nonlinear development equations in plasma.

(R2070) Poisson-Exponentiated Weibull Distribution: Properties, Applications And Extension, Alphonsa George, Dais George

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we introduce a new member of the Poisson-X family namely, the Poisson-exponentiated Weibull distribution. The statistical as well as the distributional properties of the new distribution are studied, and the performance of the maximum likelihood method of estimation is verified by a simulation study. The flexibility of the distribution is illustrated by a real data set. We develop and study a reliability test plan for the acceptance or rejection of a lot of products submitted for inspection when their lifetimes follow the new distribution. A real data example is also given to illustrate the feasibility of the …

(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni

Applications and Applied Mathematics: An International Journal (AAM)

Hyperbolic linear theory of heat propagation has been established in the framework of a Caputo time fractional order derivative. The solution of a system of integer and fractional order initial value problems is achieved by employing the Adomian decomposition approach. The obtained solution is in convergent infinite series form, demonstrating the method’s strengths in solving fractional differential equations. Moreover, the double Laplace transform method is employed to acquire the solution of a system of integer and fractional order boundary conditions in the Laplace domain. An inversion of double Laplace transforms has been achieved numerically by employing the Xiao algorithm in …

(R2071) Global Stability Analysis Of Chikv Dynamics Model With Adaptive Immunity And Distributed Time Delays, Taofeek O. Alade, Samson Olaniyi, Hassan A. Idris, Yaqoob Al Rahbi, Mohammad Alnegga

Applications and Applied Mathematics: An International Journal (AAM)

The application of mathematical biology and dynamical systems has proven to be an effective approach for studying viral infection models. To contribute to this research, our paper proposes a new CHIKV model that takes into account an adaptive immune response and distributed time delays, which accurately reflects the time lag between initial viral contacts and the production of new active CHIKV particles. By analyzing the model’s qualitative behavior, we establish a biological threshold number that can predict whether CHIKV will be cleared from or persist in the body. We demonstrate the global stability of both CHIKV-present and CHIKV-free steady states …

(R2078) Analyzing The Effects Of Fifth And Seventh Order Terms In A Generalized Henon-Heiles Potential, Nandana Madhukara

Applications and Applied Mathematics: An International Journal (AAM)

The Hénon-Heiles system is a 2-dimensional axisymmetric Hamiltonian system that was first formed to determine the third integral of motion in galactic dynamics. After its inception, it has become a paradigm in dynamical systems due to its apparent simplicity but extremely complicated dynamical behavior. In this paper, we perform a series expansion up to the seventh order of a general potential with axial and reflection symmetries. After some transformations, this becomes a generalized Hénon-Heiles (GHH) system where we separate the fifth and seventh-order terms. We qualitatively analyze this system for energies near the threshold between bounded and unbounded motion with …

(R2086) Circular Restricted Three-Body Interaction Problem With Various Perturbations, Shiv K. Sahdev, Abdullah .

Applications and Applied Mathematics: An International Journal (AAM)

The motion properties of the infinitesimal body is studied under the forces due to kerr-like oblate heterogeneous primary, continuation fractional potential for secondary, solar sail, three-body interactions, Coriolis and centrifugal forces in the circular restricted three-body problem. The equations of motion of infinitesimal body are evaluated under the above-said perturbations. Using these equations of motion, we illustrate the locations of equilibrium points, their stability, the periodic orbits and Poincaré surfaces of section. This study will applicable on the motion of the artificial satellite.

(R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, Jyoti U. Yadav, Twinkle R. Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a comparative study between two different methods for solving nonlinear timefractional coupled Boussinesq-Burger equation is conducted. The techniques are denoted as the Natural Transform Decomposition Method (NTDM) and the Variational Iteration Transform Method (VITM). To showcase the efficacy and precision of the proposed approaches, a pair of different numerical examples are presented. The outcomes garnered indicate that both methods exhibit robustness and efficiency, yielding approximations of heightened accuracy and the solutions in a closed form. Nevertheless, the VITM boasts a distinct advantage over the NTDM by addressing nonlinear predicaments without recourse to the application of Adomian polynomials. …

(R2085) Heat And Mass Transport Characteristics In Williamson Fluid Flow Over A Permeable Stretching Cylinder, Amala Olkha, Mukesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

The intention of this research endeavor is to examine heat and mass transport in Williamson fluid flow induced by a permeable stretching cylinder in a porous medium. Various physical factors (like viscous dissipation, chemical reaction, etc.) affecting the relevant fields (flow, temperature and concentration) are incorporated in the investigation. The governing PDEs are turned into nondimensional ODEs using adequate similarity transformation relations, and then tackled numerically using MATLAB based Bvp4c technique along with shooting method. The impacts of various parameters arising in the problem are exhibited on fluid flow, temperature and concentration distribution by drawing portraits and discussed. Moreover, impressions …

Pt-Symmetry And Eigenmodes, Tamara Gratcheva

University Honors Theses

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration …

Advances In Computational And Statistical Inverse Problems, Dylan Green

Dartmouth College Ph.D Dissertations

Inverse problems are prevalent in many fields of science and engineering, such as signal processing and medical imaging. In such problems, indirect data are used to recover information regarding some unknown parameters of interest. When these problems fail to be well-posed, the original problems must be modified to include additional constraints or optimization terms, giving rise to so-called regularization techniques. Classical methods for solving inverse problems are often deterministic and focus on finding point estimates for the unknowns. Some newer methods approach the solving of inverse problems by instead casting them in a statistical framework, allowing for novel point estimate …

Unconventional Computing With Photonic Oscillator Networks, Mostafa Honari Latifpour

Dissertations, Theses, and Capstone Projects

The ever-increasing demand for data processing and the challenges in scaling traditional computing architectures are driving intensive research into alternative computing paradigms. Optical computing has garnered renewed attention since the 2010s, driven by its potential to accelerate specialized computational tasks such as combinatorial optimization and neural networks.

Coherent light sources including lasers and parametric oscillators have been around for decades and become indispensable tools in modern technology, but these photonic oscillators are also nonlinear dynamical systems that can exhibit emergent, complex phenomena, especially when coupled in arrays. These nonlinear optical systems have recently been shown to be capable of doing …

Comparison Of Methods For Creating Populations Of Models By Solving Stochastic Inverse Problems, Elizabeth Epstein

Theses

Given a parametric family of models and observational data, a researcher may be faced with an inverse problem: what distribution of parameters best creates a set of models that produce the observed data? Traditionally, Markov Chain Monte Carlo (MCMC) has commonly been used as a method to solve these stochastic inverse problems. In recent years, however, Generative Adversarial Networks (GANs) have been employed. The effectiveness of Markov Chain Monte Carlo methods as compared to a conditional generative adversarial network (cGAN) when applied to a family of models produced by a system of ordinary differential equations that model viral load over …

Mathematical Modeling And Simulation Of The Photopolymerization Process In Different Industrial Applications, Maged Shaban

Doctoral

Photopolymerization is a complex physicochemical process that uses a specific wavelength of light to convert a liquid monomer resin to a solid polymer. This study investigates the evolution of photopolymerization kinetics through mathematical modeling and simulation in different industrial applications, such as stereolithography, ceramics additive manufacturing, and photonic crystal fabrication. In stereolithography, existing photopolymerization models do not fully capture the complexity of the curing process. Therefore, we develop a novel model for photopolymerization kinetics in a realistic stereolithography setting, which attempts to advance the understanding of the impact of several material properties and parameters on this process. This model significantly …

Existence And Uniqueness Results For Deformable Fractional Differential Equations, Sreedharan R

Theses and Dissertations

Fractional calculus and fractional differential equations are considered to be the valuable tools in modeling many phenomena in various fields of science and engineering. In the literature, many definitions for fractional order derivatives, such as Riemann-Liouville, Caputo, Jumarie, Hadamard, Weyl, and more, were developed to study the fractional differential equations that govern various phenomena in science and engineering. But these definitions have their own limitations, such as derivatives of constants, product of two functions, quotient of two functions, assertion laws, and limiting values of the derivatives at zero and negative numbers.

To overcome the deficiencies, researchers have recently introduced some …