Applied Mathematics Commons^™

Study On Factors Influencing The Strong Chromatic Index Of Graphs Derived From Path Graphs, Star Graphs, And Cycle Graphs, Vikram St

Theses and Dissertations

Graph coloring is a major research area in Graph Theory that has a rich collection of research articles contributed by mathematicians across the world. This thesis focuses on a specific type of Graph coloring where the edges of a graph are colored by a principle called strong edge-coloring. There have been numerous research articles published on the least number of colors required to define such a coloring for a given graph G. This least number, χ′s (G), is called as the strong chromatic index of a graph G. Though conjectures stated as early as 1989 remain unsolved, there have been …

Towards Environmentally Sustainable Preservation Of Heritage Buildings, Rozal Rozal Yousef Hanna1, Ayman Gamal El-Din Abd El- Tawab2, Walaa Abou El- Haggag Mehanna3

Journal of Engineering Research

The construction industry, characterized by its intricate processes and extensive stakeholder networks, stands at the cusp of a digital revolution. The adoption of blockchain-smart contract (BCSC) technology is at the heart of this transformation. This research delves deep into the BCSC within the construction arena to provide comprehensive insight into its probable applications, inherent challenges, and potential future trajectories. Leveraging the PRISMA analysis technique, a curated collection of relevant academic research articles was assembled, shedding light on the existing body of knowledge regarding the application of BCSC technology in construction. The authors developed an innovative user interface tool customized to …

Review: Protection Of Wooden Structures With Nano-Titanium Dioxide Coating, Zienab Zienab A. Ahmed1*, And M. M. Mosallem2

Journal of Engineering Research

Wood is widely used for various purposes with good performance. Wood works as the main material for furniture, monuments, decorations and constructions. which has the close relationship with human. Durability of wood is important in ensuring an appropriate life for the structure being designed. Wooden construction deteriorates easily due to UV radiation and weather conditions. Many of wood types need a preservative treatment. Several compounds are available for chemical protection, but not all are completely safe for human health. New technologies with low environmental impact and economically feasible are developed, which improves the life cycle of wood. Titanium dioxide is …

Urbanism Strategies For Linking Existing And New Cities, Naglaa J. Q. Mo’Men Abdel-Qader Ebrahim1, Mohsen Bayad2

Journal of Engineering Research

New cities, designed for urban growth outside existing metropolitan regions, face challenges in street infrastructure due to rapid expansion. Efficient control of mobility is crucial as cities grow. Sustainable transportation involves factors like infrastructure, public transit, delivery networks, affordability, efficiency, air quality, health, and reduced emissions. Commuting between established and new urban areas is common, leading to issues like urban sprawl, longer travel times, and congestion in developing countries. The challenge is to improve accessibility while addressing air quality, traffic, congestion, noise, built environment, emissions, and sprawl. This study aims to explore factors influencing mobility choices in Egypt, focusing on …

The Impacts Of Dimensionality, Diffusion, And Directedness On Intrinsic Cross-Model Simulation In Tile-Based Self-Assembly, Daniel Hader, Matthew J. Patitz

Computer Science and Computer Engineering Faculty Publications and Presentations

Motivated by applications in DNA-nanotechnology, theoretical investigations in algorithmic tile-assembly have blossomed into a mature theory. In addition to computational universality, the abstract Tile Assembly Model (aTAM) was shown to be intrinsically universal (FOCS 2012), a strong notion of completeness where a single tile set is capable of simulating the full dynamics of all systems within the model; however, this construction fundamentally required non-deterministic tile attachments. This was confirmed necessary when it was shown that the class of directed aTAM systems, those where all possible sequences of tile attachments result in the same terminal assembly, is not intrinsically universal (FOCS …

On Weighted Sequence Spaces, Gilbert D. Acheampong

Mathematics & Statistics Theses & Dissertations

The space ℓ^p,α of complex sequences a = (a₀,a₁,a₂, . . .) for which

∞

∥a∥p,α = ( Σ|ak|^p(k+1)^α)^1/p < ∞

k=0

is studied. Each such sequence can be identified with the analytic function with power series

∞

f (z) = ∑ akz^k.

k=0

In this setting, the point evaluation and the difference quotient mappings are shown to be bounded; the cases are identified in which ℓ^p,α is boundedly contained in ℓ^r,β . …

Accelerating The Efficiency Of Multiscale Hybridizable Discontinuos Galerkin Methods For Flows In Heterogeneous Media, Tony Charles Haines

Mathematics & Statistics Theses & Dissertations

A plethora of scientific and engineering problems encountered are multiscale in nature. This multiscale feature often influences simulation efforts wherever large disparities in spatial scales are experienced. Notable examples include composite materials, fluid flow through porous media and turbulent transport in high Reynolds number flow. Although there are promising results from the advancement of modern supercomputer, obtaining direct numerical solution of multiscale problems is very laborious. This difficulty stems from the tremendous amount of computer memory and CPU time required. Parallel computing may be one obvious choice in remedying this issue. However, the complexity and size of the discrete problem …

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 …

Parallel-In-Time Implicit Schemes For Nonlinear Pdes, Subhash Paudel

Mathematics & Statistics Theses & Dissertations

An accurate prediction of unsteady physical phenomena arising in various applications (e.g., rotorcraft and turbomachinery flows, fluid-structure interaction, maneuvering flight conditions, etc.) requires a very large number of time steps, thus considerably increasing the total computational time, because conventional time integrators are inherently sequential. Parallel-in-time methods offer a promising direction for drastically reducing the computational time and achieving such scalability that is required for solving these unsteady problems on modern supercomputers with hundreds of thousands of computing cores. The parallel performance of existing parallel-in-time algorithms for nonlinear equations especially of the hyperbolic or mixed type is far from being satisfactory. …

Existence Of Smooth Solutions For The Landau Equation With Hard Potentials, Shelly Ann Taylor

Theses and Dissertations

This dissertation is concerned with the Landau equation, an integro-differential equation that models the particle density of a plasma as it evolves in phase space. The main topic is the (large-data) local existence of classical solutions to the Landau equation in the case of hard potentials (γ ∈ (0, 1]). Solutions have previously been constructed by Chaturvedi [SIAM. J. Math. Anal., 55(5), 5345–5385, 2023] for initial data in an exponentially-weighted Sobolev space of order 10, but it is not a priori clear whether these solutions have more regularity than the initial data. We improve Chaturvedi’s existence result in two ways: …

Deep Learning In Reproducing Kernel Banach Spaces, Mingsong Yan

Mathematics & Statistics Theses & Dissertations

Deep learning has achieved immense success in the past decade. The goal of this dissertation is to understand deep learning through the framework of reproducing kernel Banach spaces (RKBSs), which were originally proposed for promoting sparse solutions. We begin by considering learning problems in a general functional setting, and establishing explicit and data-dependent representer theorems for both minimal norm interpolation (MNI) problems and regularization problems. These theorems provide a crucial foundation for the subsequent results derived for both sparse learning and deep learning. Next, we investigate the essential properties of RKBSs capable of encouraging sparsity in learning solutions. With the …

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.