Applied Mathematics Commons^™

A Neutrosophic Exploration Of Creative Ideational Dynamics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Philosophy has always tried to illuminate the complexity of existence, but often faced its own paradoxes. The emergence of philosophical schools and concepts, along with their arguments, reflect the dynamic interaction of ideas. This short note explores some nuanced principles governing philosophical thought, summarized in the proposed “philosophical formulas.” These formulas are intended to mathematically and conceptually express the tensions, complementarities, and movements intrinsec in a given philosophical system.

A Position Indicator With Applications In The Field Of Designing Forms With Artificial Intelligence, Ovidiu Ilie Șandru, Florentin Smarandache, Alexandra Șandru

Branch Mathematics and Statistics Faculty and Staff Publications

The indicators used so far within the Theory of Extension can be synthetically expressed by the notion of “position indicators”. More exactly, these indicators can be grouped in two main sub-categories: point-set position indicators and point-two sets position indicators. The secondary goal of this paper is to define these classifications, while the primary goal is that to extend the two notions to the most general notion of set-set position indicator.

Approches Neutrosophiques Et Plithogéniques En Science Des Données Et Analyse Multivariée : Contributions De La Ixe Réunion Ibéro-Américaine De Biométrie, Florentin Smarandache, Maikel Y. Leyva Vázquez, Mohamed Abdel-Basset

Branch Mathematics and Statistics Faculty and Staff Publications

Ce numéro spécial de "Neutrosophic Sets and Systems" rassemble une sélection de travaux remarquables présentés lors de la IXe Réunion Ibéro-américaine de Biométrie, qui a eu lieu les 8 et 9 juillet 2025 à Quito, en Équateur. Sous la direction d'une équipe éditoriale de prestige, ce volume explore l'application des approches neutrosophiques et plithogéniques dans divers domaines tels que la biométrie, la bioinformatique, la santé publique, l'éducation et l'économie. Les articles mettent en lumière la convergence entre les statistiques classiques et l'intelligence artificielle, illustrant comment les méthodes neutrosophiques offrent des outils puissants pour modéliser l'incertitude et la complexité des données …

Competition Super-Hypergraphs: Revealing Hierarchical Competition In Real-World Networks, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Graph theory provides a powerful language for modeling pairwise connections through vertices and edges [9, 20]. Hypergraphs generalize this idea by permitting hyperedges that join any number of vertices simultaneously [7], while super-hypergraphs iterate the Power-set operation to capture multi-level, hierarchical relationships among hyperedges [40, 22]. A competition hypergraph associates each prey species with a hyperedge containing all its predators, thereby encoding multi-way competition in ecological networks. In this work, we introduce the competition super-hypergraph, which lifts the competition concept to higher tiers of aggregation. We present its formal definition, explore theoretical properties, and illustrate its practical use in real-world …

Cvitlnn: A Hybrid Approach Based On Vision Transformer And Liquid Neural Network For Covid-19 Detection, Muhammad Waqaq, Florentin Smarandache, Muhammad Yasir, Farrukh Arslan, Anum Ali

Branch Mathematics and Statistics Faculty and Staff Publications

The COVID-19 pandemic has underscored the need for accurate and rapid diagnostic tools to assist clinical decision-making. Conventional deep learning models for COVID-19 detection in Chest X-Ray (CXR) images face challenges in poor generalization across imaging conditions and high computational demands. To address these issues, this study proposes CviTLNN, a novel hybrid model combining Vision Transformers (ViTs) and Liquid Neural Networks (LNNs) to improve feature extraction and classification. Specifically, CviTLNN employs a ViT with 24 transformer encoder blocks for efficient extraction of spatial features. The self-attention mechanism of ViTs effectively captures global and local dependencies in CXR images. Furthermore, …

Comprehensive Benchmarking Of Several Machine Learning And Bayesian Models For Early-Stage Diabetes Risk Prediction: A Large-Scale Comparative Study, Md. Iqbal Hossain, Najila Alam Porno

Mathematics & Statistics Faculty Publications

Diabetes remains a critical global health challenge, with early detection is crucial for effective management. This study presents a comprehensive benchmarking analysis of 14 diverse machine learning and Bayesian models for early-stage diabetes risk prediction using clinical data [2] from Sylhet, Bangladesh. This research evaluated traditional methods (Logistic Regression, Decision Trees), ensemble techniques (Random Forest, XGBoost, LightGBM), Bayesian approaches (BART, Bayesian Logistic Regression), and advanced neural architectures (Deep Belief Networks) using both 70-30 train-test splits and 10-fold cross-validation. The results demonstrate that ensemble methods consistently outperformed other approaches, with Random Forest(RF) achieving the highest cross-validated AUC (0.9951) and accuracy (0.9699). …

Suntan (And Other Solar Tigonometric Functions), John Adam

Mathematics & Statistics Faculty Publications

Question 1: If I₀ is the solar irradiance (power per unit area, W/m²) reaching my head, express the intensity on the side of my face (I_s) in terms of θ. Assume for now that the irradiance is independent of path length through the atmosphere and that my face is normal to the direction θ = 90°.

Using the 1962 U.S. Standard Atmosphere,² Hottel (1976)³ expressed the solar irradiance using the formula

I = I₀(a₀ + a₁e^{−k sec θ}), where A is the elevation in kilometers and

a₀ = 0.4237 − 0.00821(6 − A)²; a₁ = 0.5055 …

Golden Spirals Everywhere?, John Adam

Mathematics & Statistics Faculty Publications

The article explores different types of spirals, including Archimedean, hyperbolic, and logarithmic spirals, with a focus on the golden ratio and golden spirals. It discusses the misconception that golden rectangles and spirals can be found in various natural and man-made objects, emphasizing the importance of understanding the properties of logarithmic spirals. The text provides mathematical equations for logarithmic spirals and poses questions for readers to explore the concept further. The author, John Adam, invites readers to engage in Fermi Questions and submit ideas for consideration.

Theory And Applications Surrounding Markov Chains, Joseph J. Quisito Jr., Gallean Brown, Elijah Yoder

Capstone Showcase

This capstone project explores the Markov Chain – a mathematical model used to describe systems that transition between states based on probabilities. It begins by introducing the fundamental concepts, including transition matrices, state classifications, and stationary distributions. The paper then applies Markov Chain theory to real-world scenarios, such as simulating Snakes and Ladders games, predicting soccer match outcomes for Manchester United, and generating texts from movie lines. Finally, it discusses key findings, challenges, and potential areas for future research in the field.

Weathering And Beyond: Leveraging Mathematical Modeling To Simulate Erosion In Digital Media, Fiona Irving-Beck

Scripps Senior Theses

How might we bring an idea to life from both a mathematical and an artistic perspective? Within Weathering, I use imagery of environmental erosion to explore the differences between physical and digital forms of representation. I created a physical painting of an abandoned copper mine, digitized the work, and then used a mathematical model to digitally “erode” it, which I re-translated into paintings. While the explicit texture present in physical work speaks best to my practice/intent, the mathematical framework that is the basis for my digital work affords a powerful mode of temporal flexibility. Used in conjunction, these two …

Modelling The Formation Of Unslanted Holographic Gratings In Hybrid Photopolymer Media, Jack Lyons, Dana Mackey, Izabela Naydenova

Articles

The theoretical modelling of holographic recording in photopolymers has been an important tool in their optimisation. More complex, hybrid organic/inorganic photopolymers have been developed in pursuit of materials with higher sensitivity, low shrinkage, high dynamic range and environmental stability. Recent attempts to augment the existing models for the redistribution of inorganic nanoparticles in holographic recording were successful but there is still a knowledge gap in regards to modelling optical losses, mutual cross-diffusion, the formation of slanted holographic gratings and polymerization induced shrinkage in hybrid photopolymer media. This paper will describe a novel approach to modelling the formation of unslanted holographic …

Cfd Analysis Of Hydrodynamic Cavitation Through An Orifice: Influence Of Different Inlet Pressures And Number Of Orifice Holes, Lemthong Chanphavong, Vongsavanh Chanthaboune, Keophousone Phonhalath

ASEAN Journal on Science and Technology for Development

Hydrodynamic cavitation (HC) is considered an energy-efficient process with high potential for utilization in many chemical processes. This study presents a computational fluid dynamics (CFD) analysis of cavitating flow through an orifice with a constant flow area. The Reynolds-Averaged Navier-Stokes (RANS) equations, coupled with turbulence and cavitation models, are employed to capture the complex flow behaviors. The effects of inlet pressures and number of orifice-holes on cavitation behavior are investigated. Result of the numerical simulation is validated with the existing experimental data from the literature. The CFD study revealed that cavitation initiates just behind the inlet edge of the orifice …

Rapid Inference Of Atmospheric Feature Parameters From Light Curves Using Bayesian Neural Networks, Eugenio A. Diaz

Honors Undergraduate Theses

Mapping atmospheres using rotationally modulated light curves offers insights into cloud structures and dynamics. Current retrieval methods, primarily based on Markov Chain Monte Carlo (MCMC) techniques like Aeolus, can infer atmospheric features but are computationally prohibitive for large datasets. This project proposes a neural network (NN) framework for the rapid, variational inference of atmospheric structure from light curves, particularly those of brown dwarfs. The primary approach focuses on training a Bayesian NN (BNN) to perform regression, predicting the spot parameters that describe the object's surface brightness map. Given the scarcity of suitable observational training data, the BNN is trained on …

0th Order Solutions Of The Wavefunctions For The Quantum Elliptical Box And Microstrip Antenna, Nishtha Tikalal

Honors Undergraduate Theses

For a quantum particle confined to a two-dimensional elliptical box or electromagnetic wave in a microstrip antenna, geometrical and boundary condition interplay result in a spectrum of spatial patterns. Due to the asymmetrical nature of the ellipse, we are faced with continuous symmetry reductions, leaving both degenerate and nondegenerate solutions. Here, we present a complete derivation of an analytical solution and visualizations of the fundamental wavefunctions for both Dirichlet and Neumann boundary conditions respectively corresponding to the quantum elliptical box and the elliptical microstrip antenna.

We demonstrate that the eigenmodes, governed by eccentricity, directly correspond to the modal field distributions …

Ultrasonic Sensor-Based Sound Synthesis Using Raspberry Pi Pico W, Niraj Jaishwal

Williams Honors College, Honors Research Projects

At the intersection of Human Computer Interaction and digital art, this project transforms simple motion into musical expression. It explores an interactive real-time sound synthesis system using ultrasonic sensors to generate continuous audio. The objective is to design a system that maps physical distances into musical parameters such as pitch and amplitude, which will create a responsive audio environment. Two ultrasonic sensors are used in combination with the Raspberry Pi Pico W microcontroller running CircuitPython and Adafruit Audio Hat for real-time sound output. One sensor controls the pitch of the generated tone, while the other controls volume. This enables expressive …

Improving The Accuracy Of Neighborhood Median Pixel Method (Nmpm) In Classifying Landsat-8 Oli Images By Optimizing The Scoring System’S Point Values, Abraham T. Magpantay, Proceso L. Fernandez Jr

Department of Information Systems & Computer Science Faculty Publications

The Neighborhood Median Pixel Method has previously been introduced as an image processing technique in remote sensing, developed to classify Landsat-8 OLI satellite image pixels into categories of vegetation, water, and built-up areas. This method relies on a lookup table based on the median pixel values within a pixel’s neighborhood and a scoring system that assigns point values for classification. While a 9x9 neighborhood size was originally proposed, a succeeding study suggested a 13x13 neighborhood for better classification accuracy. This study focuses on refining the scoring system used in the Neighborhood Median Pixel Method, particularly the original set of arbitrary …

Stability And Global Dynamics Of Autonomous And Nonautonomous Discrete Population Models With Stocking, Harvesting, And Cooperation, Sam Habach

Open Access Dissertations

This dissertation investigates the local and global behavior of several classes of discrete population models involving stocking, harvesting, and cooperation. The study is divided into three major manuscripts, each offering new theoretical in sights, bifurcation results, and applications to real-world data.

In Manuscript 1, we study the Beverton-Holt population models with constant and proportional stocking and harvesting, as well as sigmoid Beverton-Holt models under constant stocking and harvesting, both in autonomous and non-autonomous settings. We analyze stability and explore global dynamics using established local and global dynamics theorems, bifurcation theory, and explicit solutions when available. Special attention is given to …

Investigations Of Conjugate Heat Transfer And Fluid Flow In Partitioned Porous Cavity Using Darcy-Forchheimer Model: Finite Element-Based Computations, Nasir Yasin, Shafee Ahmad, Muhammad Umair, Zahir Shah, Narcisa Vrinceanu, Ghadah Alhawael

Mathematics & Statistics Faculty Publications

The conjugate heat transfer and fluid flow has vast applications in thermal engineering, particularly for cooling in thermal devices, and automobile engines. This study investigates conjugate heat transfer in 2D enclosures, featuring thin solid fins attached to a porous bottom wall. The porous medium is considered isotropic and homogeneous by the Darcy-Forchheimer model, with fluid phases in local thermal equilibrium. The boundary conditions at the porous fluid interface ensure continuity of the velocities, stresses, temperature, and heat flux. The phenomenon is mathematically modelled by obtaining a set of partial differential equations. The finite element method (FEM) is used to perform …

Application Of Semantic Segmentation To An Automatic Target Recognition Problem, Bruce W. Rush Jr.

College of Graduate Studies: Theses & Dissertations

Synthetic Aperture Radar (SAR) is an active remote sensing system commonly used in aerial reconnaissance. SAR penetrates cloud cover and vegetation by recording reflected energy pulses. The resulting information content is difficult to interpret due to vast clutter data and sparse target data. The time-consuming process of analyzing SAR imagery can be greatly reduced by implementing an Automatic Target Recognition (ATR) algorithm. Convolutional Neural Networks (CNN) are capable of extracting identification features from SAR data content. Further research in this field indicates that high performing models are insufficiently robust due to high clutter correlation among classes in the Moving and …

Majority Decision Using Top-Performing Neural Networks Models For Improved Credit Risk Prediction, Vincent Dey

College of Graduate Studies: Theses & Dissertations

Credit risk prediction remains both a challenging and high-interest problem due to the inherently unbalanced nature of financial datasets and the continuous drive for higher pre- dictive precision. In this work, I build upon previous advancements in credit risk modeling and introduce an ensemble-based Artificial Neural Network (ANN) architecture designed to enhance classification performance. By leveraging a selective ensemble of decision net- works, this approach not only improves prediction accuracy but also mitigates the chal- lenges posed by imbalanced data distributions. While the primary focus is on credit risk prediction, my analysis demonstrates that the proposed model can be effectively …