Applied Mathematics Commons^™

Reducing Generalization Error In Multiclass Classification Through Factorized Cross Entropy Loss, Oleksandr Horban

CMC Senior Theses

This paper introduces Factorized Cross Entropy Loss, a novel approach to multiclass classification which modifies the standard cross entropy loss by decomposing its weight matrix W into two smaller matrices, U and V, where UV is a low rank approximation of W. Factorized Cross Entropy Loss reduces generalization error from the conventional O( sqrt(k / n) ) to O( sqrt(r / n) ), where k is the number of classes, n is the sample size, and r is the reduced inner dimension of U and V.

A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd

Mathematics Dissertations - Archive

In this dissertation, we first present a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune responses. A stochastic process that captures the system's inherent randomness determines the dynamics of colon cancer. The stochastic framework is based on the Fokker-Planck equation, which represents the evolution of the probability density function corresponding to the stochastic process. We formulate an optimization problem that takes individual patient data with randomness present and solves it to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, we perform a sensitivity analysis of the optimal parameter set to identify the …

Batch Culture Models Of The Murine Gut Microbiome & The Impact Of Simple Dormancy On Dormancy-Capable Microorganisms Models, Ana C. Mendez

Mathematics Dissertations - Archive

The proposed mathematical biology research utilizes mathematical models to gain insight into biological systems. These systems of ordinary differential equations model diverse topics, ranging from gut microbiomes to harmful algal blooms. A complete stability analysis, supporting phase plane portraits, bifurcation diagrams, and numerical simulations will accompany the models presented. In Chapter 2, the murine gut microbiome is modeled to match laboratory experiments in the literature. In these experiments, mice eat plasmid-carrying “donor” bacteria and naturally carry plasmid-free “resident” bacteria in their gut. The models aim to capture the behavior of plasmids, donor bacteria, and resident bacteria. Chapter 3 explores dormancy …

Unveiling The Power Of Shor's Algorithm: Cryptography In A Post Quantum World, Dylan Phares

CMC Senior Theses

Shor's Algorithm is an extremely powerful tool, in utilizing this tool it is important to understand how it works and why it works. As well as the vast implications it could have for cryptography

The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, Atallah El-Shenawy, Mohamed El-Gamel, Muhammad E. Anany

Mansoura Engineering Journal

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the …

Echolocation On Manifolds, Kerong Wang

Honors Theses

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.

In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …

The Precedence-Constrained Quadratic Knapsack Problem, Changkun Guan

Honors Theses

This thesis investigates the previously unstudied Precedence-Constrained Quadratic Knapsack Problem (PC-QKP), an NP-hard nonlinear combinatorial optimization problem. The PC-QKP is a variation of the traditional Knapsack Problem (KP) that introduces several additional complexities. By developing custom exact and approximate solution methods, and testing these on a wide range of carefully structured PC-QKP problem instances, we seek to identify and understand patterns that make some cases easier or harder to solve than others. The findings aim to help develop better strategies for solving this and similar problems in the future.

Adaptive Neh With Constrained Nearest Neighbor Subtours For The Electric Vehicle Routing Problem With Time Windows, Andrew Struthers

All Master's Theses

The development of electric vehicles is currently considered one of the most innovative areas in manufacturing. Largely driven by the desire to reduce greenhouse emissions, electric vehicles are seen as a viable alternative to internal combustion engine cars. Starting from consumer cars, a dedicated effort is being made to translate this into commercial vehicles for freight and delivery. This research introduces a novel adaptive Nawaz, Enscore, Ham (NEH) algorithm with constrained nearest neighbor subtour (NEH-NN). This algorithm is tested on the standard benchmark problems in literature and used as a seed solution for the Genetic Algorithm (GA). The performance and …

Discontinuous Galerkin Methods For Compressible Miscible Displacements And Applications In Reservoir Simulation, Yue Kang

Dissertations, Master's Theses and Master's Reports

This dissertation contains research on discontinuous Galerkin (DG) methods applied to the system of compressible miscible displacements, which is widely adopted to model surfactant flooding in enhanced oil recovery (EOR) techniques. In most scenarios, DG methods can effectively simulate problems in miscible displacements.
However, if the problem setting is complex, the oscillations in the numerical results can be detrimental, with severe overshoots leading to nonphysical numerical approximations. The first way to address this issue is to apply the bound-preserving
technique. Therefore, we adopt a bound-preserving Discontinuous Galerkin method
with a Second-order Implicit Pressure Explicit Concentration (SIPEC) time marching
method to …

Beyond Cryptic Equations: Reimagining Concepts In Physics Through Metaheuristics And Fantasy Stories Using Neutrosophic Venn Diagram, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Physics, the grand narrative of the universe, bas long been viewed as realm of cold, hard equations. But what if we looked beyond the formulas and considered a more imaginative origin for some of its concepts? This article explores the intriguing possibility that physics, and even cosmology, might share a surprising kinship with metaheuristics and fantastical fiction.

Ermakov Equations Can Be Derived From Zel’Dovich Pancake, And They Are Cold And Nonlocal Through Using Neutrosophic Venn Diagram, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As we argue in a previous article, the labyrinthine worlds of Jorge Luis Borges are more than captivating narratives; they are portals to a deeper understanding of existence. By weaving elements of science-fiction fantasy with philosophical and ethical inquiries, Borges's short stories bridge the seemingly disparate realms of physics and the humanities, offering fertile ground for contemporary physics research. The present-day universe consists of galaxies, galaxy clusters, one-dimensional filaments and two-dimensional sheets or pancakes, all of which combine to form the cosmic web. The so called ”Zeldovich pancakes”, are very difficult to observe, because their overdensity is only slightly greater …

New Trends In Neutrosophic Theories And Applications, Volume Iii, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

The field of neutrosophic set theory and its applications has been rapidly expanding, particularly since the introduction of the journal "Neutrosophic Sets and Systems." New theories, techniques, and algorithms are being developed at a very high rate. One of the most notable trends in neutrosophic theory is its hybridization with other set theories such as rough set theory, bipolar set theory, soft set theory, hesitant fuzzy set theory, and more. Various hybrid structures like rough neutrosophic sets, neutrosophic soft set, single valued neutrosophic hesitant fuzzy sets, among others, have been proposed in a short period. Neutrosophic sets have proven to …

Combined Plithogenic Hypersoft Sets In Decision Making On Supplier Selection With Different Mcdm Approaches., Sikkanan Sudha, Ravi Priya, Nivetha Martin, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Decision making methods integrated with Plithogenic sets are highly feasible and resilient in designing optimal solutions. This research work identifies the research gaps of limited applications of combined plithogenic hypersoft sets (CPHSS) and hence proposes a supplier selection decision problem with an integrated approach combining CPHSS with MCDM methods. A generalized form of Plithogenic accuracy function is used in determining the plithogenic accuracy matrix to which the prominent ranking methods of TOPSIS, ELECTRE, VIKOR and MAIRCA are applied. The proposed hybrid decision approach is illustrated using supplier selection decision problem as a case study. The ranking results are compared with …

Logical Pluralism And Neutrosophy: Reflections On The Nature Of Truth, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The article explores the shift from classical binary logic (true and false) to a more complex landscape of logical frameworks. It introduces logical pluralism, which suggests that no single, universally accepted system of logic exists. The paper connects this idea to neutrosophy, a framework that extends fuzzy logic by incorporating a third value: indeterminacy. This triadic approach, where every proposition has a degree of truth (T), falsity (F), and indeterminacy (I), is particularly useful for managing incomplete or contradictory information. The author argues that different logical systems, like different tools, are suited for different problems, and that the …

Associated A Nexus With A Treesoft Sets And Vice Versa, Akbar Rezae, Karim Ghadimi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We recall the definitions of a nexus and a TreeSoft Set, and investigate the relation between them. We associated a nexus with a TreeSoft Set induced by a tree graph and vice versa.

An Innovative Approach On Yao’S Three-Way Decision Model Using Intuitionistic Fuzzy Sets For Medical Diagnosis, Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Florentin Smarandache, Hamza Ghazanfar Toor, Faiza Asif

Branch Mathematics and Statistics Faculty and Staff Publications

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a …

A New Mood’S Median Test For Imprecise Data, Abdulrahman Alaita, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The existing Mood’s median test is a non-parametric test used to compare two or more sample data sets whether they are from the same population or not. There can be no application of this test to uncertain and indeterminate data. Therefore, it is necessary to find a generalization of this test that will enable us to apply it in uncertain environments. This study will present a new approach that utilizes neutrosophic statistics to apply Mood’s median test. The approach involves defining hypotheses, determining a decision rule, and performing the test in an uncertain environment. An evaluation of the performance of …

Many Extensions Of Coulomb’S Law: A Scoping Review, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, Coulomb’s Law is extended from two stationary charged particles, on linear trajectory, to: many charged particles, or quantum level particles, or objects on arbitrary motions (with velocity, acceleration, time delay), on non-linear trajectories, at even superluminal and instantaneous speeds.

Jonckheere Trend Test Under Indeterminacy With Applications, Abdulrahman Alaita, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The classical Jonckheere trend test is a non-parametric statistical tool usually employed to compare the medians of multiple independent groups, especially when there is a natural ordering or trend among the groups. This paper aims to develop a more comprehensive and adaptable version of the Jonckheere trend test, called the neutrosophic Jonckheere trend test (NJT), which can be used to analyze di_erent types of uncertainty data. This paper discusses neutrosophic hypotheses and decision rules pertaining to the NJT test. Furthermore, the practical uses of the NJT test have been discussed in the context of real-world applications with COVID-19 data. Lastly, …

A Neutrosophic Approach To Study Agnotology: A Case Study On Climate Change Beliefs, Florentin Smarandache, Maikel Leyva Vázquez

Branch Mathematics and Statistics Faculty and Staff Publications

Misinformation and biased information significantly impact public perception and political decisions, especially on critical issues such as climate change and environmental conservation. This study aims to understand how indeterminacy and contradiction influence public perception and policy formulation by applying neutrosophic theory to model the complexity and multi-dimensionality of ignorance. Using neutrosophic Likert scales, we capture a nuanced spectrum of opinions on the scientific certainty of human impact on climate change. The results are analyzed through a k-means clustering algorithm to identify patterns and segment participants into groups based on their levels of truth, indeterminacy, and falsehood. This approach reveals deeper …

A Few Lessons From Venezuela: Introducing A New Path Of Appropriate Farming And Appropriate Renewable Energy, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In development economics literatures, there is a known term for developing countries which tend to mismanage natural resources, that term is called natural resources curse. And two examples which have been discussed quite often is Venezuela and Norway. Here we also discuss other countries as well, including Argentina and a few lessons for Indonesia in choosing the next course of development path, especially with appropriate farming and appropriate renewable energy.

A Refined Neutrosophic Components Into Subcomponents With Plausible Applications To Long Term Energy Planning Predominated By Renewable Energy, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It is known that in the long-term planning of future energy supplies, in most countries, it is most likely that the energy mix will be predominated by renewable energy generation. While this feature of a predominating renewable energy mix appears too far fetched, such long term planning has been suggested, for instance, by Mark Jacobson from Stanford and also by John Blackburn. Here we consider two things, the first would be how to consider the long-term energy planning based on neutrosophic logic split into subcomponents.

The Convergence Of Ikigai And Design Thinking: Crafting A Purposeful Framework, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In an era where innovation is not just about solving problems but also about enhancing human experiences and fostering personal fulfillment, the convergence of Ikigai principles with Design Thinking methodology offers a promising avenue for holistic problem-solving and in-novation. This paper explores the intersection of Ikigai—a Japanese concept representing one's reason for being—and Design Thinking—a human-centered approach to innovation. We propose a conceptual framework, termed Ikigai-Driven Design (IDD), which integrates the principles of Ikigai with the stages of Design Thinking. IDD comprises five main stages: Empathize, Define, Ideate, Prototype, and Test, each combining elements of Ikigai and Design Thinking to …

Residual Attention Augmentation Graph Neural Network For Improved Node Classification Residual Attention Augmentation Graph Neural Network For Improved Node Classification, Muhammad Affan Abbas, Waqar Ali, Florentin Smarandache, Sultan S. Alshamrani, Muhammad Ahsan Raza, Abdullah Alshehri, Mubashir Ali

Branch Mathematics and Statistics Faculty and Staff Publications

Graph Neural Networks (GNNs) have emerged as a powerful tool for node representation learning within graph structures. However, designing a robust GNN architecture for node classification remains a challenge. This study introduces an efficient and straightforward Residual Attention Augmentation GNN (RAA-GNN) model, which incorporates an attention mechanism with skip connections to discerningly weigh node features and overcome the over-smoothing problem of GNNs. Additionally, a novel MixUp data augmentation method was developed to improve model training. The proposed approach was rigorously evaluated on various node classification benchmarks, encompassing both social and citation networks. The proposed method outperformed state-of-the-art techniques by achieving …

Bv2trs Appraiser Model: Enforcing Bharat Version2 In Tree Soft Modelling For Appraising E-Mobility Hurdles, Mona Mohamed, Florentin Smarandache, Michael Gr. Voskoglou

Branch Mathematics and Statistics Faculty and Staff Publications

Electric vehicles (EVs) are being introduced to lessen greenhouse gas (GHG) emissions, air pollution, and reliance on fossil fuels. As a result of the government's aggressive promotion of EVs and rising environmental consciousness, EVs are quickly rising to the top of the low-carbon transportation market. Several viewpoints suggested that shifting to electric vehicles has been seen as a potential way to achieve sustainable mobility. Nevertheless, many studies discussed the obstacles and hurdles that obstruct the embracing of various electric-mobility (E-mobility) as EVs and electric-scooters (E-scooters) as eco-friendly means. Herein, we discussed these hurdles and determined them through surveys for prior …

Automated Livestock Practices: Incorporation Emerging Contemporary Technologies Toward Sustainable Livestock In Era Of Smart Cities, Asmaa Elsayed, Mona Mohamed, Florentin Smarandache, Michael Gr. Voskoglou

Branch Mathematics and Statistics Faculty and Staff Publications

Currently, numerous spheres now face a wider range of needs due to the increasingly competitive and globalized global market. Moreover, digital technologies are necessary for analysis and comprehension in many sectors of contemporary society. For instance, Internet of Things (IoT) has the potential to revolutionize livestock management, including the dairy cattle industry, by providing real-time data and enabling data-driven decisions to improve animal welfare, increase productivity, and promote sustainable farming practices. The main components of IoT-enabled livestock management include sensors, communication systems, data storage, and analysis systems. These components of IoT-enabled livestock management improve animal welfare, increase productivity, and reduce …

Assuming Photon As Extended Point Particle In The Hypersoft Topological Space And Other Hypotheses: Issues And Trend Analysis, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Following our preceding article, where we discussed alternative interpretations of the advanced perihelion of Mercury, the present article revisits the 1919 solar eclipse expedition led by Arthur Eddington, which famously provided the first observational confirmation of Einstein's theory of general relativity. We focus on the deflection of starlight data obtained during the eclipse, a cornerstone of this validation. Here, we explore three alternative explanations for the observed light bending that challenge the sole attribution to general relativity. Firstly, the paper begins by arguing based on criticisms raised by Tullio Levi-Civita, a contemporary mathematician, regarding Einstein's use of pseudo-tensors in his …

Distinctions Between Various Types Of Fuzzy-Extension Hypersoft Sets, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We define the universes of discourses for all fuzzy and fuzzy-extension sets. Then present many types of Plithogenic Universes of discourse and their connections to HyperSoft Sets. Afterward, we make distinctions between various hybrid forms of HyperSoft Sets.

Neutrosophical Plant Hybridization In Decision-Making Problems, M. Arockia Dasan, E. Bementa, Florentin Smarandache, X. Tubax

Branch Mathematics and Statistics Faculty and Staff Publications

Florentin Smarandache developed the neutrosophic set theory to study inconsistency, incomplete, and uncertainty information by using truth-membership, indeterminacy-membership, and falsity-membership functions. One of the main objectives of this chapter is to develop a new methodological approach of neutrosophic sets in multi-criteria decision-making problems. This method considers neutrosophic sets with their unions in the direct direction and the complements of given neutrosophic sets with their intersections are also considered in the reverse direction. Using these collections, single-valued neutrosophic score functions are computed in both directions. After this process, all the alternatives are ranked in the ascending order arrangement to find the …