Applied Mathematics Commons^™

Privacy-Preserving Federated Learning, Dumindu Samaraweera

Math Department Colloquium Series

AI's applicability across diverse fields is hindered by data sensitivity, privacy concerns, and limited training data availability. Federated Learning (FL) addresses this challenge by enabling collaborative machine learning while preserving data privacy. FL allows clients to engage in model training with their local data, avoiding centralized storage. However, even with FL, security threats persist, jeopardizing model integrity and client data privacy. In this presentation, we will explore our latest findings in this area of research, safeguarding sensitive data from attacks through techniques like secure multiparty computation, homomorphic encryption, and differential privacy within the FL framework, enhancing data protection, and expanding …

A Low-Complexity Algorithm To Determine Spacecraft Trajectories, Sirani Perera

Math Department Colloquium Series

The growing traffic within the Cislunar region has created a need for computationally effective methods to obtain the trajectories of spacecraft in the Cislunar region. By developing algorithms with low time and arithmetic complexities, we can effectively address these needs.

In this talk, we will present a mathematical model that uses interpolation and boundary conditions to obtain trajectories for satellites based on the principles of three-body dynamics. Following the model, we propose a low- complexity algorithm to generate satellite trajectories. Once the algorithm is proposed, we will apply it to the relevant periodic orbits in the Cislunar region. Finally, we …

On Subset Labelings Of Trees, Gary Chartrand, Ebrahim Salehi, Ping Zhang

Mathematical Sciences Faculty Research

For a nontrivial graph G, a subset labeling of G is a labeling of the vertices of G with nonempty subsets of the set [r]={1, 2, ... , r} for a positive integer r such that two vertices of G have disjoint labels if and only if the vertices are adjacent. The subset index ρ(G) of G is the minimum positive integer r for which G has such a subset labeling from the set [r]. If T is a tree of diameter d, then ρ(Pd+1) ≤ ρ(T). It is shown that there are several classes of trees T of diameter …

An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, Emmanuel O. Adara, Roger B. Sidje

Northeast Journal of Complex Systems (NEJCS)

Among numerical techniques used to facilitate the analysis of biochemical reactions, we can use the method of moments to directly approximate statistics such as the mean numbers of molecules. The method is computationally viable in time and memory, compared to solving the chemical master equation (CME) which is notoriously expensive. In this study, we apply the method of moments to a chemical system with a constant rate representing a vascular endothelial growth factor (VEGF) model, as well as another system with time-dependent propensities representing the susceptible, infected, and recovered (SIR) model with periodic contact rate. We assess the accuracy of …

Forecasting Economic Growth And Movements With Wavelet Transform And Arima Model, Omar Alsinglawi, Omar Alsinglawi, Mohammad Aladwan, Mohammad Aladwan, Saddam Alwadi, Saddam Alwadi

Applied Mathematics & Information Sciences

This study uses historical data and modern statistical models to forecast future Gross Domestic Product (GDP) in Jordan. The Wavelet Transformation model (WT) and Autoregressive Integrated Moving Average (ARIMA) model were applied to the time series data and yielded a best-fitting result of (2,1,1) for estimating GDP between 2022-2031. The study concludes that GDP is expected to increase with a positive growth rate of around 3.22%, and recommends government agencies to monitor GDP, strengthen existing policies, and adopt necessary economic reforms to support growth. Additionally, the private sector is encouraged to enhance production tools to achieve economic growth that benefits …

Neutrosophic Adaptive Lsb And Deep Learning Hybrid Framework For Ecg Signal Classification, Abdallah Rezk, Ahmed S. Sakr, H. M. Abdulkader

Applied Mathematics & Information Sciences

This paper proposes a novel hybrid framework for ECG signal classification and privacy preservation. The framework includes two phases: the first phase uses LSTM+CNN with attention gate for ECG classification, while the second phase utilizes adaptive least signal bit with neutrosophic for hiding important data during transmission. The proposed framework converts data into three sets of degrees (true, false, and intermediate) using neutrosophic and passes them to an embedding layer. In the sender part, the framework hides important data in ECG signal as true and false degrees, using the intermediate set as a shared dynamic key between sender and receiver. …

Compatibility Of Clique Clustering Algorithm With Dimensionality Reduction, Ug ̆Ur Madran, Duygu Soyog ̆Lu

Applied Mathematics & Information Sciences

In our previous work, we introduced a clustering algorithm based on clique formation. Cliques, the obtained clusters, are constructed by choosing the most dense complete subgraphs by using similarity values between instances. The clique algorithm successfully reduces the number of instances in a data set without substantially changing the accuracy rate. In this current work, we focused on reducing the number of features. For this purpose, the effect of the clique clustering algorithm on dimensionality reduction has been analyzed. We propose a novel algorithm for support vector machine classification by combining these two techniques and applying different strategies by differentiating …

The Influence Of Supply Chain Management Strategies On Organizational Performance In Hospitality Industry, Omar Jawabreh, Abdullah Mahfoud Baadhem, Basel J. A. Ali, Anas Ahmad Bani Atta, Anis Ali, Fahmi Fadhl Al- Hosaini

Applied Mathematics & Information Sciences

The studys primary goal is to analyze the connection between SCM practices and organizational performance, and it also aims to evaluate the moderating role of management type. Quantitative data collected from Jordans hotel and restaurant workers via questionnaire. Structural equation modeling is used to examine the hypothesized relationships. Organizational Performance is positively impacted by effective information sharing. Information Quality (IQ) positively affects Organizational Performance (OP), and Strategic Supplier Partnerships (SSP) play a crucial role. Customer Relationship Management (CRM) had no discernible effect on OP, according to the study. OP is positively impacted by Postponement (POS) techniques. When implemented, postponement increases …

The Effect Of System Quality And User Quality Of Information Technology On Internal Audit Effectiveness In Jordan, And The Moderating Effect Of Management Support, Ahmad Yahiya Ahmad Bani Ahmad (Ayassrah), Anas Ahmad Mahmoud Bani Atta, Hanan Ali Alawawdeh, Nawaf Abdallah Aljundi, Amer Morshed, Saleh Amin Dahbour

Applied Mathematics & Information Sciences

The goal of this study is to ascertain the moderating role that management support has in internal audit effectiveness in Jordan, as well as the impact of system quality and user quality of information technology. There were 172 responders in all, and they were split across Jordanian auditors. In the data analysis process, the quantitative analysis test— which consists of the validity test, reliability test, test of conventional assumptions, and hypothesis test—is applied. Information technology system and user quality are independent variables in this study. The dependent variable in this study is internal audit effectiveness, and the moderating variable is …

Optimal Control Analysis Of The Dynamics Of Covid-19 With Application To Ethiopian Data, Temesgen Duresa Keno, Fekadu Mosisa Legesse, Ebisa Olana Bajira

Applied Mathematics & Information Sciences

In this paper, we proposed an optimal control of the COVID-19 transmission dynamics. First, we investigated system features such as solution boundedness, positivity, disease-free and endemic equilibrium, and the local and global stability of equilibrium points. Besides, a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one, and an endemic equilibrium point exists otherwise. Secondly, we have shown the sensitivity analysis of the basic reproduction number. Also the model is then fitted using COVID-19 infected reported in Ethiopia from February 1,2023 to March 2,2023. The values of model parameters are then estimated from …

Nexus Between Intellectual Capital And Financial Performance Sustainability: Evidence From Listed Jordanian Firms, Ali M. Alrabei, Leqaa N. Al-Othman, Thaer A. Abutaber, Mustafa S. Alathamneh, Tareq M. Almomani, Mohammed H. Qeshta

Applied Mathematics & Information Sciences

Purpose: The authors observe the effect of exploring the reality of Intellectual Capital (IC) and its impact on the financial performance of Jordanian industrial firms in Amman Stock Exchange. This empirical research explores the effect of intellectual capital on financial performance using data from 36 Jordanian industrial firms listed in Amman Stock Exchange for the period 2016-2020. The Value-Added Intellectual coefficient (VAIC) was adopted to measure the intellectual capital, while the return on assets (ROA), return on equity (ROE), and earnings per share (EPS) were adopted as measures of the companys financial performance. The effect of IC was tested by …

Assessing The Moderating Effect Of Innovation On The Relationship Between Information Technology And Supply Chain Management: An Empirical Examination, Heba Hatamlah, Mahmoud Allahham, Ibrahim A. Abu-Alsondos, Alaa S. Mushtaha, Ghadeer M. Al-Anati, Mustafa Al-Shaikh

Applied Mathematics & Information Sciences

This study examines how innovation (INN) influences the relationship between supply chain management and information technology in Jordan. 211 employees of Jordanian industrial enterprises who work in the Operations Department provided information for the study, which examines this subject. The findings indicate a close connection between information technology and supply chain management. Innovation also dramatically modifies the interaction between supply chain management and information technology. Management help may be the subject of future research.

The Role Of Business Intelligence Adoption As A Mediator Of Big Data Analytics In The Management Of Outsourced Reverse Supply Chain Operations, Heba Hatamlah, Mahmoud Allahham, Ibrahim A. Abu-Alsondos, Alaa Al-Junaidi, Ghadeer M. Al-Anati, Mustafa Al-Shaikh

Applied Mathematics & Information Sciences

The fluctuating and disorganized state of todays global markets is the result of several factors. COVID-19 is an illustration. Supply chain managers should re-evaluate their competitive strategy and leverage big data analytics in light of the rising volatility in demand and supply, rivalry among supply chain partners, and the requirement to deliver tailored goods and services (BDA). Supply chain firms require sophisticated BDA processes and procedures to provide useful insights from big data to better decision-making and supply chain operations, as many leaders in the sector have acknowledged the necessity for improving with data" (SCO). This research gives theoretical justification …

The Artificial Intelligence As A Decision-Making Instrument For Modeling And Predicting Small Cities’ Attractiveness: Evidence From Morocco, Sohaib Khalid, Driss Effina, Khaoula Rihab Khalid, Mohamed Salem Chaabane

Applied Mathematics & Information Sciences

This study analyzes residential attractiveness in small Moroccan cities using statistical models. Net migration rates are commonly used to assess attractiveness. The study estimated net migration rates for each city and employed a structural econometric model with logistic regression to identify influential variables that affect the net migration rate. These variables were then used in a predictive model with an artificial neural network algorithm. The logistic model revealed insights, highlighting the complexity of residential attractiveness influenced by factors like job supply, accessibility, and housing conditions. The artificial neural network model provided accurate predictions (over 80%), aiding policymakers in decision-making and …

Improving The Performance Of A Series-Parallel System Based On Lindley Distribution, Abdelfattah Mustafa, M. I. Khan, Maher. A. Alraddadi

Applied Mathematics & Information Sciences

In this article, the performance of a series-parallel system is improved. The system components are assumed to follows independently and identically Lindley distributed with three parameters. The system reliability for the given system will be improved by using reduction method, hot, cold and imperfect duplication method. Some reliability measures are derived. Two types of reliability equivalence factors and gamma fractiles are calculated. A numerical example is introduced to explain the theoretical results.

Quantization Of Fractional Constrained Systems With Wkb Approximation, Ola A. Jarabah

Applied Mathematics & Information Sciences

In this paper the constrained systems with two primary first class constraints are studied using fractional Lagrangian, after that we find the fractional Hamiltonian and the corresponding Hamilton Jacobi equation. Using separation of variables technique, we can find the action function S this function helps us to formulate the wave function which describe the behavior of our systems also from the action function S we can find the equations of motion and the corresponding momenta in fractional form. This work is illustrated using one example.

Applications Of The Ara-Residual Power Series Technique To Physical Phenomena, Aliaa Burqan

Applied Mathematics & Information Sciences

In this paper, a new analytical method called the ARA-Residual power series method (ARA- RPSM) is implemented to solve some fractional physical equations. The methodology of the proposed method based on applying the ARA-transform to the given fractional differential equations, followed by the creation of approximate series solutions using Taylor’s expansion. Then the series solution is transformed using the inverse of the ARA-transform to get the solution in the original space. Accuracy, effectiveness, and validity of the suggested method are demonstrated through the discussion of three attractive applications. The solution obtained using ARA-RPSM demonstrates good agreement when compared to the …

Generalization Of Renyi’S Entropy And Its Application In Source Coding, Ashiq Hussain Bhat, Niyamat Ali Siddiqui, Ismail A Mageed, Shawkat Alkhazaleh, Vidyanand Rabi Das, M. A. K Baig

Applied Mathematics & Information Sciences

In this paper, we introduce a new generalization of Renyis entropy β(P) and the most important feature of this generalized entropy Rαβ (P) is that it derives most important entropies that are well known and influence information theory and applied mathematics. Some significant properties of Rαβ (P) has been undertaken in this article. In addition, we introduce a new generalized exponentiated mean codeword length Lβα (P) in this article then determine how Rβα (P) and Lβα (P) are related in terms of source coding theorem.

Numerical Simulation Of Nonlinear Wave Equations With Machine Learning, Kristina O. F. Williams

Theses and Dissertations

A machine learning procedure is proposed to create numerical schemes for solutions of certain types of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. A neural network is used as a model for the stencil weights. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg - de …

Methods Of Evaluating Quantum Phase Estimation Circuit Output, Charles A. Woodrum

Theses and Dissertations

The quantum phase estimation (QPE) algorithm is one of the most important quantum computing algorithms that has been developed. The QPE algorithm estimates the phase or phases of the eigenvalue or eigenvalues of a unitary operator. It is a critical step for applications like Shor’s algorithm for factoring and the HHL algorithm for solving linear systems of equations, but it remains difficult to implement on current quantum computers due to small numbers of logical qubits and high error rates. This investigation derives a more accurate estimation of the phase of a unitary operator than would otherwise be attained with the …

Bacterial Motion And Spread In Porous Environments, Yasser Almoteri

Dissertations

Micro-swimmers are ubiquitous in nature from soil and water to mammalian bodies and even many technological processes. Common known examples are microbes such as bacteria, micro-algae and micro-plankton, cells such as spermatozoa and organisms such as nematodes. These swimmers live and have evolved in multiplex environments and complex flows in the presence of other swimmers and types, inert particles and fibers, interfaces and non-trivial confinements and more. Understanding the locomotion and interactions of these individual micro-swimmers in such impure viscous fluids is crucial to understanding the emergent dynamics of such complex systems, and to further enabling us to control and …

Fluid Dynamics Of Interacting Particles: Bouncing Droplets And Colloid-Polymer Mixtures, Lauren Barnes

Dissertations

Interacting particles are a common theme across various physical systems, particularly on the atomic and sub-atomic scales. While these particles cannot be seen with the human eye, insight into such systems can be gained by observing macroscopic systems whose physical behavior is similar. This dissertation consists of three different chapters, each presenting a different problem related to interacting particles, as follows:

Chapter 1 explores chaotic trajectories of a droplet bouncing on the surface of a vertically vibrating fluid bath, with a simple harmonic force acting on the droplet. The bouncing droplet system has attracted recent interest because it exhibits behaviors …

Boundary Integral Equation Methods For Superhydrophobic Flow And Integrated Photonics, Kosuke Sugita

Dissertations

This dissertation presents fast integral equation methods (FIEMs) for solving two important problems encountered in practical engineering applications.

The first problem involves the mixed boundary value problem in two-dimensional Stokes flow, which appears commonly in computational fluid mechanics. This problem is particularly relevant to the design of microfluidic devices, especially those involving superhydrophobic (SH) flows over surfaces made of composite solid materials with alternating solid portions, grooves, or air pockets, leading to enhanced slip.

The second problem addresses waveguide devices in two dimensions, governed by the Helmholtz equation with Dirichlet conditions imposed on the boundary. This problem serves as a …

A Variational Theory For Integral Functionals Involving Finite-Horizon Fractional Gradients, Javier Cueto, Carolin Carolin, Hidde Schönberger

Department of Mathematics: Faculty Publications

The center of interest in this work are variational problems with integral functionals depending on nonlocal gradients with finite horizon that correspond to truncated versions of the Riesz fractional gradient. We contribute several new aspects to both the existence theory of these problems and the study of their asymptotic behavior. Our overall proof strategy builds on finding suitable translation operators that allow to switch between the three types of gradients: classical, fractional, and nonlocal. These provide useful technical tools for transferring results from one setting to the other. Based on this approach, we show that quasiconvexity, which is the natural …

Efficient And Secure Digital Signature Algorithm (Dsa), Nissa Mehibel, M'Hamed Hamadouche

Emirates Journal for Engineering Research

The digital signature is used to ensure the integrity of messages as well as the authentication and non-repudiation of users. Today it has a very important role in information security. Digital signature is used in various fields such as e-commerce and e-voting, health, internet of things (IOT). Many digital signature schemes have been proposed, depending on the computational cost and security level. In this paper, we analyzed a recently proposed digital signature scheme based on the discrete logarithm problem (DLP). Our analysis shows that the scheme is not secure against the repeated random number attack to determine the secret keys …

The Quantum Mechanical Background Of Quantum Computing, Isaac Hanna

The Kabod

Quantum mechanics arose out of the question "Is light a particle or a wave?" and has laid forth a model of reality in which particles are modeled by wave functions. The particle is in a superposition of states and can be entangled with other particles to create more complex systems. Observation of the system collapses the wave function to a single point. By using quantum gates, we can manipulate these particles to create algorithms to solve computational problems. Quantum computing does not collapse the complexity hierarchy by providing an across the board exponential speedup but can provide such a speedup …

The Analytic Solution Of Non-Linear Burgers–Huxley Equations Using The Tanh Method, Kabir Oluwatobi Idowu, Adedapo Chris Loyinmi

Al-Bahir

The emergence of the Burgers-Huxley equation (which involves the famous Burgers equation and the Huxley equation) to predict response systems, dispersion moves, and nerve charge transmission in traffic patterns, sound, turbulent conditions theory, hydrodynamics has attracted the attention of scientists to provide reliable and efficient solutions to the problem. The present work employed the Tanh method to solve the Burgers-Huxley nonlinear partial differential equations. In contrast to previous results with complicated and laborious solution characteristics, this method is accurate, efficient, and requires little computational work. In showing this, we solved four Burgers-Huxley case study problems using the Tanh approach and …

Proposing A Measure Of Ethicality For Humans And Ai, Alejandro Jorge Napolitano Jawerbaum

Electronic Theses and Dissertations

Smarter people or intelligent machines are able to make more accurate inferences about their environment and other agents more efficiently than less intelligent agents. Formally: ‘Intelligence measures an agent’s ability to achieve goals in a wide range of environments.’ (Legg, 2008)

In this dissertation we extend this definition to include ethical behaviour and we will offer a mathematical formalism and a way to estimate how ethical an action is or will be, both for a human and for a computer, by calculating the expected values of random variables. Formally, we propose the following measure of ethicality, which is computable, or …

A Tale Of Two Diagonalizations: Methods To Diagonalize A 1-D Piecewise Constant Indefinite Schrödinger Operator, Sarah Wright

Dissertations

We present two numerical methods for computing the solution of a partial differential equation (PDE) for modeling acoustic pressure, known as an extra-wide angle parabolic equation, that features the square root of a differential operator. The differential operator is the negative of an indefinite Schrödinger operator with a piecewise constant potential. This work primarily deals with the 3-piece case; however, a generalization is made to the case of an arbitrary number of pieces. In the first method, the Rayleigh-Secant Method, through restriction to a judiciously chosen lower-dimensional subspace, approximate eigenfunctions are used to obtain estimates for the eigenvalues of the …

A Comparison Of Computational Perfusion Imaging Techniques, Shaharina Shoha

Masters Theses & Specialist Projects

Dynamic contrast agent magnetic resonance perfusion imaging plays a vital role in various medical applications, including tumor grading, distinguishing between tumor types, guiding procedures, and evaluating treatment efficacy. Extracting essential biological parameters, such as cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT), from acquired imaging data is crucial for making critical treatment decisions. However, the accuracy of these parameters can be compromised by the inherent noise and artifacts present in the source images.

This thesis focuses on addressing the challenges associated with parameter estimation in dynamic contrast agent magnetic resonance perfusion imaging. Specifically, we aim …