Applied Mathematics Commons^™

Mathematically Modeling Stoichiometric Drivers Of Heterotrophic N2 Fixation, Corday R. Selden, Rebecca Everett, Halvor H. Halvorson, Megan E. Berberich, Luca Schenone, Angela Peace, Renn Schipper, Edwin Cruz-Rivera, James Powell, Keisuke Inomura, Robinson W. Fulweiler, Amy M. Marcarelli, J Thad Scott

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Compartmental Model For Annual Bat Migration, Elena D. Wheatley, Rhianna Yates, Leah Glasser, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Impact Of Treatment During An Ongoing Tuberculosis Outbreak, Bach Le, Jude Shive, Erin N. Bodine

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Balancing Stability And Complexity In Boolean Models Of Biological Networks, Venkata Sai Narayana Bavisetty

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Compartmental Model For Periodic Animal Migration, Rhianna Yates, Leah Glasser, Elena Wheatley, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Optimizing The Distribution Of Fruiting Agave On Bat-Friendly Tequila Plantations, Grace Gorreck, Clarissa Azurin, Lois Carpenter

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Spatial Strategies In Ants: Modeling Polydomy, Saya Zeleznik, Fred Adler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Parameter Estimation And Simulation In Pollution-Induced Asthma Disease Model Using Physics-Informed Neural Networks, Aadi Gannavaram

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Survival Analysis Of Breast Cancer Patients In Texas Using Classical And Machine Learning Methods, Sidketa Fofana, Tamer Oraby, Salique H. Shaham, Everardo Cobos, Manish K. Tripathi

School of Medicine Publications

Background

Breast cancer is considered one of the most common cancers in women worldwide. In this study, we used an 11-year cohort of malignant breast cancer survival data in Texas to investigate the factors that might explain why some breast cancer patients live longer than others.

Methods

We performed standard survival analyses, including generating Kaplan‒Meier survival curves, using the log-rank test, and applying Cox proportional hazards regression to identify the unique features of breast cancer patients and determine the main factors influencing long-term survival. We also conducted a Random Survival Forest analysis for classification and prediction. Finally, we used Mahalanobis …

Meet Your New Math 155: A Focus On Assessment, Gabriel Tapia

Excellence in Education: Teaching Faculty Symposium

No abstract provided.

A Hybrid Data Assimilation Approach For Parameter Estimation In Dynamical Systems, Xuejian Li

Math Department Colloquium Series

In this talk, we present a hybrid data assimilation (DA) method that integrates continuous data assimilation (CDA) with particle filtering to estimate parameters in dynamical systems. Parameter estimation in such systems is particularly challenging because it involves both determining the parameters and estimating the often high-dimensional physical state. To address this difficulty, we decouple the estimation of states and parameters by employing CDA for state estimation and particle filtering for parameter estimation, with information exchanged alternately between the two. This hybrid framework leverages the strengths of CDA in handling high-dimensional state estimation and the efficiency of particle filters in estimating …

Expanding Ode Examples: Introducing Gene Regulation Dynamics Through Hill Functions, Maila Hallare, Jane M. Santamore

CODEE Journal

Gene regulation is a fundamental biological process that controls gene expression. It can explain phenomena such as cell differentiation, circadian rhythms, disease progression, and metabolic control, among many others. Despite their importance in mathematical biology, gene regulation models are rarely featured in traditional ODE textbooks, which focus mainly on examples from engineering, physics, chemistry, and population biology. This article introduces gene regulation dynamics as a valuable addition to ODE curricula, presenting the models from a mathematical perspective and building on properties of the Hill function. These models deepen the understanding of biology-inspired ODE applications, provide accessible research opportunities for students, …

Paclobutrazol Enhances Tall Fescue Salt Tolerance Via Physiological And Root System Architecture Modulation, Shugao Fan, Xindi Sun, Guohao Liang, Zhuanzhuan Ma, Jincheng Hao, Jiawei Wu, Ying Zhao

School of Mathematical & Statistical Sciences Faculty Publications

Background: Salinity represents a major global constraint on crop productivity. Promoting the cultivation of tall fescue in saline environments offers not only nutritional advantages for livestock but also enhances its potential for ornamental use. In this mesocosm study, we examined the effects of paclobutrazol (PBZ) on tall fescue performance under salt stress, focusing on key physiological traits to evaluate salt tolerance.

Results: Under high salt stress, paclobutrazol application increased the total number of lateral roots by 85%, from 18.39 to 34.04, and widened their growth angle by 24%, from 24.10° to 29.88°, fundamentally enhancing topsoil exploration. This reconfigured root system …

The Problem Of Identification Of Linear Stationary Objects With Distributed Parameters By Their Experimental Transient Characteristics, Miraziz Vorisovich Sagatov

Chemical Technology, Control and Management

A wide class of control system elements can be described with reasonable accuracy by the concept of a linear stationary dynamic object. Several mathematical descriptions of such an object are known. The traditional mathematical model is a high-order ordinary linear differential equation. In the Laplace image space, this corresponds to a fractional-rational transfer function. The latter can be decomposed into elementary fractions. Then, using the convolution theorem and tables of elementary Laplace transform functions, one can access the originals. It is crucial to ensure precise alignment of the parameters of the mathematical model of the object used in the corrector …

Tight Spherical Embeddings (Updated Version), Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

This is an updated version of the paper [14] which appeared in the proceedings of the 1979 Berlin Colloquium on Global Differential Geometry. This paper contains the original exposition together with some notes by the authors made in 2025 (as indicated in the text) that give references to descriptions of progress made in the field since the time of the original version of the paper. The main result of this paper is that every compact isoparametric hypersurface Mⁿ ⊂ Sⁿ⁺¹ ⊂ Rⁿ⁺² is tight, i.e., every non-degenerate linear height function ℓ_p, p ∈ …

A Mathematical Model On The Temporal Dynamics Of Aviation Competitive Pricing, Tichaona Chikore,, Farai Nyabadza,

Journal of Aviation/Aerospace Education & Research

This study investigates the competitive dynamics of airport pricing using U.S. airport data to validate the findings. It employs linear and nonlinear ordinary differential equation models to analyze the influence of competitive interactions and internal factors on pricing decisions. The methodology involves parameter estimation via optimization techniques and quantile regression to capture heterogeneity across market segments. Mathematical analysis and simulation results show that if competitive coupling coefficients are low then there is weak competitive influence on pricing, with airports’ pricing largely driven by internal factors. Also, if the adjustment rates exhibit consistency across airports then internal dynamics are dominant in …

Teaching Statistical Literacy Through An Excel Class Project, Patricia Berchiolli, Omar Babun Codorniu

Faculty and Staff Publications & Presentations

Lynn University’s core curriculum, The Dialogues, enables students to develop critical thinking, communication, and innovation skills. As part of this curriculum, Introductory Statistics introduces students to key statistical concepts while showing how they can be applied in real-world situations using Excel. The highlight of the course is the Statistics Excel Project, where students create their own dataset with a mix of quantitative and qualitative variables. To keep the focus on learning statistical techniques rather than data collection, students use Excel’s random number generator for quantitative data, which also avoids the need for IRB approval. From there, they calculate statistical measures, …

Cnn-Based Hybrid Model For Detecting Blight Diseases In Potato Crops With Advanced Image Processing Techniques, Farian S. Ishengoma

Tanzania Journal of Engineering and Technology (TJET)

Potato production plays a vital role in global agriculture as a major food source for large populations. However, potato crops are highly susceptible to diseases, particularly Early Blight and Late Blight, which result in substantial yield losses. Timely detection and effective control of these diseases are essential for maintaining stable crop output. This study explores the integration of Convolutional Neural Networks (CNNs) and advanced image processing techniques to differentiate between diseased and healthy potato plants accurately. Two datasets comprising original and enhanced images were used to train four CNN models: InceptionV3, Xception, Densenet201, and Resnet152V2. The original images underwent background …

Optimal Location And Sizing Of Facts Devices To Improve Voltage Profiles On A 132 Kv Mwanza-Musoma-Nyamongo Transmission Line, Peter Makolo

Tanzania Journal of Engineering and Technology (TJET)

Recently, utility companies have desired to supply quality, stable and reliable power to customers, and ensure they meet the demand. Flexible AC Transmission Systems (FACTS) dynamic compensator devices such as Static Synchronous Compensator (STATCOM), Static VAr Compensator (SVC) and Unified Power Flow Controller (UPFC) are an impeccable choice, however, cost is one of the limiting factors following these technologies. In addition, using FACTS devices in the system requires a detailed steady state, dynamic and optimisation analysis to effectively meet the purpose and ensure reduced cost. This paper proposes using an optimised FACTS device to improve voltage profile, power transfer, system …

(Si15-121) Analyzing Seitr Tuberculosis Transmission Model Using Caputo–Fabrizio Fractional Derivative With Diverse Contact Rates, S. S. Sumaiya Banu, T. Gunasekar, S. Manikandan, Kamalendra Kumar, M. Suba

Applications and Applied Mathematics: An International Journal (AAM)

In the modern age, tuberculosis remains a pressing global health concern. Our study introduces and evaluates the SEITR pandemic TB transmission model, dividing the population into five compartments to explore distinct characteristics relevant to our investigation. Additionally, we delve into the application of fractional calculus. Through the Laplace transform method, we derive series solutions for all compartments, ensuring their existence and uniqueness. We also investigate the reproduction number of the tuberculosis epidemic model, examining how varying contact rates impact disease spread. We apply the predictor-corrector method for the Caputo-Fabrizio fractional derivative to verify the accuracy of our approach. This accurately …

(Si15-093) Dynamics Of The Generalized Nonlinear Schrödinger Equation With A Source Using An Analytical Method, Manish Raghav, Manoj .

Applications and Applied Mathematics: An International Journal (AAM)

In the present article, an analytical method is used to obtain hyperbolic, trigonometric, and rational solutions of the generalized nonlinear Schrödinger (GNLS) equation with a source. The ability of solitons to preserve their shapes during propagation makes them suitable for optical fiber communication. Solutions to the generalized nonlinear Schrödinger equation with a source can also describe solitons, and understanding their dynamics helps to design communication systems based on solitons. The analytical method used is compelling and effective for finding exact solutions to various nonlinear evolution equations (NLEEs). To further understand the phenomena, we create 3−D, contour, and 2−D graphs of …

(Si15-107) Mathematical Modeling Of Cancer Dynamics Stability Analysis Of Post Therapy Protection, Rajendran Swetha, Tharmalingam Gunasekar, Kamalendra Kumar, Krishnasamy Sakthivel

Applications and Applied Mathematics: An International Journal (AAM)

The study of PSITPS mathematical model is developed to analyze cancer dynamics, focusing on post-therapy protection. The model’s solution is rigorously examined for boundedness and positivity of solutions. Equilibrium points are identified, and numerical methods are employed to study stability. Simulations using accurate cancer data demonstrate the effectiveness of post-treatment protection in controlling cancer spread and minimizing recurrence. Stability analysis confirms the model’s predictive capability, offering valuable insights into long-term patient outcomes. The results highlight the importance of continuous post-treatment care in improving survival rates and reducing disease prevalence. This study provides a framework for optimizing cancer treatment strategies by …

(Si15-113) Augmenting Cryptographic Security Through Inventive Application Of The Kharrat-Toma Transform Algorithm, Prabakaran Raghavendran, Tharmalingam Gunasekar, K. Sakthivel, Kamalendra Kumar, Shalini Gupta

Applications and Applied Mathematics: An International Journal (AAM)

This paper introduces a cryptographic technique combining the Kharrat-Toma Transform and congruence modulo operators to improve the security of message encryption. The proposed model uses the mathematical properties of the Kharrat-Toma Transform and its inverse for direct scrambling and unscrambling processes while embedding sufficient complexity to resist modern cryptanalytic attacks. The model is subjected to experimental tests, including encryption quality analysis, Shannon entropy, and NIST randomness tests, in order to prove the strength of the model. Through encryption quality analysis, symbol frequencies in the ciphertext are masked heavily from having much correlation between plaintext and ciphertext. Entropy values indicate near-theoretical …

Meshless Discrete Velocity Boltzmann Model For Porous Media Flow, Amandine Maidenberg

Doctoral Dissertations and Master's Theses

This dissertation explores the combination of two sophisticated techniques for addressing computational fluid dynamics: the discrete velocity Boltzmann equation (DVBE) and the localized collocation meshless model with upwinding (U-LCMM). The DVBE is a high-level model that describes the foundations of transport phenomena by addressing the microscale motions of particles themselves and the effect of their aggregate behaviors on continuum principles. This equation integrates multiple scales of phenomena; while it can be used for fluid flow at Navier-Stokes scales, it can also resolve fine features that can only be described at the molecular level. This type of model is necessary for …

Investigating The Market Dynamics Of Aeroponically Cultivated Products With Delay, Pulak Kundu, Uzzwal Kumar Mallick

Mathematical Modelling and Numerical Simulation with Applications

Aeroponically grown potatoes offer higher yields and year-round production but often face delayed market entry due to high setup costs, technical barriers, and logistical challenges. A delay-based mathematical model has been newly proposed in this study to analyze the dynamics of demand, supply, and pricing for aeroponically grown products. The model’s existence, stability, and sensitivity have been investigated analytically, and numerical simulations have been carried out using the Runge-Kutta 4th order method with the dde23 solver. Findings reveal that market stability is maintained when delays are below seven years, but delays beyond this threshold lead to persistent fluctuations in price, …

Stabilized Weak-Gradient Discontinuous Finite Elements With Optimal Error Estimates For Second-Order Elliptic Pdes, Aymen Laadhari

Mathematical Modelling and Numerical Simulation with Applications

This work introduces an accurate finite element approach employing a new stabilized discrete weak gradient, designed for second-order elliptic problems on arbitrary conforming meshes. We formulate the approach within a discontinuous Galerkin framework and derive a consistent and coercive bilinear form. Appropriate error analysis on a model problem confirms optimal convergence. Building on the core analysis, we extend the method to more challenging settings, including time-dependent heterogeneous scenarios and a biophysically realistic optimal-control model of photobleaching in the budding yeast cell. We further illustrate the versatility of the weak-gradient construction by applying it to an unsteady level-set equation relevant to …

High-Order Adaptive Solutions For Coupled Fractional Riccati Equations Via Daubechies Redundant Frames, Mutaz Mohammad, Alexander Trounev

Mathematical Modelling and Numerical Simulation with Applications

Coupled fractional Riccati equations play a fundamental role in modeling complex systems with memory effects and anomalous diffusion, frequently arising in engineering, control theory, finance, and quantum mechanics. Their analytical and numerical treatment remains highly challenging due to the nonlocal nature of fractional-order derivatives and the presence of nonlinear coupling terms. This study introduces an adaptive numerical framework that combines the Caputo fractional derivative with redundant Daubechies wavelet frames. The method leverages multi-resolution analysis, compact support, and controlled redundancy to achieve accurate approximation of both localized and global solution features, particularly in scenarios characterized by singular behavior and long-range memory …

The Consideration Of Two Scalarization Methods For The Multi-Objective Nurse-To-Patient Assignment Problem, Ilgın Acar, Steven E. Butt, Aydın Sipahioğlu, İslam Altın

Mathematical Modelling and Numerical Simulation with Applications

In this research, the application of two scalarization methods, namely the conic scalarization method and the $\varepsilon$-constraint method, is investigated within the context of a multi-objective optimization problem. These methods are used to address the challenge of assigning nurses to patients on a hospital unit during a shift. The two objective functions of this assignment problem are based on patient workload metrics and unit-related travel distance measures. The proposed solution approach demonstrates the ability to generate solutions that eluded the previous mathematical programming techniques that relied on simplistic weightings of conflicting objective functions. In addition, it is found that the …

Global Stability And Bifurcation Analysis Of A Predator-Prey Model Involving Allee Effect And Monod-Haldane Functional Response, Resmawan Resmawan, Agus Suryanto, Isnani Darti, Hasan S. Panigoro

Mathematical Modelling and Numerical Simulation with Applications

In this paper, the complexity of the dynamic behavior of the interaction between prey and predator is studied. The predator-prey relationship involves Allee effects and Monod-Haldane functional response. The constructed model has been shown to have validity in several respects, including the existence and uniqueness of the solution, as well as its non-negativity and boundedness. Three equilibrium points, namely trivial, axial, and coexistence points, are found, including their global dynamics using the Lyapunov function together with the LaSalle's invariance principle. The effect of the predation conversion rate causes changes in the dynamic behavior of predators and prey, which is characterized …

Solution Of Fractional Order Diffusion Equations With Clique Neural Network, Merve Zeynep Kaya, Mesut Karabacak, Ercan Çelik

Mathematical Modelling and Numerical Simulation with Applications

In this paper, the clique artificial neural network method is used to solve the fractional diffusion equation, which is a subclass of partial differential equations. The clique neural network architecture is constructed using input, hidden, and output layers. Several degrees of clique polynomials were used as activation functions, and the output layer was obtained by multiplying them with weight coefficients. Subsequently, the optimization equation was derived, and the exact solution, numerical solution, and error function graphs were obtained using a specialized algorithm. Analysis of the results demonstrates that the clique artificial neural network method provides quicker and more accurate results …