Applied Mathematics Commons^™

Emergent Dynamics In Multiplex Social Networks: Agent-Based Modeling Of Information Diffusion For Misinformation Control, Harshvardhan Prabhakar Ghongade, Anjali Ashokrao Bhadre, Shivani Agarwal, Harjitkumar Uttamrao Pawar, Harshal Subhash Rane

Northeast Journal of Complex Systems (NEJCS)

Information misrepresentation is widespread in multi-layered social networks which provide multiple avenues to communicate information. As such, it presents significant opportunities for both information integrity and public discourse to be undermined by disinformation. This paper outlines a new agent-based model, developed to capture emergent dynamics of multi-layered social networks and to help identify technical means to mitigate information misrepresentation in complex systems. A key component of this research includes a novel Multi-Layer Information Diffusion Model (MLIDM), integrating both cross-layer communication among agents, as well as heterogeneous agent behaviors and adaptive intervention strategies. Our methods employ a three-stage process to model …

Modeling Flood-Induced Cascading Disruptions In The Indian Electronics Supply Chain Using Influence Network Analysis, Surendra Orupalli, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

This study investigates flood induced disruptions in the Indian electronics supply chain using influence network analysis. Monsoon floods are recurring hazards that significantly impact economic activities, logistics, and industrial productivity. This study integrates district-level rainfall data (2020 to 2025) with supply chain network models to quantify cascading failures. The methodology applies rainfall thresholds (≥ 300 mm/month) to identify flood-prone districts and constructs a stochastic influence matrix representing inter-firm dependencies. Flood propagation dynamics are modeled iteratively with a propagation coefficient (α = 0.6) and convergence threshold (ε = 10⁻⁴). The resulting disruption profiles are mapped onto company-level revenues calibrated to India-specific …

Modeling Bitcoin Dynamics Using Differential Equations, Boone M. Fleenor

Departmental Honors & Graduate Capstone Projects

In this thesis, we develop and analyze two nonlinear systems of ordinary differential equations to model Bitcoin price dynamics. Analytical techniques are used to obtain exact or approximate solutions where possible. Then, numerical simulations using a fourth-order Runge–Kutta method are employed to explore system behavior beyond analytically tractable regimes. Finally, model outputs are compared to historical Bitcoin price data using normalized and resampled time series. These results suggest that deterministic models can provide meaningful insight into the structural behavior of Bitcoin markets, while highlighting the need for stochastic or time-dependent extensions for more realistic modeling.

Fractals Exploration Through Computer Visualization, Sihui Wei

SACAD: Scholarly Activities

This project explores the generation and visualization of fractals using computational methods. Several well-known fractal structures, including the Koch Snowflake, Sierpinski Triangle, Mandelbrot Set, and Julia Set, were implemented using C++ and the SFML graphics library.

The study focuses on how simple mathematical rules, when applied recursively or iteratively, can produce highly complex and self-similar structures. For geometric fractals, recursive algorithms were used to subdivide shapes and generate patterns. For complex-plane fractals, iterative formulas were applied pixel-by-pixel to determine set membership and visualize escape behavior.

The results demonstrate that small changes in parameters, such as recursion depth or iteration count, …

A Computational Study Of Taylor Approximation, Sihui Wei

SACAD: Scholarly Activities

This project investigates the accuracy of Taylor approximation using computational methods. Taylor polynomials of degree 1, 3, and 5 were applied to the functions e^x, sin x, and ln⁡(1+x), all centered at x=0.

Using C++, we generated both numerical data and graphical visualizations to analyze the absolute error∣f(x)−Tn(x)∣. The results show that higher-degree polynomials provide better approximation near the expansion point, while the error increases as the distance from the center grows.

In addition, the study reveals that the effectiveness of Taylor approximation depends not only on the polynomial degree but also on the structure of the function. In particular, …

A Dynamic Systems Framework For Customer Lifecycle Management: From Latent State Discovery To Robust Control Policy, Ali Nasirzonouzi

Northeast Journal of Complex Systems (NEJCS)

Traditional marketing often relies on static strategies that fail to capture dynamic customer behavior. This paper introduces an integrated framework to model and control the customer lifecycle, bridging the gap between empirical data and computational simulation. Using the Customer Personality Analysis dataset, we implemented a five-stage methodology. We first identified three distinct customer segments (At-Risk, Standard, High-Value) using Gaussian Mixture Models. To address the lack of longitudinal data, we calibrated a normative transition model based on customer inertia principles. Our analysis revealed that marketing effectiveness is highly state-dependent; notably, At-Risk customers exhibited a 33.5% lift when targeted with catalogs. Leveraging …

How To Effectively Trap Invasive Crayfish: A Discrete Life Stage Mathematical Model, Rini Pattison

Seaver College Research And Scholarly Achievement Symposium

The red swamp crayfish is an invasive species introduced into several streams within the Santa Monica Mountains (SMM). Crayfish predation decimates native aquatic species. The Mountains Restoration Trust (MRT) has worked to remove crayfish through regular trapping in Malibu Creek.

A prior student created a crayfish life cycle model with trapping, which we expand to better predict the efficacy of crayfish removal efforts in the SMM. We separate crayfish based upon life stages and sizes. We construct and parameterize this discrete crayfish population model with and without trapping. We use literature and crayfish removal data from MRT to fit the …

Irreversible K-Threshold Dynamics On Corona And Base-B Corona Product Graphs, Eric J. Moon, Soumya Bhoumik, Paul Flesher

SACAD: Scholarly Activities

This poster studies the irreversible k-threshold process on corona-type graph products, where a vertex becomes colored once at least k of its neighbors are colored and then remains colored permanently. We focus on corona, double corona, and base-b corona product graphs built from cycles and complete graphs, with particular attention to how graph structure affects complete activation from a minimum seed set.

A generalized reduction lemma is used to relate threshold dynamics on layered corona graphs to smaller residual graphs, yielding explicit formulas for the irreversible k-threshold conversion number on both corona and double corona families. The …

Transport Of Quantum Walks In Electric Fields, Yousef Mohammad Yousef Salah

Thesis/ Dissertation Defenses

This thesis presents an analysis of transport in one-dimensional discrete-time quantum walks (DTQWs) on the Hilbert space . Quantum walks serve as fundamental models of coherent quantum transport and exhibit ballistic spreading driven by superposition and interference. The primary focus of this work is the review and derivation of sharp maximal velocity bounds for several classes of quantum walk step operators, including the shift-coin walk, the split-step walk, and models with constant as well as position-dependent coin operators. We establish general a priori bounds that remain valid beyond the translation-invariant regime. For homogeneous models, Fourier and spectral analysis yield explicit …

Physics-Informed Neural Network Solution Of The 2d Helmholtz Equation With A Gaussian Source, Theodoros Panagiotakopoulos, Chris Velissaris, Aristotelis Nikolaos Rapsomanikis

Faculty Scholarship and Creative Works

We present a physics-informed neural network (PINN) framework for solving the complex-valued two-dimensional Helmholtz equation with a localized Gaussian source and spatially varying permittivity. Starting from Maxwell’s equations, the frequency-domain scalar Helmholtz formulation under transverse electric (TE) polarization is derived and enforced directly within the neural network loss function. The model employs a sinusoidal representation network (SIREN) architecture to capture the oscillatory nature of wave solutions and incorporates the Sommerfeld radiation condition to impose open boundary conditions. Training is performed using a hybrid collocation strategy combined with a two-stage optimization procedure consisting of Adam followed by L-BFGS. Numerical experiments in …

Digital Transformation And Market Microstructure: Analyzing The Impact Of Algorithmic Trading On National Stock Exchange Of India Price Discovery Mechanisms Through Complex Systems Theory., Mukesh Bhaskar Ahirrao, Harshal Anil Salunkhe, Vishal Sunil Rana

Northeast Journal of Complex Systems (NEJCS)

Abstract

This research examines the evolution of market microstructure at the National Stock Exchange of India (NSE) from 2020 to 2024, a period characterized by substantial growth in algorithmic trading from 35% to 44% of total trading volume. Using market microstructure data and analytical techniques grounded in complex systems perspectives, the study documents temporal patterns in price discovery, liquidity, volatility, and market efficiency associated with this digital transformation.

The analysis reveals several notable changes in market characteristics. Transaction costs improved significantly, with bid-ask spreads declining by 23.4% and market depth increasing by 18.1%. Price adjustment half-life decreased by 50%, indicating …

Analysis Of The Effects Of Magnetic Field, Heat Transfer, And Thermal Radiation On Blood Flow Through Bifurcated Artery To Enhance Tumor Treatments, Abdullahi Isah, Dauda Gulibur Yakubu, Ali Musa

Tanzania Journal of Science

The work presents the effects of some pertinent parameters on blood flow through bifurcated artery to enhance tumor treatments. Combining appropriately the basic equations, together with the fractionalized Maxwell fluid model allow us to determine the velocity, temperature and concentration of blood flow through bifurcated artery. The study adopted the Atangana-Baleanu fractional time derivative on fluid model to describe the non-Newtonian behavior of blood flow. The numerical simulations were performed using the combined Laplace transform and the method of undetermined coefficients and the results obtained with the aid of Mathcad software were simulated and presented graphically. From the graphical results, …

Complex Systems Mapping Of Fiscal Growth Dynamics At Strategic Maritime Chokepoints Using Time-Series Slopes, Rahul Balamurugan, Preethi Nanjundan, Avichal Sharma

Northeast Journal of Complex Systems (NEJCS)

This study examines how maritime and trading states allocate public resources between defence, health, and economic growth around three strategic chokepoints the Strait of Malacca, the Strait of Hormuz, and the Suez Canal. The analysis extends the classic “guns versus butter” framing by treating defence and health spending as co-evolving components of an interconnected fiscal-growth system. Using World Development Indicators data (1999-2024), trend slopes are estimated for military spending (% of GDP), healthcare spending (% of GDP), and GDP growth (annual %). Two derived indicators are computed, a defence-to-health slope ratio (military slope/health slope) and a fiscal-balance proxy (health slope …

Arum–D Nexus: Adaptive Reflexive Urban Metabolism For Complex Construction And Demolition Waste Governance In Bengaluru, Talat Naaz, Rosewine Joy

Northeast Journal of Complex Systems (NEJCS)

Urban material systems exhibit nonlinear dynamics governed by feedback, adaptation, and emergent coupling among institutions, markets, and behaviors. Construction and demolition (C&D) waste in Bengaluru is a great example of such complexity, where fragmented regulation, informal actors, and digital asymmetries coalesce into unstable waste flows and resource leakages. This study conceptualizes Bengaluru’s C&D waste system as a Complex Adaptive System (CAS), where institutional, market, behavioral, and metabolic subsystems co-evolve through nonlinear feedback interactions. A meta-analysis of secondary literature combined with benchmarking of government datasets is used to evaluate two key complexity indicators, i.e., response speed and feedback density. The advancement …

Solving Wordle Using Information Theory, Talal Aladaileh, Donald Stephens, Mallak Alqaisi, Congyu Wu

Northeast Journal of Complex Systems (NEJCS)

Wordle, a popular word-guessing game, challenges players to identify a five-letter secret word through iterative guesses and feedback on letter placement. The players must figure out the secret word within six guesses. After each guess, the letters will be color-coded based on different criteria. Optimizing the choice of guesses is critical for maximizing success within the limited attempts allowed. In this study, the application of Shannon entropy is explored as a strategy for selecting words that maximize information gain at each step of the game. By quantifying the uncertainty reduction achieved by potential guesses, this method prioritizes words that are …

A Multi-Layer Complex Adaptive System Framework For Ai-Driven Robo-Advisory Services, Jesty Mariam Philip, Mohit Boralkar, Alwin Joseph

Northeast Journal of Complex Systems (NEJCS)

The rapid integration of Artificial Intelligence (AI) into investment advisory services has changed financial decision-making, giving rise to adaptive robo-advisory systems capable of real-time analysis, personal recommendations, and autonomous portfolio optimization. Existing research evaluates these systems primarily through technological performance or investor adoption, overlooking the complex feedback-driven interactions that emerge when AI analytics, data environments, and human behavior operate together. This study addresses this gap by conceptualizing AI-enabled robo-advisors as a multi-layered Complex Adaptive System comprising historical data, real-time data, AI analytics, investor perception, and decision-making layers. A simulation model grounded in machine learning dynamics, behavioral finance, and complexity theory …

Regional Drought Modulation By Enso And Iod As Indicated By The Standardized Precipitation Index, Arpit Tiwari, Preethi Nanjundan, Tanu Sharma, Ravi Ranjan Kumar, Satyaban Bishoyi Ratna

Northeast Journal of Complex Systems (NEJCS)

Understanding the modulation of drought by large-scale ocean–atmosphere teleconnections is crucial for strengthening drought prediction and resilience in India. This study investigates the influence of the El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) on meteorological drought characteristics across India from 1950 to 2024 using the Standardized Precipitation Index (SPI) at a 12-month timescale. Drought events were quantified in terms of frequency, duration, severity, and intensity and linked to ENSO–IOD variability through composite, correlation, and mediation analyses. Results reveal that El Niño events consistently correspond to widespread and severe droughts, particularly over central and southern India, with drought …

Indexed Concatenation (I-Cat): A Method For Representing And Operating On Repeating Numbers*, Abigail Touma, Isaac Wolford

Campus Research Month

Our research presents Indexed Concatenation (I-Cat) notation as a structured way to represent numbers with repeating patterns, including both decimals and whole numbers. Instead of treating expressions like 0.333... or 735735735 as unstructured expansions, they are rewritten as compact repeating objects called I-Cats. The presentation demonstrates how arithmetic operations, including addition and multiplication, can be performed using hypothesized rules such as the "U = M/C" method, unpacking, and carry propagation. Examples progress from simple conversions and multiplication by integers to the multiplication of two I-Cats. A live visual demonstration will show how standard numerics transform into I-Cat form and how …

Asymmetrical S-Curve For Residual Load Sways Suppression For Double-Pendulum Rotary Crane Using Bayesian Optimization, Haryson Johanes Nyobuya

Tanzania Journal of Science

In rotary crane operations, one of the main difficulties lies in suppressing the load sway during its movement. This can be achieved using only horizontal boom motion, offering a solution that is energy-saving, simple, and safe. However, this approach renders the system under actuated, making the suppression objective more difficult to achieve. In this study, a double-pendulum model is adopted to capture the coupled dynamics of the suspended load and hook, which shows a realistic basis for sway suppression. An asymmetric S-curve velocity trajectory is proposed to shape the horizontal boom motion, effectively minimizing residual vibrations without requiring direct sway …

Quantitative Analysis Of Cholera Dynamics And The Impact Of Integrated Control Measures., Kazeem Abidoye Odeyemi, Mutairu Kayode Kolawole

Tanzania Journal of Science

A comprehensive mathematical evaluation of cholera dynamics, emphasizing the crucial role of optimal control strategies which include vaccination, treatment in endemic region and environmental hygiene in controlling the disease spread in Western and Mid-Eastern regions of African setting. Through analysis of the local and global stability of the model and assessing the reproduction number (��0), this research highlights how targeted interventions can influence transmission rates of cholera disease. Sensitivity analysis identifies key parameters driving cholera dynamics, underlining the urgency of timely and adequate intervention. Utilizing the innovative Homotopy Perturbation Method for the numerical simulation, the study explores the interplay between …

Implementing A Clustering Framework On Distributional Bee Data, Roheel Nawaz

Research and Creativity Symposium

Understanding spatial patterns in biodiversity is important for identifying how ecological communities are structured across landscapes. Clustering methods provide a useful way to detect non-random species distributions and reveal potential environmental or geographic influences. In this study, we applied a clustering framework to a large long-term bee abundance dataset from the Mid-Atlantic United States to evaluate community structure across regions of Maryland, Delaware, and Washington, D.C.

The dataset included over 1,100 sites and more than 3,000 transects. Because sampling methods were not fully standardized, abundance data were converted to presence/absence and analyzed using the Jaccard index to measure site similarity. …

Ideals And Lattices In Number Fields, Sarah Ali Alyammahi

Theses

This thesis investigates algebraic number fields and their rings of integers, which

generalize the ring of integers ℤ in ℚ. The study focuses on ideals, units, and ideal class

groups, which describe the arithmetic structure of number fields and the failure of unique factorization. Key invariants such as the norm, trace, and discriminant are developed and applied, with particular emphasis on quadratic number fields and classical examples such as the Gaussian and Eisenstein integers. Some explicit computations of ideal class groups are carried out. The thesis also explores connections with lattice theory by interpreting rings of integers as lattices and …

Low-Complexity Structured Neural Networks And Their Usage In Image And Signal Processing, Adam Kuzmicki

Doctoral Dissertations and Master's Theses

Conventional neural networks face significant challenges due to high computational costs, large parameter counts, and reliance on backpropagation, which restricts their application in resource-constrained and real-time settings. To address these challenges, this thesis proposes three structured neural network (NN) architectures grounded in the theories of sparse and self-contained factorizations of transforms, with applications to image compression, reconstruction, classification, encryption, and also adaptive wideband multi-beam beamforming. The first neural network architecture, named DCTrix-Net, replaces conventional spatial con- volution with highly sparse factorization of the discrete Cosine transform (DCT) complemented by Toeplitz-structured weight initialization, achieving at least 97% FLOP reduction over CNNs, …

Information Theory Analysis Of The Solar Wind Magnetic Structures For Space Weather Prediction, Katherine Holland

Doctoral Dissertations and Master's Theses

Forecasting space weather at Earth is highly complicated, because of the limited measurements of the dynamic processes in the Sun that span multiple temporal, spatial, and energy-scales. The solar wind is a highly structured, multi-scale, evolving plasma and consists of coronal mass ejections (CMEs), stream interaction regions (SIRs), expanding flux tubes (Borovsky, 2008), and interplanetary magnetic field (IMF) discontinuities and fluctuations. The aim of this research is to improve our understanding of the evolution and dissipation of different scale-size solar wind magnetic structures as they move from the Sun-Earth Lagrange point 1 (L1) to Earth's bow shock and, ultimately, to …

Employing Effective Solution Methods For Caputo-Based Sequential Fractional Models, Eman A. A. Ziada, Mohamed F. Abouelenein, Hijaz Ahmad, Monica Botros

Mathematical Modelling and Numerical Simulation with Applications

This paper investigates a class of nonlinear sequential singular fractional differential equations (FDEs) involving Caputo derivatives. This type of equation has several key advantages that enhance its value, such as capturing memory and hereditary effects. Viscoelastic materials and anomalous diffusion, as well as biological systems, can take advantage of this feature. In addition, fractional derivatives possess a sequential structure that enables the implementation of multiscale processes and hierarchical memory responses. Moreover, it provides an effective and flexible framework for solving differential equations compared to classical differential equations. It can therefore be used to model complex systems in physics, biology, and …

Optimal Control Strategies For Infectious Diseases: A Numerical Simulation Approach, M. Abu Salek, Jannatun Nayeem, Romana Yesmin, M. Haider Ali Biswas, M. Humayun Kabir

Mathematical Modelling and Numerical Simulation with Applications

Various infectious diseases, such as Tuberculosis and Hepatitis B virus (HBV), caused by Mycobacterium bacteria and hepatitis B virus, respectively, pose serious threats worldwide. This paper examines the spread of these diseases using a mathematical model that incorporates control measures, including vaccination and awareness programs. We use a system of differential equations with control variables and apply Pontryagin's principle to determine optimal control strategies. The stability of the Disease Free Equilibrium (DFE) has been analysed and demonstrated to be both locally and globally asymptotically stable when the basic reproduction number remains below unity, thereby ensuring disease elimination. Furthermore, the Endemic …

Exact Soliton Solutions Of The Nonlinear Time-Fractional Schrödinger Equation Via Atangana–Baleanu And M-Truncated Operators, Bahadır Kopçasiz, Fatma Nur Kaya Sağlam, Mehmet Şenol

Mathematical Modelling and Numerical Simulation with Applications

The main objective of this work is to obtain exact soliton solutions for a nonlinear time-fractional equation model describing wave profiles arising in various physical systems. To derive different wave structures associated with the considered model, two analytical techniques are employed: the extended G'\G^2-expansion method and the modified auxiliary equation (MAE) approach. A wave transformation is applied to reduce the nonlinear time-fractional equation to a nonlinear ordinary differential equation (NLODE) by means of the M-truncated and Atangana-Baleanu (AB) fractional operators. Several classes of solutions, including exponential, hyperbolic, and trigonometric wave forms, are obtained. Over and above the analytical results, graphical …

Dynamical Analysis And Optimal Control Of The Mpox Transmission Model With Stratified Susceptibility, Tuhfatul Janan, Fatmawati Fatmawati, Cicik Alfiniyah, Santi Martini, Dipo Aldila, Agus Hasan

Mathematical Modelling and Numerical Simulation with Applications

This study develops a mathematical model of Mpox transmission that combines stratified susceptibility (low-risk and high-risk groups) with vaccinated and asymptomatically infected compartments. The analysis of the model begins with examining the well-posedness, boundedness, and nonnegativity conditions for the solutions. The local stabilities of the equilibria are examined through the Jacobian matrix and phase plane analysis, while the global stabilities are provided through Lyapunov functions. The estimated parameters are verified using epidemiological data on Mpox cases in the United States, with an MAPE of 2.20% and R_0 > 1, indicating that Mpox remains endemic. Sensitivity analysis indicates that the contact rate …

Bifurcation Exploration Of Ion Acoustic Solitons Formation Of A Nonlinear Beta Fractional Kadomtsev-Petviashvili Burger Model In Plasma State, Mst. Razia Pervin, Alrazi Abdeljabbar, Fahad Sameer Alshammari, Mst. Shekha Khatun, Harun Or-Roshid

Mathematical Modelling and Numerical Simulation with Applications

This research presents an extensive investigation of Ion acoustic soliton dynamics governed by a Beta-fractional Kadomtsev-Petviashvili-Burgurs (KPB) model. By engaging the planar dynamical system scheme in aggregation with the extended $(\phi, \psi)$ expansion, Kudryashov expansion, and the NMKM analytic schemes, we create a broad class of exact nonlinear pattern wave solutions. The local stability edifice of the fractional plasma model is explored through bifurcation theory, enabling the far-reaching classification of all admissible phase diagrams. Conforming Ion acoustic wave structures allied with every detour alignment are systematically assembled. Owing to the fractional and dissipative appearances of the model, an all-embracing assortment …

Numerical Simulations And Hyers-Ulam Stability Of A Novel Nonlocal Anthropogenic Cutaneous Leishmaniasis Mathematical Model, Khalid Fanoukh Al Oweidi, Zakirullah -, Kamal Shah, Thabet Abdeljawad

Mathematical Modelling and Numerical Simulation with Applications

In this work, the fractal-fractional Atangana-Baleanu derivative with the Mittag-Leffler kernel is employed to capture the memory and hereditary effects inherent to anthropogenic cutaneous leishmaniasis transmission dynamics. The Banach fixed-point theorem and contraction mapping principle are used to prove the existence and uniqueness of solutions, while Hyers-Ulam stability of the system is analyzed to demonstrate the robustness of solutions with respect to small perturbations. Using a nonlinear least-squares approach, model parameters and fractional order are estimated using epidemiological data from the World Health Organization. The basic reproduction number $R_0 = 0.53$ indicates that the disease is under control after adding …