Numerical Analysis and Computation Commons^™

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 …

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 …

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, …

Measuring Market Risk Through Entropic Var, Dragomir Nedeltchev, Tsvetelin Zaevski

Mathematical Modelling and Numerical Simulation with Applications

The article aims to measure the market risk beyond the basic risk measures like the Value-at-Risk (VaR) and the Expected Shortfall (ES). The Entropic Value-at-Risk is selected among the available measures based on its advantages -- it is the coherent upper bound of the VaR and ES. This risk measure is applied to the classical Black-Scholes model as well as to some more realistic ones, such as the exponential tempered stable model (the log-returns are presented by a tempered stable L\'evy process), the stochastic volatility model of Heston, its jump extension of Bates, and another stochastic volatility model but with …

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 …

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 …

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 …

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 …

(Si16-04) Some Fixed Point Theorems On Chatterjea Type Contractions, Irom Shashikanta Singh, Y. Mahendra Singh

Applications and Applied Mathematics: An International Journal (AAM)

This paper establishes the existence of fixed points related to strict Chatterjee contractive mappings by relaxing the compactness of the underlying spaces and the continuity of the mapping involved, using altering distance functions and comparison functions in the general setting of metric spaces. Several non-trivial and illustrative examples are provided to demonstrate, support, and validate the obtained theoretical results. In addition, a theorem that can characterize the completeness of metric spaces through the existence of fixed points is rigorously proven and discussed. Furthermore, a theorem on strict Chatterjea-type modulus contractive mappings without continuity assumptions and with relaxed compactness conditions is …

A Coupled Fractional Thermistor System Demonstrating Existence, Uniqueness, And Simulation Results With Two-Point Boundary Conditions, Yahia Awad, Angela Khattar, Hussein Fakih, Sami Hammoud, Karim Amin

Mathematical Modelling and Numerical Simulation with Applications

This paper studies a coupled system of Caputo fractional differential equations of orders $\alpha, \beta\in(1,2]$, subject to two-point boundary conditions. The model incorporates nonlinear nonlocal integral terms that capture the memory-dependent interactions between thermal and electrical dynamics in thermistor materials. We rigorously establish existence via Schaefer’s fixed-point theorem and uniqueness through Banach’s contraction principle in a Banach space of continuous and continuously differentiable functions. Additionally, we analyze Ulam–Hyers stability to quantify solution sensitivity to initial perturbations. A numerical example highlights the effects of fractional orders and nonlocal feedback on system behavior. This work generalizes classical thermistor models and provides a …

The Butterfly Effect In Economics: Exploring Chaos With A Simple Financial Model, Sandy Hs Herho

CODEE Journal

Wild swings in financial markets need not result from external shocks like earthquakes or wars—they can emerge from deterministic chaos. This article introduces kalimusada, an open-source Python library that lets students and instructors explore this phenomenon through a simple three- equation model of financial dynamics. The model couples interest rates, investment, and prices through nonlinear feedback, generating bounded but unpredictable oscillations characteristic of chaos. Tiny differences in starting conditions—smaller than any measurement could detect—grow exponentially until two initially identical economies follow completely different paths. The library provides ready-to-use tools for visualizing this “butterfly effect” in economics, computing divergence metrics, and …

Eigenvalue Bound Preservation: Numerical Experiments On The 2d Q-Tensor Flow, Marcel C. Deguzman

Knowledge and Creativity Expo

We study the evolution of nematic liquid crystals in two dimensions using the Q-tensor model, a continuum framework that describes the orientational order of rod-like molecules via symmetric, traceless matrices. Focusing on the Landau-de Gennes energy and its associated gradient flow, we consider a reduced two-dimensional formulation in which the Q-tensor is fully described by two scalar functions. This reduction simplifies the system to a nonlinear, coupled PDE for the scalars, while preserving essential physical features. A key question is whether the eigenvalues of the Q-tensor remain within the physically admissible range under this flow. Building on a theoretical result …

Computationally Modelling Nmda Blockages Within A Neural Network, Anya Raetsch

UNH URC Open (2026 and after)

The N-Methyl-D-Aspartate (NMDA) Receptor is fundamentally important to memory formation within the brain due to its control of calcium entry into the cell.  In recent years, there has been an increased interest in long-term effects of NMDA blockages on the brain, due to the “re-wiring” of communication channels (synapses) between neurons. This project models the effects of NMDA blockages due to drugs such as Ketamine, and how the blocking of NMDA receptors affects firing rates, which can then be applied to studying long-term plasticity within the neural hierarchies. Using the Nest Online Simulator, a 50x50 grid of neurons was created …

Using Ai To Analyze Survey Data, Sara Martucci

Open Educational Resources

This assignment in Methodology in Sociology/Criminology engages students in the full research process by guiding them through variable selection, data analysis, interpretation, and critical reflection on AI-assisted decision-making. Using a class-generated survey dataset (or an existing dataset), students develop a research question, identify independent and dependent variables, and formulate a hypothesis. They then compare their selections with those suggested by an AI tool, analyzing differences in reasoning and variable choice. Through SPSS, students generate frequency tables, charts, and scatterplots to examine relationships between variables, including potential intervening factors. The assignment culminates in a group presentation and reflective analysis on the …

Using L1-Magic For Feature Enhancement And Reduced Redundancy In Hyperspectral Data, Ashley Alfred

Mathematics Dissertations

Hyperspectral imaging offers detailed spectral information, but achieving high spatial resolution typically requires large and expensive equipment. This study explores an alternative approach: enhancing low-quality hyperspectral bands using an L1-norm minimization technique known as L1-magic. The goal is to improve the utility of low-cost hardware by preserving discriminative features, promoting sparsity, and reducing spectral redundancy. We apply L1-magic to enhance low-quality bands and hypothesize that this method selectively amplifies key features while suppressing redundant information. Experimental results indicate that the enhanced bands approach the quality of high-resolution data, enabling robust feature extraction without reliance on high-end hyperspectral cameras.

Microgravity-Induced Alterations In Left Atrial Hemodynamics And Thrombogenic Risk: Insights From Healthy And Atrial Fibrillation Models, Grace M. Hoeppner

Dissertations, Master's Theses and Master's Reports

Background: Microgravity exposure alters cardiovascular loading, yet its impact on left atrial flow dynamics and thrombotic risk remains poorly understood. This study investigates how spaceflight-relevant microgravity-induced changes in cardiac outflow affect left atrial hemodynamics in healthy individuals and patients with atrial fibrillation.

Methods: Patient-specific left atrial models were generated for three healthy individuals and three AF patients. Computational fluid dynamics (CFD) simulations were performed using each patient’s baseline mitral outflow waveform and two modified waveforms representing short- and long-duration post-flight cardiac loading changes derived from echocardiographic observations. Hemodynamic metrics included left atrial velocity, time averaged wall shear stress, oscillatory shear …

A Bayesian Late-Fusion Supportability Framework For Rare-Disease Severity Prediction In Glut1 Deficiency Syndrome, Jordan M. Rodriguez

Mathematics Dissertations

Glucose transporter type 1 deficiency syndrome (GLUT1-DS) is a rare neurometabolic disorder with heterogeneous neurological and developmental severity. Because patient-level severity is not observed as a single validated outcome, this dissertation develops a Bayesian late-fusion supportability framework for constructing and predicting an ordered latent severity phenotype from clinical, genetic, and EEG-derived evidence. The primary target was constructed in a larger clinical cohort using age-5 symptom burden and learning cognition, then assigned to an aligned multimodal prediction cohort. Target-defining variables were excluded from supervised predictors, and models were evaluated using patient-exclusive cross-validation with training-fold preprocessing and fold-wise EEG PCA.

The primary …

A Mathematical Frameworks For Singular, Nonlinear Phenomena: Applications To Nematocyst Firing And Inhomogeneous Nls With Coulomb Potential, Abdulrahman Alharbi

Theses and Dissertations

Nematocysts are specialized cellular organelles found in all cnidarians, including corals and jellyfish, as well as in some single-celled protists such as dinoflagellates. These organelles display remarkable diversity in morphology and function, playing roles in prey capture and defense. The firing of a nematocyst is one of the fastest accelerations in nature, yet the underlying physical mechanisms remain not fully understood. In this work, we address key questions: how sufficient force is generated to overcome the fluid boundary layer, whether fluid–structure interaction models can reproduce observed dynamics, and what mechanisms trigger discharge.

Our research investigates models based on osmotic pressure …

Performance Of Numerical Methods Applied To The Black–Scholes Model, Scott Cameron Williams

UNF Graduate Theses and Dissertations

We compare five numerical approaches for approximating solutions to the Black–Scholes partial differential equation for pricing European call options: FTCS, BTCS, Crank– Nicolson, Monte Carlo simulation, and a physics–informed neural network (PINN). These methods span finite difference techniques, probabilistic simulation, and machine learning. Performance is evaluated based on computational efficiency and accuracy relative to the analytical Black–Scholes solution.

Among the methods, Crank–Nicolson and the PINN demonstrated the strongest overall performance. Crank–Nicolson achieved the highest accuracy but exhibited increased runtime as the number of underlying stock price grid points grew. In contrast, the PINN produced slightly less accurate results but with …