Numerical Analysis and Computation Commons^™

From Homogeneous To Heterogeneous Adaptive Bounded-Confidence Opinion Dynamics On Networks, Sally Hafez, Fatma R. Farag, Amira S. N. Tawadros

Northeast Journal of Complex Systems (NEJCS)

Adaptive bounded-confidence models (ABCMs) elucidate the coevolution of agent states and network structure via local interactions and rewiring mechanisms. Traditional formulations assume uniform interaction parameters, leading to distinct regime shifts encompassing fragmentation, polarization, and consensus. A symmetric heterogeneous extension of the adaptive bounded-confidence model is introduced, in which interaction parameters vary according to whether agents belong to the same or different groups. The model retains the original update and rewiring protocols but integrates within-group and between-group confidence bounds alongside tolerance thresholds. Initially, the classic homogeneous model is replicated to establish a reference point. Subsequently, the heterogeneous extension is assessed under …

Sustainable Consumer Behavior Modeling: A Complex-Systems Approach To Neuromarketing, Preethi Nanjundan, Nupoor Sanjay Bhute, Ragini Topre, Lijo Thomas

Northeast Journal of Complex Systems (NEJCS)

This study examines the application of complex-systems modeling to neuromarketing data for gaining deeper insights into the mechanisms underlying sustainable consumer behavior. It investigates how neural and biometric responses, interpreted through a systems-based perspective, can uncover dynamic interactions, feedback mechanisms, and emergent behavioral patterns influencing sustainable purchase decisions. The research explores the impact of sustainability-oriented marketing stimuli on long-term behavioral intentions by emphasizing the interconnected roles of cognitive processing, emotional engagement, implicit associations, and collective consumer dynamics. Through simulation-based modeling and structural analysis, the study demonstrates how subconscious neural responses and affective mechanisms mediate the relationship between marketing interventions, consumer …

Provocable Forgiveness In Noisy Brand--Consumer Systems:An Agent-Based Study Of Repeated Interaction, Tahere Ahmadiyan, Hamidreza Navidi, Behbod Keshavarzi

Northeast Journal of Complex Systems (NEJCS)

Repeated brand--consumer exchange is often treated as a managerial problem of loyalty, recovery, and trust. It can also be read as a small complex system: many local decisions about cooperation, retaliation, and forgiveness accumulate into market-level selection. This study uses that perspective to examine which relational rules survive when communication is imperfect. Eight canonical Iterated Prisoner's Dilemma strategies are translated into marketing archetypes and evaluated through round-robin tournaments, a six-level noise sweep, proportional-fitness ecological dynamics, and finite-population Moran invasion tests. The tournament leaderboard is calculated without same-strategy self-play, so that reported payoffs reflect inter-archetype competition rather than homogeneous self-coordination. At …

Numerical Method For Strongly Variable-Density Flows At Low Mach Number: Flame-Sheet Regularisation And A Mass-Flux Immersed Boundary Method, Matheus P. Severino, Fernando F. Fachini, Elmer M. Gennaro, Daniel Rodríguez, Leandro F. Souza

Mathematical Modelling and Numerical Simulation with Applications

A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the disparity between the flow and acoustic speed. Therefore, low-Mach-number flows impose mathematical and computational challenges in their description. Standard numerical methods for compressible flows, which are typically designed for problems with a single dominant spatial and temporal scale, require alternative approaches, such as preconditioning techniques or solvers tailored for low-Mach-number equations. The present work introduces a simplified fluid dynamics model for flows …

Hybrid Solar - Coal Thermal Energy System For Industrial Process Heat At Sayona Drinks Limited In Tanzania, Santos Kihwele, Elisha D. Bitesigirwe

Tanzania Journal of Engineering and Technology (TJET)

Over the past two decades, global efforts to mitigate pollution from conventional energy sources have intensified, with coal remaining a major contributor to carbon emissions. While fossil fuels cannot be eliminated from thermal generation in manufacturing industries, particularly in middle‑income countries such as Tanzania, they continue to dominate as the primary energy source. Industries including food and beverage, paper, textile, paints, chemicals, and pharmaceuticals require substantial thermal energy for heating and drying, and typically rely on coal and natural gas.This study introduces a unique application of a parabolic trough solar thermal system with integrated thermal energy storage, specifically tailored to …

(R2072) A Method To Sample From Transition Densities Of Diffusion Processes With Unknown Densities, Yasin Kikabi, Juma Kasozi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a reliable method that can be used to sample paths of a diffusion process described by a system of stochastic differential equations. These are types of processes whose transition density is not known in closed form. This reliable method involves solving a partial differential equation of the Fokker-Planck type by rejection sampling techniques applied to the associated densities. We then use the novel method to sample from the Ornstein-Uhlenbeck (OU) process whose transition density is known and has unbounded drift. The results obtained compare excellently with the analytical results, thus rendering the method reliable and …

(R2153) Advanced Numerical Method For One Dimensional Burgers Equation With A Source Term, Yahaya Alassane Mahaman Nouri, Djibo Moustapha, Maman Yarodji Abdoul, Saley Bisso

Applications and Applied Mathematics: An International Journal (AAM)

This paper investigates a numerical strategy for the one-dimensional Burgers equation with a nonzero source term. Such equations arise in simplified models of transport and diffusion processes and are often used to assess the performance of numerical schemes for nonlinear evolution problems. The proposed approach combines a second-order Crank–Nicolson time discretization with a projection-based procedure that separates the nonlinear convective contribution from diffusive effects. Spatial approximation is carried out using a Chebyshev spectral collocation method, which provides high accuracy for smooth solutions with a limited number of degrees of freedom. The resulting fully discretized system is solved through an iterative …

(R2155) Mathematical Insights Into Cancer Cells Growth Stability And Chaos, Pardeep Kumar, Kashish Agarwal, Tripti Anand, Sarita Jha

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we examined a recently proposed three-dimensional dynamical model of cancer cell growth that explicitly couples the populations of tumour cells, healthy host cells, and immune cells (Pardeep et al.). We aim to elucidate the model’s novel biological features relative to classical tumour–immune interaction models and to characterize its dynamical regimes. This model is governed by nonlinear differential equations featuring a quadratic tumour proliferation term and bilinear coupling terms for tumour–immune and tumour–host interactions. Then, we performed the rigorous analysis by solving the fixed-point equations and from the Jacobian matrices at the resulting equilibria to identify the …

(R2167) Global Stability Of Seirs Model With Single Dose Vaccination In Varying Population, Govind Jha, Prabhat Mandal, Sarita Jha

Applications and Applied Mathematics: An International Journal (AAM)

Understanding the evolution of infectious diseases within a dynamic population is essential for formulating effective public health strategies. This work introduces an enhanced SEIRS epidemic model that incorporates demographic variation and a single-dose vaccination strategy, supporting that immunity can be reduced over time. The model reflects diseases in which individuals may return to the susceptible state after recovery. Extending prior reduced three-dimensional models, this study develops a complete four-dimensional SEIRS framework, thereby increasing the model’s applicability to real-world scenarios. The inclusion of the full system presents greater analytical challenges. To overcome this, we extend the second additive compound matrix and …

(R2187) Analysis Of Neurological Impairments In Hospitalized Patients Using Cubic Neutrosophic Sets, B. Anitha, M. Lavanya

Applications and Applied Mathematics: An International Journal (AAM)

This study introduces an MCDM-based framework for identifying neurological diseases in hospitalized patients using symptom-based evaluations. A team of interns, guided by the chief doctor, was responsible for determining each patient’s precise condition from the presented neurological symptoms. To enhance diagnostic accuracy, the interns employed the TOPSIS and WASPAS methods to assess and rank the potential disease options. The combined analysis yielded a clear identification of the highest ranked disease for every patient, highlighting the effectiveness of these MCDM techniques in supporting clinical decision making.

(R2129) Layer Resolving Classical Scheme For A System Of N Time-Dependent Singularly Perturbed Problems With Spatial Delay And Robin Initial Conditions, K. Ramiya Bharathi, G. E. Chatzarakis, M. Joseph Paramasivam

Applications and Applied Mathematics: An International Journal (AAM)

This article deals with solving a system of n time-dependent singularly perturbed problems with spatial delay and robin initial conditions. Each equation’s leading term is multiplied by a distinct small positive parameter, inducing overlapping initial layers. Due to presence of these parameters and delay terms, intricate layers occur at interior regions of the domain. To capture the behavior of these layers the solution is decomposed into two components and layer functions are also formulated. The formulation of the layer resolving numerical scheme involves temporal and spatial discretization on uniform and piecewise uniform Shishkin meshes respectively. The proposed framework is found …

Qualitative Analysis Of Solutions To A General Class Of Nonlinear Difference Equations With Applications, Osama Moaaz, Mohamed F. Abouelenein, Mona Anis

Mathematical Modelling and Numerical Simulation with Applications

This work examines the qualitative behavior of a general class of difference equations. We establish criteria guaranteeing the stability, periodicity, and boundedness of the solutions of the equation under consideration. In addition, we identify its invariant intervals. The theoretical results are subsequently applied to various special cases, among them the May--Host model. Numerical simulations are presented to demonstrate the dynamics of the solutions and to validate the theoretical analysis.

Adaptive Intervention Strategies In Co-Evolving Multiplex Networks: A Reinforcement Learning Approach To Real-Time Misinformation Containment, Anjali Ashokrao Bhadre Dr., Harshvardhan Prabhakar Ghongade Dr.

Northeast Journal of Complex Systems (NEJCS)

The growing transmission of misinformation via social media creates serious challenges to public health, democracy and social cohesion. To date, methods used to contain misinformation rely upon static representations of networks and set rules for interventions. In contrast, this study presents the first Multiplex Adaptive Reinforcement Intervention Network (MARIN), a framework for real-time adaptive intervention in the context of dynamic misinformation transmission using co-evolving multiplex networks and deep reinforcement learning. Unlike past studies that have assumed static network structures, MARIN has the ability to allow for dynamic changes in network topology as a result of both misinformation transmission and intervention …

Pinnlab: An Interactive Dashboard For Teaching Data-Driven Parameter Estimation In Differential Equations Using Physics-Informed Neural Networks, Mohan J. Parthasarathy, Padmanabhan Seshaiyer

CODEE Journal

Undergraduate instruction in ordinary differential equations (ODEs) is typically organized around the forward problem: finding solution trajectories when the governing equation and its parameters are known. In scientific practice, however, inverse problems are often more relevant, requiring unknown parameters to be inferred from noisy observations while assessing whether a proposed model is consistent with the data. We introduce PINNLab, an open-source MATLAB dashboard designed to help undergraduate students explore inverse modeling through physics-informed neural networks (PINNs). PINNLab presents PINNs as a complementary data-driven framework that connects differential equations, optimization, empirical data, and scientific machine learning. The instructional sequence is organized …

The Dynamics Of Educational Change: A Complex Systems Perspective, Preethi Nanjundan, Lijo Thomas, Abith K. Sunil

Northeast Journal of Complex Systems (NEJCS)

The perception of university teachers toward educational reforms plays an important role in determining the success of changes introduced in the education sector. This study focuses on teachers’ attitudes toward change, their emotional responses, and their overall views on educational reforms. Across the world, many educational reforms have failed to achieve their expected outcomes in improving teaching practices and student learning. As education systems are highly complex, the approach toward implementing reforms has also changed over time. Some reforms are introduced gradually, while others involve major innovations within the system. Complexity theory provides useful insights and tools that help educators …

A Professional Development Course On Data-Driven Dynamical Systems At A Primarily Undergraduate Institution: Part A - Scientific Content, Alessandro M. Selvitella, Jeffrey R. Anderson

CODEE Journal

In the age of data-driven decision making, ordinary differential equations (ODEs) remain a powerful and interpretable framework for modeling dynamic processes, especially when integrated with modern tools from statistical learning and data-driven dynamical systems. Yet, general undergraduate and graduate curricula do not typically address key opportunities in data-driven dynamical systems.

This first paper in a series focuses on the mathematical and methodological core of a professional development course first developed in the academic year 2025-2026 at a Primarily Undergraduate Institution, Purdue University Fort Wayne. The curriculum developed in this course emphasized how regression, regularization, and sparse identification can be used …

Decoding Stock Market Movements: The Role Of Unemployment And Volatility, Bipllab Roy, Suparna Bhattacharjee

Northeast Journal of Complex Systems (NEJCS)

This study investigates how unemployment and market volatility interact with stock prices in the Indian context, framing the stock–labour–volatility nexus as a complex adaptive system (CAS) rather than a set of linear, time-invariant relationships. Using verified secondary data on unemployment, India VIX, and NSE stock indices for 2013–2023, we first apply simple and multiple regression as a descriptive baseline. Results show a strong negative association between unemployment and stock prices (R ≈ 0.824, R² ≈ 0.68, p < 0.05), consistent with Keynesian demand-side channels, while the linear VIX–stock relationship is weak and statistically insignificant (R² ≈ 0.07, p > 0.05), consistent with the expectation that volatility operates through non-linear, regime-dependent mechanisms not captured by OLS.

Importantly, we document and transparently disclose critical …

Developing A Framework For Mooc Dropout: The Role Of Utilitarian And Hedonic Values In Student Retention, Bipllab Roy, Mave D'Souza, Madhura Laghane

Northeast Journal of Complex Systems (NEJCS)

Massive Open Online Courses (MOOCs) have expanded access to higher education but continue to face persistently high dropout rates, raising concerns about their long‑term effectiveness and sustainability. This study develops and empirically tests a structural framework that links utilitarian values (perceived usefulness, certificate value, time flexibility), hedonic values (enjoyment, variety and novelty, personal interest alignment), and individual characteristics (goal orientation, self‑efficacy, motivation type) to MOOC student retention. Data were collected through a structured questionnaire administered to 200 MOOC learners from Christ University, Lavasa Campus, and analyzed using Structural Equation Modelling (SEM) in AMOS. The results show that goal orientation, self‑efficacy …

Distributed Self-Control Of Dynamical Networks By Adaptive Link Weight Adjustments, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

Conventional control theory considers controlling the behavior of a dynamical system toward a desired state by injecting externally designed inputs into the system. Meanwhile, most complex systems exhibit self-organization through local information exchanges among individual dynamical components that are embedded within a complex network of interactions. The self-organizing dynamics of those systems are realized in a highly distributed manner using locally available information only, and therefore, their behaviors have not been discussed much from a control theoretic viewpoint. Meanwhile, adaptive networks, i.e., dynamical networks whose states and topologies coevolve at similar time scales, can offer a promising theoretical framework in …

Exploring Maximal Length Cellular Automata To Generate Primitive Polynomials In Gf(2), Sumit Adak, Subhrajit Deb, Anurag Ghosh, Angshuman Roy, Souvik Roy

Northeast Journal of Complex Systems (NEJCS)

We present a simple method that uses cellular automata (CAs) to find primitive polynomials over GF(2). We used maximal length CAs as tools to generate primitive polynomials. It is usually very difficult to find maximal length CAs or primitive polynomials since they require exponential time, and there is no linear time method. However, in our work, given an n-size specific sequence of CA with reasonable probability, our technique computes a cycle of length at most 2^n-1 (maximal length) in O(n) time. The characteristic polynomials of synthesized maximal length CAs are claimed to be primitive since it was previously established that …

Evaluating Optimal Capacity And Investment Strategies For Renewable Energy Projects: A Combined Technical And Financial Approach, Helen Josephine, Indhumathi Shanmugasundaram, Sharad Gupta, Manjari Sharma

Northeast Journal of Complex Systems (NEJCS)

The global shift toward clean energy is accelerating, and by 2050 renewable sources are expected to supply more than 85% of the world’s electricity. This transition, however, introduces new layers of complexity. Wind and solar energy behave as interconnected subsystems whose output fluctuates with weather, season, and geography. Their interaction with fixed hourly demand, capital-intensive investments, and financing structures creates a multi-dimensional system in which small changes can trigger significant operational and economic consequences.  This study presents a simulation-driven framework designed to understand and optimize this complex behaviour. The framework models hourly wind and solar generation alongside projected demand to …

Decision Making At Triage Classification Using Svm With Smote Technique, Mehanas Shahul, Pushpalatha Kp

Northeast Journal of Complex Systems (NEJCS)

The efficient functioning of triage gates in overcrowded emergency departments (EDs) occurs in the context of the complex adaptive system (CAS) framework, where diverse system elements – patients, medical personnel, resources, patients’ inflow patterns, and patients themselves – simultaneously and dynamically influence the decision process. This study addresses the automated incorporation of machine learning triage algorithms as part of the system triage process to support automated classified risk-level recognition based on a limited set of vital signs. Patients are dynamically subsumed under high and low-risk categories enhanced by sensitivity, which enables optimal diagnosis and triage response to the critical clinician …

Uncovering Discrete States From Multimodal Psychophysiological Data Using Gaussian Latent Dirichlet Allocation (Glda), Congyu Wu, Aaron Fisher, David Schnyer

Northeast Journal of Complex Systems (NEJCS)

In this article we explore and validate the utility of an unsupervised probabilistic model, Gaussian Latent Dirichlet Allocation (GLDA), for discovering discrete states from repeated, multimodal psychophysiological samples collected from multiple individuals. Psychology and medical research heavily involves measuring potentially related but individually inconclusive variables from a cohort of participants to derive diagnosis, necessitating clustering analysis for state identification. Traditional probabilistic clustering models such as Gaussian Mixture Model (GMM) assume a global mixture of component distributions, which may not be realistic for observations from different patients. The GLDA model borrows the individual-specific mixture structure from a popular topic model Latent …

Asymmetric Opinion Formation Of Emotional Excitable Agents, Irene Ferri, Emanuele Cozzo, Aleix Nicolás-Olivé, Albert Díaz-Guilera, Luce Prignano

Northeast Journal of Complex Systems (NEJCS)

The bounded confidence model represents a widely adopted framework for modeling opinion dynamics wherein actors have a continuous-valued opinion and interact and approach their positions in the opinion space only if their opinions are within a specified confidence threshold. Here, we propose a novel framework where the confidence bound is determined by a decreasing function of their emotional arousal, an additional independent variable distinct from the opinion value. Additionally, our framework accounts for agents' ability to broadcast messages, with interactions influencing the timing of each other's message emissions. Our findings underscore the significant role of synchronization in shaping consensus formation. …

The Digital Neuron: Neural Cellular Automata For Neural–Symbolic Translation, Nicole Assenza

SMU Data Science Review

A neural cellular automata (NCA) architecture, referred to as Pluto’s NCA, was developed to characterize bilateral communication and semantic reciprocity between symbolic representations and a spatially distributed update field. The architecture employs an encoder–automata–decoder pipeline that maps symbolic inputs into a multichannel state field and reconstructs them through agreement-driven attractor convergence within a stable semantic attractor landscape. System behavior was evaluated under controlled perturbations, including rhythmic desynchronization, graded ablations, correlated and independent noise, and percolation-based structural degradation. Quantities such as Agreement(t), internal coherence Aᵢ(t), the recovery time constant τ, and the critical percolation threshold pc were measured to assess stability, …

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 …

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 …