Numerical Analysis and Computation Commons^™

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. …

Conditional Product Sampling For Gaussian Process Implicit Surfaces, Song Shi

Dartmouth College Master’s Theses

Gaussian Process Implicit Surfaces (GPISes) provide a powerful and unified stochastic geometry representation for rendering surfaces, volumes, and the rich continuum between them. Recent work has shown that GPISes can model a broad space of visual appearances under a unified light transport framework. However, practical rendering with GPISes remains challenging: existing estimators can become inefficient for particular correlation structures, and highly anisotropic or heightfield-like GPISes require specialized treatment to obtain robust variance reduction.

This thesis extends recent work on GPIS rendering by introducing a new next-event estimation (NEE) technique for anisotropic GPISes.We show that standard NEE provides diminishing benefits as …

Stochastic Derivative-Free Deep Learning Methods For Solving High Dimensional Partial Differential Equations, Qing He Mr.

Mathematics Theses and Dissertations

Solving high-dimensional partial differential equations (PDEs) is a fundamental challenge in scientific computing, with applications ranging from quantum chemistry and computational finance to statistical physics and stochastic optimal control.  Classical numerical methods such as finite element or finite difference schemes suffer from the curse of dimensionality, rendering them computationally infeasible when the dimension $d$ exceeds a handful. Physics-informed neural network (PINN) methods alleviate this by embedding the PDE residual directly into a loss function, but they require computing derivatives of the network with respect to its spatial inputs---an operation that scales poorly in high dimensions and demands that the approximate …

Dynamics Of A Two-Stage Epidemiological Model With Post-Infection Mortality And Transmission Heterogeneity, B Sagar

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Multiscale Computational Framework Coupling Pulmonary Arterial Blood Flow And Lung Tissue Perfusion, Nigar Sultana, Hangjie Ji, Mette Sofie Olufsen

Biology and Medicine Through Mathematics Conference

No abstract provided.

Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard

LSU Doctoral Dissertations

Numerical algorithms for computing the electronic structure of incommensurate 2D-materials using ab initio models are critical for predicting material properties and guiding experiments. For bilayers, momentum space and continuum models have been introduced to approximate observables of ab initio tight-binding models using a momentum description, despite the lack of periodicity in the tight-binding model required for Bloch theory. A similar structure has been introduced for double-incommensurate trilayers using a continuum model, where the three lattices are mutually incommensurate. However, this description leads to a four-dimensional lattice space, and numerical convergence of the density of states has been observed to be …

Phenological Overlap In Obligate Plant-Pollinator Mutualism, Austin J. Carlson

2026 Spring Honors Capstones Projects

Plant-pollinator mutualisms require temporal overlap between flowering and pollinator activity, so climate-driven timing shifts can weaken the interaction and, in severe cases, destabilize the system. This work investigates how reduced overlap affects persistence in an obligate plant-pollinator pair using a coupled differential equation model in which a phenological overlap factor scales the saturating mutualistic benefit. Simplification with a constant overlap enables closed-form equilibrium and stability analysis, revealing that below a critical overlap threshold, coexistence is no longer maintained. Rescaling reduces the parameter space from ten quantities to seven dimensionless groups, and sensitivity analysis identifies the degree of species dependence and …

Safe Control Design For Quadruped Locomotion In Unstructured Environments Using Linear Transfer Operators, Sriram Sundar Krishnamoorthy Shankara Narayanan

All Dissertations

Deploying quadruped robots in unstructured, obstacle-rich environments requires control and planning methods that remain safe and reliable despite complex terrain geometry, limited sensing, and inevitable modeling errors. This thesis develops operator-theoretic tools for safe control design of robotic systems using linear transfer operators, with a focus on quadruped locomotion in unstructured environments. The central goal is to develop a unified operator-theoretic framework for safe control design based on the Perron–Frobenius (P–F) and Koopman operators. In particular, the thesis leverages \emph{density functions} to develop safe navigation frameworks in the dual space of densities. In the operator-theoretic perspective, the P–F operator governs …

Advances In Computational Methods For Sparsity-Promoting Linear Inverse Problems, Jonathan Lindbloom

Dartmouth College Ph.D Dissertations

Inverse problems arise throughout science and engineering, where indirect, incomplete, and noisy observations are used to recover unknown parameters of interest. In these applications, the corresponding forward or measurement models are often ill-conditioned or underdetermined, so direct inversion is unstable and regularization is required. This thesis develops computational methods for linear inverse problems in which the unknown is assumed to be approximately sparse in a transformed domain defined by a linear, possibly rank-deficient operator, such as a finite-difference matrix, with particular emphasis on large-scale problems.

The thesis makes three main contributions. First, it generalizes hierarchical Bayesian maximum a posteriori estimation …

Stochastic Universal Differential Equations For Epidemiological Modeling: Uncertainty Quantification In Disease Transmission Dynamics, Alice Menaya Armah-Bonney

Electronic Theses and Dissertations

Epidemic forecasting requires not only predictions of expected case counts, but also quantification of uncertainty, although existing surrogate modeling frameworks for agent-based models remain fundamentally deterministic. In this thesis a Stochastic Universal Differential Equation framework is presented that extends the deterministic Universal Differential Equation approach by incorporating a learnable stochastic diffusion term, enabling calibrated probabilistic forecasts while preserving the mechanistic interpretability and computational efficiency of the deterministic baseline. In doing so, a two-phase training algorithm is introduced to ensure stable convergence and the framework is validated against the ensemble output from ExaEpi, an exascale agent-based model of a COVID-19 outbreak …

Intermediate-Scale Outflow Dynamics Of Eta Carinae, Edmund J. Garcia, Matthew C. Fleenor

Departmental Honors & Graduate Capstone Projects

η Carinae (η Car) is a binary system, with the larger star being an extremely massive, luminous blue variable (LBV) beyond the Eddington Limit. Surrounding the η Car system, numerous multi-wavelength imaging campaigns reveal axisymmetric structures with the expanding bipolar Homunculus Nebula (¡1 pc). In combination with the episodic eruptive history of the η Car system, our initial intermediate-scale imaging revealed further axisym- metric structures (1-5 pc). To gain a more expansive view of how the small scale structure connects to panoramic imaging of the η Car region, we constructed a deep, optical, narrowband mosaic of 189 images utilizing the …

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 …

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 …

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 …