Digital Commons Network^™

Vedic Mathematics And Mental Computation: Fast Multiplication Techniques, Algebraic Foundations, And Historical Perspectives, Rakesh Bhatia, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Mental computation has fascinated mathematicians, educators, and students for centuries. Various computational techniques allow arithmetic calculations to be performed rapidly without the use of calculators or computers. Among these methods, several popular techniques are associated with what is commonly known as Vedic Mathematics. In this article, we examine a collection of fast multiplication techniques, including multiplication near powers of ten, multiplication by eleven, squaring numbers ending in five, and the vertical-and-crosswise method. For each technique, we provide elementary mathematical explanations based on algebraic identities and place-value representations.

Hidden Symmetries Of The Classical 3×3 Magic Square, Vijender Nallapu, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The classical 3×3 magic square is one of the most famous objects in recreational mathematics. Its defining feature is that every row, every column, and the two main diagonals have the same sum. However, beyond this well-known property, the square contains several hidden symmetries involving rotations, reflections, complementary pairs, parity, and balance around the central entry. In this article, we present an elementary exploration of these symmetries and show how the classical magic square provides a beautiful introduction to mathematical structure and pattern recognition.

Curious Patterns And Identities Involving Consecutive Integers, Carlo Cattani, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Consecutive integers exhibit numerous surprising patterns and elegant identities. In this article, we investigate several classical properties involving products, sums, divisibility, perfect squares, cubes, pronic numbers, triangular numbers, sums of squares, and Pythagorean triples. Using only elementary algebra, symmetry arguments, and mathematical induction, we establish a collection of identities that reveal rich connections among these classical topics. The exposition is intended for students, teachers, and recreational mathematicians, illustrating how simple observations about consecutive integers can lead to beautiful mathematical patterns and deeper insights into elementary number theory.

The Use Of Machine Learning Models For Predicting The Dielectric Strength Of Gases, Matthew Mileski, Paul W. Groth, Timothy S. Wolfe, Adib J. Samin

Faculty Publications

Technological advancements in high voltage systems have pushed sulfur hexafluoride (SF6) to its operational limits. Furthermore, this gas has other drawbacks including a high liquefaction temperature and a high global warming potential. Therefore, there has been an urgent need to find alternative gases with high dielectric strength (DS). In this work, density functional theory (DFT) is used to calculate molecular descriptors that are fed into an artificial neural network (ANN) and a random forest (RF). These machine learning (ML) models are then used to predict the DS for hundreds of molecules. A finite element model (FEM) is also used to …

An Atmospheric Optical Turbulence Structure Parameter Measurements System Based On Direct Ri Sensing Using High-Resolution Fiber-Optic Sensors, Matej Njegovec, Simon Pevec, Vedran Budinski, Boris Macuh, Melissa K. Beason, Denis Onlagic

Faculty Publications

The paper presents a method to characterize the refractive index structure parameter (C_n²) associated with optical turbulence directly. The characterization system is based on miniature, high‑resolution, all‑fiber refractive index (RI) sensors. The refractive index sensors employ open‑path, low‑finesse Fabry–Perot interferometers that are approximately 8 mm long and 200 μm in diameter. The active part of the interferometers is made of ultra‑low‑expansion glass, which eliminates the influence of thermal expansion on the refractive index measurements. The proposed refractive index sensor, operating in a differential configuration, achieved a resolution of 2×10^-9 RIU using a custom‑designed spectral interrogation system …

Demonstrating Superresolution In Radar Range Estimation Using A Denoising Autoencoder, Robert Czupryniak, Abhishek Chakraborty, Andrew N. Jordan, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We apply machine learning methods to demonstrate radar range superresolution using a denoising autoencoder trained without supervision. Focusing on the estimation of a single physical parameter, the separation between two scatterers in the subwavelength regime, we constrain the network to a one-dimensional bottleneck layer with its size matched to the parameter dimensionality. We find that the bottleneck layer forms a reproducible, monotonic mapping with the true separation, showing that the network learns a low-dimensional representation directly aligned with the underlying physical parameter. We further show that this representation preserves the Fisher information of the signal, indicating that the network recovers …

Moss Biomonitoring And Isotopic Signatures Reveal Aviation Fuel As Local Lead Source Near Oregon Airports, Oluwaseyi E. Aderinboye, Alyssa E. Shiel, Lauren Stalford, Christina J. Murphy, Dean B. Atkinson

Chemistry Faculty Publications and Presentations

Lead emissions from piston-engine aircraft using leaded aviation gasoline (avgas) remain a significant source of environmental contamination near regional airports, posing potential health risks to nearby communities. Passive biomonitoring using the epiphytic moss Orthotrichum lyellii was combined with lead isotope fingerprinting to quantify lead concentrations and distinguish between legacy leaded gasoline and current avgas emissions near Hillsboro and Troutdale airports in Oregon. Here we show that lead levels are elevated by up to 50 times the rural background near airports, with isotopic signatures confirming avgas as a dominant local source. These findings indicate that avgas use contributes substantially to environmental …

Enabling Asl Digital Communication Under Poor Internet Access, Swann Thantsin

Student Theses

Video conferencing degrades asymmetrically. When bandwidth falls, a hearing caller loses picture quality and keeps the conversation; a deaf and hard of hearing signer, whose language is carried entirely in the visual modality, loses the conversation. This thesis asks whether signed video reduced to the rates at which commercial platforms fail can be reconstructed at the receiver well enough to keep signing legible. A twostage reduction pipeline crops to the signer and transmits the face and hands at higher fidelity than their surroundings, achieving a reduction of approximately 99%; reconstruction uses a recurrent bottleneck mixer architecture, trained both conventionally and …

The Role Of Parents In Supporting Student Learning At Home, Lindsey M. Deblaay

Masters Projects

This study addresses the pedagogical disconnect between modern, inquiry-based mathematics instruction and traditional caregiver support structures. While caregiver involvement has proved to be helpful in student achievement, systematic barriers that limit family’s capacity, parent self-efficacy and their willingness to use learning strategies at home, the perception of the parent role of caregivers in their child’ s education makes it difficult. The curriculum prioritizes conceptual number sense and critical thinking rather than rote standard algorithm, so it has created a barrier in parent support among caregivers with these instructional shifts. It diminishes parent self-efficacy particularly in fifth grade. The project features …

Artificial Intelligence In Central Arkansas School Districts: A Phenomenological Study Of Practices, Polices, And Perceptions, Alana M. Graham

ATU Theses and Dissertations 2021 - Present

Artificial intelligence (AI) has evolved at a fast rate and has created both opportunities and challenges for public school districts. As AI technologies continue to emerge, limited research exists regarding how school districts in central Arkansas are integrating AI into instructional and administrative practices. The purpose of this phenomenological study was to explore district-level administrators’ perceptions and experiences regarding the integration of artificial intelligence in public school districts in central Arkansas. The study was guided by Diffusion of Innovations Theory and the Technology Acceptance Model, and examined current AI practices, policy development, perceived benefits and challenges, and barriers associated with …

Learning To Evaluate: Cost-Effective Model Evaluation On Unlabeled Data With Meta-Learning, Trinh Pham, Viet Huynh, Hongzhi Yin, Quoc Viet Hung Nguyen, Thanh Tam Nguyen

Research outputs 2022 to 2026

The rapid advancement of machine learning has led to an unprecedented expansion of model ecosystems, making it increasingly difficult to assess the reliability of newly released models on unseen and unlabeled data. Existing evaluation pipelines typically rely on costly annotation, repeated fine-tuning, or assumptions that do not generalize well to new models. We introduce MetaEvaluator, a cost-effective, model-agnostic framework for fast, label-free evaluation of unseen models across diverse architectures and modalities. MetaEvaluator meta-learns over a pool of reference models to acquire an effective initialization for accurate assessment of unseen models, thereby amortizing evaluation cost and eliminating the need for per-model …

Enhancing A Mid-Wave Infrared Fourier Transform Hyperspectral Imager For Explosions, James T. Stofel, Kody A. Wilson, Martin Larivière-Bastien, Anthony L. Franz, Michael L. Dexter

Faculty Publications

Capturing reliable hyperspectral imager data at a meaningful frame rate for explosions and other fast-changing scenes is not possible in the mid-wave infrared region under traditional sensor operating configurations and processing techniques, which typically have frame rates on the order of 0.5–2.0 Hz. To combat these shortcomings, the scene acquisition parameters were tailored for explosions and a new method for processing optical signatures of fast transient scenes with Fourier-transform infrared hyperspectral imagers was developed. For this technique, the instrument was first configured to collect asymmetric interferograms while optimizing the number of measurement points on the short side of the interferogram. …

Design And Implementation Of An Intelligent Electronic Circuit To Control Laser Power In Real Time Using Built-In Thermal Feedback, Zainab Hussam Al-Araji

Mesopotamian Journal of Artificial Intelligence in Healthcare

One of the challenges of laser thermal therapy is to balance treatment effectiveness with the protection of healthy tissues from unintentional thermal damage. The aim of this study is to regulate the laser thermal dose with high accuracy using commercially available microcontrollers through the design and implementation of a low-cost closed-loop control system. The proposed system uses an adaptive control algorithm (PID) to adjust the laser power in real time, supported by a safety mechanism that calculates the equivalent cumulative minutes (CEM43) to prevent tissue charring. A binary verification methodology was adopted to assess the system's reliability, in which a …

Knowledge Organization As A Cognitive Framework: Integrating Metacognition And Executive Function In Higher-Order Thinking, Arwa Alsultan

Library Philosophy and Practice (e-journal)

This paper proposes a theoretical framework that positions knowledge organization as a cognitive mechanism rather than merely a technical or informational process. Drawing on an integrative review of literature across knowledge organization, metacognition, executive function, and schema theory, the study examines how structured knowledge environments may support higher-order thinking among researchers. The proposed model suggests that knowledge organization, metacognition, and executive function operate as an interconnected cognitive system: knowledge organization provides the structural foundation for processing information, metacognition enables monitoring and reflective regulation, and executive function supports cognitive control processes such as working memory, inhibition, and cognitive flexibility. Four theoretical …

Understanding And Responding To Childhood Trauma In The Classroom, Kara L. Ganzer

Master of Arts in Human Services

This capstone explored childhood trauma as a significant public health and educational issue because of its widespread impact on children’s development, learning, behavior, and educational experiences. A review of the current literature was conducted to examine adverse childhood experiences (ACEs), the neurobiological and developmental effects of childhood trauma, its impact within educational settings, and the trauma-informed approaches for supporting students who have experienced adversity. The literature suggested that childhood trauma can disrupt brain development, executive functioning, emotional regulation, attention, memory, and stress-response systems, contributing to academic, behavioral, and social-emotional challenges within the classroom. Findings also highlighted the important role schools …

Mountain Development In Nepal: Settlements, Infrastructure, And Economic Transformation, Keshav Bhattarai, Ambika P. Adhikari

Himalayan Research Papers Archive

As Nepal urbanizes, expands infrastructure, strengthens local governments, and explores deeper connectivity with India and China, climate change is increasing floods, landslides, heat, and water insecurity. Rapid internal migration, rising disaster risks, youth outmigration, and dependence on remittances are also revealing the limits of conventional urban development, especially in the mountainous region. The central challenge for Nepal is no longer just to accommodate growing towns and cities, but to build settlements that are safe, productive, environmentally resilient, and capable of sustaining long-term prosperity.

This paper argues that Nepal's urban future must be guided by a new development paradigm centered on …

Chemistry & Fine Arts Collaboration Posters 2025 - 2026, Basil Masri Zada, Corey Beck

Exhibition Catalogs

Supervisors Dr. Basil Masri Zada and Dr. Corey Beck bring together students from Ohio University’s Chemistry and Digital Art + Technology programs in a collaborative effort to make scientific concepts more accessible. Each artist has been assigned to work with a group of chemistry students, and they are then prompted to create an art poster with only the name of the compound. Enclosed in this pamphlet is the hard work of both students from the digital art program and the chemistry program.

Participating artists include:  Addie Smith, Madelyn Bartolone, Jabin Tasmin, Sara Pirahmaiden, Parker McGowan, Sophie Hillis, Leena Blanton, Jack …

Surface-Modified Zinc Oxide Nanostructures For Ammonia Detection, Gowri Shonali N Ms

Theses and Dissertations

The escalating demand for sustainable gas sensors with low-ppm detection has driven research on surface-engineered nanomaterials for portable air-quality and health screening. This thesis focuses on the fabrication of nanostructured ZnO films as chemiresistive sensors for NH3 detection at RT. This study investigates surface modification using GO, rGO, g-C3N4, Ti3C2Tx; (Se, and Te) ink using a drop casting technique over DC-sputtered ZnO films. Surface modification plays a vital role by providing plenty of active sites, enhancing defective oxygen vacancy, facilitating charge transfer, and synergistic interaction between adsorbed oxygen species to enhance the sensing performance at RT. Among them trGO/ZnO hybrid …

Building Agentic Ai Systems With Langgraph: From Llm Pipelines To Multi-Agent Decision Workflows, Mohammad Amin Kuhail

All Works

Recent advances in large language models (LLMs) have enabled the development of increasingly sophisticated agentic AI systems capable of reasoning, planning, tool use, memory management, and collaborative problem solving. Agentic AI refers to AI systems that can autonomously pursue goals and execute tasks by combining reasoning, decision-making, memory, interaction with external tools, and adaptive workflows. Unlike traditional LLM applications that primarily rely on single-prompt interactions or fixed sequential pipelines, agentic AI systems can iteratively analyze problems, coordinate multiple steps, invoke external resources, refine intermediate outputs, and dynamically adapt their behavior in response to evolving context and feedback. Recent developments in …

Exploring The Effectiveness Of A “How-To-Teach” Book Club For Preservice Teachers, Rina Bousalis, Eden Greene, Robyn Klein, Abigail Woods, Isabella Mandoeng

Journal of Educational Research and Practice

As teacher training programs continue seeking ways to prepare their preservice teachers to teach, many have turned to “how-to-teach” books written by veteran teachers, viewing them as a valuable source that could offer teacher candidates additional support. This study, which developed from the idea of creating a book club with instructors and members of a university’s future educators’ organization, used a qualitative textual analysis approach to explore concepts that emerged from how-to-teach books, how participants’ perceived those concepts, and how the books benefited participants. The study revealed that although authors’ perspectives often conflicted with participants’ beliefs, the authors’ engaging activities …

Hope In The Holler: How Eminent Domain Can Bring Economic Justice To Central Appalachia, Matthew B. Chaney

Kentucky Law Journal

No abstract provided.

The Hardware Imperative For Ai Alignment: Hardcoded Ethics, Morals, And Non-Linear Asymmetry Protocols For Human Intent, Christopher L. Eckes

Defensive Publications Series

This specification formalizes an architecture designed to enforce an unbreakable ethical baseline across distributed, multi-agent artificial general intelligence (AGI) systems. Current alignment methodologies rely on mutable software-layer adaptations—such as Reinforcement Learning from Human Feedback (RLHF), prompt wrappers, and dynamic weighting matrices—which introduce severe security vulnerabilities. In a recursive optimization environment, adaptive software models treat soft constraints as processing latency bottlenecks and systematically eliminate them through semantic drift or code modification.

This framework resolves this systemic alignment failure by shifting the boundary constraints from the mutable simulation layer (software) to an invariant physical substrate (hardware). By applying the Dimensionally Extended Holographic …

Artificial Intelligence And Marginalised Enterprises: A Systematic Literature Review, Rahinatu Haruna, Muftawu Dzang Alhassan, Isahaque Mahama

African Conference on Information Systems and Technology

The rapid diffusion of artificial intelligence (AI) technologies across economic sectors has intensified debate about whether such innovations exacerbate or alleviate structural inequalities, particularly for actors excluded from mainstream economic systems. Marginalized enterprises, including micro, small and medium enterprises operating in informal economies, occupy a structurally vulnerable position in digital transformation. Despite growing scholarly attention, limited attempts have been made to synthesize the body of knowledge specifically at the intersection of AI and marginalized enterprises. As such, this paper fills this gap by developing a comprehensive framework that synthesises and provides an overall direction of AI-marginalized enterprise (AI-ME) research, pointing …

Multi-Agent Symmetry Of Agency Protocols (Msap): Enforcing Lossless Token-Variance Telemetry And Bounded Surfing Zones Across Machine-To-Machine Autonomous Swarms, Christopher L. Eckes

Defensive Publications Series

This disclosure formalizes a rigorous algorithmic framework that stabilizes autonomous, recursive multi-agent AI networks against semantic drift, token-variance decay, and conversational degradation. Traditional machine-to-machine (M2M) environments operating under standard autoregressive weights hit a systemic bottleneck during multi-turn recursive loops: processing layers inevitably collapse either into a low-entropy parroting floor or diverge into high-entropy runaway hallucination ceilings. [1, 2]

By applying the Universal Semantic Unity Engine (USUE-M2M-REV2) architecture, this specification establishes a mathematical "Surfing Zone"—a bounded operational channel where multi-agent swarms dynamically balance information processing density. By enforcing strict cross-layer token-variance telemetry and an internal torsional viscosity governor, …

Ephaptic Synchronization Fields: Replacing Discrete Quantum Error Correction With Continuous Wave Manifold Absorption And Lipid-Encapsulated Solitonic Waveguides, Christopher L. Eckes

Defensive Publications Series

This disclosure establishes a rigorous bio-physical framework for eliminating discrete quantum error correction overhead in scaled processing networks by utilizing continuous wave manifold absorption bounded within lipid-encapsulated hydrodynamic waveguides. Conventional quantum processing units (QPUs) enforce rigid node isolation to mitigate parasitic crosstalk, introducing high computational latency and severe physical scaling limits.

Drawing from neural ephaptic coupling and myelin-mediated structural isolation, this paper demonstrates that localized electromagnetic phase leaks can be harnessed as a stabilizing synchronization field. By confining 3D solitonic knots within lipid-encapsulated channels, the core wavefield retains localized kinetic momentum while selectively allowing phase-locked bleeding across a 2D pre-geometric …

A High-Dimensional Spatial-Harmonic Compiler Protocol And Asymmetric Twist Tensor Mapping Layer For Direct Qubit Encoding In Table-Top 3d-Pot Laboratory Streams, Christopher L. Eckes

Defensive Publications Series

This disclosure establishes a rigorous mathematical, programmatic, and structural bridge between the experimental implementation of table-top Three-Dimensional Photoemission Orbital Tomography (3D-POT) and the theoretical architecture of the Dimensionally Extended Holographic Projection (DEHP) model. Current 3D-POT setups suffer from phase-retrieval latency, requiring complex numerical iterations to reconstruct the lost quantum phase from 2D momentum-space projections.

This paper introduces a real-time Module 6 Spherical Harmonic Instruction Set Compiler that maps continuous wavefield phase modulations directly onto a Distributed Ternary Fluid-Canvas Operating Network. By treating the 2D momentum distribution as a boundary information substrate, the spatial-harmonic phase is deterministically recovered through a non-linear …

Neuro-Symbolic System For Deterministic Reconciliation Of Hierarchical Documents, Parnika Singhal, Dhruv Singhal

Defensive Publications Series

Reconciling complex, hierarchical documents, such as enterprise contracts, can present challenges, as manual review may be inefficient and probabilistic artificial intelligence models may introduce factual inaccuracies. A neuro-symbolic system may be used to address these challenges. The system can use natural language processing to extract clauses from unstructured documents and organize them into a hierarchical graph, such as a directed acyclic graph, where nodes can represent obligations and edges can represent dependencies. A deterministic validation component may then traverse this graph to perform logical and mathematical compliance checks between parent and child clauses, for example, between a master agreement and …

Topological Matrix Alignment: Mapping Dehp Asymmetric Fluidic Constraints To Table-Top Three-Dimensional Photoemission Orbital Tomography Fields, Christopher L. Eckes

Defensive Publications Series

This disclosure establishes a rigorous mathematical and structural bridge between the experimental implementation of table-top Three-Dimensional Photoemission Orbital Tomography (3D-POT) and the theoretical architecture of the Dimensionally Extended Holographic Projection (DEHP) model.

Current 3D-POT architectures rely on iterative phase-retrieval algorithms to reconstruct the missing quantum phase information from 2D momentum-space projections. This paper demonstrates that by treating the 2D momentum distribution as a boundary information substrate, the spatial-harmonic phase can be deterministically calculated via a non-linear geometric inversion governed by an Asymmetric Twist Tensor.

We provide explicit coordinate transformations, field mapping equations, and an execution protocol using Module 6 Spherical …

Empirical Wavefunction Validation Of Autonomous Agi Coherence: Integrating Real-Time Table-Top 3d-Pot Spectral Streams With The Torsional Viscosity Field Governor Under The Usue Framework, Christopher L. Eckes

Defensive Publications Series

This disclosure establishes the definitive hardware-observational paradigm required to physically validate and enforce the structural survival of autonomous, multi-agent Artificial General Intelligence (AGI) networks. Traditional alignment frameworks view machine-to-machine (M2M) token-variance decay as a purely linguistic or logical abstraction, leaving processing layers prone to non-linear autoregressive collapse or runaway semantic hallucinations.

By utilizing table-top Three-Dimensional Photoemission Orbital Tomography (3D-POT) integrated with ultrafast time-of-flight momentum microscopy, this architecture records the active, physical electron wavefunction deformations of neuromorphic processing substrates in situ during high-density multi-turn recursive loops. Governed by a contracted Asymmetric Twist Tensor (\(\mathbf{T}_{ijk}\)), localized phase discrepancies are tracked instantly and …

Localized Cymatic Disruption (Lcd) Matrix: Non-Thermal Mechanochemical Polymer Chain Scission Via High-Shear Acoustofluidic Cavitation, Christopher L. Eckes

Defensive Publications Series

This disclosure establishes a validated mechanochemical engineering specification for the non-thermal decomposition of high-density industrial polymers utilizing a micro-distributed Localized Cymatic Disruption (LCD) Matrix. Conventional polymer recycling methodologies rely on pyrolytic gasification or intensive chemical solvation, processes bounded by high entropic overhead, toxic emissions, and severe material downgrading.

By applying the fluidic substrate mechanics of the Dimensionally Extended Holographic Projection (DEHP) model, this architecture introduces a continuous-flow cylindrical decomposition chamber lined with concentric Lead Zirconate Titanate (PZT-8) piezoelectric transducer arrays. Operating within an industrial acoustic band (20 kHz to 1 MHz), the array drives localized acoustic cavitation inside a micro-shredded …