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Articles 301 - 330 of 91357
Full-Text Articles in Entire DC Network
Clark Tailings Consolidated Waste Management Area Site Investigation Quality Assurance Project Plan (Qapp), Woodard & Curran
Clark Tailings Consolidated Waste Management Area Site Investigation Quality Assurance Project Plan (Qapp), Woodard & Curran
Silver Bow Creek/Butte Area Superfund Site
No abstract provided.
Sludge-To-Sod: Sustainability In Action At Bull Creek Water Treatment Plant, Ava Baker
Sludge-To-Sod: Sustainability In Action At Bull Creek Water Treatment Plant, Ava Baker
Goal 6: Clean Water and Sanitation
No abstract provided.
Pseudo-Riesz Bases, Deborpita Biswas
Pseudo-Riesz Bases, Deborpita Biswas
All Dissertations
In this dissertation, we will introduce the concept of pseudo-Riesz bases, extending the influential notion of near-Riesz bases first proposed by J. Holub in the 1990s. Our goal is to develop an analogous theory for pseudo-Riesz bases, obtaining results parallel to those known for near-Riesz bases, with suitable modifications.
We will develop the foundational theory of pseudo-Riesz bases. Unlike classical Riesz bases, these sequences need not be complete or independent; however, they still retain meaningful expansion properties. We will investigate the conditions under which a Bessel sequence can be transformed into a Riesz basis through finite modifications. In particular, we …
An Open-Source Evaluation Framework For Risc-V Co-Design-Based Decimal Arithmetic, Riaz Ul Haque Mian, Michiko Inoue
An Open-Source Evaluation Framework For Risc-V Co-Design-Based Decimal Arithmetic, Riaz Ul Haque Mian, Michiko Inoue
Research outputs 2022 to 2026
Hardware–software co-design is a balanced strategy for computationally intensive algorithms such as decimal computing. It can provide several Pareto points for the development of embedded systems in terms of hardware cost and performance. In this study, we propose an efficient and accurate evaluation framework for decimal computing. The framework was designed and developed for hardware–software co-design decimal arithmetic using the RISC-V ecosystem. New binary and decimal-oriented instructions supported by an accelerator were developed. The framework can perform cycle-accurate analysis for performance and assess hardware overhead for co-design-based decimal arithmetic. Unlike previous studies that focused primarily on implementing and evaluating individual …
Efficient And Universal Watermarking For Llm-Generated Code Detection, Boquan Li, Zirui Fu, Mengdi Zhang, Peixin Zhang, Jun Sun, Xingmei Wang
Efficient And Universal Watermarking For Llm-Generated Code Detection, Boquan Li, Zirui Fu, Mengdi Zhang, Peixin Zhang, Jun Sun, Xingmei Wang
Research Collection School Of Computing and Information Systems
Large language models (LLMs) have significantly enhanced the usability of AI-generated code, providing effective assistance to programmers. This advancement also raises ethical and legal concerns, such as academic dishonesty and the generation of malicious code. For accountability, it is imperative to detect whether a piece of code is AI-generated. Watermarking is broadly considered a promising solution and has been successfully applied to identify LLM-generated text. However, existing efforts on code are far from ideal, suffering from limited universality and excessive time and memory consumption. In this work, we propose a plugand- play watermarking approach for AI-generated code detection, named ACW …
Continuous Query For Top-K Maximal Sum Intervals Over Streaming Data, Zhongshuai Zhang, Xiaochun Yang, Baihua Zheng, Rui Zhu, Haomin Li, Bin Wang
Continuous Query For Top-K Maximal Sum Intervals Over Streaming Data, Zhongshuai Zhang, Xiaochun Yang, Baihua Zheng, Rui Zhu, Haomin Li, Bin Wang
Research Collection School Of Computing and Information Systems
The continuous identification of top-k maximal sum intervals using a sliding window over a data stream is a critical operation for applications in IoT and beyond. A maximal sum interval is a non-overlapping, contiguous subsequence with the maximal sum in a sequence of signed values. Existing algorithms are ill-suited for streaming contexts: they either exhaustively enumerate all intervals even for small k values, or depend on indexes that require frequent and costly restructuring. We propose a novel partition-based strategy. Our core insight is a partitioning scheme that guarantees that any maximal sum interval is fully contained within a single partition, …
Timeradar: A Domain-Rotatable Foundation Model For Time Series Anomaly Detection, Hui He, Hezhe Qiao, Yutong Chen, Kun Yi, Guansong Pang
Timeradar: A Domain-Rotatable Foundation Model For Time Series Anomaly Detection, Hui He, Hezhe Qiao, Yutong Chen, Kun Yi, Guansong Pang
Research Collection School Of Computing and Information Systems
Current time series foundation models (TSFMs) primarily focus on learning prevalent and regular patterns within a predefined time or frequency domain to enable supervised downstream tasks (\eg, forecasting). Consequently, they are often ineffective for inherently unsupervised downstream tasks—such as time series anomaly detection (TSAD), which aims to identify rare, irregular patterns. This limitation arises because such abnormal patterns can closely resemble the regular patterns when presented in the same time/frequency domain. To address this issue, we introduce TimeRadar, an innovative TSFM built in a fractional time–frequency domain to support generalist TSAD across diverse unseen datasets. Our key insight is that …
Task-Aligned Haze Removal With Semantic-Aware Fusion And Contrast Self-Correction, Jinbin Wang, Aiping Yang, Guosong Jiang, Wenlong Yu, Dongwei Ren, Qinghua Hu
Task-Aligned Haze Removal With Semantic-Aware Fusion And Contrast Self-Correction, Jinbin Wang, Aiping Yang, Guosong Jiang, Wenlong Yu, Dongwei Ren, Qinghua Hu
Research Collection School Of Computing and Information Systems
Adverse haze conditions introduce complex degradations that obscure scene details and distort structural cues critical for object detection, posing persistent challenges for vision‐based sensing systems. Although existing haze removal methods have achieved notable improvements in visual clarity, their optimisation objectives are often misaligned with downstream detection requirements, leading to limited detection performance in real‐world scenarios. To address this issue, this work proposes a task‐aligned weakly supervised haze removal framework, termed Dehaze4Detection, which explicitly aligns low‐level restoration with high‐level detection objectives. The framework incorporates a Semantic‐Aware Multi‐Scale Fusion Module (SMFM) that embeds pixel‐level semantic knowledge into the dehazing process, enabling selective …
Hvi-Cidnet+: Beyond Extreme Darkness For Low-Light Image Enhancement, Kangbiao Shi, Xiaowen Ma, Yixu Feng, Tao Hu, Peng Wu, Guansong Pang, Qingsen Yan
Hvi-Cidnet+: Beyond Extreme Darkness For Low-Light Image Enhancement, Kangbiao Shi, Xiaowen Ma, Yixu Feng, Tao Hu, Peng Wu, Guansong Pang, Qingsen Yan
Research Collection School Of Computing and Information Systems
Low-Light Image Enhancement (LLIE) aims to recover visually pleasing content and details from degraded low-light images. However, existing RGB-based methods often suffer from color bias and brightness artifacts due to inherent high color sensitivity. Although the HSV color space can decouple brightness and color, it introduces noticeable red and black noise artifacts. To address these challenges, we adopt the Horizontal/Vertical-Intensity (HVI) color space for LLIE, which is defined by the HV color map and learnable intensity. The former enforces small distances for red coordinates to alleviate red noise artifacts, while the latter adaptively compresses low-light regions to suppress black noise …
Continuous Authentication For Industrial System Access: Evaluating Bluetooth Low Energy Direction Finding And Channel Sounding For Tailgating And Relay Attacks, Mitchell Mennelle
Continuous Authentication For Industrial System Access: Evaluating Bluetooth Low Energy Direction Finding And Channel Sounding For Tailgating And Relay Attacks, Mitchell Mennelle
LSU New Orleans Theses and Dissertations
In physical access control, authentication is often viewed as a one-time event, where, once an authorized user crosses a protected boundary, downstream systems assume the user remains physically present. Tailgating and relay attacks violate this assumption. In this thesis we propose a continuous authentication layer based on two Bluetooth Low Energy spatial signals. Angle of Arrival direction finding follows the trail of a worn credential to determine when an operator exits a work zone. Bluetooth Channel Sounding measures a physical property of the radio path and verifies distance during stationary periods. Limiting Relay Attacks with Event-Driven Distance Verification. A stream …
Insect Abundance And Bat Use Of Fields For Foraging In The Cumberland Plateau, Caroline M. Abramowitz
Insect Abundance And Bat Use Of Fields For Foraging In The Cumberland Plateau, Caroline M. Abramowitz
All Theses
Bat populations and their insect prey are declining, making it urgent to understand how habitat features and management support both groups. Early successional habitat (ESH), grasslands and shrublands with reduced vegetative clutter and abundant flowering resources, may benefit foraging bats and nocturnal insects. This study examined how landscape context, patch characteristics, microhabitat features, and management (mechanical mastication and prescribed burns) affected insects and bats across 29 managed fields in Big South Fork National River and Recreation Area (TN/KY) from 2024–2025. Flight-intercept traps collected 25,297 insects across five orders. Though results were order-specific, vegetative composition and height were the strongest predictors …
When The Best-Fit Model Is Not Best: The Glass Slipper Fallacy And Latent Growth Mixture Modelling, Jonathan L. Chia, Markus Wettstein, Andree Hartanto
When The Best-Fit Model Is Not Best: The Glass Slipper Fallacy And Latent Growth Mixture Modelling, Jonathan L. Chia, Markus Wettstein, Andree Hartanto
Research Collection School of Social Sciences
Despite the use of latent growth mixture modelling (LGMM) to study longitudinal changes, existing practices may inadvertently impede this very investigation. Although subgroup trajectories may theoretically differ in their structure (e.g., some subgroups being linear, some curvilinear), the current convention advocates overreliance on the baseline model to derive subsequent profile trajectories, which may obscure these structural differences. In this article, we provide a brief description of extant LGMM practices, after which we explicate the pitfalls of the current approach. Finally, we provide a principled approach for LGMM research moving forward. Specifically, we recommend specifying a set of theoretically plausible models …
Artificial Intelligence (Ai) In Forensic Psychology: An Umbrella Review Of Potentials And Pitfalls, Ysabel Thereze Ang Guevarra, Nur Eva Alisha Binte Mohamed Hisham, Andree Hartanto
Artificial Intelligence (Ai) In Forensic Psychology: An Umbrella Review Of Potentials And Pitfalls, Ysabel Thereze Ang Guevarra, Nur Eva Alisha Binte Mohamed Hisham, Andree Hartanto
Research Collection School of Social Sciences
Artificial intelligence (AI) is becoming increasingly embedded within forensic psychological practice, shaping how criminal risk, legal responsibility and public safety are assessed. AI tools are now used in recidivism prediction, behavioural analysis, deception detection and investigative support, high-stakes domains where errors can have profound consequences. Despite this rapid adoption, the existing literature remains fragmented, with most reviews confined to narrow subdomains and offering limited integrated synthesis of AI′s broader role in forensic psychology. Thus, this umbrella review addresses this gap by synthesising findings from 43 reviews obtained from five major databases, namely EBSCOhost ERIC, EBSCOhost PsycInfo, PubMed, Scopus and Web …
Long-Term Spatiotemporal Change In Coral Reef Fish Populations And Communities In The Philippines, John Christopher Whalen
Long-Term Spatiotemporal Change In Coral Reef Fish Populations And Communities In The Philippines, John Christopher Whalen
Biological Sciences Theses & Dissertations
The Visayas Region of the Philippines is a global epicenter of marine fish biodiversity. Hypotheses attribute this peak of species richness within the Coral Triangle to processes that occur at geological time scales. However, changes in biodiversity may occur on ecological time scales, allowing for the assessment of the potential impact of anthropogenic activities. Recent declines in genetic, species, and ecosystem diversity have been observed in the tropics, including the Philippines. Within the Philippines the Visayas Region is considered the epicenter of species adversity due to anthropogenic stressors such as habitat degradation, overfishing, and harvesting individuals for the aquarium trade. …
Simulations Of Inverse Compton Scattering With Radiation Reaction, Elizabeth Breen-Lee
Simulations Of Inverse Compton Scattering With Radiation Reaction, Elizabeth Breen-Lee
Physics Theses & Dissertations
Inverse Compton scattering (ICS) is a versatile mechanism for producing bright, tunable, and quasi-monochromatic x-ray and gamma-ray radiation through the interaction of relativistic electrons with intense laser pulses. These sources have applications spanning medicine, archaeological studies, materials science, and fundamental research, motivating continued efforts to improve both their performance and the accuracy of theoretical models used to describe them. As nextgeneration laser and accelerator facilities continue to reach increasingly intense regimes, efficient and accurate simulation techniques have become essential for the design and optimization of ICS sources. This dissertation presents the development of analytical and computational methods for modeling inverse …
Enhancing Stem Education With Modeling, Simulation, And Ai Technologies: From Virtual Laboratories To Intelligent Teaching Assistants, Yiyang Li
Electrical & Computer Engineering Theses & Dissertations
Rapid advancements in modeling and simulation (M&S) and artificial intelligence (AI) present new opportunities to enhance various aspects of STEM education, from virtual laboratories that simulate physical lab environments in software to intelligent teaching assistants that provide on-demand, curriculum-aligned instructional support. Virtual laboratories offer a potential solution to the access and scalability challenges of laboratory courses by allowing students to conduct experiments without physical equipment or geographical constraints. AI-powered teaching assistants, particularly those grounded in course-specific materials, can help mitigate the instructional support gap that arises when students work independently in digital learning environments. This dissertation presents three-phase research into …
Quantitative Surface-Enhanced Raman Spectroscopy For Antiretroviral Drug Monitoring: Novel Quality Index And Distributional Approaches In Aqueous And Plasma Matrices, Marguerite Rose Butler
Quantitative Surface-Enhanced Raman Spectroscopy For Antiretroviral Drug Monitoring: Novel Quality Index And Distributional Approaches In Aqueous And Plasma Matrices, Marguerite Rose Butler
Chemistry & Biochemistry Theses & Dissertations
Surface-enhanced Raman spectroscopy (SERS) offers high sensitivity for molecular detection but is limited for quantitative applications by spatial heterogeneity in signal enhancement on dried colloidal substrates. This Dissertation addresses these limitations through the development and evaluation of novel quantitative methods applied to the antiretroviral drugs tenofovir and emtricitabine.
A quality index (Qi) metric was developed to rank individual SERS spectra within each well based on analyte peak prominence relative to local baseline. SERS spectra were acquired from evaporated silver colloid deposits on aluminum well plates using a custom raster-scanning Raman system. Calibration curves were constructed using the top-ranked spectra (Top-Qi …
Interpretable Sparse Modeling Of Longitudinal Signals Via Critical-Range Rectification And Anytime Rule Compression, Jason Orender
Interpretable Sparse Modeling Of Longitudinal Signals Via Critical-Range Rectification And Anytime Rule Compression, Jason Orender
Computer Science Theses & Dissertations
High-dimensional longitudinal data arise in clinical monitoring, industrial control systems, and other sensor-driven domains where outcomes are often governed by threshold-and-lag behavior. Traditional longitudinal workflows frequently depend on expert guessing to nominate candidate variables, lag windows, and threshold hypotheses, followed by repeated hypothesis testing over a limited set of manually specified relationships. While such approaches can be useful in narrow settings, they are often less robust in high-dimensional regimes because important interactions may be missed, multicollinearity can destabilize inference, and the resulting process can be labor-intensive and difficult to scale. This dissertation develops an end-to-end framework for interpretable sparse longitudinal …
Experimental Investigation Of The Discharge Modes Of Nanosecond Pulsed Plasmas At Atmospheric Pressure, Md Ziaur Rahman
Experimental Investigation Of The Discharge Modes Of Nanosecond Pulsed Plasmas At Atmospheric Pressure, Md Ziaur Rahman
Electrical & Computer Engineering Theses & Dissertations
The generation of repeatable and stable nanosecond pulsed atmospheric pressure plasmas is important to non-thermal plasma applications in various fields including medicine, material processing, food processing, and plasma ignition for combustion. This dissertation investigates the atmospheric pressure plasma initiation and formation under 10 – 200 ns pulsed power for electrode configurations applicable for transient plasma ignition (TPI) for combustion. The impacts of pulsed power parameters, gas condition, and electrode geometry on the discharge initiation and modes (i.e., streamer, transient spark and spark) are systematically evaluated for applying TPI for combustion. We evaluated the discharge modes driven by both longer and …
Physics-Guided Deep Learning For Predictive Modeling Of Spatiotemporal Dynamical Systems, Niharika Deshpande
Physics-Guided Deep Learning For Predictive Modeling Of Spatiotemporal Dynamical Systems, Niharika Deshpande
Engineering Management & Systems Engineering Theses & Dissertations
Many physical and networked systems evolve under continuously changing spatial and temporal conditions. Transportation networks respond to fluctuating demand, atmospheric fields reorganize as storms intensify, and coastal response depends on localized forcing pathways. Modeling such systems requires learning formulations that adapt to evolving structure, operate on irregular geometries, and provide interpretable measures of predictive uncertainty. This dissertation develops a physics-guided spatiotemporal learning framework designed for structured dynamical systems whose governing interactions are neither static nor Euclidean. The central premise is that spatial relationships in these systems are dynamic and geometry-dependent. To represent this behavior, system states are modeled on time-varying …
Computational And Ai Tools For Understanding Telomere-Associated Cancer Mechanisms, Eleni Adam
Computational And Ai Tools For Understanding Telomere-Associated Cancer Mechanisms, Eleni Adam
Computer Science Theses & Dissertations
Telomeres are the protective caps of the human chromosomes and are critical for genome stability. Dysfunctional telomeres caused by their erosion with age and cell proliferation as well as by defects in their maintenance is a major early event leading to genome changes and cancer. Subtelomeres possess the critical role of regulating adjacent telomeres. Due to their complex repeat structure and high variance from one person to another, these areas have not been analyzed in detail. We present a set of computational and machine learning tools to aid in the understanding of subtelomere structure and its rearrangements in cancer.
Initially, …
Tagged J/Ψ Photoproduction Near Threshold, Mariana Tenorio Pita
Tagged J/Ψ Photoproduction Near Threshold, Mariana Tenorio Pita
Physics Theses & Dissertations
J/ψ production (heavy quarkonium in general) is sensitive to the gluonic content of the nucleon. Recent theoretical studies have suggested that near-threshold J/ψ production is sensitive to the gravitational form factors (GFFs) of the nucleon, which parametrize the matrix elements of the QCD energy-momentum tensor (EMT). The energy-momentum tensor of the nucleon encodes its mechanical properties through the gravitational form factors, which give access to quantities such as the mass radius and pressure distribution of the proton. Previous J/ψ electroproduction measurements were either performed near-threshold at very low Q2 (in the quasi-real photoproduction regime) or far above threshold at …
Multi-Particle Reactions In Lattice Field Theories: From Euclidean To Quantum Computations, Marco Antonio Carrillo Bernal
Multi-Particle Reactions In Lattice Field Theories: From Euclidean To Quantum Computations, Marco Antonio Carrillo Bernal
Physics Theses & Dissertations
Amplitudes of multi-particle processes provide a probe of the dynamics described by relativistic quantum field theories. In the context of quantum chromodynamics, these amplitudes encode the way in which quarks and gluons are bound together by the strong nuclear force to form hadrons and govern their interactions. The non-perturbative nature of the strong interactions complicates the study of hadronic amplitudes from first principles. The most effective way of studying hadronic reactions non-perturbatively is the numerical framework known as lattice quantum chromodynamics. This method relies on theoretical formalisms that establish relations between numerical observables, such as finite-volume energy levels and matrix …
Macroscopic Classical And Quantum Models Of Inverse Compton Scattering, Emerson Penn Rogers
Macroscopic Classical And Quantum Models Of Inverse Compton Scattering, Emerson Penn Rogers
Physics Theses & Dissertations
Inverse Compton sources — in which a relativistic electron beam scatters a laser pulse to produce tunable, collimated, high-energy radiation—have emerged as among the most promising compact radiation sources, with applications ranging from nuclear photonics to medical and nanoscale imaging and metrology. The most viable current tabletop configuration couples laser-wakefield acceleration with inverse Compton scattering, producing GeV-scale electron beams over millimeter distances. As laser intensities increase and electron energies grow, the interaction enters the radiation reaction regime, where the energy radiated by the electron becomes a significant fraction of its kinetic energy. Predicting the scattered electron energy spectrum — the …
Efficient Test-Time Retrieval Augmented Generation, Hailong Yin, Bin Zhu, Jingjing Chen, Chong-Wah Ngo
Efficient Test-Time Retrieval Augmented Generation, Hailong Yin, Bin Zhu, Jingjing Chen, Chong-Wah Ngo
Research Collection School Of Computing and Information Systems
Although Large Language Models (LLMs) demonstrate significant capabilities, their reliance on parametric knowledge often leads to inaccuracies. Retrieval Augmented Generation (RAG) mitigates this by incorporating external knowledge, but these methods may introduce irrelevant retrieved documents, leading to inaccurate responses. While the integration methods filter out incorrect answers from multiple responses, but lack external knowledge like RAG methods, and their high costs require balancing overhead with performance gains. To address these issues, we propose an Efficient Test-Time Retrieval-Augmented Generation Framework named ET2RAG to improve the performance of LLMs while maintaining efficiency. Specifically, ET2RAG is a training-free method, that first retrieves the …
Paleolimnology And Diatom Taxonomy From Lake Tanganyika, Sristika Adhikari
Paleolimnology And Diatom Taxonomy From Lake Tanganyika, Sristika Adhikari
All-Inclusive List of Electronic Theses and Dissertations
Lake Tanganyika is one of the world's largest freshwater ecosystems, supporting rich aquatic biodiversity and providing several ecosystem services to surrounding communities. Environmental changes such as rising lake surface temperatures, pollution, and land-use alterations threaten the lake’s sustainability. This research examines spatial and temporal variations in nutrient dynamics and primary productivity of Lake Tanganyika using diatom assemblages from multiple locations. Our findings indicate reduced nutrient levels and longer stratification periods in the lake’s central basin during most of the Common Era, as indicated by a remarkable increase in the relative abundance of long, needle-shaped planktonic Nitzschia species. In the southern …
Lessons From The Club Homeschool Capstone: Testing, Data Discipline, And The Computer Science Curriculum, Shane Brown
Lessons From The Club Homeschool Capstone: Testing, Data Discipline, And The Computer Science Curriculum, Shane Brown
University Honors Theses
This thesis looks at the CLUB Homeschool Capstone project to argue that Portland State University's Computer Science curriculum should introduce testing and data quality discipline earlier and more intentionally than it does now. As team lead of a seven-person team, I coordinated sprint planning, communicated with the sponsor, and developed custom Discourse plugins that enhanced an existing forum platform instead of creating a separate application database, as requested by the sponsor. The project's requirements document called for a formal testing plan, but our team lacked the practical experience to implement one. This gap became evident through my internships as a …
Reconstructing Stand-Age Structure In A Wet Miombo Woodland Using Dendrochronology, Zambia, Clara Tiyembekeze Zulu
Reconstructing Stand-Age Structure In A Wet Miombo Woodland Using Dendrochronology, Zambia, Clara Tiyembekeze Zulu
All-Inclusive List of Electronic Theses and Dissertations
Dendrochronological research in tropical Africa has remained limited, leaving critical gaps in stand-age structure and climate-growth relationships in seasonally dry tropical woodlands. This study reconstructed stand-age structure and assessed climate sensitivity in the wet Miombo woodland of African Explosives Limited (AEL) forest, Copperbelt Province, Zambia. Field sampling was conducted during four African Dendrochronology Fieldschools (2021-2024) using a Modified Variable Area Transect (MVAT) design across nine plots. The series intercorrelation was 0.351; the average mean sensitivity was 0.423. The oldest tree was 170 years old, and more than 70% of the sampled species showed potential for dendrochronology. Markhamia obtusifolia was the …
Opening The Lantern: The Leiden Declaration, Mark Huber
Opening The Lantern: The Leiden Declaration, Mark Huber
Journal of Humanistic Mathematics
The Leiden Declaration on Artificial Intelligence and Mathematics provides insight into how mathematicians view their discipline. However, when positioning mathematics against AI, the declaration falls short in recognizing recent advances. This column introduces the reader who might be unfamiliar with these new methods through the formal language Lean and discusses how these new abilities might change the way journals operate.
Riding The Rails Of Reason: A Dialogue On Truth, Logic, And Proof, Surinder Pal Singh Kainth
Riding The Rails Of Reason: A Dialogue On Truth, Logic, And Proof, Surinder Pal Singh Kainth
Journal of Humanistic Mathematics
On a quiet train ride, I found myself in conversation with Noor, an inquisitive teenager with sharp questions about truth, logic, and mathematical proof. As we talked, I used the train itself as a metaphor to explain how mathematical proofs provide certainty, far beyond what repetitive verification alone can offer. Our discussion ranged from common misconceptions about the foundations of logic to the need for clear definitions and axioms. We also touched on fundamental ideas such as the challenges posed by the Axiom of Choice and the limitations revealed by Gödel’s incompleteness theorem.