Physical Sciences and Mathematics Commons^™

Certified Continual Learning For Neural Network Regression, Hong Long Pham, Jun Sun

Research Collection School Of Computing and Information Systems

On the one hand, there has been considerable progress on neural network verification in recent years, which makes certifying neural networks a possibility. On the other hand, neural network in practice are often re-trained over time to cope with new data distribution or for solving different tasks (a.k.a. continual learning). Once re-trained, the verified correctness of the neural network is likely broken, particularly in the presence of the phenomenon known as catastrophic forgetting. In this work, we propose an approach called certified continual learning which improves existing continual learning methods by preserving, as long as possible, the established correctness properties …

Toi–757 B: An Eccentric Transiting Mini–Neptune On A 17.5–D Orbit, A Alqasim, N Grieves, N M. Rosário, D Gandolfi, J H. Livingston, S Sousa, K A. Collins, J K. Teske, M Fridlund, Ryan J. Oelkers

Physics and Astronomy Faculty Publications and Presentations

We report the spectroscopic confirmation and fundamental properties of TOI 757 b, a mini Neptune on a 17.5 d orbit transiting a bright star (⁠ mag) discovered by the TESS mission. We acquired high precision radial velocity measurements with the HARPS, ESPRESSO, and PFS spectrographs to confirm the planet detection and determine its mass. We also acquired space borne transit photometry with the CHEOPS space telescope to place stronger constraints on the planet radius, supported with ground based LCOGT photometry. WASP and KELT photometry were used to help constrain the stellar rotation period. We also determined the fundamental parameters of …

Reimagining Education With Ai, Margherita Pagani, Steven Miller, Jerry Wind

Research Collection School Of Computing and Information Systems

This chapter examines AI’s transformative potential in education, focusing on Generative AI (GenAI) and Large Language Models (LLMs) while at the same time emphasizing the importance of grounding and guiding AI efforts with learning science and education research findings. It synthesizes analyses and expert recommendations, highlighting opportunities like personalized learning and enhanced teacher productivity, alongside challenges such as over-reliance on AI. Practical steps for instructors include adopting a question-first approach, utilizing AI for personalized feedback, designing AI-enhanced learning experiences, fostering critical thinking, and ensuring ethical AI use. The chapter concludes with strategic recommendations for leveraging AI to sustainably improve educational …

Granular3d: Delving Into Multi-Granularity 3d Scene Graph Prediction, Kaixiang Huang, Jingru Yang, Jin Wang, Shengfeng He, Zhan Wang, Haiyan He, Qifeng Zhang, Guodong Lu

Research Collection School Of Computing and Information Systems

This paper addresses the significant challenges in 3D Semantic Scene Graph (3DSSG) prediction, essential for understanding complex 3D environments. Traditional approaches, primarily using PointNet and Graph Convolutional Networks, struggle with effectively extracting multi-grained features from intricate 3D scenes, largely due to a focus on global scene processing and single-scale feature extraction. To overcome these limitations, we introduce Granular3D, a novel approach that shifts the focus towards multi-granularity analysis by predicting relation triplets from specific sub-scenes. One key is the Adaptive Instance Enveloping Method (AIEM), which establishes an approximate envelope structure around irregular instances, providing shape-adaptive local point cloud sampling, thereby …

2024 Draft Blacktail Creek Remediation And Contaminated Groundwater Hydraulic Control Site Pre-Design Investigation Work Plan, Stantec Consulting Services, Inc.

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.

Appendix D Comparison Of Historical Coc Results To Groundwater Remedial Goals, Stantec Consulting Services, Inc.

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.

Satirical Deepfakes, Surreal Dreamscapes & Nostalgic Pixels: The Rapid Evolution And Cultural Commentary Of Ai-Aesthetics, Andrew Smith, James Hutson

Faculty Scholarship

The rapid evolution of visual aesthetics driven by AI, shared globally through the internet and social media, has dramatically accelerated what once took centuries to develop. This article explores the unique visual tropes emerging from AI-generated content, characterized by surreal, uncanny, and often unsettling imagery. Examples range from the Dor Brothers' stylized narrative videos to horrifying depictions of transformations, such as people morphing into motorcycles. The article contextualizes this aesthetic within historical developments in creative experimentation, drawing parallels with David Bowie's unconventional approach to sound creation in the 1970s. It also considers how AI-driven art, free from copyright constraints in …

Twisted Spatiotemporal Optical Vortex Beams In Dispersive Media, Milo W. Hyde Iv

Faculty Publications

We derive a closed-form expression for the mutual coherence function (MCF) of a twisted spatiotemporal optical vortex (STOV) beam after propagating a distance in a linear dispersive medium. A twisted STOV beam is a partially coherent optical field that possesses a coherent STOV and a stochastic twist coupling its space and time dimensions. These beams belong to a special class of space–time-coupled light fields that carry transverse (to the direction of propagation) orbital angular momentum, making them potentially useful in numerous applications including quantum optics, optical manipulation, and optical communications. After presenting the derivation, we validate our new general MCF …

Generalized Periodicity And Applications To Logistic Growth, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

Classically, a continuous function f:R→R is periodic if there exists an ω>0 such that f(t+ω)=f(t) for all t∈R. The extension of this precise definition to functions f:Z→R is straightforward. However, in the so-called quantum case, where f:qN0→R (q>1), or more general isolated time scales, a different definition of periodicity is needed. A recently introduced definition of periodicity for such general isolated time scales, including the quantum calculus, not only addressed this gap but also inspired this work. We now return to the continuous case and present the concept of ν-periodicity that connects these different formulations of periodicity for …

The Cubic-Quintic Nonlinear Schrödinger Equation With Inverse-Square Potential, Alex H. Ardila, Jason Murphy

Mathematics and Statistics Faculty Research & Creative Works

We consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of [11] in the setting of the standard cubic-quintic NLS.

Introduction To The Virtual Special Issue: Mathematics That Underpins Social Issues, Eva Thanheiser, Ami Mamolo

Mathematics and Statistics Faculty Publications and Presentations

This Virtual Special Issue on Mathematics in Society: Exploring the Mathematics that Underpins Social Issues features 13 articles which expand our understanding of how people build, retain, communicate, apply, and comprehend mathematical ideas as they relate to social and societal issues. The focus is on education research that explores the ways in which mathematics and a mathematical worldview can influence choices, on educational, personal and societal levels. We take a broad view and raise questions about what it means to be mathematical in society, and we consider the multifaceted ways in which abilities to derive and interpret information presented mathematically …

Unraveling The Dynamics Of Stable And Curious Audiences In Web Systems, Rodrigo Alves, Antoine Ledent, Renato Assunção, Pedro Vaz-De-Melo, Marius Kloft

Research Collection School Of Computing and Information Systems

We propose the Burst-Induced Poisson Process (BPoP), a model designed to analyze time series data such as feeds or search queries. BPoP can distinguish between the slowly-varying regular activity of a stable audience and the bursty activity of a curious audience, often seen in viral threads. Our model consists of two hidden, interacting processes: a self-feeding process (SFP) that generates bursty behavior related to viral threads, and a non-homogeneous Poisson process (NHPP) with step function intensity that is influenced by the bursts from the SFP. The NHPP models the normal background behavior, driven solely by the overall popularity of the …

Bridging Disciplines With Ai-Powered Coding: Empowering Non-Stem Students To Build Advanced Apis In The Humanities, Daniel Plate, James Hutson

Faculty Scholarship

The integration of AI-powered coding assistants, such as Cursor AI, GitHub Copilot, and Replit’s Ghostwriter AI, represents a transformative shift in programming education, particularly for non-STEM students. These tools democratize coding by enabling natural language code generation, intelligent error correction, and context-aware assistance within familiar coding environments. This article explores how these technologies empower educators across disciplines to introduce basic and advanced coding concepts to humanities students, a demographic traditionally underserved in programming education. By leveraging AI, instructors can teach non-STEM students the foundational principles of coding and guide them through the development of sophisticated projects, such as building APIs …

Exact Solutions Of Stochastic Burgers–Korteweg De Vries Type Equation With Variable Coefficients, Kolade Adjibi, Allan Martinez, Miguel Mascorro, Carlos Montes, Tamer Oraby, Rita Sandoval, Erwin Suazo

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We will present exact solutions for three variations of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equation featuring variable coefficients. In each variant, white noise exhibits spatial uniformity, and the three categories include additive, multiplicative, and advection noise. Across all cases, the coefficients are time-dependent functions. Our discovery indicates that solving certain deterministic counterparts of KdV–Burgers equations and composing the solution with a solution of stochastic differential equations leads to the exact solution of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equations.

Solving Fractional Differential Equations On A Quantum Computer: A Variational Approach, Fong Yew Leong, Dax Enshan Koh, Jian Feng Kong, Siong Thye Goh, Jun Yong Khoo, Wei Bin Ewe, Hongying Li, Jayne Thompson, Dario Poletti

Research Collection School Of Computing and Information Systems

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap history states. The proposed algorithm is not only efficient in terms of time complexity but also has lower memory costs compared to classical methods. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation costs scale economically with the number of time steps. As a proof of concept, we apply our algorithm to solve a range of fractional partial differential equations commonly encountered in engineering …

Ai Satire And Digital Dystopia: The Dor Brothers Crafting Imperfection And Political Commentary In Contemporary Video Art, James Hutson, Andrew Smith

Faculty Scholarship

The Dor Brothers' AI-generated video content exemplifies an inflection point in digital creativity, where technological limitations are repurposed as aesthetic tools. Drawing on recent interviews with Yonatan Dor, this article explores the innovative techniques of the brothers, such as masking visual imperfections with retro filters and embracing the unpredictability of AI outputs. Through generating numerous clips and meticulously editing selections, they create a unique aesthetic that juxtaposes surrealism with a gritty realism, often reminiscent of early CCTV or VHS footage. Their work not only transcends the typical "morphing face" trope of AI videos but also engages in satire, using deepfake-like …

Technoculture And Language Models In Archaeology: Reconstructing And Preserving Cultural Narratives Through Digital Humanities, James Hutson

Faculty Scholarship

Technoculture, which examines the intersection of culture and technology, has increasingly permeated archaeological practice, transforming both scholarly research and public engagement [1-3]. The introduction of digital tools such as virtual reality (VR), geographic information systems (GIS), and large language models (LLMs) has democratized access to archaeological knowledge, enabling communities to engage more actively with their cultural heritage [4-6]. This short article explores the mutual influence of technocultural studies and AI technologies on archaeology, with a focus on the preservation and reconstruction of cultural narratives through digital means.

The first aspect of this intersection lies in how technocultural tools are creating …

Enhancing History Education With Google Notebooklm: Case Study Of Mary Easton Sibley’S Diary For Multimedia Content And Podcast Creation, Paul Huffman, James Hutson

Faculty Scholarship

This article explores new features of Google’s NotebookLM, an AI-powered tool designed for advanced document analysis and educational content generation. Tested on the 92-page transcribed diary of Mary Easton Sibley, the founder of Lindenwood University, NotebookLM effectively generated FAQs, a study guide, a table of contents, a briefing document, and an audio overview in podcast format. By transforming static historical documents into dynamic learning materials, the document-based AI model provides a user-friendly interface for educators and students, especially those without experience in audio editing or podcasting. While successful in creating study guides and audio formats, the tool faced challenges in …

Efficient Neural Collaborative Search For Pickup And Delivery Problems, Detian Kong, Yining Ma, Zhiguang Cao, Tianshu Yu, Jianhua Xiao

Research Collection School Of Computing and Information Systems

In this paper, we introduce Neural Collaborative Search (NCS), a novel learning-based framework for efficiently solving pickup and delivery problems (PDPs). NCS pioneers the collaboration between the latest prevalent neural construction and neural improvement models, establishing a collaborative framework where an improvement model iteratively refines solutions initiated by a construction model. Our NCS collaboratively trains the two models via reinforcement learning with an effective shared-critic mechanism. In addition, the construction model enhances the improvement model with high-quality initial solutions via curriculum learning, while the improvement model accelerates the convergence of the construction model through imitation learning. Besides the new framework …

Certified Quantization Strategy Synthesis For Neural Networks, Yedi Zhang, Guangke Chen, Jun Sun, Jun Sun

Research Collection School Of Computing and Information Systems

Quantization plays an important role in deploying neural networks on embedded, real-time systems with limited computing and storage resources (e.g., edge devices). It significantly reduces the model storage cost and improves inference efficiency by using fewer bits to represent the parameters. However, it was recently shown that critical properties may be broken after quantization, such as robustness and backdoor-freeness. In this work, we introduce the first method for synthesizing quantization strategies that verifiably maintain desired properties after quantization, leveraging a key insight that quantization leads to a data distribution shift in each layer. We propose to compute the preimage for …

Investigation Of The Distribution Of Transuranic Radionuclides In Marine Sediment At The Montebello Islands, Western Australia, Madison Williams-Hoffman, Megan Cook, Jack K. Clegg, Ross Kleinschmidt, Pere Masqué, Mathew P. Johansen

Research outputs 2022 to 2026

Three nuclear weapons tests were conducted in the 1950s at the Montebello Islands, Western Australia. The detonations were of different yields and configurations (two tower tests, one ship test), and led to substantial radionuclide contamination within the surrounding terrestrial and marine ecosystems. The region possesses great ecological and recreational significance, particularly within the marine environment. However, studies conducted so far have largely neglected the marine ecosystem which makes up the majority of the Montebello Island Marine Park and in which most test fallout would have deposited. Here we investigated the distribution of the transuranic radionuclides 238Pu, 239,240Pu and 241Am in …

Solving Water Scarcity Challenges In Arid Regions: A Novel Approach Employing Human-Based Meta-Heuristics And Machine Learning Algorithm For Groundwater Potential Mapping, Seyed Vahid Razavi-Termeh, Abolghasem Sadeghi-Niaraki, Farbod Farhangi, Mehdi Khiadani, Saied Pirasteh, Soo Mi Choi

Research outputs 2022 to 2026

Addressing water scarcity challenges in arid regions is a pressing concern and demands innovative solutions for accurate groundwater potential mapping (GPM). This study presents a comprehensive evaluation of advanced modeling techniques to enhance the precision of GPM. This study, conducted in the Zayandeh Rood watershed, Iran, employed a spatial database comprising 16 influential factors on groundwater potential and data from 175 wells. This study introduced an innovative approach to GPM by enhancing the Random Forest (RF) algorithm. This enhancement involved integrating three metaheuristic algorithms inspired by human behavior: ICA (Imperialist Competitive Algorithm), TLBO (Teaching-Learning-Based Optimization), and SBO (Student Psychology Based …

Putting Gpt-4o To The Sword: A Comprehensive Evaluation Of Language, Vision, Speech, And Multimodal Proficiency, Sakib Shahriar, Brady D. Lund, Nishith Reddy Mannuru, Muhammad Arbab Arshad, Kadhim Hayawi, Ravi Varma Kumar Bevara, Aashrith Mannuru, Laiba Batool

All Works

As large language models (LLMs) continue to advance, evaluating their comprehensive capabilities becomes significant for their application in various fields. This research study comprehensively evaluates the language, vision, speech, and multimodal capabilities of GPT-4o. The study employs standardized exam questions, reasoning tasks, and translation assessments to assess the model’s language capability. Additionally, GPT-4o’s vision and speech capabilities are tested through image classification and object-recognition tasks, as well as accent classification. The multimodal evaluation assesses the model’s performance in integrating visual and linguistic data. Our findings reveal that GPT-4o demonstrates high accuracy and efficiency across multiple domains in language and reasoning …

Attention-Based Load Forecasting With Bidirectional Finetuning, Firuz Kamalov, Inga Zicmane, Murodbek Safaraliev, Linda Smail, Mihail Senyuk, Pavel Matrenin

All Works

Accurate load forecasting is essential for the efficient and reliable operation of power systems. Traditional models primarily utilize unidirectional data reading, capturing dependencies from past to future. This paper proposes a novel approach that enhances load forecasting accuracy by fine tuning an attention-based model with a bidirectional reading of time-series data. By incorporating both forward and backward temporal dependencies, the model gains a more comprehensive understanding of consumption patterns, leading to improved performance. We present a mathematical framework supporting this approach, demonstrating its potential to reduce forecasting errors and improve robustness. Experimental results on real-world load datasets indicate that our …

A New Fractional Derivative Extending Classical Concepts: Theory And Applications, Mutaz Mohammad, Mohamed Saadaoui

All Works

In this paper, a novel general definition for the fractional derivative and fractional integral based on an undefined kernel function is introduced. For 0<α≤1, this definition aligns with classical interpretations and is applicable for calculating the derivative in an open negative interval I⊆[a,+∞),a∈R. Additionally, when α=1, the definition coincides with the classical derivative. Fundamental properties of the fractional integral and derivative, including the product rule, quotient rule, chain rule, Rolle's theorem, and the mean value theorem, are derived. These properties are illustrated through various applications to demonstrate their applicability. Furthermore, some applications of solving fractional nonlinear systems of integro-differential equations using framelets are presented.

Oer Textbook Review For Calculus - Openstax Calculus, Jing Hu Ph.D.

Open Educational Resources Publications

This OER textbook review provides a comprehensive evaluation of the "Calculus" textbook series published by OpenStax. The reviewer, Jing Hu, an adjunct lecturer at Bentley University, highlights the textbook's strengths, including its thorough coverage of essential calculus topics, accurate and well-established mathematical principles, practical relevance, and user-friendly design. The open-access nature of the resource is seen as a significant advantage, contributing to its long-term utility and accessibility for both students and educators. Overall, the review concludes that the OpenStax Calculus textbook is a high-quality, comprehensive, and freely available resource that effectively supports the learning and teaching of calculus.

Health Benefits And Adverse Effects Of Kratom: A Social Media Text-Mining Approach, Abdullah Wahbeh, Mohammad A. Al-Ramahi, Omar El-Gayar, Tareq Nasralah, Ahmed El Noshokaty

All Faculty Scholarship

Background: Kratom is a substance that alters one’s mental state and is used for pain relief, mood enhancement, and opioid withdrawal, despite potential health risks. In this study, we aim to analyze the social media discourse about kratom to provide more insights about kratom’s benefits and adverse effects. Also, we aim to demonstrate how algorithmic machine learning approaches, qualitative methods, and data visualization techniques can complement each other to discern diverse reactions to kratom’s effects, thereby complementing traditional quantitative and qualitative methods. Methods: Social media data were analyzed using the latent Dirichlet allocation (LDA) algorithm, PyLDAVis, and t-distributed stochastic neighbor …

Comment Letter For The Butte Priority Soils Operable Unit (Bpsou) Residential Metals Abatement Program (Rmap) Yard Submittals Round 2 (Dated July 25, 2024), Brandon Warner

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.

Re: Conditional Approval Letter For The Butte Priority Soils Operable Unit (Bpsou) Silver Bow Creek Conservation Area Repository Data Gap Quality Assurance Project Plan Request For Change To Install Additional Test Pits And Perform Material Characterization (Dated August 28, 2024), Emma Rott

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.

Graph And Group Theoretic Properties Of The Soma Cube And Somap, Kyle Asbury, Ben Glancy

Mathematical Sciences Technical Reports (MSTR)

The SOMA Cube is a puzzle toy in which seven irregularly shaped blocks must be fit together to build a cube. There are 240 distinct solutions to the SOMA Cube. One rainy afternoon, Conway and Guy created a graph of all the solutions by manually building each solution. They called their graph the SOMAP. We studied how the geometric structure of the SOMA Cube pieces informs the graph theoretic properties of the SOMAP, such as subgraphs that can or cannot appear and vertex centrality. We have also used permutation group theory to decipher notation used by Knuth in previous work …