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Articles 80071 - 80100 of 1826527
Full-Text Articles in Entire DC Network
Ef21 With Bells & Whistles: Six Algorithmic Extensions Of Modern Error Feedback, Ilyas Fatkhullin, Igor Sokolov, Eduard Gorbunov, Zhize Li, Peter Richtarik
Ef21 With Bells & Whistles: Six Algorithmic Extensions Of Modern Error Feedback, Ilyas Fatkhullin, Igor Sokolov, Eduard Gorbunov, Zhize Li, Peter Richtarik
Research Collection School Of Computing and Information Systems
First proposed by Seide (2014) as a heuristic, error feedback (EF) is a very popular mechanism for enforcing convergence of distributed gradient-based optimization methods enhanced with communication compression strategies based on the application of contractive compression operators. However, existing theory of EF relies on very strong assumptions (e.g., bounded gradients), and provides pessimistic convergence rates (e.g., while the best known rate for EF in the smooth nonconvex regime, and when full gradients are compressed, is O(1/T2/3), the rate of gradient descent in the same regime is O(1/T)). Recently, Richtàrik et al. (2021) proposed a new error feedback mechanism, EF21, based …
Less Is More: On The Importance Of Data Quality For Unit Test Generation, Junwei Zhang, Xing Hu, Shan Gao, Xin Xia, David Lo, Shanping Li
Less Is More: On The Importance Of Data Quality For Unit Test Generation, Junwei Zhang, Xing Hu, Shan Gao, Xin Xia, David Lo, Shanping Li
Research Collection School Of Computing and Information Systems
Unit testing is crucial for software development and maintenance. Effective unit testing ensures and improves software quality, but writing unit tests is time-consuming and labor-intensive. Recent studies have proposed deep learning (DL) techniques or large language models (LLMs) to automate unit test generation. These models are usually trained or fine-tuned on large-scale datasets. Despite growing awareness of the importance of data quality, there has been limited research on the quality of datasets used for test generation. To bridge this gap, we systematically examine the impact of noise on the performance of learning-based test generation models. We first apply the open …
Adapting Large Language Models For Parameter-Efficient Log Anomaly Detection, Ying Fu Lim, Jiawen Zhu, Guansong Pang
Adapting Large Language Models For Parameter-Efficient Log Anomaly Detection, Ying Fu Lim, Jiawen Zhu, Guansong Pang
Research Collection School Of Computing and Information Systems
Log Anomaly Detection (LAD) seeks to identify atypical patterns in log data that are crucial to assessing the security and condition of systems. Although Large Language Models (LLMs) have shown tremendous success in various fields, the use of LLMs in enabling the detection of log anomalies is largely unexplored. This work aims to fill this gap. Due to the prohibitive costs involved in fully fine-tuning LLMs,we explore the use of parameter-efficient fine-tuning techniques (PEFTs) for adapting LLMs to LAD.To have an in-depth exploration of the potential of LLM-driven LAD, we present a comprehensive investigation of leveraging two of the most …
Verify All Traffic: Towards Zero-Trust In-Network Intrusion Detection Against Multipath Routing, Ziming Zhao, Zhaoxuan Li, Xiaofei Xie, Zhipeng Liu, Tingting Li, Jiongchi Yu, Fan Zhang, Binbin Chen
Verify All Traffic: Towards Zero-Trust In-Network Intrusion Detection Against Multipath Routing, Ziming Zhao, Zhaoxuan Li, Xiaofei Xie, Zhipeng Liu, Tingting Li, Jiongchi Yu, Fan Zhang, Binbin Chen
Research Collection School Of Computing and Information Systems
With the popularity of encryption protocols, machine learning (ML)-based traffic analysis technologies have attracted widespread attention. To adapt to modern high-speed bandwidth, recent research is dedicated to advancing zero-trust intrusion detection by offloading feature extraction and model inference into the network dataplane. Especially, with the rise of programmable switches, achieving line-speed ML inference becomes promising. However, existing research only considers a single switch node as a relay to conduct evaluation. This is far from real-world deployments involving multiple switches (given that zero-trust security assumes that threats can originate from anywhere, including within the network), particularly the multipath routing phenomenon that …
The Financial Effects Of Enrolling Students With Disabilities In Catholic High Schools In States That Offer Vouchers Or Scholarships For Students With Disabilities, Susan M. Noonan
Electronic Theses and Dissertations
This study investigated the financial effect of enrolling students with disabilities in Catholic high schools located in states that offer vouchers or scholarships for these students. Furthermore, the research aimed to understand the school’s experience in collaborating with the U.S. Department of Education to meet the criteria for voucher acceptance. It is important to note that enrollment and tuition revenue is the key to a school’s financial stability. Using an exploratory case study approach, information was gathered from a variety of stakeholders including the superintendent, administration, business manager, admissions coordinator, teachers, and counselors. The findings indicated that parents of children …
Weight Recidivism Post-Bariatric Surgery: A Lifestyle Modifications Educational Intervention, Kimeshia N. Johnson
Weight Recidivism Post-Bariatric Surgery: A Lifestyle Modifications Educational Intervention, Kimeshia N. Johnson
Electronic Theses and Dissertations
Weight recidivism after bariatric surgery is a frustrating phenomenon for bariatric surgery patients and healthcare professionals. A 90-day lifestyle modification intervention for patients at least 18 months postsurgery was performed in the primary care setting to determine if a structured program could promote or maintain weight loss. The intervention aimed to investigate if participation in a structured lifestyle modification program would impact the body mass index of bariatric patients at least 18 months postsurgical intervention. In coordination with a nutritionist specializing in addiction and obesity education, a booklet detailing the guidelines for a 12-week program was provided to 41 bariatric …
Exploring New Mexico 4-H Volunteers’ Acceptance And Use Of Technology: A Qualitative Approach, Kayla Dawn Hinrichs
Exploring New Mexico 4-H Volunteers’ Acceptance And Use Of Technology: A Qualitative Approach, Kayla Dawn Hinrichs
Electronic Theses and Dissertations
Integrating technology into youth development programs like 4-H is increasingly vital for enhancing communication, education, and engagement. However, technology adoption among 4-H volunteers remains inconsistent. This qualitative study explored the barriers to technology adoption among New Mexico 4-H volunteers. The researcher aimed to understand the factors influencing their willingness and ability to integrate digital tools into their volunteer roles. Guided by Rogers’s (2003) diffusion of innovation theory and framed by Creswell and Poth’s (2024) qualitative research design, this study employed semistructured interviews with a purposive sample of 4-H volunteers across the state. Following Braun and Clarke’s (2006) six- phase approach, …
Interplanetary Risk Regulation, Jonathan B. Wiener, Charles (Chase) Hamilton
Interplanetary Risk Regulation, Jonathan B. Wiener, Charles (Chase) Hamilton
Chicago Journal of International Law
Space exploration promises new opportunities but also new risks. After centuries of national settlements and international conflicts on Earth, and the Cold War era of two great power states racing to the Moon, today we see a rapidly proliferating arena of actors, both governmental and non-governmental, undertaking bold new ventures off-Earth while posing an array of new risks. These multiple activities, actors, and risks raise the prospects of regulatory gaps, costs, conflicts, and complexities that warrant reconsideration and renovation of legacy legal regimes such as the international space law agreements. New approaches are needed, beyond current national and international law, …
Battlefield Evidence In The Age Of Artificial Intelligence-Enabled Warfare, Winthrop Wells
Battlefield Evidence In The Age Of Artificial Intelligence-Enabled Warfare, Winthrop Wells
Chicago Journal of International Law
A number of emerging technologies increasingly prevalent on contemporary battlefields—notably unmanned autonomous systems (UAS) and various military applications of artificial intelligence (AI)—are working a sea change in the way that wars are fought. These technological developments also carry major implications for the investigation and prosecution of serious crimes committed in armed conflict, including for an under-examined yet potentially valuable form of evidence: information and material collected or obtained by military forces themselves.
Such “battlefield evidence” poses various legal and practical challenges. Yet it can play an important role in justice and accountability processes, in which it addresses the longstanding obstacle …
Revolutions In Justice: Advancing The Rome Statute System To Fight Impunity In Future Wars, Lindsay Freeman
Revolutions In Justice: Advancing The Rome Statute System To Fight Impunity In Future Wars, Lindsay Freeman
Chicago Journal of International Law
The modern system of international criminal justice, which was born out of World War II and built in its current form during the early 1990s, is both revolutionary and a relic. The ideals, innovation, and vision that created the international legal order were ground-breaking at the time but have failed to evolve at a pace that ensures its relevance and efficacy. The challenges we face today are drastically different from those in the period in which the framework was conceived, the institutions were formed, and the laws were drafted. While these changes have been incremental over several decades, technological advances …
Two Terribles: A Day Without Space And Ai Enabled Synthetic Biological Weapons A Warning Order, James E. Baker
Two Terribles: A Day Without Space And Ai Enabled Synthetic Biological Weapons A Warning Order, James E. Baker
Chicago Journal of International Law
A day without space, a term used to describe the loss or destruction of America’s space assets, and the potential generation of novel biological threats using AI and synthetic biology present catastrophic and potentially existential threats to U.S. security in a way that nuclear weapons did before and continue to do so today. Yet they have not received the level of attention from national security lawyers or commentators they warrant. This article describes the threats. It describes the current and inchoate nature of the law to address these threats. And it makes initial recommendations to policymakers and lawyers about how …
Distinction, Proportionality, And Precautions In Attacks At Sea In The New Era Of The Law Of Naval Warfare, James Kraska
Distinction, Proportionality, And Precautions In Attacks At Sea In The New Era Of The Law Of Naval Warfare, James Kraska
Chicago Journal of International Law
China has upset the security balance in East Asia through the development of a long- range strike complex composed of anti-ship ballistic missiles, drones and cruise missiles, and hypersonic missiles that put U.S. naval fleets at risk. Beijing’s innovative approach to sea control through the projection of power from land-based fires highlights three important differences between the law applicable to naval warfare and the law of armed conflict (LOAC) as it is implemented on land.1 These legal distinctions are subtle in law, but they shape concrete choices available to naval commanders and could determine the outcome of war at sea. …
Balancing Breadth And Depth: An Analysis Of General Engineering Programs, Gayle Ermer
Balancing Breadth And Depth: An Analysis Of General Engineering Programs, Gayle Ermer
University Faculty Publications and Creative Works
One of the goals of the Multidisciplinary Engineering Division of ASEE has been to promote engineering programs that are multidisciplinary, interdisciplinary, or otherwise categorized as general engineering. This is based on the conviction that graduating engineers would benefit from more breadth than might be available within traditional disciplinary programs. Non-disciplinary programs are currently accredited by ABET under the Criteria: Engineering, General Engineering, Engineering Physics, and Engineering Science. These programs are not evaluated using discipline-specific program criteria in addition to the general criteria. ASEE has served as the lead society for evaluating these programs since 2006.
This project involves an examination …
Understanding Anti-Racism In Counselor Education: A Narratology Of Anti-Racist Pedagogy In Sociocultural Courses, Danielle G. Rodgers
Understanding Anti-Racism In Counselor Education: A Narratology Of Anti-Racist Pedagogy In Sociocultural Courses, Danielle G. Rodgers
Counseling & Human Services Theses & Dissertations
Counselors have the privilege to join children, adolescents, and adults from all walks of life in a journey of working towards mental and emotional wellness. Our code of ethics outlines “honoring diversity and embracing a multicultural approach in support of the worth, dignity, potential, and uniqueness of people within their social and cultural contexts” (p.3) and promoting social justice as two of our core professional values (American Counseling Association [ACA], 2014). The ACA also stated in their Antiracist Statement in 2020 that “we have a moral and professional obligation to deconstruct institutions which have historically been designed to benefit White …
Belknap County Fair Book 2025, Alison Coleman
Belknap County Fair Book 2025, Alison Coleman
UNH Cooperative Extension
No abstract provided.
Epidemiology Of Hip Dislocations In The United States From 1990 To 2019: A Temporal Study Using The Global Burden Of Disease Database., Ambrose Loc T Ngo, Gabrielle Dykhouse, Taylor J Manes, Phillip C Mckegg, Cameron J Sabet, Brett Barthman, Robert Golden
Epidemiology Of Hip Dislocations In The United States From 1990 To 2019: A Temporal Study Using The Global Burden Of Disease Database., Ambrose Loc T Ngo, Gabrielle Dykhouse, Taylor J Manes, Phillip C Mckegg, Cameron J Sabet, Brett Barthman, Robert Golden
Trauma and Acute Care Articles
Introduction Hip dislocations are devastating injuries that require urgent intervention to minimize the development of severe complications. This study aimed to evaluate the epidemiology of hip dislocations in the United States (U.S.) from 1990 to 2019. Methods This study is a descriptive retrospective epidemiological study. The Global Burden of Disease (GBD) database was used to collect epidemiological data on hip dislocation in the U.S. from 1990 to 2019. Data included years lived with disability (YLDs), prevalence, and incidence rates per 100,000 people. Data were regionally stratified into Northeast, Midwest, South, and West by the U.S. Census definition. Bartlett's test was …
Poa Annua Ecology, Biology, And Integrated Weed Management Practices In Turfgrass, David Ervin
Poa Annua Ecology, Biology, And Integrated Weed Management Practices In Turfgrass, David Ervin
Environmental Science and Management Faculty Publications and Presentations
Poa annua L. is one of the most widespread and troublesome weeds of turfgrass. It persists as both an annual and perennial and is adaptable to almost any static maintenance regime, including adaptation to mowing heights and evolution of herbicide resistance. This management guide is intended to provide stakeholders with a summary of new and existing knowledge on integrated Poa annua management. Here we review the basic biology and ecology, as well as practical integrated weed management (IWM) strategies developed for its control.
Clinical Trial Readiness In Limb Girdle Muscular Dystrophy R1 (Lgmdr1): A Grasp Consortium Study, Stephanie M Hunn, Amanda Clause, Conrad C Weihl, Et Al.
Clinical Trial Readiness In Limb Girdle Muscular Dystrophy R1 (Lgmdr1): A Grasp Consortium Study, Stephanie M Hunn, Amanda Clause, Conrad C Weihl, Et Al.
2020-Current year OA Pubs
OBJECTIVE: Identifying functional measures that are both valid and reliable in the limb girdle muscular dystrophy (LGMD) population is critical for quantifying the level of functional impairment related to disease progression in order to establish clinical trial readiness in the context of anticipated therapeutic trials.
METHODS: Through the Genetic Resolution and Assessments Solving Phenotypes in LGMD (GRASP-LGMD) Consortium, 42 subjects with LGMDR1 were enrolled in a 12-month natural history study across 11 international sites. Each subject completed a battery of clinical outcome assessments (COA), including the North Star Assessment for Limb Girdle-Type Dystrophies (NSAD), 10-m walk/run, and Performance of the …
Radiation Nephropathy Complicated By Tubulointerstitial Nephritis With Predominantly Lymphocyte And Plasma Cell Infiltration, Tatsuaki Kosaka, Koji Takaori, Azusa Izumiya, Daisuke Hirai, Mitsuteru Koizumi, Shinya Yamamoto, Akiko Mii, Akira Shimizu, Kiyonao Nakamura, Norio Araki, Koichi Seta
Radiation Nephropathy Complicated By Tubulointerstitial Nephritis With Predominantly Lymphocyte And Plasma Cell Infiltration, Tatsuaki Kosaka, Koji Takaori, Azusa Izumiya, Daisuke Hirai, Mitsuteru Koizumi, Shinya Yamamoto, Akiko Mii, Akira Shimizu, Kiyonao Nakamura, Norio Araki, Koichi Seta
Faculty, Staff and Students Publications
A 64-year-old Japanese woman presented with gross hematuria and was diagnosed with stage IVB cervical cancer. Renal dysfunction was observed following chemoradiation therapy, and a renal biopsy revealed renal thrombotic microangiopathy (TMA) and tubulointerstitial nephritis (TIN), which are atypical features of radiation nephropathy. Contrast-enhanced computed tomography revealed wedge-shaped areas of high contrast, consistent with areas of high radiation dose in the kidneys, thus leading to the diagnosis of radiation nephropathy. This case underscores the importance of integrating clinical, pathological, and radiological findings for the diagnosis of radiation nephropathy, atypical renal biopsy findings, and a combination of TIN and renal TMA.
Residential Factors Associated With Mental Health In United States Veterans, Air Force Military, And Air Force Employees, Andrew J. Hoisington, Christopher A. Stamper, Molly Penzenik, Meredith Reitter, Elizabeth J. Kovacs, Nazanin H. Bahraini, Lisa A. Brenner
Residential Factors Associated With Mental Health In United States Veterans, Air Force Military, And Air Force Employees, Andrew J. Hoisington, Christopher A. Stamper, Molly Penzenik, Meredith Reitter, Elizabeth J. Kovacs, Nazanin H. Bahraini, Lisa A. Brenner
Faculty Publications
Individuals in Westernized countries spend most of their time indoors. However, exploration of residential building factors that may influence occupants’ mental health is limited in scientific literature. The purpose of this study was to explore investigator's perceived areas of importance in residences to mental health via survey methods. To that end, we administered the Housing, Occupancy, Materials, and Environment (HOME) survey to assess factors that may influence mental health to those working in the United States (US) Air Force (n = 230) or past military members, US Veterans (n = 180). Self-reported mental health surveys were also administered to the …
Equiangularity From Compatible Orthobiangularity, Tyler J. Myers
Equiangularity From Compatible Orthobiangularity, Tyler J. Myers
Theses and Dissertations
An equiangular tight frame (ETF) is an equal norm sequence of vectors in a Hilbert space whose coherence achieves equality in the Welch bound. Such sequences necessarily have minimal coherence and thus are, in some sense, as "spread out" in space as possible. ETFs have a variety of applications, such as compressed sensing and waveform design. The main problem in the study of ETFs is determining the pairs (D, N) for which an ETF with N vectors in a D-dimensional space exists. Real ETFs are moreover equivalent to a special subset of a well-studied class of graphs known as strongly …
Constraining Nuclear Data Uncertainty Requirements For The 19F(A, N)22Na Reaction For Non-Proliferation Applications, Tyler R. M. Smith
Constraining Nuclear Data Uncertainty Requirements For The 19F(A, N)22Na Reaction For Non-Proliferation Applications, Tyler R. M. Smith
Theses and Dissertations
This thesis explores the requirements on nuclear data uncertainties needed for the use of the 19F(α, n)22Na reaction for nuclear non-proliferation applications. An overview of how neutrons are produced from alpha decays in a UF6 medium is discussed. Calculation demonstrate the role nuclear data uncertainties effect the neutron yield and energy spectra as a function of enrichment.
Isotope Production Modeling In Sodium-Cooled Fast Reactors, Aaron W. Burkhardt
Isotope Production Modeling In Sodium-Cooled Fast Reactors, Aaron W. Burkhardt
Theses and Dissertations
The accurate prediction of isotopic compositions in Sodium-Cooled Fast Reactors (SFRs) is essential for nuclear forensic analyses and international nuclear treaty monitoring, particularly with the increased global deployment of Generation-IV reactors. This research developed and validated a detailed computational model tailored specifically to the Prototype Fast Breeder Reactor (PFBR), employing advanced Monte Carlo neutron transport methods, sophisticated burnup modeling, and variance reduction techniques. Validation against empirical data from the Experimental Breeder Reactor-II confirmed the model’s accuracy, producing a comprehensive database of isotopic compositions across 301 assembly locations and 580 isotopes through the reactor’s initial operation and equilibrium cycle. The model …
Contract Quality Feature Extraction Using Llm, Aaron C. Washington
Contract Quality Feature Extraction Using Llm, Aaron C. Washington
Theses and Dissertations
This study explored the potential insights generated from linguistic complexity measurements and large language model (LLM) based assessments on the quality of contract documents. By combining structured True/False prompts with log-probability analysis and ambiguity scoring, the study introduced novel contract-quality assessment methods. Results support a feature-driven approach to contract evaluation, one that offers automated, scalable insights for triaging risk and improving drafting practices. These assessment methods contribute to the growing field of legal natural language processing by offering modular tools for effective contract analysis.
Rotating Scatter Mask System Optimization Study For Determining Optimal Image Recreation, Seth L. Grover
Rotating Scatter Mask System Optimization Study For Determining Optimal Image Recreation, Seth L. Grover
Theses and Dissertations
The Rotating Scatter Mask (RSM) system is a radiation imaging technology currently limited by the mask design and governing identification algorithm parameters. To optimize the RSM design, Dakota—an optimization software—was integrated with a ray tracing code that simulates particle interactions with the RSM detector, and with the Locally Competitive Algorithm (LCA), which reconstructs the source image based on the ray tracing code’s Detector Response Matrix (DRM). Since the original ray tracing code was developed in MATLAB, it was translated into Python to improve compatibility with both Dakota and LCA. The Python version of the ray tracing code was then integrated …
Fused-Silica Microelectromechanical Systems For Relative Gravimetry, Ethan Doerstling
Fused-Silica Microelectromechanical Systems For Relative Gravimetry, Ethan Doerstling
Theses and Dissertations
Gravimeters are devices that measure gravitational acceleration which can be used by the United States Air Force (USAF) in the areas of navigation and remote sensing. Fused-silica microelectromechanical systems (MEMS) devices offer capabilities to make inexpensive relative gravimeters with higher thermal stability than common silicon devices while maintaining good gravitational sensitivity. The fused-silica devices in this research were designed, simulated, fabricated, and tested to observe their performance as gravimeters. The devices exhibit properties of highly sensitive accelerometers but the current designs do not qualify as gravimeters. This study provides information to improve the sensitivity and stability of these fused-silica MEMS …
Dynamics-Award Reward Balancing And Waypoint Navigation Using Deep Reinforcement Learning, Justin D. Merrick
Dynamics-Award Reward Balancing And Waypoint Navigation Using Deep Reinforcement Learning, Justin D. Merrick
Theses and Dissertations
The return of Great Power Competition to United States national security strategy necessitates renewed focus on a modern and more lethal military force. The United States Air Force has identified artificial intelligence and autonomy as key to delivering transformational strategic capabilities. This need, paired with the rapid advancement of machine learning, especially deep reinforcement learning (RL), led to questions concerning the optimality of reinforcement learning policies, the use of vehicle dynamics information in the creation of reinforcement learning rewards, and whether research conducted using environments with simple dynamics can be quickly and successfully scaled to more complex, more accurate dynamics, …
Perceived Adherence-Related Barriers For Youth Living With Hiv In The Southern United States, Kate Weaver, Sarah J. Miller, Sayward Harrison
Perceived Adherence-Related Barriers For Youth Living With Hiv In The Southern United States, Kate Weaver, Sarah J. Miller, Sayward Harrison
Faculty Publications
Objective: Youth are at high risk for HIV, accounting for 19% of new diagnoses in the United States (US) in 2021. Highly effective HIV treatment is available in the form of antiretroviral therapy (ART), which enables individuals with HIV to achieve viral suppression. However, youth living with HIV (YLHIV) have poorer ART adherence and lower rates of viral suppression than adults. This study aimed to explore the perspectives of YLHIV and their HIV care providers on barriers and facilitators to ART adherence for YLHIV in the southern US. Methods: Semi-structured qualitative interviews were conducted with YLHIV (n = 16) …
On The Sensitivity Of Short Design Waves For Semi-Submersible Wind Platforms, S.A. Brown, T. Tosdevin, M. Hann, D.M. Greaves
On The Sensitivity Of Short Design Waves For Semi-Submersible Wind Platforms, S.A. Brown, T. Tosdevin, M. Hann, D.M. Greaves
School of Engineering, Computing and Mathematics
Determining ultimate loads and platform motions is essential for both survivability and cost-effectiveness in the development of floating offshore wind. Current design standards utilise time-consuming methodologies that rely on irregular sea state simulations to determine design loads. Design waves offer the potential to accelerate the design process through the simulation of shorter wave profiles that specifically target extreme responses. However, it is not well understood how reliable design waves are for floating devices. Using a mid-fidelity numerical tool, this paper explores the characteristic loads produced by four design wave methods for a semi-submersible floating wind device over a wide range …
Analytical Modelling Of Chloride Diffusion In Circular Section Concrete Columns With Binding Effects, Zaiwei Li, Long-Yuan Li
Analytical Modelling Of Chloride Diffusion In Circular Section Concrete Columns With Binding Effects, Zaiwei Li, Long-Yuan Li
School of Engineering, Computing and Mathematics
– Reinforced concrete structures in marine environments face significant durability challenges due to chloride-induced corrosion of the steel reinforcement. Understanding and modelling chloride ingress are critical for the prediction of the service life of these structures. This study presents an analytical model for chloride diffusion in circular section concrete columns, addressing a critical gap in existing research by incorporating the effects of chloride binding. The model employs a bilinear chloride binding isotherm to derive an analytical solution in cylindrical coordinates, which captures the nonlinear interaction between free and bound chlorides. Validation is performed by comparing the model's predictions with numerical …