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Valid Confidence Intervals For Μ,Σ When There Is Only One Observation Available, Anirban Dasgupta, Stephen Portnoy May 2024

Valid Confidence Intervals For Μ,Σ When There Is Only One Observation Available, Anirban Dasgupta, Stephen Portnoy

Mathematics and Statistics Faculty Publications and Presentations

Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation X ∼ N(µ, σ2). Here we extend this result to obtaining 1-sample confidence intervals for σ and to cases of symmetric unimodal distributions and of distributions with compact support. Finally, we extend the multivariate result in Portnoy (2019) to allow a sample of size m from a multivariate normal distribution where m may be less than the dimension.


The Lewis Acidity Of Imidazole-Derived Diaryliodonium Zwitterions, Cyrus Rose May 2024

The Lewis Acidity Of Imidazole-Derived Diaryliodonium Zwitterions, Cyrus Rose

University Honors Theses

Diaryliodonium salts can be used as effective aryl-transfer agents in reactions to form novel molecules with diverse applications including pharmaceuticals and agrochemicals without using harsh reaction conditions and transition metal reagents. In recent years, interest in the applications of the Lewis acidity of iodonium ion catalysts has increased. Despite this, the quantification of the Lewis acidities of diaryliodonium salts are scarce. Even rarer, there has not been much study into the Lewis acidities of zwitterionic diaryliodonium salts. For zwitterions, there is no counter anion that would come into consideration in regard to its Lewis acidity. To expand the understanding of …


Multi-Scale Variability Of Heavy Metals In A Snowpack In The Triple Divide Region Of The Western United States, Kelsey Hefner May 2024

Multi-Scale Variability Of Heavy Metals In A Snowpack In The Triple Divide Region Of The Western United States, Kelsey Hefner

University Honors Theses

Natural and anthropogenically sourced particulates are deposited from the atmosphere to landscapes via dry and wet deposition, making frozen winter snowpack a natural archive of atmospheric elemental composition. In the Western United States, wildfires are increasing in extent, duration, and severity. Severe fires remove forest canopy, impacting how atmospheric elements are dispersed and stored across snow-dominated watersheds. We evaluated concentrations of twelve elements in 397 winter snow core samples from a chronosequence of eight forests that burned with mixed severity from 2000 to 2018 in the Triple Divide region of Western Wyoming, the headwaters of the Columbia, Colorado, and Missouri …


Rheological Properties And 3d Printing Behavior Of Pcl And Dmso2 Composites For Bio-Scaffold, Jae-Won Jang, Kyung-Eun Min, Cheolhee Kim, Chien Wern, Sung Yi May 2024

Rheological Properties And 3d Printing Behavior Of Pcl And Dmso2 Composites For Bio-Scaffold, Jae-Won Jang, Kyung-Eun Min, Cheolhee Kim, Chien Wern, Sung Yi

Mechanical and Materials Engineering Faculty Publications and Presentations

The significance of rheology in the context of bio three-dimensional (3D) printing lies in its impact on the printing behavior, which shapes material flow and the layer-by-layer stacking process. The objective of this study is to evaluate the rheological and printing behaviors of polycaprolactone (PCL) and dimethyl sulfone (DMSO2) composites. The rheological properties were examined using a rotational rheometer, employing a frequency sweep test. Simultaneously, the printing behavior was investigated using a material extrusion 3D printer, encompassing varying printing temperatures and pressures. Across the temperature range of 120–140 °C, both PCL and PCL/DMSO2 composites demonstrated liquid-like behavior, …


Some Hypergeometric Identities And Related Leonard Pairs, Taiyo Summers Terada May 2024

Some Hypergeometric Identities And Related Leonard Pairs, Taiyo Summers Terada

Dissertations and Theses

The notion of a Leonard pair was introduced by Terwilliger in 2001 to simplify Leonard's theorem, which classifies the orthogonal polynomials in the terminating branch of the Askey-Wilson scheme. In the same year, Kresch and Tamvakis made a conjecture about a certain 4F3 hypergeometric series while studying the arithmetic analogues of the standard conjectures for the Grassmanian G(2,n). The 4F3 series appearing in their conjecture is closely related to a family of orthogonal polynomials in the Askey-Wilson scheme. Consequently, the theory of Leonard pairs provides a useful framework for understanding their conjecture.

In …


Extended Producer Responsibility: Successes, Failures, And The Future Of Oregon Recycling, Zoe Vandal May 2024

Extended Producer Responsibility: Successes, Failures, And The Future Of Oregon Recycling, Zoe Vandal

University Honors Theses

Extended Producer Responsibility (EPR) is a waste management program used globally to improve the recovery, recycling, and management of solid waste materials. There are three types of EPR programs defined by their target materials: electronic and electrical waste (WEEE) EPR, hazardous waste EPR, and packaging EPR. Europe has implemented all three types with relative success. The US has implemented WEEE EPR and hazardous waste EPR and is currently in the process of implementing packaging EPR on a state scale in Oregon, California, Colorado, Maine, and Maryland with 10 more bills being introduced in 2024 alone. Oregon's EPR program will be …


Computational Tools For Exploring Eigenvector Localization, Robyn Ashley Markee Reid May 2024

Computational Tools For Exploring Eigenvector Localization, Robyn Ashley Markee Reid

Dissertations and Theses

We develop computational tools for exploring eigenvector localization for a class of selfadjoint, elliptic eigenvalue problems regardless of the cause for localization. The user inputs a desired region R (not necessarily connected), a tolerance for the amount localization in R, and the desired energy range [a,b]. The tool outputs eigenvectors concentrated within the tolerance inside R and within [a, b]. We develop ample theory that justifies our algorithm, which involves a complex, compact perturbation of the operator L, Ls = L+isχR, for some (small) s > 0. Our central idea can be summarized as follows: if (λ,ψ) is an eigenpair of …


Atmospheric Circulation, Climate Change, And Related Impacts Over The Western United States, Graham Patrick Taylor May 2024

Atmospheric Circulation, Climate Change, And Related Impacts Over The Western United States, Graham Patrick Taylor

Dissertations and Theses

This dissertation characterizes the range of atmospheric circulation patterns and select associated meteorology impacting the northwest United States, the onset timing of rain and wind relevant to wildfire across the western United States, and how these may respond to global warming. The ability of a suite of models contributing to the sixth phase of the Coupled Model Intercomparison Project (CMIP6) to simulate observed large-scale atmospheric circulation patterns over the Pacific Northwest of North America is evaluated. Climate model projections of atmospheric circulation patterns, their frequency, and associated temperature and precipitation anomalies under a high-end global warming scenario are assessed over …


Extreme Heat & Public Perception In Portland, Oregon: Evidence Of A Compounding Vulnerability Effect For Climate Hazards, Brianne Suldovsky, Molly Baer Kramer, Jonathan Fink May 2024

Extreme Heat & Public Perception In Portland, Oregon: Evidence Of A Compounding Vulnerability Effect For Climate Hazards, Brianne Suldovsky, Molly Baer Kramer, Jonathan Fink

Geology Faculty Publications and Presentations

Extreme heat events are a global public health threat, and the frequency of these events are projected to increase significantly in the coming decades. Responding to extreme heat requires that municipalities communicate with public audiences. Generally speaking, risk communication and public engagement efforts are more effective when they are responsive to current risk perception trends. This social scientific study examines extreme heat risk perceptions, emergency response needs, and level of trust in first responders among residents of the Portland (OR) Metro Area. Using quantitative survey data, it demonstrates the compounding influence of three previously identified vulnerability indicators–poverty, disability, and race–on …


Geochemistry And Geochronology Of The Steens And Monument Dike Swarm: Implications And Relationships To Magmatic Storage And To Lava Flows Of The Picture Gorge And Steens Basalt, Rachel Anne Sweeten May 2024

Geochemistry And Geochronology Of The Steens And Monument Dike Swarm: Implications And Relationships To Magmatic Storage And To Lava Flows Of The Picture Gorge And Steens Basalt, Rachel Anne Sweeten

Dissertations and Theses

The Columbia River Basalt Group (CRBG) is the youngest and best-preserved example of a continental flood basalt province. Vents and dikes for the four main eruptive units (Steens, Imnaha, Grande Ronde, and Picture Gorge Basalt) are the Monument, Steens and Chief Joseph Dike Swarms located in eastern Oregon, southeastern Washington, and northern Nevada.

Here we report on the compositions and timing of the dikes and sills of the Monument Dike Swarm (MDS), as well as their relationship to the subaerial lava flows of the Picture Gorge Basalt (PGB) with implications for crustal storage of these magmas. We evaluate data from …


A Deep Learning Framework For Blockage Mitigation In Mmwave Wireless, Ahmed Hazaa Almutairi May 2024

A Deep Learning Framework For Blockage Mitigation In Mmwave Wireless, Ahmed Hazaa Almutairi

Dissertations and Theses

Millimeter-Wave (mmWave) communication is a key technology to enable next generation wireless systems. However, mmWave systems are highly susceptible to blockages, which can lead to a substantial decrease in signal strength at the receiver. Identifying blockages and mitigating them is thus a key challenge to achieve next generation wireless technology goals, such as enhanced mobile broadband (eMBB) and Ultra-Reliable and Low-Latency Communication (URLLC). This thesis proposes several deep learning (DL) frameworks for mmWave wireless blockage detection, mitigation, and duration prediction. First, we propose a DL framework to address the problem of identifying whether the mmWave wireless channel between two devices …


Living On The Outskirts Of Things: Women And Nonbinary People Of Color With Cognitive Disabilities Describe Their Employment Experiences, Laura Spura Rodriguez May 2024

Living On The Outskirts Of Things: Women And Nonbinary People Of Color With Cognitive Disabilities Describe Their Employment Experiences, Laura Spura Rodriguez

Dissertations and Theses

This study examines the experiences of discrimination and the strategies used to navigate employment for women of color and nonbinary people of color (POC) with cognitive disabilities (CD) through their own narratives. Using Dis/ability Critical Race Theory and an interpretive description methodology, this study engaged 10 women of color and/or nonbinary POC with CD in semi-structured interviews in order to answer the following research questions: 1) What stories do women of color and nonbinary POC with CD tell about their experiences seeking employment? 2) What are the narratives of women and nonbinary POC with CD about their experiences of racism, …


Immigration Policy Evaluation For Technology Professionals Immigrants In The United States, Angel Contreras Cruz May 2024

Immigration Policy Evaluation For Technology Professionals Immigrants In The United States, Angel Contreras Cruz

Dissertations and Theses

The U.S. Immigration System is complex for technology professionals seeking to relocate to the United States for employment or education. The United States relies on its employment-based immigration to attract and select the best talent to fill the shortage of skilled jobs. Technology professionals, a stream of highly skilled immigrants, tend to contribute and be more beneficial to the U.S. economy, which is one of the principles of U.S. immigration policies. Although U.S. immigration policies are constantly updating, policymakers, experts, and scholars suggest that the United States needs significant immigration reform to solve current issues, such as improving technological capabilities …


H1-Conforming Finite Elements On Nonstandard Meshes, Samuel Edward Reynolds May 2024

H1-Conforming Finite Elements On Nonstandard Meshes, Samuel Edward Reynolds

Dissertations and Theses

We present a finite element method for linear elliptic partial differential equations on bounded planar domains that are meshed with cells that are permitted to be curvilinear and multiply connected. We employ Poisson spaces, as used in virtual element methods, consisting of globally continuous functions that locally satisfy a Poisson problem with polynomial data. This dissertation presents four peer-reviewed articles concerning both the theory and computation of using such spaces in the context of finite elements. In the first paper, we propose a Dirichlet-to-Neumann map for harmonic functions by way of computing the trace of a harmonic conjugate by numerically …


Exploring The Curriculum And Institutional Contexts Of Stem Future Faculty Programs, Amy Mae Forester May 2024

Exploring The Curriculum And Institutional Contexts Of Stem Future Faculty Programs, Amy Mae Forester

Dissertations and Theses

While there are a multitude of contributing factors, under-represented student success in STEM appears to be critically interdependent with teaching and learning practices that are responsive to diverse epistemologies and inclusive pedagogies. However, the professional literature has yet to identify a set of faculty development best practices that might guide the field. Furthermore, the institutional supports required to drive the success of STEM-oriented future faculty programs remain unknown. This inquiry proposal intended to address these concerns through a critical comparative qualitative study in seeking evidence-based practices and institutional elements of STEM faculty professional development programs that support diverse graduate and …


Accord: Constraint-Driven Mediation Of Multi-User Conflicts In Cloud Services, Abhiroop Tippavajjula, Primal Pappachan, Anna Squicciarini, Jose Such May 2024

Accord: Constraint-Driven Mediation Of Multi-User Conflicts In Cloud Services, Abhiroop Tippavajjula, Primal Pappachan, Anna Squicciarini, Jose Such

Computer Science Faculty Publications and Presentations

When multiple users adopt collaborative cloud services like Google Drive to work on a shared resource, incorrect or missing permis- sions may cause conflicting or inconsistent access or use privileges. These issues (or conflicts) compromise resources confidentiality, integrity, or availability leading to a lack of trust in cloud services. An example conflict is when a user with editor permissions changes the permissions on a shared resource without consent from the orig- inal resource owner. In this demonstration, we introduce ACCORD, a web application built on top of Google Drive able to detect and resolve multi-user conflicts. ACCORD employs a simulator …


Fea Simulations For Thermal Distributions Of Large Scale 3dic Packages, Suxia Chen, Qiang Wu, Wayne Xun, Jiachen Zhang, Jianping Xun May 2024

Fea Simulations For Thermal Distributions Of Large Scale 3dic Packages, Suxia Chen, Qiang Wu, Wayne Xun, Jiachen Zhang, Jianping Xun

Computer Science Faculty Publications and Presentations

As the market increases for Artificial Intelligence and High-Performance Computing applications, the geometry of 3-Dimensional Integrated Circuit packages becomes more complicated; therefore, predicting the thermal distributions of the structures becomes not only more important but also more challenging. The physics governing the thermal distribution is a 3-dimensional partial differential equation. In order to predict the thermal distributions, various approaches such as the layer modeling method have been invented. While practical, these approaches solve a simplified version of the differential equation placing an inherent limitation on their capabilities which may be improved upon. In this research we solve the actual differential …


Assessing The Reliability Of The Pairwise Variability Index For Differential Diagnosis Of Apraxia Of Speech, Celeste Sinko May 2024

Assessing The Reliability Of The Pairwise Variability Index For Differential Diagnosis Of Apraxia Of Speech, Celeste Sinko

University Honors Theses

Differential diagnosis of apraxia of speech (AOS) from other speech and language disorders is a prevailing challenge in the field of speech language pathology. Presently, existing measures for assessing AOS consist of perceptual rating scales, such as the Apraxia of Speech Rating Scale developed by Duffy, Strand, Clark, and Josephs. While perceptual rating scales are the current gold standard for assessment and diagnosis of AOS, they require a high degree of clinical expertise, and are susceptible to rater bias and rater drift. Thus, there exists a need for quantitative, objective measures for differential diagnosis of AOS. The purpose of this …


Motion History Images: A New Method For Tracking Microswimmers In 3d, Max Riekeles, Hadi Albalkhi, Megan Marie Dubay, Jay Nadeau, Christian A. Lindensmith May 2024

Motion History Images: A New Method For Tracking Microswimmers In 3d, Max Riekeles, Hadi Albalkhi, Megan Marie Dubay, Jay Nadeau, Christian A. Lindensmith

Physics Faculty Publications and Presentations

Quantitative tracking of rapidly moving micron-scale objects remains an elusive challenge in microscopy due to low signal-to-noise. This paper describes a novel method for tracking micron-sized motile organisms in off-axis Digital Holographic Microscope (DHM) raw holograms and/or reconstructions. We begin by processing the microscopic images with the previously reported Holographic Examination for Life-like Motility (HELM) software, which provides a variety of tracking outputs including motion history images (MHIs). MHIs are stills of videos where the frame-to-frame changes are indicated with color time-coding. This exposes tracks of objects that are difficult to identify in individual frames at a low signal-to-noise ratio. …


Flexible Strain Gauge Sensors As Real-Time Stretch Receptors For Use In Biomimetic Bpa Muscle Applications, Rochelle Jubert May 2024

Flexible Strain Gauge Sensors As Real-Time Stretch Receptors For Use In Biomimetic Bpa Muscle Applications, Rochelle Jubert

Student Research Symposium

This work presents a novel approach to real-time length sensing for biomimetic Braided Pneumatic Actuators (BPAs) as artificial muscles in soft robotics applications. The use of artificial muscles enables the development of more interesting robotic designs that no longer depend on single rotation joints controlled by motors. Developing robots with these capabilities, however, produces more complexities in control and sensing. Joint encoders, the mainstay of robotic feedback, can no longer be used, so new methods of sensing are needed to get feedback on muscle behavior to implement intelligent controls. To address this need, flexible strain gauge sensors from Portland company, …


Extreme Precipitation Climatology Of The Contiguous U.S., Amy M. Johnson May 2024

Extreme Precipitation Climatology Of The Contiguous U.S., Amy M. Johnson

Student Research Symposium

Extreme precipitation can cause flooding, landslides, loss of life and assets. Across the Contiguous United States (CONUS), concurrent to global warming, many communities have experienced increases in the amount of rain falling during the most extreme precipitation events and climate models project further increases for most of the CONUS. There is a need to comprehensively study the extreme precipitation climatology across the CONUS to understand what is within the observed range of extreme precipitation and the weather that drives it. Modern Era Retrospective analysis for Research and Applications 2 (MERRA-2) atmospheric reanalysis data for the period of 1980-2023 is used …


Effects Of Language Status, Community Advice, And Parent Beliefs On Heritage Language Maintenance In The U.S.: A Scoping Review, Isabelle Trujillo, Jasmine Loeung, Carolyn Quam May 2024

Effects Of Language Status, Community Advice, And Parent Beliefs On Heritage Language Maintenance In The U.S.: A Scoping Review, Isabelle Trujillo, Jasmine Loeung, Carolyn Quam

Student Research Symposium

This scoping review of qualitative research examines effects of language status, community advice to parents, and parents' beliefs on heritage language maintenance within a U.S. context. The review was guided by three research questions: 1. What is the nature of the relationship between a heritage language’s (HL) status in society and language maintenance across generations? 2. How does information parents receive from community members (e.g., health professionals, teachers, friends/family) influence their beliefs about the HL? 3. How do parents’ beliefs about the impact of a HL on academic/career success influence HL transmission? Thirty-four articles met inclusion criteria. Three themes were …


Performance-Based Risk Assessment For Large-Scale Transportation Networks, Anteneh Deriba, David Y. Yang May 2024

Performance-Based Risk Assessment For Large-Scale Transportation Networks, Anteneh Deriba, David Y. Yang

Student Research Symposium

Efficiently assessing the risk of asset failure due to deterioration or extreme events is crucial for transportation asset management. Traditional methods often lack effectiveness in directly evaluating system performance-based risks, facing challenges like the exponential increase in system states and the emergence of low-probability high-consequence events ("grey swan" events). To address these, this paper introduces a novel performance-based risk assessment approach for large-scale transportation networks, inspired by the Transitional Markov Chain Monte Carlo (TMCMC) method. This method transforms the risk assessment problem into a high-dimensional posterior distribution, with system risk acting as the normalization factor (evidence). It also provides risk-based …


Improving Tattle-Tale K-Deniability, Nicholas G.E. Morales May 2024

Improving Tattle-Tale K-Deniability, Nicholas G.E. Morales

Student Research Symposium

Ensuring privacy for databases is an ongoing struggle. While the majority of work has focused on using access control lists to protect sensitive data these methods are vulnerable to inference attacks. A set of algorithms, referred to as Tattle-Tale, was developed that could protect sensitive data from being inferred however its runtime performance wasn’t suitable for production code. This set of algorithms contained two main subsets, Full Deniability and K-Deniability. My research focused on improving the runtime or utility of the K-Deniability algorithms. I investigated the runtime of the K-Deniability algorithms to identify what was slowing the process down. Aside …


Evaluation Of Us Immigration Policies For Technology Professionals, Angel Contreras Cruz May 2024

Evaluation Of Us Immigration Policies For Technology Professionals, Angel Contreras Cruz

Student Research Symposium

The U.S. Immigration System is complex for technology professionals seeking to relocate to the United States for employment or education. The United States relies on its employment-based immigration to attract and select the best talent to fill the shortage of skilled jobs. Technology professionals, a stream of highly skilled immigrants, tend to contribute and be more beneficial to the U.S. economy, which is one of the principles of U.S. immigration policies. Although U.S. immigration policies are constantly updating, policymakers, experts, and scholars suggest that the United States needs significant immigration reform to solve current issues, such as improving technological capabilities …


Integration Of Agent Models And Meta Reinforcement Learning (Meta-Rl) Algorithms For Car Racing Experiment, Vidyavarshini Holenarasipur Jayashankar May 2024

Integration Of Agent Models And Meta Reinforcement Learning (Meta-Rl) Algorithms For Car Racing Experiment, Vidyavarshini Holenarasipur Jayashankar

Student Research Symposium

Introduction: Achieving optimal performance in 2D racing games presents unique challenges, requiring adaptive strategies and advanced learning algorithms. This research explores the integration of sophisticated agent models with Meta Reinforcement Learning (Meta-RL) techniques, specifically Model-Agnostic Meta-Learning (MAML) and Proximal Policy Optimization (PPO), to enhance decision-making and adaptability within these simulated environments. We hypothesize that this innovative approach will lead to marked improvements in game performance and learning efficiency.

Methods: In our experimental setup, we applied MAML for its rapid adaptation capabilities and PPO for optimizing the agents' policy decisions within a 2D racing game simulator. The objective was …


Comparative Life Cycle Assessment Of Hydrogen Production Via Various Pv-Assisted Electrochemical Water Splitting Techniques, Achyuth Ravilla, Ilke Celik May 2024

Comparative Life Cycle Assessment Of Hydrogen Production Via Various Pv-Assisted Electrochemical Water Splitting Techniques, Achyuth Ravilla, Ilke Celik

Student Research Symposium

Photoelectrochemical (PEC) and photovoltaic-electrochemical (PV-EC) water-splitting technologies have emerged as cost-effective options for large-scale green hydrogen production in industrial applications. Solar to hydrogen (STH) efficiencies of these technologies have reached up to 20% and several pathways have been explored to drive down the cost of hydrogen using these technologies to less than $2/kg. However, the environmental impact assessment of these technologies for industry-scale deployment has not been explored in previous studies. This study assesses the environmental impacts of PEC and PV-EC technologies by conducting a cradle-to-gate life cycle assessment. The functional unit considered for this assessment is 1 kg of …


A Novel Caching Algorithm For Efficient Fine-Grained Access Control In Database Management Systems, Anadi Shakya May 2024

A Novel Caching Algorithm For Efficient Fine-Grained Access Control In Database Management Systems, Anadi Shakya

Student Research Symposium

Fine-grained access Control (FGAC) in DBMS is vital for restricting user access to authorized data and enhancing security. FGAC policies govern how users are granted access to specific resources based on detailed criteria, ensuring security and privacy measures. Traditional methods struggle with scaling policies to thousands, causing delays in query responses. This paper introduces a novel caching algorithm designed to address this challenge by accelerating query processing and ensuring compliance with FGAC policies. In our approach, we create a circular hashmap and employ different replacement techniques to efficiently manage the cache, prioritizing entries that are visited more frequently. To evaluate …


Beavers Beyond Boundaries: Perceptions Of Beaver-Related Restoration, Matthew V. Guziejka May 2024

Beavers Beyond Boundaries: Perceptions Of Beaver-Related Restoration, Matthew V. Guziejka

Student Research Symposium

The study "Beavers Beyond Boundaries: Perceptions of Beaver-Related Restoration" conducted by Matt Guziejka and Heejun Chang from the WISE Lab, Department of Geography at Portland State University, delves into the social, cultural, and environmental dimensions of Beaver-Related Restoration (BRR) within the urban setting of the Tualatin River watershed. Utilizing a voluntary survey with 187 participants across three urban watershed sites, the research aimed to analyze community perceptions concerning beavers and their impact on the environment, particularly in relation to their proximity to watercourses. Findings indicate that proximity significantly affects attitudes towards beavers, with those living closer to watercourses demonstrating more …


The Effect Of Metabolic Modulators On The Rate Of Steady State Water Exchange In S. Cerevisiae Grown In Chemostat Bioreactors, Samantha Mumford, Mark Woods, Johnathan Dutra May 2024

The Effect Of Metabolic Modulators On The Rate Of Steady State Water Exchange In S. Cerevisiae Grown In Chemostat Bioreactors, Samantha Mumford, Mark Woods, Johnathan Dutra

Student Research Symposium

Water transport across the lipid bilayer due to osmotic stress causes a change in intracellular volume over time. At isotonic equilibrium there is no change in cell volume and yet water exchange does not stop. Water molecules continue to exchange rapidly with those of the extracellular space. The rate constant for steady state water efflux (kio) can be measured using contrast enhanced magnetic resonance (MR) and the two-site exchange (2SX) model. kio is known to correlate with the cellular energy molecule ATP making it a probable biomarker for metabolic diseases such as cancer. Measurements of k …