Physical Sciences and Mathematics Commons^™

Probability Axioms And Set Theory Paradoxes, Ari Herman, John Caughman

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we show that Zermelo–Fraenkel set theory with Choice (ZFC) conflicts with basic intuitions about randomness. Our background assumptions are the Zermelo–Fraenekel axioms without Choice (ZF) together with a fragment of Kolmogorov’s probability theory. Using these minimal assumptions, we prove that a weak form of Choice contradicts two common sense assumptions about probability—both based on simple notions of symmetry and independence.

Rock Glaciers And Related Cold Rocky Landforms: Overlooked Climate Refugia For Mountain Biodiversity, Stefano Brighenti, Scott Hotaling, Debra S. Finn, Andrew G. Fountain, Masaki Hayashi, David Herbst, Jasmine E. Saros, Lusha M. Tronstad, Constance I. Millar

Geology Faculty Publications and Presentations

Mountains are global biodiversity hotspots where cold environments and their associated ecological communities are predicted to be threatened by climate warming. Considerable research attention has been devoted to understanding the ecological effects of alpine glacier and snowfield recession. However, much less attention has been given to identifying climate refugia in mountain ecosystems where present-day environmental conditions will be maintained, at least in the near-term, as other habitats change. Around the world, montane communities of microbes, animals, and plants live on, adjacent to, and downstream of rock glaciers and related cold rocky landforms (CRL). These geomorphological features have been overlooked in …

From Ideas To Items: A Primer On The Development Of Ordered Multiple-Choice Items For Investigating The Progression Of Learning In Higher Education Stem, Katherine Lazenby, Morgan E. Balabanoff, Nicole M. Becker, Alena Moon, Jack Barbera

Chemistry Faculty Publications and Presentations

Identifying effective methods of assessment and developing robust assessments are key areas of research in chemistry education. This research is needed to evaluate instructional innovations and curricular reform. In this primer, we advocate for the use of a type of assessment, ordered multiple-choice (OMC), across postsecondary chemistry. OMC assessments are grounded in a developmental perspective, which treats students’ knowledge as developing in sophistication over time. This is in contrast to a dichotomous perspective, which asserts that students’ knowledge is either aligned or misaligned with scientifically accepted knowledge. By drawing on a developmental perspective, OMC assessments offer insights into student understanding …

Occam Manual, Martin Zwick

Systems Science Faculty Publications and Presentations

Occam is a Discrete Multivariate Modeling (DMM) tool based on the methodology of Reconstructability Analysis (RA). Its typical usage is for analysis of problems involving large numbers of discrete variables. Models are developed which consist of one or more components, which are then evaluated for their fit and statistical significance. Occam can search the lattice of all possible models, or can do detailed analysis on a specific model.

In Variable-Based Modeling (VBM), model components are collections of variables. In State-Based Modeling (SBM), components identify one or more specific states or substates.

Occam provides a web-based interface, which …

Boolean Network Control With Ideals, Ian H. Dinwoodie

Mathematics and Statistics Faculty Publications and Presentations

A method is given for finding controls to transition an initial state x0 to a target set in deterministic or stochastic Boolean network control models. The algorithms use multivariate polynomial algebra. Examples illustrate the application.

Ecohydrology Of Epiphytes: Modelling Water Balance, Cam Photosynthesis, And Their Climate Impacts, Gretta Miller, Samantha Hartzell, Amilcare Porporato

Civil and Environmental Engineering Faculty Publications and Presentations

Epiphytes are aerial plants, often characterized by CAM (crassulacean acid metabolism) photosynthesis, which make up a significant portion of the biomass in some rainforests. Their unique characteristics have not yet been included in ecohydrological models, and their potential impact on local hydrometeorology is largely unexplored. This work introduces a water balance model for epiphytes, which adapts the soil‐plant‐atmosphere continuum model to represent a plant system without soil and couples it to the Photo3 photosynthesis model, which includes CAM photosynthesis. The model, which is parameterized with field data of Guzmania monostachia, accurately captures the observed hydraulic and photosynthetic behaviour of …

The Case For A Long-Lived And Robust Yellowstone Hotspot, Victor E. Camp, Ray E. Wells

Geology Faculty Publications and Presentations

The Yellowstone hotspot is recognized as a whole-mantle plume with a history that extends to at least 56 Ma, as recorded by offshore volcanism on the Siletzia oceanic plateau. Siletzia accreted onto the North American plate at 51–49 Ma, followed by repositioning of the Farallon trench west of Siletzia from 48 to 45 Ma. North America overrode the hotspot, and it transitioned from the Farallon plate to the North American plate from 42 to 34 Ma. Since that time, it has been genetically associated with a series of aligned volcanic provinces associated with ageprogressive events that include Oligocene high-K calc-alkaline …

Toward An Integrative Geological And Geophysical View Of Cascadia Subduction Zone Earthquakes, Maureen A.L. Walton, Lydia M. Staisch, Tina Dura, Jessie K. Pearl, Brian Sherrod, Joan Gomberg, Simon Engelhart, Ray E. Wells, Multiple Additional Authors

Geology Faculty Publications and Presentations

The Cascadia subduction zone (CSZ) is an exceptional geologic environment for recording evidence of land-level changes, tsunamis, and ground motion that reveals at least 19 great megathrust earthquakes over the past 10 kyr. Such earthquakes are among the most impactful natural hazards on Earth, transcend national boundaries, and can have global impact.Reducing the societal impacts of future events in the US Pacific Northwest and coastal British Columbia, Canada, requires improved scientific understanding of megathrust earthquake rupture, recurrence, and corresponding hazards. Despite substantial knowledge gained from decades of research, large uncertainties remain about the characteristics and frequencies of past CSZ earthquakes. …

Simulations Of Single- And Two-Tone Tm-Doped Optical Fiber Laser Amplifiers, Tathagata Goswami, J. Grosek, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

This work uses numerical simulations of a thulium-doped optical fiber amplifier to predict various performance characteristics such as peak temperatures, expected output powers and efficiencies, presence of amplified spontaneous emission (ASE), and transverse mode instability (TMI) onset power thresholds. Single- and two-tone configurations are studied. In the latter case, the two laser sources are separated in frequency by the amount that corresponds to the peak Raman gain, and a few seed ratios at various total seed powers are examined. The goal is to provide the field with pertinent information on what is feasible for this type of amplifier.

Torsion And Curvature In Continuously Defective Solid Crystals, Marek Z. Elźanowski

Mathematics and Statistics Faculty Publications and Presentations

I show how one can utilize the concept of a canonical connection on a homogeneous space to describe defectiveness of a continuous elastic crystal solid.

Five Ps (Policies, Practices, Power Structures, Places; And People): A Framework To Analyze Systemic Inequalities, Eva Thanheiser, Lisa Weasel, Idowu Ajibade, Larry Martinez, Gina Greco

Mathematics and Statistics Faculty Publications and Presentations

This chart is part of a framework to establish institutional equity and is part of the following National Science Foundation grant project:

The Spaces of Empowerment for Equity and Diversity: Advancement Through Access (SEE-DATA) project at Portland State University (PSU) aims to identify, understand, and improve the workplace experiences and retention of faculty in STEM fields who have been traditionally minoritized and marginalized based on gender, race/ethnicity, and other intersectional identities (e.g., sexual orientation, disability, socioeconomic status, national origin, immigrant status). The project will collect, analyze, and map data about faculty’s experiences at PSU to inform programs and policies that …

Poised For Change: University Students Are Positively Disposed Toward Food Waste Diversion And Decrease Individual Food Waste After Programming, Manar Arica Alattar, Jennifer L. Morse

Environmental Science and Management Faculty Publications and Presentations

Eaters (consumers of food) are responsible for 60% of waste along the food cycle in developed countries. Programs that target individual and household food waste behavior change are essential to addressing such waste. School cafeterias worldwide offer an opportune microcosm in which to educate on food and nutrition skills and change related behavior. No Scrap Left Behind, a cafeteria food waste diversion program, was developed, piloted, and assessed based on measures of both direct and indirect food waste behavior, and attitudes, knowledge, and emotions related to food waste. Participants had positive attitudes towards food waste reduction, engaged in food waste …

Towards Formally Verified Compilation Of Tag-Based Policy Enforcement, Chr Chhak, Andrew Tolmach, Sean Anderson

Computer Science Faculty Publications and Presentations

Hardware-assisted reference monitoring is receiving increasing attention as a way to improve the security of existing software. One example is the PIPE architecture extension, which attaches metadata tags to register and memory values and executes tag-based rules at each machine instruction to enforce a software-defined security policy. To use PIPE effectively, engineers should be able to write security policies in terms of source-level concepts like functions, local variables, and structured control operators, which are not visible at machine level. It is the job of the compiler to generate PIPE-aware machine code that enforces these source-level policies. The compiler thus becomes …

View Synthesis Of Dynamic Scenes Based On Deep 3d Mask Volume, Kai-En Lin, Guowei Yang, Lei Xiao, Feng Liu, Ravi Ramamoorthi

Computer Science Faculty Publications and Presentations

Image view synthesis has seen great success in reconstructing photorealistic visuals, thanks to deep learning and various novel representations. The next key step in immersive virtual experiences is view synthesis of dynamic scenes. However, several challenges exist due to the lack of high-quality training datasets, and the additional time dimension for videos of dynamic scenes. To address this issue, we introduce a multi-view video dataset, captured with a custom 10-camera rig in 120FPS. The dataset contains 96 high-quality scenes showing various visual effects and human interactions in outdoor scenes. We develop a new algorithm, Deep 3D Mask Volume, which enables …

Sensitivity Analysis Of An Agent-Based Simulation Model Using Reconstructability Analysis, Andey M. Nunes, Martin Zwick, Wayne Wakeland

Systems Science Faculty Publications and Presentations

Reconstructability analysis, a methodology based on information theory and graph theory, was used to perform a sensitivity analysis of an agent-based model. The NetLogo BehaviorSpace tool was employed to do a full 2^k factorial parameter sweep on Uri Wilensky’s Wealth Distribution NetLogo model, to which a Gini-coefficient convergence condition was added. The analysis identified the most influential predictors (parameters and their interactions) of the Gini coefficient wealth inequality outcome. Implications of this type of analysis for building and testing agent-based simulation models are discussed.

Estimating Posterior Quantity Of Interest Expectations In A Multilevel Scalable Framework, Hillary R. Fairbanks, Sarah Osborn, Panayot S. Vassilevski

Mathematics and Statistics Faculty Publications and Presentations

Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large‐scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element‐agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state‐of‐the‐art scalable AMG. To showcase the applicability …

From Forests To Fish: Mercury In Mountain Lake Food Webs Influenced By Factors At Multiple Scales, Ariana M. Chiapella, Collin A. Eagles-Smith, Angela L. Strecker

Environmental Science and Management Faculty Publications and Presentations

Mountain lakes, while seemingly pristine, have been subjected to historical fish stocking practices and exposure to atmospherically deposited contaminants like mercury. Mercury bioaccumulation in these ecosystems varies widely due to strong environmental gradients, and there are complex, hierarchical factors that affect mercury transport and loading, methylmercury production, and food web biomagnification. We sought to assess how representative variables associated with watershed, lake, and food web-scale processes—specifically, catchment tree cover, lake benthic primary production, and fish diet, respectively—are associated with mercury concentrations in mountain lake fish. Mean fish mercury concentrations varied threefold between lakes, with nearshore tree cover and fish diet …

Nonlinear Multigrid Based On Local Spectral Coarsening For Heterogeneous Diffusion Problems, Chak Shing Lee, Francois Hamon, Nicola Castelletto, Panayot S. Vassilevski, Joshua A. White

Mathematics and Statistics Faculty Publications and Presentations

This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of freedom and spectral decomposition of reference linear operators associated with the aggregates. For rapid convergence, it is important that the resulting coarse spaces have good approximation properties. In our approach, the approximation quality can be directly improved by including more spectral degrees of freedom in the coarsening process. Further, by exploiting local coarsening and a piecewise-constant approximation when evaluating the nonlinear component, the coarse level problems are assembled and …

Projected Impact Of Mid-21st Century Climate Change On Wildfire Hazard In A Major Urban Watershed Outside Portland, Oregon Usa, Andy Mcevoy, Max Nielsen-Pincus, Andres Holz, Arielle J. Catalano, Kelly E. Gleason

Environmental Science and Management Faculty Publications and Presentations

Characterizing wildfire regimes where wildfires are uncommon is challenged by a lack of empirical information. Moreover, climate change is projected to lead to increasingly frequent wildfires and additional annual area burned in forests historically characterized by long fire return intervals. Western Oregon and Washington, USA (westside) have experienced few large wildfires (fires greater than 100 hectares) the past century and are characterized to infrequent large fires with return intervals greater than 500 years. We evaluated impacts of climate change on wildfire hazard in a major urban watershed outside Portland, OR, USA. We simulated wildfire occurrence and fire regime characteristics under …

Clarity On Cronbach’S Alpha Use, Jack Barbera, Nicole Naibert, Regis Komperda, Thomas C. Pentecost

Chemistry Faculty Publications and Presentations

The Cronbach’s alpha (α) statistic is regularly reported in science education studies. However, recent reviews have noted that it is not well-understood. Therefore, this commentary provides additional clarity regarding the language used when describing and interpreting alpha and other estimates of reliability.

A Posteriori Error Estimates For Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques, Stefano Giani, Luka Grubišić, Harri Hakula, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

We propose an a posteriori error estimator for high-order p- or hp-finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for estimating the error in the approximation of an eigenvalue cluster and the corresponding invariant subspace. The estimator is based on the computation of approximate error functions in a space that complements the one in which the approximate eigenvectors were computed. These error functions are used to construct estimates of collective measures of error, such as the Hausdorff distance between the true and approximate clusters of eigenvalues, and the subspace gap between the corresponding true and approximate …

The Gauge Principle From The Schrodinger-Born Wave Mechanics, P. T. Leung

Physics Faculty Publications and Presentations

We propose an elementary way of introducing the gauge principle to beginners with a background in only mechanics, electromagnetism, and quantum mechanics. This evolves from an apparent conflict in the Schrodinger-Born formulation of wave mechanics, and does not have to resort to advanced concepts like covariant derivative and minimal coupling. With such an approach, one would have appreciated how interactions can be dictated from consideration of internal symmetry of a physical system, which serves as a principle underlying the foundation of almost all modern physics. In addition, the gauge principle also serves as a resource providing consistency between the Born …

Extending The Functional Subnetwork Approach To A Generalized Linear Integrate-And-Fire Neuron Model, Nicholas Szczecinski, Roger Quinn, Alexander J. Hunt

Mechanical and Materials Engineering Faculty Publications and Presentations

Engineering neural networks to perform specific tasks often represents a monumental challenge in determining network architecture and parameter values. In this work, we extend our previously-developed method for tuning networks of non-spiking neurons, the “Functional subnetwork approach” (FSA), to the tuning of networks composed of spiking neurons. This extension enables the direct assembly and tuning of networks of spiking neurons and synapses based on the network’s intended function, without the use of global optimization ormachine learning. To extend the FSA, we show that the dynamics of a generalized linear integrate and fire (GLIF) neuronmodel have fundamental similarities to those of …

The Cycle Structure Of Unicritical Polynomials, Andrew Bridy, Derek Garton

Mathematics and Statistics Faculty Publications and Presentations

A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: for any prime p" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">pp⁠, reduce its coefficients mod p" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; …

Nicotine In Tobacco Product Aerosols: 'It's Deja Vu All Over Again', Anna K. Duell, James F. Pankow, David H. Peyton

Chemistry Faculty Publications and Presentations

Introduction: The distribution of nicotine among its free-base (fb) and protonated forms in aerosolised nicotine affects inhalability. It has been manipulated in tobacco smoke and now in electronic cigarettes by the use of acids to de-freebase nicotine and form ‘nicotine salts’.

Methods: Measurements on electronic cigarette fluids (e-liquids) were carried out to determine (1) the fraction of nicotine in the free-base form (α fb) and (2) the levels of organic acid(s) and nicotine. Samples included JUUL ‘pods’, ‘look-a-like/knock-off’ pods and some bottled ‘nicotine salt’ and ‘non-salt’ e-liquids.

Results: α fb= 0.12 ±0.01 at 40°C (≈ 37°C) for 10 JUUL products, …

Newton Polygons Of Hecke Operators, Liubomir Chiriac, Andrei Jorza

Mathematics and Statistics Faculty Publications and Presentations

In this computational paper we verify a truncated version of the Buzzard–Calegari conjecture on the Newton polygon of the Hecke operator T2 for all large enough weights. We first develop a formula for computing p-adic valuations of exponential sums, which we then implement to compute 2-adic valuations of traces of Hecke operators acting on spaces of cusp forms. Finally, we verify that if Newton polygon of the Buzzard–Calegari polynomial has a vertex at n≤15, then it agrees with the Newton polygon of T2 up to n.

Approximate Computing With Emerging Devices, Richard Atherton

Undergraduate Research & Mentoring Program

Approximate computation is a new trend that explores and harnesses trade-offs between the precision and energy/power consumption of computing systems. In this project a feed-forward neural network was designed as well as several reservoir networks using different network topologies to compare the accuracy and resilience of the network against the computational complexity required.

Genetically Encoded Phase Contrast Agents For Digital Holographic Microscopy, Arash Farhadi, Manuel Bedrossian, Justin Lee, Gabrielle H. Ho, Mikhail G. Shapiro, Jay Nadeau

Physics Faculty Publications and Presentations

Quantitative phase imaging and digital holographic microscopy have shown great promise for visualizing the motion, structure and physiology of microorganisms and mammalian cells in three dimensions. However, these imaging techniques currently lack molecular contrast agents analogous to the fluorescent dyes and proteins that have revolutionized fluorescence microscopy. Here we introduce the first genetically encodable phase contrast agents based on gas vesicles. The relatively low index of refraction of the air-filled core of gas vesicles results in optical phase advancement relative to aqueous media, making them a “positive” phase contrast agent easily distinguished from organelles, dyes, or microminerals. We demonstrate this …

Convex Analysis Of Minimal Time And Signed Minimal Time Functions, D. V. Cuong, B. S. Mordukhovich, Mau Nam Nguyen, M. L. Wells

Mathematics and Statistics Faculty Publications and Presentations

In this paper we first consider the class of minimal time functions in the general setting of locally convex topological vector (LCTV) spaces. The results obtained in this framework are based on a novel notion of closedness of target sets with respect to constant dynamics. Then we introduce and investigate a new class of signed minimal time functions, which are generalizations of the signed distance functions. Subdifferential formulas for the signed minimal time and distance functions are obtained under the convexity assumptions on the given data.

Electromagnetic Reciprocity In The Presence Of Topological Insulators, Huai-Yi Xie, P. T. Leung

Physics Faculty Publications and Presentations

Electromagnetic reciprocity is studied in the presence of topological insulators (TI) with application of axion electrodynamics for harmonic electromagnetic fields. The corresponding generalized Lorentz and Feld-Tai type lemmas are derived in terms of the axion coupling parameter, and their correlation to the conditional symmetry in source-observer coordinates for the various Green dyadics is established subjected to different types of boundary conditions. Possible application of the results to the probing of the topological magneto-electric effects from TI is discussed.