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Full-Text Articles in Physical Sciences and Mathematics

Semantically Structured Creative Computer Systems & Automated Evaluation Of Creative Artifacts, Brad Spendlove Aug 2023

Semantically Structured Creative Computer Systems & Automated Evaluation Of Creative Artifacts, Brad Spendlove

Theses and Dissertations

Computational creativity seeks, in part, to develop autonomous agents that exhibit creativity. Language is an ideal creative domain for studying computer agents due to its rich interconnectedness and immense space of possible combinations. This dissertation explores the design, testing, and theory of creative computer systems that write microfiction and play the board game Codenames. The designs of these systems are all similarly based on building up creative artifacts from the underlying structure of the relationships between words. A critical component of the creative process is the ability to evaluate the quality of creative output. Human and automated assessment of our …


The Student Becomes The Teacher: Training High-Performance Language Models More Sample-Efficiently From Small Models Via Superstilling, Chaz Allen Gundry Aug 2023

The Student Becomes The Teacher: Training High-Performance Language Models More Sample-Efficiently From Small Models Via Superstilling, Chaz Allen Gundry

Theses and Dissertations

Recent advances including the Transformer architecture have revolutionized the Natural Language Processing community by providing immense performance improvements across many tasks, including the development of Large Language Models (LLMs). LLMs show enormous promise as few-shot learners, common-sense knowledge repositories, conversational agents, writing assistants, and coding tools, and are gaining widespread traction in commercial industry. However, LLMs are expensive and time-consuming to train, requiring many passes over terabytes of data for the largest models. In this paper, we present Superstilling, a method for reducing the sample complexity of language model training by distilling the knowledge from a previously-trained model (the teacher) …


Improving Xrd Analysis With Machine Learning, Rachel E. Drapeau Aug 2023

Improving Xrd Analysis With Machine Learning, Rachel E. Drapeau

Theses and Dissertations

X-ray diffraction analysis (XRD) is an inexpensive method to quantify the relative proportions of mineral phases in a rock or soil sample. However, the analytical software available for XRD requires extensive user input to choose phases to include in the analysis. Consequently, analysis accuracy depends greatly on the experience of the analyst, especially as the number of phases in a sample increases (Raven & Self, 2017; Omotoso, 2006). The purpose of this project is to test whether incorporating machine learning methods into XRD software can improve the accuracy of analyses by assisting in the phase-picking process. In order to provide …


Groundwater Flow Across The Coyote Wash Fault And Cedar Mesa Anticline Near St. Johns, Arizona, Stephanie Lynn Latour Aug 2023

Groundwater Flow Across The Coyote Wash Fault And Cedar Mesa Anticline Near St. Johns, Arizona, Stephanie Lynn Latour

Theses and Dissertations

As the demand for water increases across the southwestern United States, the region's utilization of and dependence on water stored in groundwater aquifers has risen in kind. The Coconino Aquifer (C-aquifer) underlies much of the southwestern Colorado Plateau and is a primary source of groundwater in northeastern Arizona. One of the largest commercial users of water from the C-aquifer in Apache County, Arizona, is Springerville Generating Station, a coal-fired power plant owned and operated by Tucson Electric Power. The area surrounding the power plant, located between the cities of Springerville and St. Johns, Arizona (the Springerville-St. Johns area), is geologically …


Geochemistry Of Zircon And Apatite In Rhyolites From The Central Snake River Plain: Genetic Implications, Chesley Philip Gale Aug 2023

Geochemistry Of Zircon And Apatite In Rhyolites From The Central Snake River Plain: Genetic Implications, Chesley Philip Gale

Theses and Dissertations

Whole-rock and mineral compositions of three eruptive deposits from the Twin Falls caldera, associated with the Yellowstone hotspot, provide a window into melt generation and evolution for hot, dry, A-type rhyolites. Three rhyolitic units were sampled via the Kimberly drill-core as a part of project HOTSPOT, a study focused on mantle plume and continental lithosphere interaction. Previous work has been done to collect high resolution U-Pb zircon ages, and Hf- and O-isotopic compositions. This study examined the geochemistry of apatite and zircon along with host rock compositions in the context of this previous work. The Kimberly core sampled the Shoshone …


Exploring New Horizons In Microwave-Promoted Iminyl Radical Chemistry And Synthesis Of Bulky Dehydroamino Acids, Jatinder Singh Aug 2023

Exploring New Horizons In Microwave-Promoted Iminyl Radical Chemistry And Synthesis Of Bulky Dehydroamino Acids, Jatinder Singh

Theses and Dissertations

The first project in this dissertation presents a simplified and efficient protocol for synthesizing pyrrolines through 5-exo iminyl radical cyclizations. The microwave irradiation of O-Phenyloximes tethered to alkenes causes N-O homolysis resulting in iminyl radical generation, which subsequently undergoes 5-exo-trig cyclizations furnishing pyrrolines. This eliminates the need for toxic radical initiators (AIBN, benzoyl peroxide), propagating agents (Bu3SnH, (Me3Si)3SiH), and expensive catalysts or single-electron transfer (SET) cycles. We explored the scope of diverse traps and substrates for iminyl radical cyclizations. The iminyl radical cyclizations formed versatile pyrrolines with moderate to excellent yields. The diastereoselectivity also ranged from low to high. Moreover, …


Parents' Perceptions Of The Importance Of Teaching Mathematics: A Q-Study, Ashlynn M. Holley Aug 2023

Parents' Perceptions Of The Importance Of Teaching Mathematics: A Q-Study, Ashlynn M. Holley

Theses and Dissertations

Mathematics education has gone through multiple reform efforts over the last century and continues to be the target of improvement efforts. Past changes in curriculum and goals have sometimes led to heated debates between various stakeholders. Knowing the views of different stakeholders can help determine what common ground there is between these different groups and where areas of disagreement might arise. Parents are especially important to understand because they have been influential in past reform efforts. Despite the importance of parents' opinions, little research has been conducted concerning their perspectives on the importance of mathematics teaching. Using Q-methodology, I was …


Engagement In Secondary Mathematics Group Work: A Student Perspective, Rachel H. Jorgenson Aug 2023

Engagement In Secondary Mathematics Group Work: A Student Perspective, Rachel H. Jorgenson

Theses and Dissertations

In the realm of academic engagement research, students are valuable sources of information to learn how and why students often engage unproductively in mathematics group work. However, although secondary mathematics students are often expected to engage in meaningful mathematical discourse in a small group setting, little research has been conducted to better understand student engagement in this setting from the perspective of the students themselves. This thesis attempts to understand how one junior high student described his own engagement in mathematics small group work as well as what factors influenced this engagement. By conducting several cycles of observations and interviews …


Computational Modeling Of Energy Landscapes And Trajectory Studies Of Fundamental Organometallic Reactions, Joshua I. Wheeler Aug 2023

Computational Modeling Of Energy Landscapes And Trajectory Studies Of Fundamental Organometallic Reactions, Joshua I. Wheeler

Theses and Dissertations

Organometallic reactions are a fundamental class of chemical transformations. The mechanisms of organometallic reactions are routinely modeled by calculating intermediates and transition-state structures on a potential energy surface with density functional theory (DFT). The translation of these calculated structures to a reaction mechanism is typically done under the umbrella of statistical transition state theory. This dissertation reports the use of DFT calculations and quasiclassical direct dynamics trajectories to explore the possibility of nonstatistical dynamic effects in organometallic reactions. Chapter 1 provides a brief review of potential energy surfaces, transition state theory, dynamics trajectories, and a review of previous dynamics studies …


Physics-Guided Modeling Of Acoustic Environments Using Limited Spatio-Spectro-Temporal Data, Mylan Ray Cook Aug 2023

Physics-Guided Modeling Of Acoustic Environments Using Limited Spatio-Spectro-Temporal Data, Mylan Ray Cook

Theses and Dissertations

When creating data-based models it is important to include the underlying physical characteristics and constraints of the data. If physical characteristics are not properly included in the model, results may be infeasible or physically impossible. Acoustic environments are better characterized by ensuring that models include the fundamental spatial, spectral, and temporal characteristics of noise sources, or how they change based on location, frequency, and time. When model data are limited, in availability or in reliability, additional care must be taken to ensure models predict feasible results. This dissertation focuses on physics-guided modeling of acoustic environments using limited data, taking into …


A Step Into Structural Biology: Structural Determination Of Tnk1-Uba And Computational Design Of A Radical Sam Cyclase, Yi-Jie Tseng Aug 2023

A Step Into Structural Biology: Structural Determination Of Tnk1-Uba And Computational Design Of A Radical Sam Cyclase, Yi-Jie Tseng

Theses and Dissertations

Structural biology uncovers life's secrets by studying protein structures via techniques like X-ray crystallography. This knowledge drives advancements in protein engineering for the improvement of human lives. Yet, obtaining high-quality crystals in X-ray crystallography is challenging. To overcome this, we used Translocation ETS Leukemia protein Sterile Alpha Motif domain (TELSAM), a promising polymer-forming crystallization chaperone (PFCC), to enhance protein crystallization. Human thirty-eight-negative kinase-1 (TNK1), a key player in cancer progression, possess a ubiquitin association (UBA) domain that binds polyubiquitin and regulates TNK1 activity and stability. Although sequence analysis hints at an unconventional TNK1 UBA domain architecture, its molecular structure lacks …


Synthesis And Characterization Of Redox-Noninnocent Pyrazine(Diimine) Iron Complexes And An Inverted Pyridine(Diimine) Ligand, Jaylan Billups Aug 2023

Synthesis And Characterization Of Redox-Noninnocent Pyrazine(Diimine) Iron Complexes And An Inverted Pyridine(Diimine) Ligand, Jaylan Billups

Theses and Dissertations

Cooperativity between the metal center and the ligand has been shown in nature to be an important feature of systems that catalyze two-electron processes that first-row transition metals usually cannot catalyze on their own. In these cases, the ligand acts as a site of reactivity that in many instances can store electrons or react directly with substrates in solution. The design and study of systems where there is synergy between the metal and the ligand have been leveraged to catalyze polymerization and hydrogenation-type reactions as well as the activation of small molecules such as dihydrogen. Specifically, the pyridine(diimine) ligand scaffold …


Trace Metal Analysis Of Pond Sediments To Measure Deposition From A Coal-Fired Power Plant In Ackerman Mississippi, Charles Bills Aug 2023

Trace Metal Analysis Of Pond Sediments To Measure Deposition From A Coal-Fired Power Plant In Ackerman Mississippi, Charles Bills

Theses and Dissertations

Trace element sediment pollution due to coal power plants have been reported in many countries. In this study, pond sediment samples collected from locations around a coal fired power plant in Ackerman, MS, were evaluated for their trace element concentration and pollution status. The samples were collected at two depths to study changes in element accumulation over time. The samples were digested and the elements, As, Cd, Cr, Cu, Pb, Hg, and Zn were analyzed using ICP-MS. Results were then compared to known background concentrations as well as sediment quality guidelines and pollution thresholds. The sample locations downwind of the …


Improved Stoichiometric Synthesis Of Ccc-Nhc Pincer Rh Complexes And Catalytic Activity Towards Dehydrogenative Silylation And Hydrosilylation Of Alkenes, Enock Amoateng Aug 2023

Improved Stoichiometric Synthesis Of Ccc-Nhc Pincer Rh Complexes And Catalytic Activity Towards Dehydrogenative Silylation And Hydrosilylation Of Alkenes, Enock Amoateng

Theses and Dissertations

N-Heterocyclic carbenes (NHCs) have attracted growing interest not only as successful ancillary ligands in a wide variety of transition-metal-catalyzed reactions but have also shown to offer photophysical and electrochemical properties. The metalation/transmetalation strategy using [Zr(NMe2)4] as initial metalating reagent offers an efficient approach to the preparation of CCC-NHC pincer complexes of the late transition metals such as Rh and Ir. In the process of investigating an intermediate and the mechanism of the metalation/transmetalation to Rh sequence, a mixed valent bimetallic CCC-NHC pincer Rh complex with two chloro ligands bridged between a [(CCC-NHC)Rh(III)] and a [Rh(I)(COD)] fragment …


Direct Measurement Of The 114cd(N, Gamma)115cd Cross Section In The 1 Ev To 300 Kev Energy Range, Kofi Tutu Addo Assumin-Gyimah Aug 2023

Direct Measurement Of The 114cd(N, Gamma)115cd Cross Section In The 1 Ev To 300 Kev Energy Range, Kofi Tutu Addo Assumin-Gyimah

Theses and Dissertations

The large thermal cross section of cadmium makes it ideal for many practical applications where screening of thermal neutrons is desired. For example, in non-destructive assay techniques, or for astrophysical studies of the s-process. All such applications require precise knowledge of the neutron-capture cross section on cadmium. Although there are some data on neutron-capture cross sections particularly at thermal energies and at energies relevant for astrophysics, there is very little data at most other energies. Further, the evaluated cross sections from the ENDF and JENDL databases disagree at high energies. Therefore, there is a critical need for precise knowledge of …


A Four-Pronged Approach To Addressing A Wild Pig Invasion In A Bottomland And Upland Forested Landscape, Tyler Scott Evans Aug 2023

A Four-Pronged Approach To Addressing A Wild Pig Invasion In A Bottomland And Upland Forested Landscape, Tyler Scott Evans

Theses and Dissertations

Among exotic species that are capable of invading, establishing, and reaching pest status, few pose the range of impacts to biotic (e.g., competition with native species, predation, herbivory, introduction of other exotics) and abiotic (e.g., soil, hydrology) ecosystem components that can be attributed to the wild pig (Sus scrofa). Despite the presence of wild pigs throughout the southeastern United States for centuries, new invasions continue to occur in previously uninhabited and often under-investigated landscapes, including bottomland and upland forests. The recent invasion of the Sam D. Hamilton Noxubee National Wildlife Refuge (hereafter, NNWR) in east-central Mississippi represents an …


Investigating The Role Of Plant Traits And Interactions In Emergent Wetland Nutrient Removal, Andrew Ryan Sample Aug 2023

Investigating The Role Of Plant Traits And Interactions In Emergent Wetland Nutrient Removal, Andrew Ryan Sample

Theses and Dissertations

Increasing wetland restoration in the Lower Mississippi Alluvial Valley has been identified as a method to reduce nutrient loading in the Gulf of Mexico. Wetlands have historically been used to treat water through processes facilitated by wetland plants, and relatively few species and plant traits have been identified as important in carrying out these processes. This study focuses on some of those species and traits and aims to identify species differences and plant traits that may be important for wetland nutrient mitigation. Chapter I provides background information on nutrient pollution, wetland biogeochemical mechanisms for nutrient sequestration, and the focal species …


Expanding One-Dimensional Game Theory-Based Group Decision Models: Extension To N-Dimension And Integration Of Distributed Position Function, Mirhossein Mousavi Karimi Aug 2023

Expanding One-Dimensional Game Theory-Based Group Decision Models: Extension To N-Dimension And Integration Of Distributed Position Function, Mirhossein Mousavi Karimi

Theses and Dissertations

This dissertation aims to expand the current one-dimensional game theory based model to a multidimensional model for multi-actor predictive analytics and generalize the concept of position to address problems where actors’ positions are distributed over a position spectrum. The one-dimensional models are used for the problems where actors are interacting in a single issue space only. This is less than an ideal assumption since, in most cases, players’ strategies may depend on the dynamics of multiple issues when dealing with other players. In this research, the one-dimensional model is expanded to N-Dimensional model by considering different positions, and separate salience …


Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri Aug 2023

Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri

Theses and Dissertations

In this dissertation, we investigate various aspects of signed graphs, with a particular focus on signings and sign-symmetric signed graphs. We begin by examining the complete graph on six vertices with one edge deleted ($K_6$\textbackslash e) and explore the different ways of signing this graph up to switching isomorphism. We determine the frustration index (number) of these signings and investigate the existence of sign-symmetric signed graphs. We then extend our study to the $K_6$\textbackslash 2e graph and the McGee graph with exactly two negative edges. We investigate the distinct ways of signing these graphs up to switching isomorphism and demonstrate …


Visual And Spatial Audio Mismatching In Virtual Environments, Zachary Lawrence Garris Aug 2023

Visual And Spatial Audio Mismatching In Virtual Environments, Zachary Lawrence Garris

Theses and Dissertations

This paper explores how vision affects spatial audio perception in virtual reality. We created four virtual environments with different reverb and room sizes, and recorded binaural clicks in each one. We conducted two experiments: one where participants judged the audio-visual match, and another where they pointed to the click direction. We found that vision influences spatial audio perception and that congruent audio-visual cues improve accuracy. We suggest some implications for virtual reality design and evaluation.


Identifying Student Challenges In Organic Chemistry: Supporting Student Understanding Through Eye-Tracking, Think-Aloud Interviews And Alternative Questions, Lisa Ann Smith Aug 2023

Identifying Student Challenges In Organic Chemistry: Supporting Student Understanding Through Eye-Tracking, Think-Aloud Interviews And Alternative Questions, Lisa Ann Smith

Theses and Dissertations

Think-aloud interviews are a strategy used to identify misconceptions held by students. We incorporated think-aloud interviews and studied representational competence of novice and expert participants with identifying alkyl halides with multiple representations. We hypothesized that the participants would approach representations differently and think-aloud interviews would reveal misconceptions. Eye-tracking results showed that novice and expert participants differ in their approaches to representations and that novice participants spend more time on representations. Think-aloud interviews revealed that novice participants contain misconceptions on alkyl halide identification. This research provided insights on student understanding in identifying alkyl halides and representations, allowing instructors to use student …


Ide-Based Learning Analytics For Assessing Introductory Programming Skill, Phyllis J. Beck Aug 2023

Ide-Based Learning Analytics For Assessing Introductory Programming Skill, Phyllis J. Beck

Theses and Dissertations

Providing a sufficient level of personalized feedback on students' current level of strategic knowledge within the context of the natural programming environment through IDE-based learning analytics would transform learning outcomes for introductory programming students. However, providing sufficient insight into the programming process was previously inaccessible due to the need for more complex and scalable data collection methods and metrics with a wider variety for understanding programming metacognition and the full programming process.

This research developed a custom-built web-based IDE and event compression system to investigate two of the five components of a five-dimensional model of cognition for programming skill estimation …


Optimizing Edge-Of-Field Water Quality Monitoring Methods To Determine The Effects Of Best Management Practices On Nutrient And Sediment Runoff, Mark Hill Aug 2023

Optimizing Edge-Of-Field Water Quality Monitoring Methods To Determine The Effects Of Best Management Practices On Nutrient And Sediment Runoff, Mark Hill

Theses and Dissertations

This study investigates the impact on water quality of combined agricultural best management practices cover crop and minimum tillage, alongside an examination of techniques used to collect those samples. Edge-of-field (EOF) water quality samples were collected from 11 working farms during a two-year paired field experiment. Results showed significant reductions in nutrient concentrations, increased discharge, and mixed findings regarding nutrient mass transport post-treatment. A suite of EOF collection techniques were compared using in-situ automated water sampling systems sampling the same runoff events. Sampling protocols influenced nutrient concentrations in composite samples, but unexpected variance in velocity sensors affected measured discharge, making …


Vertical Federated Learning Using Autoencoders With Applications In Electrocardiograms, Wesley William Chorney Aug 2023

Vertical Federated Learning Using Autoencoders With Applications In Electrocardiograms, Wesley William Chorney

Theses and Dissertations

Federated learning is a framework in machine learning that allows for training a model while maintaining data privacy. Moreover, it allows clients with their own data to collaborate in order to build a stronger, shared model. Federated learning is of particular interest to healthcare data, since it is of the utmost importance to respect patient privacy while still building useful diagnostic tools. However, healthcare data can be complicated — data format might differ across providers, leading to unexpected inputs and incompatibility between different providers. For example, electrocardiograms might differ in sampling rate or number of leads used, meaning that a …


More Is Better Than One: The Effect Of Ensembling On Deep Learning Performance In Biochemical Prediction Problems, Jacob A. Stern Aug 2023

More Is Better Than One: The Effect Of Ensembling On Deep Learning Performance In Biochemical Prediction Problems, Jacob A. Stern

Theses and Dissertations

This thesis presents two papers addressing important biochemical prediction challenges. The first paper focuses on accurate protein distance predictions and introduces updates to the ProSPr network. We evaluate its performance in the Critical Assessment of techniques for Protein Structure Prediction (CASP14) competition, investigating its accuracy dependence on sequence length and multiple sequence alignment depth. The ProSPr network, an ensemble of three convolutional neural networks (CNNs), demonstrates superior performance compared to individual networks. The second paper addresses the issue of accurate ligand ranking in virtual screening for drug discovery. We propose MILCDock, a machine learning consensus docking tool that leverages predictions …


Enumerative Problems Of Doubly Stochastic Matrices And The Relation To Spectra, Julia A. Vandenlangenberg Aug 2023

Enumerative Problems Of Doubly Stochastic Matrices And The Relation To Spectra, Julia A. Vandenlangenberg

Theses and Dissertations

This work concerns the spectra of doubly stochastic matrices whose entries are rational numbers with a bounded denominator. When the bound is fixed, we consider the enumeration of these matrices and also the enumeration of the orbits under the action of the symmetric group.

In the case where the bound is two, we investigate the symmetric case. Such matrices are in fact doubly stochastic, and have a nice characterization when we are in the special case where the diagonal is zero. As a central tool to this investigation, we utilize Birkhoff's theorem that asserts that the doubly stochastic matrices are …


Nutrient Dynamics Of Freshwater Estuarine Sediments Disturbed By Dredging, Ryan Allan John Roekle Aug 2023

Nutrient Dynamics Of Freshwater Estuarine Sediments Disturbed By Dredging, Ryan Allan John Roekle

Theses and Dissertations

This study examined the nutrient environment of sediments in the Milwaukee River estuary and the dynamics of those nutrients during simulated disturbance experiments within the context of large-scale dredging remediation. Surface sediments were collected from throughout the Milwaukee estuary (including river, harbor, and nearshore stations) by PONAR, centrifuged to separate porewater (interstitial water) from solid material, and filtered to further isolate and stabilize dissolved material. Porewaters were analyzed for dissolved nutrients including ammoniacal nitrogen (AN), nitrate, nitrite, and soluble reactive phosphorus (SRP). Surface sediment porewaters within the estuary were often highly enriched in AN and SRP, which were often 10-2000x …


Benthic Algal And Macroinvertebrate Response To The Removal Of Dreissenid Mussels In The Nearshore Zone Of Lake Michigan, Tyler Alexander Kunze Aug 2023

Benthic Algal And Macroinvertebrate Response To The Removal Of Dreissenid Mussels In The Nearshore Zone Of Lake Michigan, Tyler Alexander Kunze

Theses and Dissertations

Dreissenid mussels (Dreissena polymorpha and Dreissena rostriformis bugensis) have changed the fundamental community structure and biogeochemical processes of the Lake Michigan nearshore zone. There is evidence that dreissenids promote the nuisance growth of benthic algae, especially Cladophora sp. In addition, benthic macroinvertebrates have benefitted from the presence of dreissenid mussels due to the increased structural complexity along with greater nutrient availability in the benthos. These effects of the dreissenid mussel invasion are well documented; however, little is known about how these systems respond to the removal of dreissenid mussels from a once-populated area. Therefore, it is important to further our …


The Vanishing Discount Method For Stochastic Control: A Linear Programming Approach, Brian Hospital Aug 2023

The Vanishing Discount Method For Stochastic Control: A Linear Programming Approach, Brian Hospital

Theses and Dissertations

Under consideration are convergence results between optimality criteria for two infinite-horizon stochastic control problems: the long-term average problem and the $\alpha$-discounted problem, where $\alpha \in (0,1]$ is a given discount rate. The objects under control are those stochastic processes that arise as (relaxed) solutions to a controlled martingale problem; and such controlled processes, subject to a given budget constraint, comprise the feasible sets for the two stochastic control problems.

In this dissertation, we define and characterize the expected occupation measures associated with each of these stochastic control problems, and then reformulate each problem as an equivalent linear program over a …


Collapsibility And Z-Compactifications Of Cat(0) Cube Complexes, Daniel L. Gulbrandsen Aug 2023

Collapsibility And Z-Compactifications Of Cat(0) Cube Complexes, Daniel L. Gulbrandsen

Theses and Dissertations

We extend the notion of collapsibility to non-compact complexes and prove collapsibility of locally-finite CAT(0) cube complexes. Namely, we construct such a cube complex $X$ out of nested convex compact subcomplexes $\{C_i\}_{i=0}^\infty$ with the properties that $X=\cup_{i=0}^\infty C_i$ and $C_i$ collapses to $C_{i-1}$ for all $i\ge 1$.

We then define bonding maps $r_i$ between the compacta $C_i$ and construct an inverse sequence yielding the inverse limit space $\varprojlim\{C_i,r_i\}$. This will provide a new way of Z-compactifying $X$. In particular, the process will yield a new Z-boundary, called the cubical boundary.