Physical Sciences and Mathematics Commons^™

Method Development For The Quantification Of Critically Valuable Elements In Permian Basin Produced Waters, Carley Oliver

Open Access Theses & Dissertations

Produced waters (PW) are a major byproduct of the oil and gas industrial hydraulic fracturing processes that create a major waste disposal issue with a need for disposal, treatment, and reuse method developments. The current primary disposal method is subsurface injection, which can lead to high pressures in the subsurface. PWs are often highly saline from mineral leaching due to long residence in subsurface reservoirs. According to the USGS National Minerals Information Center, bromine, calcium chloride, iodine, lithium, magnesium, and sodium chloride have been found in and extracted from these domestic subsurface brines, suggesting that there may be other economically …

Investigation Of Seasonal Trends And Source Apportionment Of Particulate Matter (Pm2.5) In El Paso-Juarez Airshed, Fatema Tuz Zohora

Open Access Theses & Dissertations

Using the data from Texas Commission on Environmental Quality (TCEQ) for the El Paso city throughout the years from 2021 to 2024 Particulate Matter (PM2.5) was measured to examine the seasonal distribution and sources. This study aims to understand the seasonal variability of PM2.5 concentrations, identify the significant impact of wildfire events on this and source apportionment.The analysis begins with a comprehensive examination of PM2.5 data from TCEQ highlighting the seasonal pattern, it was found that fine particulate matter was more prevalent in winter and tends to be down in spring, and in summer it is relatively lower, subsequently in …

Improving Cyber Defense Using Detailed Bayesian Models Of Attacker Reconnaissance., Nazia Sharmin

Open Access Theses & Dissertations

The continued success of cyber-attacks motivates the need for continued innovation in cyber defense. In particular, there is a need for novel methods to mitigate attacker reconnaissance, usually the first stage in planning an attack. One of the few general approaches in this stage is using deception and information manipulation to affect what the attacker can learn about a system or network. Existing work in moving target defense, game-theoretic models of cyber deception/camouflage, and adversarial learning has provided a framework for optimizing deception strategies. However, most of the current literature is based on limited models of how attackers actually perform …

Neural Networks For Decisions Under Uncertainty, Edwin Tomy George

Open Access Theses & Dissertations

Neural networks are used in many real-world applications, ranging from classification tasks to medical diagnostics. For each task, a neural network is typically able to make predictions due to its ability to extract meaningful patterns from processing large amounts of data. Thus, given the increases in available data in recent decades, the performance of neural networks in making accurate predictions has greatly increased. However, this data often comes with ingrained uncertainties due to measurement errors or the inherent variability of individual data points. Neural networks can learn despite the errors in the overall data, but what if we want them …

Design Of Engineered Nanomaterials For Pfas Adsorption And Catalytic Degradation From Relevant Environmental Conditions, Sheng Yin

Open Access Theses & Dissertations

Poly- and per-fluoroalkyl substances (PFAS) are a class of artificially made chemicals whose carbon chains are fully or partially fluorinated. Due to their persistent and pervasive distribution and their adverse effects on human health, the removal of PFAS from the environment has been the focus of current research. This project explores the use of engineered nanomaterials for the effective removal of PFAS through various adsorption and catalytic degradation methods. First, a comprehensive review of recent studies highlights the significant potential of various nanomaterials, including carbon-based, non-metal, single-metal, and multi-metal nanomaterials, for PFAS remediation. These materials are evaluated for their performance, …

Investigating Styles Of Contraction And Overprinting By Rio Grande Rift Extension In The Southern Indio Mountains, Western Texas, David W. West

Open Access Theses & Dissertations

Laramide-style intracontinental deformation occurred throughout a large area in the western United States from the late Cretaceous through the Eocene. This event is largely investigated and viewed from classic exposures in Colorado and Wyoming, extending south to southern New Mexico. In this region the Laramide orogen merges with the Mexican fold and thrust belt (MFTB) and the northern limits of the Mexican orogen along a blurry boundary. In the Indio Mountain range in western Texas, Cretaceous sediments were deposited in the Jurassic-Cretaceous Chihuahua trough. They were inverted due to contraction and emplaced adjacent to the Diablo Plateau. This region lies …

Determining Heterogeneous Growth Rates Of Brucite On Magnesia Using Multiharmonic Qcm-D And X-Ray Scattering Methods, Pedro Josue Hernandez Penagos

Open Access Theses & Dissertations

The Earth’s temperature has increased in the last six decades mainly due to the emissions of greenhouse gases, including carbon dioxide (CO2). Mineral looping using magnesium oxide (MgO) is a promising approach for direct air capture (DAC) of CO2 from the atmosphere at the GtCO2/yr scale. The presence of humidity during the carbonation process will lead to a reaction between the MgO and water resulting in magnesium hydroxide formation, Mg(OH)2, growing over the MgO surface forming a shell-like structure. The influence of temperature and relative humidity variation on heterogeneous nucleation and crystal growth kinetics of Mg(OH)2 on MgO is not …

Staying Fresh: Unconventional Approaches Towards Advancing Energy Sustainability, Water Resources, And Community Resiliency In The Southwestern United States, Judith Hoyt

Open Access Theses & Dissertations

This dissertation addresses critical challenges in urban heat management, sustainable energy resource utilization, and water quality communication through three studies. Study 1 investigates the impact of roof color on urban heat islands in Tucson, Arizona where approximately 70% of roofs display high albedo (i.e., light) colors. Energy consumption simulations conducted indicate that converting dark- to light-colored roofs could save Tucson approximately $1,400,000 annually in energy costs, highlighting the potential of cool roofs for energy savings and improved thermal comfort. Study 2 assesses the sources of lithium in subsurface waters in West Texas and South Central New Mexico. Water chemistry data …

Zebra Limestone From The Gypsum Valley Salt Diapir, Colorado, Rebecca Navarrette

Open Access Theses & Dissertations

Zebra rocks displaying alternating light and dark-colored millimeter to centimeter thick bands of crystals have been found at the Gypsum Valley salt diapir, Colorado in the Paradox Basin where they are associated with gypsic diapiric caprock. Elucidating their origin may provide crucial information about intermittent fluid flow at the margin of salt diapirs and about Zebra rock formation, which often is associated with carbonate-hosted lead-zinc mineralization (Mississippi Valley Type, MVT) and hydrothermal dolomite -hosted hydrocarbon reservoirs.

The Gypsum Valley Zebra rocks consist of calcite, i.e., it is a Zebra limestone. It shows a finely crystalline light banding and coarsely crystalline …

Robust Multivariate Estimation And Inference With The Minimum Density Power Divergence Estimator, Ebenezer Nkum

Open Access Theses & Dissertations

The estimation of the location vector and scatter matrix plays a crucial role in many multivariate statistical methods. However, the classical likelihood-based estimation is greatly influenced by outliers, potentially leading to unreliable decisions. Hence, a fundamental challenge in multivariate statistics is to develop robust alternatives that can maintain performancein the presence of outliers and deviations from the assumed data distribution. Unfortunately, methods with good global robustness often substantially sacrifice efficiency. To address this, we propose the adoption of Minimum Density Power Divergence (MDPD) estimation, a well-established robust technique known for its efficiency and statistical robustness to outliers and model violations. …

Semantic Linguistic User Profiles For Automatic Computational Narrative Creation For Scientific Models, Angel Uriel Ortega Castillo

Open Access Theses & Dissertations

The outcomes of scientific models can be hard to understand given the need for context, domain knowledge, and many variables and data being used. This research aims to provide users of scientific models with understandable information that can be automatically generated. For the context of this research, understandable is defined as being correctly interpreted (i.e., with respect to the original intent of the data). Scientific information can be conveyed to users in the form of a narrative or visualizations, and these are not necessarily separate from each other, but rather complimentary. One of the objectives of this research is to …

Random Forest For High-Dimensional Data, George Ekow Quaye

Open Access Theses & Dissertations

The exponential growth of data has led to a rapid increase in high-dimensional datasets across various domains, presenting significant challenges in data analysis, particularly in predictive modeling tasks. Traditional Random Forest (RF), while robust, often struggles with datasets filled with numerous noisy or non-informative features, compromising both performance and accuracy. This study introduces an advanced algorithm, High-Dimensional Random Forests (HDRF), designed to address these challenges by integrating robust multivariate feature selection techniques directly into the decision tree construction process. Unlike standard RF, HDRF incorporates ridge regression-based variable screening at each decision split, enhancing its ability to identify and utilize the …

Quantum Circuit Optimization Leveraging Multi-Qubit Exchange Interactions In Spin Qubits, Miguel Gonzalo Rodriguez

Open Access Theses & Dissertations

This thesis looks into how multi-qubit exchange interactions can be used to improve quantumcircuits in semiconductor quantum devices. Pairwise interactions between qubits are a common tenet of traditional quantum computing paradigms, although they can impose complexity and depth constraints on circuits. In order to improve the efficiency and scalability of quantum circuits, this research explores the theoretical underpinnings and practical uses of multi-qubit interactions. A thorough theoretical framework is formulated, outlining the mathematical equivalence of a unitary matrix representing interactions between multiple qubits. We obtain the timeevolution operator by analyzing the Hamiltonian of three spin-1/2 particles. A number of quantum …

Seismic Imaging Of Mcmurdo Ice Shelf Near Williams Airfield, Yeshey Seldon

Open Access Theses & Dissertations

Seismic exploration has played a crucial role in understanding the Earth's interior and has been successfully employed in various regions, including Antarctica. This research focuses on analyzing a 1000-m seismic line on McMurdo Ice Shelf near Williams Airfield, as part of the Thwaites Interdisciplinary Margin Evolution (TIME) project. The McMurdo Ice Shelf, covering an expansive area within the Ross Ice Shelf, has undergone significant changes due to evolving oceanic and atmospheric conditions. The presence of Circumpolar Deep Water (CDW) has recently impacted the ice shelf, with warmer ocean waters causing basal melting and changes in wind patterns affecting ice flow …

Stochastic Dominance: Cases Of Interval And P-Box Uncertainty, Kittawit Autchariyapanikul, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional decision theory recommendation about making a decision assume that we know both the probabilities of different outcomes of each possible decision, and we know the utility function -- that describes the decision maker's preferences. Sometimes, we can make a recommendation even when we only have partial information about utility. Such cases are known as cases of stochastic dominance. In other cases, in addition to not knowing the utility function, we also only have partial information about the probabilities of different outcomes. For example, we may only known bounds on the outcomes (case of interval uncertainty) or bounds on the …

If Subsequent Results Are Too Easy To Obtain, The Proof Most Probably Has Errors: Explanation Of The Empirical Observation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many modern mathematical proofs are very complex, checking them is difficult; as a result, errors sneak into published proofs, even into proofs published in highly reputable journals. Sometimes, the errors are repairable, but sometimes, it turns out that the supposedly proven result is actually wrong. When the error is not noticed for some time, the published result is used to prove many other results -- and when the error is eventually found, all these new results are invalidated. This happened several times. Since it is not realistic to more thoroughly check all the proofs, and we want to minimize the …

For 2 X N Cases, Proportional Fitting Problem Reduces To A Single Equation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, for each of two classifications, we know the probabilities that a randomly selected object belong to different categories. For example, we know what proportion of people are below 20 years old, what proportion is between 20 and 30, etc., and we also know what proportion of people earns less than 10K, between 10K and 20K, etc. In such situations, we are often interested in proportion of people who are classified by two classifications into two given categories. For example, we are interested in the proportion of people whose age is between 20 and 30 and whose …

Is Alaska Negative-Tax Arrangement Fair? Almost: Mathematical Analysis, Chon Van Le, Vladik Kreinovich

Departmental Technical Reports (CS)

In the State of Alaska there is no state income tax. Instead, there is a negative tex: every year every resident gets some money from the state. At present, every resident -- from the poorest to the richest -- gets the exact same amount of money: in 2024, it is expected to be around $1500. A natural question is: Is this fair? Maybe poor people should get more since their needs are greater? Maybe the rich people should get proportionally more, since fairness means equal added happiness for all, and for rich people, extra $1500 is barely noticeable? There have …

Why Angles Between Galactic Center Filaments And Galactic Plane Follow A Bimodal Distribution: A Symmetry-Based Explanation, Julio C. Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

Recent observations have shown that the angles between the Galaxy Center filaments and the Galactic plane follow a bimodal distribution: a large number of filaments are approximately orthogonal to the Galactic plane, a large number of filaments are approximately parallel to the Galactic plane, and much fewer filaments have other orientations. In this paper, we show this bimodal distribution can be explained by natural geometric symmetries.

Why Seismicity In Ireland Is Low: A Possible Geometric Explanation, Julio C. Urenda, Aaron Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

For each geographic location, its seismicity level is usually determined by how close this location is to the boundaries of tectonic plates. However, there is one notable exception: while Ireland and Britain are at approximately the same distance from such boundaries, the seismicity level in Ireland is much lower than in Britain. A recent paper provided a partial explanation for this phenomenon: namely, it turns out that the lithosphere under Ireland is unusually thick, and this can potentially lead to lower seismicity. However, the current explanation of the relation between the lithosphere thickness and seismicity level strongly depends on the …

For Discrete-Time Linear Dynamical Systems Under Interval Uncertainty, Predicting Two Moments Ahead Is Np-Hard, Luc Jaulin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the first approximation, when changes are small, most real-world systems are described by linear dynamical equations. If we know the initial state of the system, and we know its dynamics, then we can, in principle, predict the system's state many moments ahead. In practice, however, we usually know both the initial state and the coefficients of the system's dynamics with some uncertainty. Frequently, we encounter interval uncertainty, when for each parameter, we only know its range, but we have no information about the probability of different values from this range. In such situations, we want to know the range …

What To Do If An Inflexible Tolerance Problem Has No Solutions: Probabilistic Justification Of Piegat's Semi-Heuristic Idea, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, it is desirable to select the control parameters x1, ..., xn in such a way that the resulting quantities y1, ..., ym of the system lie within desired ranges. In such situations, we usually know the general formulas describing the dependence of yi on xj, but the coefficients of these formulas are usually only known with interval uncertainty. In such a situation, we want to find the tuples for which all yi's are in the desired intervals for all possible tuples of coefficients. But what if no such parameters are possible? Since we cannot guarantee the …

How To Make Ai More Reliable, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the reasons why the results of the current AI methods (especially deep-learning-based methods) are not absolutely reliable is that, in contrast to more traditional data processing techniques which are based on solid mathematical and statistical foundations, modern AI techniques use a lot of semi-heuristic methods. These methods have been, in many cases, empirically successful, but the absence of solid justification makes us less certain that these methods will work in other cases as well. To make AI more reliable, it is therefore necessary to provide mathematical foundations for the current semi-heuristic techniques. In this paper, we show that …

Why Magenta Is Not A Real Color, And How It Is Related To Fuzzy Control And Quantum Computing, Victor L. Timchenko, Yuriy P. Kondratenko, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is well known that every color can be represented as a combination of three basic colors: red, green, and blue. In particular, we can get several colors by combining two of the basic colors. Interestingly, while a combination of two neighboring colors leads to a color that corresponds to a certain frequency, the combination of two non-neighboring colors -- red and blue -- leads to magenta, a color that does not correspond to any frequency. In this paper, we provide a simple explanation for this phenomenon, and we also show that a similar phenomenon happens in two other areas …

How To Propagate Uncertainty Via Ai Algorithms, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Any data processing starts with measurement results. Measurement results are never absolutely accurate. Because of this measurement uncertainty, the results of processing measurement results are, in general, somewhat different from what we would have obtained if we knew the exact values of the measured quantities. To make a decision based on the result of data processing, we need to know how accurate is this result, i.e., we need to propagate the measurement uncertainty through the data processing algorithm. There are many techniques for uncertainty propagation. Usually, they involve applying the same data processing algorithm several times to appropriately modified data. …

Why Empirical Membership Functions Are Well-Approximated By Piecewise Quadratic Functions: Theoretical Explanation For Empirical Formulas Of Novak's Fuzzy Natural Logic, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Empirical analysis shows that membership functions describing expert opinions have a shape that is well described by a smooth combination of two quadratic segments. In this paper, we provide a theoretical explanation for this empirical phenomenon.

Why Fully Consistent Quantum Field Theories Require That The Space-Time Be At Least 10-Dimensional: A Commonsense Field-Based Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that quantum field theories that describe fields in our usual 4-dimensional space-times are not fully consistent: they predict meaningless infinite values for some physical quantities. There are some known tricks to avoid such infinities, but it is definitely desirable to have a fully consistent theory, a theory that would produce correct results without having to use additional tricks. It turns out that the only way to have such a theory is to consider space-times of higher dimensions, the smallest of which is 10. There are complex mathematical reasons for why 10 is the smallest such dimension. However, …

Why Is Grade Distribution Often Bimodal? Why Individualized Teaching Adds Two Sigmas To The Average Grade? And How Are These Facts Related?, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To make education more effective, to better use emerging technologies in education, we need to better understand the education process, to gain insights on this process. How can we check whether a new idea is indeed a useful insight? A natural criterion is that the new idea should explain some previously-difficult-to-explain empirical phenomenon. Since one of the main advantages of emerging educational technologies -- such as AI -- is the possibility of individualized education, a natural phenomenon to explain is the fact -- discovered by Benjamin Bloom -- that individualization adds two sigmas to the average grade. In this paper, …

Towards A More Subtle (And Hopefully More Adequate) Fuzzy "And"-Operation: Normalization-Invariant Multi-Input Aggregation Operators, Yusuf Güven, Vladik Kreinovich

Departmental Technical Reports (CS)

Many reasonable conditions have been formulated for a fuzzy "and"-operation: idempotency, commutativity, associativity, etc. It is known that the only "and"-operation that satisfies all these conditions is minimum, but minimum is not the most adequate description of expert's "and", and it often does not lead to the best control or the best decision. Many other more adequate "and"-operations (t-norms) have been proposed and effectively used, but they do not satisfy the natural idempotency condition. In this paper, we show that a small relaxation of the usual description of "and"-operations leads to the possibility of non-minimum idempotent operations. We also show …

How To Make A Neural Network Learn From A Small Number Of Examples -- And Learn Fast: An Idea, Chitta Baral, Vladik Kreinovich

Departmental Technical Reports (CS)

Current deep learning techniques have led to spectacular results, but they still have limitations. One of them is that, in contrast to humans who can learn from a few examples and learn fast, modern deep learning techniques require a large amount of data to learn, and they take a long time to train. In this paper, we show that neural networks do have a potential to learn from a small number of examples -- and learn fast. We speculate that the corresponding idea may already be implicitly implemented in Large Language Models -- which may partially explain their (somewhat mysterious) …