Physical Sciences and Mathematics Commons^™

The P-Laplacian Problem Via An Euler Equation And The Basis Properties Of Its Eigenfunctions, Luis Suarez Salas

Open Access Theses & Dissertations

The Laplacian operator is used in many fields of science, such as fluidodynamics, mechanics and elasticity. Mathematically, much research has been devoted to develop a theory with which it and other variations can be understood. In this work, we present the p-Laplacian problem via an Euler equation. We then study the properties of its eigenfunctions which generalize the trigonometric functions sine and cosine. In connection with a Fourier series, we then show the generalized trigonometric functions possess basis properties for L^r((0,1)^d), d=1,2,3. Finally, we introduce the spaces of variable exponent and the analogue p(x)-Laplacian problem which has immense applications such …

Decision Making For Dynamic Systems Under Uncertainty: Predictions And Parameter Recomputations, Leobardo Valera

Open Access Theses & Dissertations

In this Thesis, we are interested in making decision over a model of a dynamic system. We want to know, on one hand, how the corresponding dynamic phenomenon unfolds under different input parameters (simulations). These simulations might help researchers to design devices with a better performance than the actual ones. On the other hand, we are also interested in predicting the behavior of the dynamic system based on knowledge of the phenomenon in order to prevent undesired outcomes. Finally, this Thesis is concerned with the identification of parameters of dynamic systems that ensure a specific performance or behavior.

Understanding the …

Massively Parallel Computational Studies Of Material Response At High Strain Rate Deformation, Jayalath Abeywardhana Mudiyanselage Madawa Abeywardhana

Open Access Theses & Dissertations

Large scale molecular dynamics (MD) simulations are now commonly utilized to study materials at extreme conditions: high pressure and/or temperatures and ultra-high strain rates of deformation. A variety of emerging architectures such as general purpose graphics processing units (GP-GPU) and many-integrated core (MIC) architecture as well as new execution models have changed the traditional approach of high-performance computing. ExMatEx, the DoE initiative for enabling exa-scale (10^18 flops) performance in scientific applications, has developed several proxy applications to facilitate co-design of novel algorithms and hardware by software developers and microchip vendors.

We have used CoMD, a proxy application for classical MD, …

Effects Of Increasing Deciduous Shrub Litter On Ecosystem Functioning In Alpine Tundra, Alejandro Emmanuel Benhumea

Open Access Theses & Dissertations

Rising temperatures due to global warming have resulted in rapid environmental changes in northern environments, resulting in an increase in deciduous shrub growth which has the potential to alter soil ecosystem properties and processes. In order to address some potential mechanisms by which shrubs alter ecosystem properties and processes, we designed an experiment which separated the effects of physical shrub presence and the effects of litter quantity in a fully factorial experiment on a north facing alpine plateau in the southwest Yukon, Canada. Specifically, we asked the following questions: What are effects of shrub litter, independent of shrub presence, on …

Magnetotelluric Analysis Of Central Kenya Kenyan Rift Volcanoes For Geothermal Development, Anna Wairimu Mwangi

Open Access Theses & Dissertations

Abstract

High temperature geothermal resources are vast along rift margins because of emplacement of magma in shallow crust. This is the case along the Kenyan Rift valley also known as the Gregory Rift. It is the Eastern arm of the East African rift and a chain of volcanoes along the rift graben characterizes it. We use (MT) magnetotelluric method to image beneath the peralkaline province of the Kenya Rift i.e. Olkaria, Eburru, Badlands, and Longonot volcanoes. The resistivity structure shows active geothermal activity happening at the upper 3km from the subsurface as evidenced by low resistivity cap rock comprised of …

Experimental Laser Powder Bed Fusion System For Difficult To Process Metallic Materials, Syed Zia Uddin

Open Access Theses & Dissertations

The focus of this research was twofold, such as development of defect free fabrication parameters for laser powder bed fusion (LPBF) processing of crack prone or difficult to process metallic materials, and study of the temperature dependence of emissivity for some commonly used metal alloy powders in LPBF process. The later objective extends to the implementation of multiwavelength (MW) pyrometer technology for in situ true surface temperature measurement in LPBF process. LPBF is an additive manufacturing (AM) process capable of layer-by-layer manufacturing by successive laser melting of each layer according to CAD data. AM manufacturing has the inherent advantages of …

Detection Of Pharmaceuticals And Personal Care Products In The Rio Grande And Their Effects On A Model Aquatic Invertebrate (Rotifera, Monogononta: Plationus Patulus), Enrique David Garcia

Open Access Theses & Dissertations

Rivers, including the Rio Grande, receive discharges from urban, agricultural, and industrial areas. These discharges have potentially harmful contaminants that may affect life span, fecundity, and/or behaviors of aquatic organisms. In this project, water quality was analyzed near a discharge point source and impacts of pharmaceuticals and personal care products (PPCPs) on a non-target organism (Plationus patulus) were investigated. Long-term and integrative organic samplers (POCIS) were left in situ for about 1 month near a wastewater treatment plant that discharges effluent into the Rio Grande. Over 40 PPCPs, including carbamazepine (ranging from 17.50 to 584.29 ng/L), erythromycin (ranging from 0.51 …

Trace Metal And Metalloid Behavior In The Submicron Scale Components Of Coal Fly Ashes: Insights From Combined Microscopic And Microbiological Studies, Matthew Costa

Open Access Theses & Dissertations

For over a century, coal has been used worldwide to meet ever-growing energy demands. Coal combustion accounts for over 30% of electricity generation in the United States. In the U.S., coal combustion produces annually over 100 million tons of coal combustion products (CCPs) of which only 30% are used in beneficial and economic ways. One of the primary CCPs from coal-burning power plants is fly ash, typically fine-sized and enriched in many trace elements (e.g., arsenic, chromium, lead, and vanadium). When disposed in the environment, fly ash may release significant concentrations of trace elements into surrounding ecosystems and induce toxicity …

The Hierarchical Structure Of Nanoporous Carbon Electrode Materials Elucidated By Water Sorption: A Comparison Of Multiple Structural Models, Jose Ali Espitia

Open Access Theses & Dissertations

The total amount of energy that an electrical double layer capacitor (EDLC) can store depends on the voltage and the accessible surface area for ion electrosorption. Nanoporous carbon materials with a high specific surface area, such as carbide derived carbon (CDC), make ideal electrodes for EDLC devices. CDC materials have fine-tuned pore sizes in the subnanometer range which are controlled by the initial carbide (TiC) and annealing conditions. Water can enter TiC-CDC pores and give filling fractions in excess of 0.6 g/g (H2O/C). Recent reports of water's diffusional dynamics dependence on CDC pore size indicate confinement effects similar to that …

Environmental And Genetic Factors Affecting Antibiotic Resistance Of Extended Spectrum Î?-Lactamase Bacteria From The Rio Grande River In El Paso, Tx And Cd. Juarez, Mexico, Maria D. Fuentes

Open Access Theses & Dissertations

Background: The Rio Grande River provides a major source of potable and agricultural water for the population of the Texas/Mexico border region. Cattle farming and ranching are the most prevalent activities, which may contribute to the microbial burden of pharmaceuticals into our state's water resources. Antibiotics, presumably released into the environment by discharges originating from waste-water treatment plants, septic disposal systems, animal feeding operations and urban runoff have a definite impact on the ecosystem and may contribute to an increase in antibiotic resistance. We hypothesized that waters of the Rio Grande River contained Multi Drug Resistant Organisms (MDRO) and mobile …

Gravitational Waves Research At Toros Utrgv, Pamela Ivonne Lara

Open Access Theses & Dissertations

The detection of gravitational waves (GW) has directly opened a new era in the observation of cosmic events. One hundred years after its theoretical prediction we find ourselves immerged in the multi-messenger study of the signals at the root of gravitational wave detection. The electromagnetic (EM) counterpart to GW is the optical portion of that signal and the main objective in the organization of TOROS Collaboration: finding and studying kilonovas, the name given by Metzger (Metzger et al, 2010), to the EM counterpart to gravitational waves.

In order for TOROS to find kilonovas, it needed to create a python language …

Assessing The Hydrologic Impacts Of Extreme Rainfall And Land Use Change On A Semiarid Watershed, Tahneen Jahan Neelam

Open Access Theses & Dissertations

Abstract: Intense precipitation events increase the risk of flash floods in the New Mexico-Texas-Mexico border region. Compounding effects of changing land use and precipitation pattern can influence rainfall-runoff processes that govern flash flooding. Paradoxically, this southwestern semiarid watershed has substantial water conflict that may get worse by 2025 due to changing climate and increasingly competitive demands for over-appropriated water resources. Using Soil and Water Assessment Tool (SWAT), we investigate the impact of changes in precipitation intensity and land use on runoff and arroyo flows in the dry, mountainous terrains. The baseline watershed simulation model shows that for a statistically insignificant …

Synthesis And Application Of Photoreactive Collagen Peptides, And Antiparasitic Agents, Alfredo Ornelas

Open Access Theses & Dissertations

Since the introduction of solid phase peptide synThesis in 1963, peptides and post-translationally modified peptides can be conveniently synthesized in the chemistry laboratory. In the past decade, there has been a remarkable increase in bioactive peptide research and the therapeutic peptide market value is expected to hit $25 billion this year. Peptides can also provide structural and biological functions and have emerged as promising novel biomaterials in tissue engineering. Here we will describe three different projects, which deal with different aspects of peptide chemistry, i.e. synthetic method development, exploration of new peptide biomaterials, and the use of cell penetrating peptides …

Why Rectified Linear Neurons Are Efficient: Symmetry-Based, Complexity-Based, And Fuzzy-Based Explanations, Olac Fuentes, Justin Parra, Elizabeth Y. Anthony, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, neural networks used a sigmoid activation function. Recently, it turned out that piecewise linear activation functions are much more efficient -- especially in deep learning applications. However, so far, there have been no convincing theoretical explanation for this empirical efficiency. In this paper, we show that, by using different uncertainty techniques, we can come up with several explanations for the efficiency of piecewise linear neural networks. The existence of several different explanations makes us even more confident in our results -- and thus, in the efficiency of piecewise linear activation functions.

Z-Numbers: How They Describe Student Confidence And How They Can Explain (And Improve) Laplacian And Schroedinger Eigenmap Dimension Reduction In Data Analysis, Vladik Kreinovich, Olga Kosheleva, Michael Zakharevich

Departmental Technical Reports (CS)

Experts have different degrees of confidence in their statements. To describe these different degrees of confidence, Lotfi A. Zadeh proposed the notion of a Z-number: a fuzzy set (or other type of uncertainty) supplemented by a degree of confidence in the statement corresponding to fuzzy sets. In this chapter, we show that Z-numbers provide a natural formalization of the competence-vs-confidence dichotomy, which is especially important for educating low-income students. We also show that Z-numbers provide a natural theoretical explanation for several empirically heuristic techniques of dimension reduction in data analysis, such as Laplacian and Schroedinger eigenmaps, and, moreover, show how …

Why Deep Learning Methods Use Kl Divergence Instead Of Least Squares: A Possible Pedagogical Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most applications of data processing, we select the parameters that minimize the mean square approximation error. The same Least Squares approach has been used in the traditional neural networks. However, for deep learning, it turns out that an alternative idea works better -- namely, minimizing the Kullback-Leibler (KL) divergence. The use of KL divergence is justified if we predict probabilities, but the use of this divergence has been successful in other situations as well. In this paper, we provide a possible explanation for this empirical success. Namely, the Least Square approach is optimal when the approximation error is normally …

Why Triangular Membership Functions Are Often Efficient In F-Transform Applications: Relation To Interval Uncertainty\\ And Haar Wavelets, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy techniques describe expert opinions. At first glance, we would therefore expect that the more accurately the corresponding membership functions describe the expert's opinions, the better the corresponding results. In practice, however, contrary to these expectations, the simplest -- and not very accurate -- triangular membership functions often work the best. In this paper, on the example of the use of membership functions in F-transform techniques, we provide a possible theoretical explanation for this surprising empirical phenomenon.

Beyond Integration: A Symmetry-Based Approach To Reaching Stationarity In Economic Time Series, Songsak Sriboonchitta, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many efficient data processing techniques assume that the corresponding process is stationary. However, in areas like economics, most processes are not stationery: with the exception of stagnation periods, economies usually grow. A known way to apply stationarity-based methods to such processes -- integration -- is based on the fact that often, while the process itself is not stationary, its first or second differences are stationary. This idea works when the trend polynomially depends on time. In practice, the trend is usually non-polynomial: it is often exponentially growing, with cycles added. In this paper, we shod how integration techniques can be …

Why Sparse?, Thongchai Dumrongpokaphan, Olga Kosheleva, Vladik Kreinovich, Aleksandra Belina

Departmental Technical Reports (CS)

In many situations, a solution to a practical problem is sparse, i.e., corresponds to the case when most of the parameters describing the solution are zeros, and only a few attain non-zero values. This surprising empirical phenomenon helps solve the corresponding problems -- but it remains unclear why this phenomenon happens. In this paper, we provide a possible theoretical explanation for this mysterious phenomenon.

How To Best Apply Neural Networks In Geosciences: Towards Optimal "Averaging" In Dropout Training, Afshin Gholamy, Justin Parra, Vladik Kreinovich, Olac Fuentes, Elizabeth Y. Anthony

Departmental Technical Reports (CS)

The main objectives of geosciences is to find the current state of the Earth -- i.e., solve the corresponding inverse problems -- and to use this knowledge for predicting the future events, such as earthquakes and volcanic eruptions. In both inverse and prediction problems, often, machine learning techniques are very efficient, and at present, the most efficient machine learning technique is deep neural training. To speed up this training, the current learning algorithms use dropout techniques: they train several sub-networks on different portions of data, and then "average" the results. A natural idea is to use arithmetic mean for this …

Why Taylor Models And Modified Taylor Models Are Empirically Successful: A Symmetry-Based Explanation, Mioara Joldes, Christoph Lauter, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that symmetry-based ideas can explain the empirical success of Taylor models and modified Taylor models in representing uncertainty.

How To Store Tensors In Computer Memory: An Observation, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, after explaining the need to use tensors in computing, we analyze the question of how to best store tensors in computer memory. Somewhat surprisingly, with respect to a natural optimality criterion, the standard way of storing tensors turns out to be one of the optimal ones.

How To Make A Proof Of Halting Problem More Convincing: A Pedagogical Remark, Benjamin W. Robertson, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

As an example of an algorithmically undecidable problem, most textbooks list the impossibility to check whether a given program halts on given data. A usual proof of this result is based on the assumption that the hypothetical halt-checker works for all programs. To show that a halt-checker is impossible, we design an auxiliary program for which the existence of such a halt-checker leads to a contradiction. However, this auxiliary program is usually very artificial. So, a natural question arises: what if we only require that the halt-checker work for reasonable programs? In this paper, we show that even with such …

Do It Today Or Do It Tomorrow: Empirical Non-Exponential Discounting Explained By Symmetry And Fuzzy Ideas, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

At first glance, it seems to make sense to conclude that when a 1 dollar reward tomorrow is equivalent to a D < 1 dollar reward today, the day-after-tomorrow's 1 dollar reward would be equivalent to D * D = D² dollars today, and, in general, a reward after time t is equivalent to D(t) = D^t dollars today. This exponential discounting function D(t) was indeed proposed by the economists, but it does not reflect the actual human behavior. Indeed, according to this formula, the effect of distant future events is negligible, and thus, it would be reasonable for a person to take on huge loans or get engaged in unhealthy behavior even when the long-term consequences …

Quantum Econometrics: How To Explain Its Quantitative Successes And How The Resulting Formulas Are Related To Scale Invariance, Entropy, Fuzzy, And Copulas, Hung T. Nguyen, Kittawit Autchariyapanitkul, Olga Kosheleva, Vladik Kreinovich, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Many aspects of human behavior seem to be well-described by formulas of quantum physics. In this paper, we explain this phenomenon by showing that the corresponding quantum-looking formulas can be derived from the general ideas of scale invariance, fuzziness, and copulas. We also use these ideas to derive a general family of formulas that include non-quantum and quantum probabilities as particular cases -- formulas that may be more adequate for describing human behavior than purely non-quantum or purely quantum ones.

Sudoku App: Model-Driven Development Of Android Apps Using Ocl?, Yoonsik Cheon, Aditi Barua

Departmental Technical Reports (CS)

Model driven development (MDD) shifts the focus of software development from writing code to building models by developing an application as a series of transformations on models including eventual code generation. Can the key ideas of MDD be applied to the development of Android apps, one of the most popular mobile platforms of today? To answer this question, we perform a small case study of developing an Android app for playing Sudoku puzzles. We use the Object Constraint Language (OCL) as the notation for creating precise models and translate OCL constraints to Android Java code. Our findings are mixed in …

Propagation Of Probabilistic Uncertainty: The Simplest Case (A Brief Pedagogical Introduction), Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The main objective of this text is to provide a brief introduction to formulas describing the simplest case of propagation of probabilistic uncertainty -- for students who have not yet taken a probability course.

Need For A Large-N Array (And Wavelets And Differences) To Determine The Assumption-Free 3-D Earth Model, Solymar Ayala Cortez, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main objectives of geophysical seismic analysis is to determine the Earth's structure. Usually, to determine this structure, geophysicists supplement the measurement results with additional geophysical assumptions. An important question is: when is it possible to reconstruct the Earth's structure uniquely based on the measurement results only, without the need to use any additional assumptions? In this paper, we show that for this, one needs to use large-N arrays -- 2-D arrays of seismic sensors. To actually perform this reconstruction, we need to use differences between measurements by neighboring sensor and we need to apply wavelet analysis to …

An Ancient Bankruptcy Solution Makes Economic Sense, Anh H. Ly, Michael Zakharevich, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

While econometrics is a reasonable recent discipline, quantitative solutions to economic problem have been proposed since the ancient times. In particular, solutions have been proposed for the bankruptcy problem: how to divide the assets between the claimants? One of the challenges of analyzing ancient solutions to economics problems is that these solutions are often presented not as a general algorithm, but as a sequence of examples. When there are only a few such example, it is often difficult to convincingly extract a general algorithm from them. This was the case, for example, for the supposedly fairness-motivated Talmudic solution to the …

Impacts Of Java Language Features On The Memory Performances Of Android Apps, Yoonsik Cheon, Adriana Escobar De La Torre

Departmental Technical Reports (CS)

Android apps are written in Java, but unlike Java applications they are resource-constrained in storage capacity and battery lifetime. In this document, we perform an experiment to measure quantitatively the impact of Java language and standard API features on the memory efficiency of Android apps. We focus on garbage collection because it is a critical process for performance affecting user experience. We learned that even Java language constructs and standard application programming interfaces (APIs) may be a source of a performance problem causing a significant memory overhead for Android apps. Any critical section of code needs to be scrutinized on …