Physical Sciences and Mathematics Commons^™

Invariance-Based Approach Explains Empirical Formulas From Pavement Engineering To Deep Learning, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many application areas, there are effective empirical formulas that need explanation. In this paper, we focus on two such challenges: neural networks, where a so-called softplus activation function is known to be very efficient, and pavement engineering, where there are empirical formulas describing the dependence of the pavement strength on the properties of the underlying soil. We show that similar scale-invariance ideas can explain both types of formulas -- and, in the case of pavement engineering, invariance ideas can lead to a new formula that combines the advantages of several known ones.

How Probable Is A Revolution? A Natural Relu-Like Formula That Fits The Historical Data, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In his recent book "Principles for Dealing with the Changing World Order", Ray Dalio considered many historical crisis situations, and came up with several data points showing how the probability of a revolution or a civil war depends on the number of economic red flags. In this paper, we provide a simple empirical formula that is consistent with these data points.

How Can The Opposite To A True Theory Be Also True? A Similar Talmudic Discussion Helps Make This Famous Bohr's Statement Logically Consistent, Miroslav Svitek, Vladik Kreinovich

Departmental Technical Reports (CS)

In his famous saying, the Nobelist physicist Niels Bohr claimed that the sign of a deep theory is that while this theory is true, its opposite is also true. While this statement makes heuristic sense, it does not seem to make sense from a logical viewpoint, since, in logic, the opposite to true is false. In this paper, we show how a similar Talmudic discussion can help come up with an interpretation in which Bohr's statement becomes logically consistent.

How To Estimate The Present Serviceability Rating Of A Road Segment: Explanation Of An Empirical Formula, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

An accurate estimation of the road quality requires a lot of expertise, and there is not enough experts to provide such estimates for all the road segments. It is therefore desirable to estimate this quality based on easy-to-estimate and easy-to-measure characteristics. Recently, an empirical formula was proposed for such an estimate. In this paper, we provide a theoretical explanation for this empirical formula.

From Historically First "Unary" Numbers, Through Egyptian Fractions, Roman Numerals, Leibniz's Binary Numbers And Kepler's Fractions To Modern Ideas Such As Calkin-Wilf Tree: A Unified Approach To Representing Natural Numbers And Fractions, Olga Kosheleva, Vladik Kreinovich, Christian Servin

Departmental Technical Reports (CS)

In elementary mathematics classes, students are often overwhelmed by different representations of numbers and corresponding operations: usual fractions, decimal representations, binary numbers, etc. What often helps is when students learn the history of these representations, see the limitations of seemingly reasonable representations like Roman numerals, and how other representations overcame these limitations. Still, history was developed somewhat randomly, so the historical sequence is still somewhat chaotic. We believe that providing a unified approach for all these representations would help describe their sequence in a more logical way and thus, help the students even more.

In our analysis, we explore the …

Economy-Related Emotional Attitudes Towards Other People: How Can We Explain Them?, Christopher Reyes, Vladik Kreinovich, Chon Van Le

Departmental Technical Reports (CS)

Research has shown that to properly understand people's economic behavior, it is important to take into account their emotional attitudes towards each other. Behavioral economics shows that different attitudes results in different economy-related behavior. A natural question is: where do these emotional attitudes come from? We show that, in principle, such emotions can be explained by people's objective functions. Specifically, we show it on the example of a person whose main objective is to increase his/her country's GDP: in this case, the corresponding optimization problem leads exactly to natural emotions towards people who contribute a lot or a little towards …

Grid-Connected Renewable Energy Systems For Residential Hvac Load Management, Oscar Samuel Acosta

Open Access Theses & Dissertations

With an ongoing mission of utility operators to maintain a resilient and reliable power grid in the face of continuously increasing load demand, it is essential that advancements be made in developing both technology and methodology to help account for the increasing energy requirements. According to the U.S. Department of Energy (DOE) and Energy Information Administration (EIA), the residential end-use sector alone counted for 22% of all electricity used in the U.S. in 2020. Of this, approximately 32% of household electricity load is the direct result of air conditioning and space heating units (HVAC). One way to account for this …

Context Dependence Of Warming Induced Shifts In Alpine Soil Microbial Functions, Sydne Rose Spinella

Open Access Theses & Dissertations

Atmospheric warming is occurring due to anthropogenic release of carbon dioxide. Climate change has the potential to increase microbial activity in soil, where a significant amount of terrestrial carbon is stored, which may lead to release of this soil carbon into the atmosphere, positively feeding back to global temperature rise. Understanding how the indirect impacts of climate warming, like shifts in plant community composition, affect soil microbes can improve predictions of ecosystem functions and services under climate change. This project examined direct and indirect consequences of warming on microbial processes using independent and combined treatments of experimental warming and dominant …

Developing And Applying Computational Algorithms To Reveal Health-Related Biomolecular Interactions, Yixin Xie

Open Access Theses & Dissertations

Computational biology is an interdisciplinary area that applies computational approaches in biological big data, including protein amino acid sequences, genetic sequences, etc., which is widely used to analyze protein-protein interactions, make predictions in drug discovery, develop vaccines, etc. Popular methods include mathematical modeling, molecular dynamics simulations, data science mythology, etc. With the help of computational algorithms and applications, drug development is much faster than traditional processes, as it reduces risks early on in a drug discovery process and helps researchers select target candidates that have the highest potential for success. In my doctoral research, I applied multi-scale computational approaches to …

Low-Lying Spin-Flip Excitonic States Of ����12��12 (��������)16 [��2��]4 Molecule (Mn12 − ����), Karma Dema

Open Access Theses & Dissertations

Molecules and materials constructed from Mn atoms offer diverse assortments of geomet- rical and spin structures. The diversity of structures, in comparison with other transition metals, along with nature’s decision to use a Mn-based molecule to catalyze solar-driven water splitting and oxygen evolution, suggests that there is indeed something special about the location of Mn valence electrons, both energetically and geometrically, that endows Mn with its multifaceted behaviors that, in turn, provide such chemical, physical and mag- netic diversity. Based upon recent work on the Mn3 monomer and the Mn(taa) there is an expectation that Mn�� �� �� centers can …

A Central Compact Hybrid-Variable Method With Spectral-Like Resolution, Md Mahmudul Hasan

Open Access Theses & Dissertations

Numerical methods for hyperbolic conservation laws have been a driving force for theresearch in scientific computing and simulation science in the past decades, as many physical, biological, and engineering systems are governed by these equations, such as fluid mechanics, tumor growth, and virtual wind tunnel simulations. Despite the existence of many schemes in the literature, people have never stopped searching for more accurate and efficient methods for these problems. Indeed, the increasing complexity of systems in emerging applications demands better resolution of sub-grid scale phenomenon whereas classical methods usually fail to deliver high-fidelity simulation results of such systems within realistic …

Method Development For Preconcentration And Quantification Of Critical And Valuable Elements In Permian Basin Produced Waters, Joshua Matthew Lewis

Open Access Theses & Dissertations

Produced waters are a voluminous byproduct of unconventional oil and gas production. Produced water volumes are primarily addressed by subsurface reinjection through saltwater disposal wells (SWDs) and reuse within the oil and gas industry. Oil and gas operators continue to evaluate and trial novel methods to improve produced water handling, and reduce freshwater use, and disposal volumes. Here, we present results for method development to quantify Critical and Valuable Elements (CVEs; defined here as the lanthanide series, high field strength elements, industrial elements and precious metals in brines. CVE concentrations in produced waters and other high-salinity waters are poorly understood …

Rational Design Of Composite Nanomaterials For Water Treatment Applications, Mariana Marcos-Hernandez

Open Access Theses & Dissertations

Water quantity and quality have been affected in communities all around the world due to population growth, pollution, changes in land use, and climate change. In order to cope with existing and anticipated water demands and shortages, the use of treated or reclaimed water is an ongoing alternative that has helped communities all over the world address this problem. The adaptation of nanotechnology to traditional water and wastewater treatment processes offers new opportunities in technological developments. Unique size-dependent properties such as: high surface to mass ratio, high reactivity, high sorption capacities, fast dissolution, superparamagnetism, among others, provide high-tech efficient materials …

Material Synthesis And Machine Learning For Additive Manufacturing, Jaime Eduardo Regis

Open Access Theses & Dissertations

The goal of this research was to address three key challenges in additive manufacturing (AM), the need for feedstock material, minimal end-use fabrication from lack of functionality in commercially available materials, and the need for qualification and property prediction in printed structures. The near ultraviolet-light assisted green reduction of graphene oxide through L-ascorbic acid was studied with to address the issue of low part strength in additively manufactured parts by providing a functional filler that can strengthen the polymer matrix. The synthesis of self-healing epoxy vitrimers was done to adapt high strength materials with recyclable properties for compatibility with AM …

Covid Synergy: A Machine Learning Approach Uncovering Potential Treatment Combinations For Sars-Cov-2, Jason Eden Sanchez

Open Access Theses & Dissertations

For more than two years, the COVID-19 pandemic has upended the lives of billions of individualsworldwide leading to disruptions in healthcare, the economy and society at large. As the pandemic enters its third year, the human impact cannot be overstated and the need to develop effective pharmaceuticals remains. Though there currently exits FDA-approved medications for COVID-19, the emergence of novel variants, such as Omicron, highlights the importance of discovering new therapies which will continue to be effective regardless of the pandemicâ??s progression. Because discovering new medications is a costly and timeintensive endeavor, my approach entails drug repurposing to test medications …

A Machine Learning Approach To Stochastic Optimal Control, Pablo Ever Avalos

Open Access Theses & Dissertations

Merton's portfolio optimization problem is a well-renowned problem in financial mathematics which seeks to optimize the investment decision for an investor. In the simplest situation, the market consists of a risk-less asset (i.e. a bond) that pays back a relatively low interest rate, and a risky asset (i.e. a stock) that follows a geometric Brownian motion. The optimal allocation strategy of the investor's wealth is found by optimizing the expected utility along the stochastic evolution of the market. This thesis focuses on several different applications of this optimization problem. We look at pre-constructed analytical solutions and showcase the results. We …

Suitability Of Low-Cost Additive Manufacturing For Polymer Electrolyte Fuel Cells, David Alexander

Open Access Theses & Dissertations

The purpose of this dissertation is to study the feasibility of low-cost additive manufacturing to fabricate polymer electrolyte fuel cell bipolar plate materials. Traditional manufacturing techniques include molding, milling, hollow embossing, hydro-forming, rolling, and electromagnetic forming. These processes are employed when a design has been selected due to higher costs at low volumes. The combination of high initial costs and bipolar plates being the most expensive component of the polymer electrolyte fuel cell creates incentive to mitigate this obstacle. The feasibility of low-cost additive manufactured bipolar plates will be proven by fabrication, post-processing, and characterization of printed test specimen. The …

Tuning Nanoscale Molecular Heterogeneity To Improve Co2 Transport And Binding In Co2 Capture Solvents, Omar Avina

Open Access Theses & Dissertations

Aqueous amine-based technology has been considered the most promising carbon capture solution for post-combustion gas from fossil fuel plants. However, solvent degradation and the high energy cost associated with removing CO2 from the solvent, known as regeneration, have hindered its widespread implementation. It has been proposed that utilizing a water lean solvent, in contrast to aqueous amines, can decrease the required heat to regenerate the solvent. Additionally, Malhotra et al. proposed that controlling the viscosity can help increase the mass transport properties of CO2 in the solvent. A recent study on CO2 binding organic liquids (CO2BOLs) found them to exist …

Game-Theoretic Deception Modeling For Distracting Network Adversarie, Mohammad Sujan Miah

Open Access Theses & Dissertations

In this day and age, adversaries in the cybersecurity space have become alarmingly capable of identifying network vulnerabilities and work out various targets to attack where deception is becoming an increasingly crucial technique for the defenders to delay these attacks. For securing computer networks, the defenders use various deceptive decoy objects to detect, confuse, and distract attackers. By trapping the attackers, these decoys gather information, waste their time and resources, and potentially prevent future attacks. However, we have to consider that an attacker with the help of smart techniques may detect the decoys and avoid them. One of the well-known …

Nanotechnology-Based Approaches To Mitigate Environmental Pollutants -- Induced Neurological Disorders, Jyoti Ahlawat

Open Access Theses & Dissertations

Neurodegenerative diseases such as Parkinson's disease (PD), Alzheimerâ??s Disease (AD) and Huntingtonâ??s Disease (HD) have no cure despite intensive research efforts geared towards therapeutics development. In the USA, patients with PD and AD alone cost the nation ~ $200 billion annually in patient care and lost productivity. Therefore, there remains an urgent and unmet need to develop novel drugs and drug carriers with the potential to slow down, halt and ideally reverse the course of neurodegenerative disorders. The dissertation focuses on developing approaches towards targeting PD using multifactorial mechanisms including the targeting of protein aggregation and oxidative stress. This is …

Exploring Tunable Magnetization And High-Temperature Ferromagnetism In Ternary Transition Metal-Based Chalcogenides, Hector Iturriaga

Open Access Theses & Dissertations

The discovery of long-range magnetic ordering in ultrathin transition metal-based compounds shows great promise for the development of nanoscale memory and spintronic devices. Composed of cost-effective materials and boasting from strong chemical and thermal stability at low dimensions, van der Waals (vdW) ternary transition metal chalcogenide magnets like CrSiTe3 (CST), Fe2.7GeTe2 (FGT), and Mn3Si2Te6 (MST), provide not only possible energy solutions, but also a broad platform to explore the versatile magnetic character of this family of compounds. Although they have great potential, it has been found that their long-range magnetic ordering exists at temperatures far too low (the highest of …

What About Generic "And"- And "Or"-Operations: From Levels Of Certainty (Philosophical-Physical-Mathematical) To A Natural Interpretation Of Quantum-Like Negative Degrees Of Certainty, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy techniques -- techniques designed to convert imprecise human knowledge into precise computer-understandable terms -- have many successful applications. Traditional applications of fuzzy techniques use only important general features of human reasoning and, to make an implement more efficient, ignore subtle details, details which are not important for the corresponding application. But from the more fundamental viewpoint, it is desirable to understand, in all the detail, how people actually reason. In this paper, we use general ideas of fuzzy approach to answer this question. Interestingly -- and somewhat unexpectedly -- the resulting analysis leads to a natural explanation of existence …

Shape Of An Egg: Towards A Natural Simple Universal Formula, Sofia Holguin, Vladik Kreinovich

Departmental Technical Reports (CS)

Eggs of different bird species have different shapes. There exists formulas for describing the usual egg shapes -- e.g., the shapes of chicken eggs. However, some egg shapes are more complex. A recent paper proposed a general formula for describing all possible egg shapes; however this formula is purely empirical, it does not have any theoretical foundations. In this paper, we use the theoretical analysis of the problem to provide an alternative -- theoretically justified -- general formula. Interestingly, the new general formula is easier to compute than the previously proposed one.

Freedom Of Will, Non-Uniqueness Of Cauchy Problem, Fractal Processes, Renormalization, Phase Transitions, And Stealth Aircraft, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

We all know that we can make different decisions, decisions that change -- at least locally -- the state of the world. This is what is known as freedom of will. On the other hand, according to physics, the future state of the world is uniquely pre-determined by its current state, so there is no room for freedom of will. How can we resolve this contradiction? In this paper, we analyze this problem, and we show that many physical phenomena can help resolve this contradiction: fractal character of equations, renormalization, phase transitions, etc. Usually, these phenomena are viewed as somewhat …

In The Absence Of Information, The Only Reasonable Negotiation Scheme Is Offering A Certain Percentage Of The Original Request: A Proof, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the case of complete information, a reasonable solution to a negotiation process is Nash's bargaining solution, in which we maximize the product of all agents' utility gains. This is the only solution that does not depend on the order in which we list the agents, and does not change if we use a different scale for describing each agent's utility. In this paper, we apply similar invariance criteria to a situation when practically all information is absent, and all we know is the smallest and largest possible gains. We show that in this situation, the only invariant negotiation strategy …

Education In The Era Of Google, Wikipedia, And Deep Learning: Are We Humans Still Needed And If Yes For What?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main purposes of education is to teach skills needed in future life and future jobs. What is important and what is useful changes with time. Before the industrial revolution, routine mechanical work was an important part of human activity – now machines can do it (and do it better). Before printing, copying was an important activity – now copy machines do it. Before computers, humans were needed for computing – now computer do it better. With Wikipedia and Google, there is not much need for scholars being erudite. Even extracting dependencies from data – one of the …

Characterization And Evolution Of The Professor Valley Pennsylvanian Salt Body (Paradox Basin, Ut) Using Gravity And Magnetotellurics, Derek Scott

Open Access Theses & Dissertations

Syndepositional halokinetic movement of the Pennsylvanian Paradox Formation in the Paradox Basin, UT & CO behaved as a control over the development of depositional systems during the Late Paleozoic and early Mesozoic periods (Trudgill, 2011). Understanding the controls on halokinetic evolution in the area serves as an invaluable outcrop analogue for similar subsurface salt bodies in petroleum-bearing basins and provides key insights for hydrocarbon exploration in salt basins world wide. Professor Valley, located 15 miles Northeast of Moab, UT is situated between the Fisher Valley (Onion Creek) and Cache/Salt Valley salt walls. It includes an anomalous, isolated 0.5 km² outcrop …

Integration Of Genetic Isothermal Amplification On Low-Cost Hybrid Paper/Polymer Microfluidic Biochips For High Sensitivity Point-Of-Care Disease Diagnosis, Hamed Tavakoli

Open Access Theses & Dissertations

Infectious diseases and cancer have been two main causes of global death and disability, leading to a significant impact on public health and economies globally. Early diagnosis of these diseases can improve prevention, treatment, and prognosis in clinical practice. However, current laboratory diagnostic approaches require expensive and bulky equipment, well-trained personnel, and time-consuming processes, which puts a great challenge to conventional methods to address, especially in resource-limited settings. Microfluidic lab-on-a-chip presents a unique opportunity for various biomedical applications due to multiple advantages such as low reagent consumption, integration, miniaturization, portability, and automation. Since different microfluidic platform substrates have their advantages …

Fair Bankruptcy Solutions Under Interval Uncertainty, Uyen Pham, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

If the overall amount of the company's assets is smaller than its total debts, then a fair solution is to give, to each creditor, the amount proportional to the corresponding debt, e.g., 10 center for each dollar or 50 cents for each dollar. But what if the debt amounts are not known exactly, and for some creditors, we only know the lower and upper bounds on the actual debt amount? What division will be fair in such a situation? In this paper, we show that the only fair solution is to make payments proportional to an appropriate convex combination of …

Why Some Theoretically Possible Representations Of Natural Numbers Were Historically Used And Some Were Not: An Algorithm-Based Explanation, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Historically, people have used many ways to represent natural numbers: from the original "unary" arithmetic, where each number is represented as a sequence of, e.g., cuts (4 is IIII) to modern decimal and binary systems. However, with all this variety, some seemingly reasonable ways of representing natural numbers were never used. For example, it may seem reasonable to represent numbers as products -- e.g., as products of prime numbers -- such a representation was never used in history. So why some theoretically possible representations of natural numbers were historically used and some were not? In this paper, we propose an …