Mathematics Commons^™

Modeling The Spread Of Covid-19 Over Varied Contact Networks, Ryan L. Solorzano

Master's Theses

When attempting to mitigate the spread of an epidemic without the use of a vaccine, many measures may be made to dampen the spread of the disease such as physically distancing and wearing masks. The implementation of an effective test and quarantine strategy on a population has the potential to make a large impact on the spread of the disease as well. Testing and quarantining strategies become difficult when a portion of the population are asymptomatic spreaders of the disease. Additionally, a study has shown that randomly testing a portion of a population for asymptomatic individuals makes a small impact …

A Gate-Based Monte Carlo Simulation Of A Dual-Layer Pixelized Gadolinium Oxyorthosilicate (Gso) Detector Performance And Response For Micro Pet Scanner, Leonid L Nkuba, Innocent J Lugendo, Idrissa S Amour

Tanzania Journal of Science

The purpose of this study was to simulate the GSO detector of a micro PET using GATE simulation platform. The performance and responses of the simulated GSO detector assembly were evaluated by comparing the simulated data to the experimental and XCOM data to validate the simulation platform and procedure. Based on NEMA NU-4 2008 protocols, the performance of GSO detector in terms of sensitivity was simulated and compared to the experimental data. Similarly, the GSO detector response to photons interaction was simulated and compared against the XCOM data for absorbed intensity ratio in the GSO detector and survived intensity ratio …

Knowing What We Know: Leveraging Community Knowledge Through Automated Text-Mining, Justin Gardner, Jonathan Tory Toole, Hemant Kalia, Garry Spink Jr., Gordon Broderick

Advances in Clinical Medical Research and Healthcare Delivery

No abstract provided.

Revolt Pimenov Taught Us How To Be Scientists, Vladik Kreinovich

Departmental Technical Reports (CS)

In 2021, we are celebrating the 90th birthday of Revolt Pimenov, a specialist in space-time geometry. He was my teacher. In this article, I am trying to summarize what he taught to his students.

Why Kappa Regression?, Julio C. Urenda, Orsolya Csiszár, József Dombi, György Eigner, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent book provide examples that a new class of probability distributions and membership functions -- called kappa-regression distributions and membership functions -- leads to better data processing results than using previously known classes. In this paper, we provide a theoretical explanation for this empirical success -- namely, we show that these distributions are the only ones that satisfy reasonable invariance requirements.

Fuzzy Techniques, Laplace Indeterminacy Principle, And Maximum Entropy Approach Explain Lindy Effect And Help Avoid Meaningless Infinities In Physics, Julio C. Urenda, Sean R. Aguilar, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, the only information that we have about some quantity S is a lower bound T ≤ S. In such a situation, what is a reasonable estimate for S? For example, we know that a company has survived for T years, and based on this information, we want to predict for how long it will continue surviving. At first glance, this is a type of a problem to which we can apply the usual fuzzy methodology -- but unfortunately, a straightforward use of this methodology leads to a counter-intuitive infinite estimate for S. There is an empirical …

What Is Wrong With Micromanagement: Economic View, Sean R. Aguilar, Olga Kosheleva

Departmental Technical Reports (CS)

Purpose: It is well known that micromanagement -- excessive control of employees -- is detrimental to the employees' morale and thus, decreases their productivity. But what if the managers keep people happy -- will there still be negative consequences of micromanagement? This is the problem analyzed in this paper.

Design/methodology/approach: To analyze our problem, we use general -- but simplified -- mathematical models of how productivity depends on the working rate.

Findings: We show that even in the absence of psychological discomfort, micromanagement is still detrimental to productivity. Interestingly, the negative effect of micromanagement increases as the population becomes more …

Is Our World Becoming Less Quantum?, Lidice Castro, Vladik Kreinovich

Departmental Technical Reports (CS)

According to the general idea of quantization, all physical dependencies are only approximately deterministic, and all physical "constants" are actually varying. A natural conclusion -- that some physicists made -- is that Planck's constant (that determines the magnitude of quantum effects) can also vary. In this paper, we use another general physics idea -- the second law of thermodynamics -- to conclude that with time, this constant can only decrease. Thus, with time (we are talking cosmological scales, of course), our world is becoming less quantum.

Order Relations Are Ubiquitously Fundamental: Alexandrov(-Zeeman) Theorem Extended From Space-Time Physics To Logical Reasoning And Decision Making, Vladik Kreinovich, Olga Kosheleva, Laxman Bokati, Laura Berrout

Departmental Technical Reports (CS)

In all areas of human activity, there are natural ordering relations: causality in space-time physics, preference in decision making, and logical inference in reasoning. In space-time physics, a 1950 theorem by A. D. Alexandrov proved that causality relation is fundamental: many other features, including numerical characteristics of time and space, can be reconstructed from this relation. In this paper, we provide simple proofs that, similarly, the corresponding ordering relations are fundamental in decision making and in logical reasoning.

Shall We Ignore All Intermediate Grades?, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most European universities, the overall student's grade for a course is determined exclusively by this student's performance on the final exam. All intermediate grades -- on homework, quizzes, and previous texts -- are, in effect, ignored. This arrangement helps gauge the student's performance by the knowledge that the student shows at the end of the course. The main drawback of this approach is that some students do not start studying until later, thinking that they can catch up and even get an excellent grade -- and this hurts their performance. To motivate students to study hard throughout the semester, …

Extension To Multidimensional Problems Of A Fuzzy-Based Explainable & Noise-Resilient Algorithm, Javier Viana, Stephan Ralescu, Kelly Cohen, Anca Ralescu, Vladik Kreinovich

Departmental Technical Reports (CS)

While Deep Neural Networks (DNNs) have shown incredible performance in a variety of data, they are brittle and opaque: easily fooled by the presence of noise, and difficult to understand the underlying reasoning for their predictions or choices. This focus on accuracy at the expense of interpretability and robustness caused little concern since, until recently, DNNs were employed primarily for scientific and limited commercial work. An increasing, widespread use of artificial intelligence and growing emphasis on user data protections, however, motivates the need for robust solutions with explainable methods and results. In this work, we extend a novel fuzzy based …

Applying Emotional Analysis For Automated Content Moderation, John Shelnutt

Computer Science and Computer Engineering Undergraduate Honors Theses

The purpose of this project is to explore the effectiveness of emotional analysis as a means to automatically moderate content or flag content for manual moderation in order to reduce the workload of human moderators in moderating toxic content online. In this context, toxic content is defined as content that features excessive negativity, rudeness, or malice. This often features offensive language or slurs. The work involved in this project included creating a simple website that imitates a social media or forum with a feed of user submitted text posts, implementing an emotional analysis algorithm from a word emotions dataset, designing …

Why Too Much Interaction Between Different Parts Of The Brain Leads To Unhappiness, Ricardo Alvarez, Yamel Hernandez, Vladik Kreinovich

Departmental Technical Reports (CS)

Reasonably recent experiments show that unhappiness is strongly correlated with the excessive interaction between two parts of the brain -- amygdala and hippocampus. At first glance, in situations when outside signals are positive, additional interaction between two parts of the brain that get signals from different sensors should only reinforce the positive feeling. In this paper, we provide a simple explanation of why, instead of the expected reinforcement, we observe unhappiness.

The Generalized Riemann Hypothesis And Applications To Primality Testing, Peter Hall

University Scholar Projects

The Riemann Hypothesis, posed in 1859 by Bernhard Riemann, is about zeros
of the Riemann zeta-function in the complex plane. The zeta-function can be repre-
sented as a sum over positive integers n of terms 1/ns when s is a complex number
with real part greater than 1. It may also be represented in this region as a prod-
uct over the primes called an Euler product. These definitions of the zeta-function
allow us to find other representations that are valid in more of the complex plane,
including a product representation over its zeros. The Riemann Hypothesis says that
all …

Randomized Tax Deadlines Can Help Economy, Julio C. Urenda, Olga Kosheleva

Departmental Technical Reports (CS)

Purpose: While the main purpose of reporting -- e.g., reporting for taxes -- is to gauge the economic state of a company, the fact that reporting is done at pre-determined dates distorts the reporting results. For example, to create a larger impression of their productivity, companies fire temporary workers before the reporting date and re-hire then right away. The purpose of this study is to decide how to avoid such distortion.

Design/methodology/approach: We want to make our solution applicable for all possible reasonable optimality criteria. Thus, we use a general formalism for describing and analyzing all such criteria.

Findings: We …

Godel's Proof Of Existence Of God Revisited, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In his unpublished paper, the famous logician Kurt Godel provided arguments in favor of the existence of God. These arguments are presented in a very formal way, which makes them difficult to understand to many interested readers. In this paper, we describe a simplifying modification of Godel's proof which will hopefully make it easier to understand. We also describe, in clear terms, why Godel's arguments are just that -- arguments -- and not a convincing proof.

Five Revolutionary Ideas In The 1950s-70s Science: 90th Birthday Of Revolt Pimenov, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

This year, Revolt Pimenov, a philosophical thinker whose main ideas were in geometry of space-time, would have turned 90. In this essay, we explain how in the 1950s-70s, when he was most productive, his were two of the five natural and important revolutionary scientific ideas -- along with fuzzy logic, constructive mathematics, and scalar-tensor theory of gravitation, ideas that, in our opinions, still have potential to change the world.

How To Teach Advanced Highly Motivated Students: Teaching Strategy Of Iosif Yakovlevich Verebeichik, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The paper describes and explains the teaching strategy of Iosif Yakovlevich Verebeichik, a successful mathematics teacher at special mathematical high schools -- schools for students interested in and skilled in mathematics. The resulting strategy seems counterintuitive and contrary to all the pedagogical advice. Our explanation is not complete: it worked well for this teacher, but others who tried to follow seemingly the same strategy did not succeed. How he made it work, how can others make it work -- this is still not clear. In the words of Verebeichik himself, while mathematics itself is a science, teaching mathematics is an …

Visual Analysis Of Historical Lessons Learned During Exercises For The United States Air Force Europe (Usafe), Samantha O'Rourke

Theses/Capstones/Creative Projects

Within the United States Air Force, there are repeated patterns of differences observed during exercises. After an exercise is completed, forms are filled out detailing observations, successes, and recommendations seen throughout the exercise. At the most, no two reports are identical and must be analyzed by personnel and then categorized based on common themes observed. Developing a computer application will greatly reduce the time and resources used to analyze each After Action Report. This application can visually represent these observations and optimize the effectiveness of these exercises. The visualization is done through graphs displaying the frequency of observations and recommendations. …

Defect Detection In Atomic Resolution Transmission Electron Microscopy Images Using Machine Learning, Philip Cho, Aihua W. Wood, Krishnamurthy Mahalingam, Kurt Eyink

Faculty Publications

Point defects play a fundamental role in the discovery of new materials due to their strong influence on material properties and behavior. At present, imaging techniques based on transmission electron microscopy (TEM) are widely employed for characterizing point defects in materials. However, current methods for defect detection predominantly involve visual inspection of TEM images, which is laborious and poses difficulties in materials where defect related contrast is weak or ambiguous. Recent efforts to develop machine learning methods for the detection of point defects in TEM images have focused on supervised methods that require labeled training data that is generated via …

Lecture 08: Partial Eigen Decomposition Of Large Symmetric Matrices Via Thick-Restart Lanczos With Explicit External Deflation And Its Communication-Avoiding Variant, Zhaojun Bai

Mathematical Sciences Spring Lecture Series

There are continual and compelling needs for computing many eigenpairs of very large Hermitian matrix in physical simulations and data analysis. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenvalues. To improve the performance of the Lanczos method, in this talk, we will present a combination of explicit external deflation (EED) with an s-step variant of thick-restart Lanczos (s-step TRLan). The s-step Lanczos method can achieve an order of s reduction in data movement while the EED enables to compute eigenpairs in batches along with a number …

Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman

Mathematical Sciences Spring Lecture Series

Opening remarks for the 46th Annual Mathematical Sciences Spring Lecture Series at the University of Arkansas, Fayetteville.

Why Decimal System? Why Communities With More Than 150 Folks Tend To Split? New Consequences Of The Seven Plus Minus Two Law, Leobardo Orea Amador, Vladik Kreinovich

Departmental Technical Reports (CS)

Why are we using the decimal system to describe numbers? Why all over the world, communities with more than 150 folks tend to split? In this paper, we show that both phenomena -- as well as some other phenomena -- can be explained if we take into account the seven plus minus two law, according to which a person can keep in immediate memory from 5 to 9 items.

Why, In Deep Learning, Non-Smooth Activation Function Works Better Than Smooth Ones, Daniel Cruz, Richard Godoy, Vladik Kreinovich

Departmental Technical Reports (CS)

Since in the physical world, most dependencies are smooth (differentiable), traditionally, smooth functions were used to approximate these dependencies. In particular, neural networks used smooth activation functions such as the sigmoid function. However, the successes of deep learning showed that in many cases, non-smooth activation functions like max(0,z) work much better. In this paper, we explain why in many cases, non-smooth approximating functions often work better -- even when the approximated dependence is smooth.

Why Semi-Supervised Learning Makes Sense: A Pedagogical Note, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The main idea behind semi-supervised learning is that when we do not enough human-generated labels, we train a machine learning system based on what we have, and we add the resulting labels (called pseudo-labels) to the training sample. Interesting, this idea works well, but why is somewhat a mystery: we did not add any new information so why is this working? There exist explanations for this empirical phenomenon, but most these explanations are based on complicated math. In this paper, we provide a simple intuitive explanation.

Why ∞ Is A Reasonable Symbol For Infinity, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The fact that ∞ is actively used as a symbol for infinity shows that this symbol is probably reasonable in this role, but why? In this paper, we provide a possible explanation for why this is indeed a reasonable symbol for infinity.

Lev Landau's Marital Advice Explained, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Nobelist physicist Lev Landau was known for applying mathematical and physical reasoning to human relations. His advices may have been somewhat controversial, but they were usually well motivated. However, there was one advice for which no explanation remains -- that a person should not marry his/her first and second true loves, and only start thinking about marriage starting with the third true love. In this paper, we provide a possible Landau-style motivation for this advice.

Limit Theorems As Blessing Of Dimensionality: Neural-Oriented Overview, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

As a system becomes more complex, at first, its description and analysis becomes more complicated. However, a further increase in the system's complexity often makes this analysis simpler. A classical example is Central Limit Theorem: when we have a few independent sources of uncertainty, the resulting uncertainty is very difficult to describe, but as the number of such sources increases, the resulting distribution get close to an easy-to-analyze normal one -- and indeed, normal distributions are ubiquitous. We show that such limit theorems often make analysis of complex systems easier -- i.e., lead to blessing of dimensionality phenomenon -- for …

What Is 1/0 From The Practical Viewpoint: A Pedagogical Note, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

What is 1/0? Students are first taught -- in elementary school -- that it is undefined, then -- in calculus -- then it is infinity. In both cases, the answer is usually provided based on abstract reasoning. But what about the practical meaning? In this paper, we show that, depending on the specific practical problem, we can have different answers to this question: in some practical problems, the correct answer is that 1/0 is undefined, in others, the correct answer is that 1/0 =0 -- and there are probably other practical problems where we can have different answers. Bottom line: …

Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, David J. Wooten, Jorge Gómez Tejeda Zañudo, David Murrugarra, Austin M. Perry, Anna Dongari-Bagtzoglou, Reinhard Laubenbacher, Clarissa J. Nobile, Réka Albert

Mathematics Faculty Publications

Candida albicans, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which C. albicans can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how C. albicans causes infections in the host. Here we build and analyze a Boolean dynamical model of the C. albicans yeast to hyphal transition, integrating …