Mathematics Commons^™

Instances Of Undecidability In The Semigroup Word Problem, Timothy C. Grosky

Honors Theses and Capstones

We will examine the decidability of the word problem in semigroups, which is a yes/no question. We will examine tools that have been developed to help answer it, and then look at some examples where the word problem is decidable or undecidable.

Signatures Of Time Interval Reproduction In The Human Electroencephalogram (Eeg), Harvey Mccone, John. S. Butler, Redmond. G. O'Connell

Articles

No abstract provided.

Probing A Neural Unreliability Account Of Auditory Sensory Processing Atypicalities In Rett Syndrome, Tufikameni Brima, Shlomit Beker, Kevin D. Prinsloo, John Butler, Aleksandra Djukic, Edward G. Freedman, Sophie Molholm, John J. Foxe

Articles

Background: In the search for objective tools to quantify neural function in Rett Syndrome (RTT), which are crucial in the evaluation of therapeutic efficacy in clinical trials, recordings of sensory-perceptual functioning using event-related potential (ERP) approaches have emerged as potentially powerful tools. Considerable work points to highly anomalous auditory evoked potentials (AEPs) in RTT. However, an assumption of the typical signal-averaging method used to derive these measures is “stationarity” of the underlying responses – i.e. neural responses to each input are highly stereotyped. An alternate possibility is that responses to repeated stimuli are highly variable in RTT. If so, this …

Snow Spheres And Ice Cubes: Solutions For Fermi Questions, February 2024, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Infusing Machine Learning And Computational Linguistics Into Clinical Notes, Funke V. Alabi, Onyeka Omose, Omotomilola Jegede

Mathematics & Statistics Faculty Publications

Entering free-form text notes into Electronic Health Records (EHR) systems takes a lot of time from clinicians. A large portion of this paper work is viewed as a burden, which cuts into the amount of time doctors spend with patients and increases the risk of burnout. We will see how machine learning and computational linguistics can be infused in the processing of taking clinical notes. We are presenting a new language modeling task that predicts the content of notes conditioned on historical data from a patient's medical record, such as patient demographics, lab results, medications, and previous notes, with the …

Utility In Time Description In Priority Best-Worst Discrete Choice Models: An Empirical Evaluation Using Flynn's Data, Sasanka Adikari, Norou Diawara

Mathematics & Statistics Faculty Publications

Discrete choice models (DCMs) are applied in many fields and in the statistical modelling of consumer behavior. This paper focuses on a form of choice experiment, best-worst scaling in discrete choice experiments (DCEs), and the transition probability of a choice of a consumer over time. The analysis was conducted by using simulated data (choice pairs) based on data from Flynn's (2007) 'Quality of Life Experiment'. Most of the traditional approaches assume the choice alternatives are mutually exclusive over time, which is a questionable assumption. We introduced a new copula-based model (CO-CUB) for the transition probability, which can handle the dependent …

Sparse Representer Theorems For Learning In Reproducing Kernel Banach Spaces, Rui Wang, Yuesheng Xu, Mingsong Yan

Mathematics & Statistics Faculty Publications

Sparsity of a learning solution is a desirable feature in machine learning. Certain reproducing kernel Banach spaces (RKBSs) are appropriate hypothesis spaces for sparse learning methods. The goal of this paper is to understand what kind of RKBSs can promote sparsity for learning solutions. We consider two typical learning models in an RKBS: the minimum norm interpolation (MNI) problem and the regularization problem. We first establish an explicit representer theorem for solutions of these problems, which represents the extreme points of the solution set by a linear combination of the extreme points of the subdifferential set, of the norm function, …

A Copula Discretization Of Time Series-Type Model For Examining Climate Data, Dimuthu Fernando, Olivia Atutey, Norou Diawara

Mathematics & Statistics Faculty Publications

The study presents a comparative analysis of climate data under two scenarios: a Gaussian copula marginal regression model for count time series data and a copula-based bivariate count time series model. These models, built after comprehensive simulations, offer adaptable autocorrelation structures considering the daily average temperature and humidity data observed at a regional airport in Mobile, AL.

Pigeon Strike!, John Adam

Mathematics & Statistics Faculty Publications

This article, titled "Pigeon strike!" from the Physics Teacher journal, discusses an incident where a bird, likely a pigeon, struck a window leaving an imprint. The author went outside to check but found no trace of the bird, hoping it had flown away after receiving medical care. The article also includes questions for readers to estimate the momentum, kinetic energy, force, pressure, and wingspan of the bird. The answers to these questions can be found online in the current issue of the journal. The article concludes with information about Fermi Questions and how to submit ideas.

The Weighty Words Of Lord Rayleigh: Solutions For Fermi Questions, January 2024, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Earthquakes And Seismic Waves, John Adam

Mathematics & Statistics Faculty Publications

This article discusses earthquakes and seismic waves. It explains that earthquakes occur in the crust or upper mantle, with "shallow" earthquakes happening above a depth of 70 km in the crust. The article also introduces the slider-block model, which is a simple model used to understand earthquake behavior. It provides equations to calculate the displacement and maximum slip velocity of the fault based on various factors. The article then presents two questions related to earthquake calculations. Additionally, it mentions Fermi Questions, which are brief questions with estimation techniques.

Analysis Of Sir Model With Optimal Control Strategy For A Simple Traffic Congestion Process, Ratna Herdiana, Zani Anjani Rafsanjani, R. Heru Tjahjana, Yogi Ahmad Erlangga, Moch Fandi Ansori

All Works

Traffic analysis on highways at the macroscopic level is very similar to the analysis of the spread of infectious diseases, namely the susceptible-infected-recover (SIR) model. We propose the SIR model with a control variable. The dynamics with fixed control and stability of the model are analyzed. Sensitivity analysis was also carried out. Variable control is applied as an effort to regulate or change the duration of the green light at an intersection. We obtain an optimal control strategy when the control is time-dependent. Numerical results show the positive impacts of implementing the control to susceptible vehicles and treatment for congested …

Maximizing The Number Of H-Colorings Of Graphs With A Fixed Minimum Degree, John Engbers

Mathematical and Statistical Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is an adjacency-preserving map from the vertex set of G to the vertex set of H.

Nonequational Stable Groups, Isabel Müller, Rizos Sklinos

Faculty Journal Articles

We introduce a combinatorial criterion for verifying whether a formula is not the conjunction of an equation and a co-equation. Using this, we give a proof for the nonequationality of the free group. Furthermore, we generalize the latter result to the first-order theory of any free product of groups of the form G * Fω.

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly

College of Graduate Studies: Theses & Dissertations

In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …

Optimizing Microbe-Infected Mosquito Release: A Stochastic Model For Malaria Prevention, Steeven Belvinos Affognon, Henri E.Z. Tonnang, Philip Ngare, Benard Kipchumba Kiplangat, Shirley Abelman, Jeremy K. Herren

All Peer-Reviewed Publications

Malaria remains a critical public health challenge in Africa, demanding innovative control strategies. This study introduces a novel approach using Microsporidia MB-infected mosquitoes and stochastic optimal control within a Lévy process framework to regulate mosquito release strategies. The primary goal is to optimize Microsporidia MB prevalence within mosquito populations to disrupt Plasmodium transmission to humans. By incorporating Lévy noise into the modeling process, we capture the inherent randomness of mosquito dynamics, improving intervention accuracy. The model, guided by the Hamilton–Jacobi–Bellman (HJB) equation, optimizes release protocols while accounting for key environmental factors like seasonality and temperature fluctuations. Results show that intervention …

Sky Smiley Face, John Adam

Mathematics & Statistics Faculty Publications

The article discusses the formation of a circumzenithal arc (CZA) in the sky, caused by specific light ray paths through hexagonal ice crystals in cirrus clouds. The CZA is visible when the Sun's altitude is about 32° or less. The text includes questions for readers to explore the physics behind the formation of CZAs and circumhorizontal arcs (CHAs). The author acknowledges photographers for providing images and invites readers to find answers online.

Earthquakes And Seismic Waves: Solutions For Fermi Questions, March 2024, John Adam

Mathematics & Statistics Faculty Publications

Solution to Question 1: To estimate h, we take the geometric mean of 1 km and 70 km, or ~8 km, and take ρ ≈ 2500 kg/m³.

Hence, δl ≈ 4 × 0.05 × (2.5 × 10³ kg/m³) × (10 m/s²) × (8 × 10³ m) × (2 × 10⁴ m) × 0.1 ÷ (3 × 10¹⁰ kg · m⁻¹ · s⁻²) ≈ 1.3 m. (Note that this is not meant to be an estimate of the width of the Icelandic rock fracture in the photograph, though it appears to be of the right order …

Cats, Dogs, And Roll Waves, John Adam

Mathematics & Statistics Faculty Publications

This article discusses the phenomenon of roll waves, which are shock-like patterns separated by smooth profiles that occur in flood waves. The author mentions that in a steady-state situation, the drag forces on the water in the channel are balanced by the down-slope gravitational force. The article also includes questions for readers to estimate the speed and length of the roll waves, as well as determine the stability of the flow. The author provides additional information about the Chezy formula, an empirical equation used in fluid mechanics to estimate the mean flow velocity of open channel flow.

Cats, Dogs, And Roll Waves: Solutions For Fermi Questions, April 2024, John Adam

Mathematics & Statistics Faculty Publications

On a hot afternoon in western North Carolina, the heavens opened and (to mix metaphors) it started raining “cats and dogs.” The rain was torrential, and soon a river of water was flowing downhill into the parking lot. In rivers and dam spillways, these are known as flood waves. The picture shows a particular type of flood waves known s roll waves—shock-like patterns separated by smooth profiles. In a steady-state situation, the drag forces on the water in the channel are balanced by the down-slope gravitational force. The dimensionless friction coefficient is C, the stream depth is h, v is …