Mathematics Commons^™

Soft Sets Extensions Used In Bioinformatics, Florentin Smarandache, Daniela Gifu

Branch Mathematics and Statistics Faculty and Staff Publications

This comprehensive review delves into the intricate realm of Soft Sets and their extensions, including HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set, within the context of biomedical data analysis. Soft Sets serve as a foundational framework for managing the inherent uncertainty and imprecision inherent in biological data, thereby facilitating informed decision-making and knowledge discovery. The exploration of Soft Set Products, particularly in the context of multiple soft sets, underscores their pivotal role in advancing biomedical research. By extending these concepts to HyperSoft Sets, researchers can unlock deeper insights into complex biological phenomena, enabling more accurate predictions and classification.

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 …

Shadow Hands, John Adam

Mathematics & Statistics Faculty Publications

The article titled "Shadow hands" discusses a statement made by authors Dave Lynch and Bill Livingston in their book "Color and Light in Nature." The authors state that when you cast a shadow with your hand onto a piece of paper, the sharpness of the shadow's edge diminishes as you raise your hand above the surface. This fuzzy outer edge of the shadow is called the penumbra, and its width divided by its distance from your hand is always a constant fraction of about 1/112. The article poses two questions related to this statement and asks readers to explain it …

Numerical Investigation And Statistical Analysis Of The Flow Patterns Behind Square Cylinders Arranged In A Staggered Configuration Utilizing The Lattice Boltzmann Method, M. Abid, N. Yasin, M. Saqlain, S. Ul-Islam, S. Ahmad

Mathematics & Statistics Faculty Publications

Flow past bluff bodies like square cylinders is important in engineering applications, but flow patterns behind staggered cylinder arrangements remain poorly understood. Existing studies have focused on tandem or side-by-side configurations, while offset orientations have received less attention. The aim of this paper is to numerically investigate flow dynamics and force characteristics behind two offset square cylinders using the single relaxation time lattice Boltzmann method. The effects of changing both the Reynolds number (Re = 1-150) and gap spacing ratio (g* = 0.5-5) between the cylinders are analyzed. Instantaneous vorticity contours, time histories of drag and lift coefficients, power spectra …

Shadow Hands: Solutions For Fermi Questions, September 2024, John Adam

Mathematics & Statistics Faculty Publications

The article titled "Shadow hands: Solutions for Fermi Questions, September 2024" discusses the enigmatic statement made by authors Dave Lynch and Bill Livingston in their book "Color and Light in Nature." The statement explains that the fuzzy outer edge of a shadow, known as the penumbra, is always a constant fraction of about 1/112 of its width divided by its distance from the object casting the shadow. The article provides a solution to Question 1, which asks for an explanation of this statement using elementary geometry. It also offers a solution to Question 2, which asks why the shadow of …

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 …

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.

Modeling Inflation Using A Fast Fourier Transform (Fft), Blake Smith

Williams Honors College, Honors Research Projects

This paper utilizes a Fast Fourier Transform (FFT) algorithm to construct a trigonometric interpolant for the Consumer Price Index (CPI), which is then differentiated and used to obtain a continuous function for “instantaneous” (i.e., month-wise) inflation, as opposed to a 12-month percent-change. Fourier coefficients are analyzed to investigate underlying periodicities in the newly constructed function. This metric does not hold significant predictive value but it may prove helpful in retroactive analysis of inflation trends.

Continuous-Variable Quantum Computation Of The O(3) Model In 1+1 Dimensions, Raghav G. Jha, Felix Ringer, George Siopsis, Shane Thompson

Physics Faculty Publications

We formulate the O(3) nonlinear sigma model in 1+1 dimensions as a limit of a three-component scalar field theory restricted to the unit sphere in the large squeezing limit. This allows us to describe the model in terms of the continuous-variable (CV) approach to quantum computing. We construct the ground state and excited states using the coupled-cluster Ansatz and find excellent agreement with the exact diagonalization results for a small number of lattice sites. We then present the simulation protocol for the time evolution of the model using CV gates and obtain numerical results using a photonic quantum simulator. We …

Integrable Symplectic Maps With A Polygon Tessellation, T. Zolkin, Y. Kharkov, S. Nagaitsev

Physics Faculty Publications

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this …

Multiple Imputation For Robust Cluster Analysis To Address Missingness In Medical Data, Arnold Harder, Gayla R. Olbricht, Godwin Ekuma, Daniel B. Hier, Tayo Obafemi-Ajayi

Mathematics and Statistics Faculty Research & Creative Works

Cluster Analysis Has Been Applied To A Wide Range Of Problems As An Exploratory Tool To Enhance Knowledge Discovery. Clustering Aids Disease Subtyping, I.e. Identifying Homogeneous Patient Subgroups, In Medical Data. Missing Data Is A Common Problem In Medical Research And Could Bias Clustering Results If Not Properly Handled. Yet, Multiple Imputation Has Been Under-Utilized To Address Missingness, When Clustering Medical Data. Its Limited Integration In Clustering Of Medical Data, Despite The Known Advantages And Benefits Of Multiple Imputation, Could Be Attributed To Many Factors. This Includes Methodological Complexity, Difficulties In Pooling Results To Obtain A Consensus Clustering, Uncertainty Regarding …

Recommendations To Internal Auditors Regarding The Auditing And Attestation Of Mathematical Programming Models, Jose Rincón, Greg Akai, Daryl Ono

Librarian Publications & Presentations

Mathematical programming planning models increase operational efficiency and minimize operating costs, but the underlying mathematics generally is complex. Combinatorial optimization is technically sophisticated which requires a strong quantitative background to successfully implement. Most internal auditors will not have the technical training to critically assess the underlying mathematics of mathematical programming planning models, but the internal auditor can still provide insight and attestation which can increase the efficiency of mathematical programming planning models.

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.

Id Numbers Of Lobster Graphs, Mark Anthony C. Tolentino, Luis Silvestre Jr, Richwell T. Chan Sim, Amir Jann Erikson Diga, Althea Julia R. Loyola

Mathematics Faculty Publications

No abstract provided.

Can't We Just Use Computers? Initial Efforts On Technology-Enhanced Learning Of Operations Research In A Philippine University, Lester Hao, Jeric C. Briones, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Operations Research (OR) is a required course in any applied math program in the Philippines. It involves complex and computation-heavy algorithms to guide and improve decision-making in organizations and relevant contexts. Despite the advent of software that have automated the computations or the implementation of algorithms, the teaching and learning of OR may still be rife with procedures being performed manually by hand. In this paper, we report on our initial progress on a research project that aims to revise the OR syllabi in one Philippine university, by integrating more technological tools in the teaching and learning of OR for …

Adjusting For Participation Bias In Case-Control Genetic Association Studies For Rare Diseases, Le Wang, Ben Fitzpatrick, Zhengbang Li, Clarice Weinberg, Jinbo Chen

Mathematics, Statistics and Data Science Faculty Works

Collection of genotype data in case-control genetic association studies may often be incomplete for reasons related to genes themselves. This non-ignorable missingness structure, if not appropriately accounted for, can result in participation bias in association analyses. To deal with this issue, Chen et al. [7] proposed to collect additional genetic information from family members of individuals whose genotype data were not available, and developed a maximum likelihood method for bias correction. In this study, we develop an estimating equation approach to analyzing data collected from this design that allows adjustment of covariates. It jointly estimates odds ratio parameters for genetic …

Rising Plant Demand Strengthens Nitrogen Limitation In Tidal Marsh, Le Wang, Adam Langley, Bella Yedman, Patrick Megonigal

Mathematics, Statistics and Data Science Faculty Works

Nitrogen (N) is a limiting nutrient for primary productivity in most terrestrial ecosystems, but whether N limitation is strengthening or weakening remains controversial because both N sources and sinks are increasing in magnitude globally. Temperate marshes are exposed to greater amounts of external N inputs than most terrestrial ecosystems and more than in preindustrial times owing to their position downstream of major sources of human-derived N runoff along river mouths and estuaries. Simultaneously, ecosystem N demand may also be increasing owing to other global changes such as rising atmospheric [CO2]. Here, we used interannual variability in external drivers and variables …

Persistent Relative Homology For Topological Data Analysis, Christian J. Lentz

Mathematics, Statistics, and Computer Science Honors Projects

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via the language of persistent homology, which encodes features of interest as holes within a filtration of the data. The recently presented U-Match Decomposition places the standard persistence computation in a flexible form, allowing for straight-forward extensions of the algorithm to variations of persistent homology. We describe U-Match Decomposition in the context of persistent homology, and extend it to an algorithm for persistent relative homology, providing proofs for the correctness and stability of the presented algorithm.

An Investigation Of Students' Modes Of Thinking Concerning Linearity In Linear Algebra, Noa Levy

Honors Undergraduate Theses

The intent of this thesis is to investigate student approaches to linearity within a linear algebra context, focusing on definitional, computational, and theoretical skills. Linear algebra’s abstract nature constitutes a major challenge for a significant sector of STEM students, with the course often serving as undergraduates’ first encounter with mathematical proofs and extrapolations. The current student struggle is reflected through the prominent gap in knowledge derived from a lack of a concrete understanding of rudimentary concepts (like linearity), pivotal to student success. As such, this investigation aimed to bridge this gap by considering students’ modes of thinking regarding the elementary …