Mathematics Commons^™

Graph Convolutional Networks Enable Fast Hemorrhagic Stroke Monitoring With Electrical Impedance Tomography, J. Toivanen, V. Kolehmainen, A. Paldanius, A. Hänninen, A. Hauptmann, Sarah J. Hamilton

Mathematical and Statistical Science Faculty Research and Publications

Objective: To develop a fast image reconstruction method for stroke monitoring with electrical impedance tomography with image quality comparable to computationally expensive nonlinear model-based methods. Methods: A post-processing approach with graph convolutional networks is employed. Utilizing the flexibility of the graph setting, a graph U-net is trained on linear difference reconstructions from 2D simulated stroke data and applied to fully 3D images from realistic simulated and experimental data. An additional network, trained on 3D vs. 2D images, is also considered for comparison. Results: Post-processing the linear difference reconstructions through the graph U-net significantly improved the image quality, resulting in images …

Stability Analysis Of The Eulerian-Lagrangian Finite Volume Methods For Nonlinear Hyperbolic Equations In One Space Dimension, Yang Yang, Jiajie Chen, Jing Mei Qiu

Michigan Tech Publications

In this paper, we construct a novel Eulerian-Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine-Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still …

Dissections Of Lacunary Eta Quotients And Identically Vanishing Coefficients, Timothy Huber, James Mclaughlin, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

For any function A(q)=∑∞n=0anqn defineA(0):={n∈N:an=0}.Now suppose C(q) and D(q) are two functions whose m-dissections are given byC(q)=c0G0(qm)+c1qG1(qm)+…+cm−1qm−1Gm−1(qm),D(q)=d0G0(qm)+d1qG1(qm)+…+dm−1qm−1Gm−1(qm).If it is the case that ci=0⟺di=0, i=0,1,…,m−1, then we say that C(q) and D(q) have similar m-dissections, and then it is also clear that C(0)=D(0), in which case we say that C(q) and D(q) have identically vanishing coefficients. In the present paper some new 4-dissections of particular eta quotients are developed. These are used in conjunction with known 2- and 3-dissections to prove many results on the identical vanishing of coefficients of various eta quotients, results which were found experimentally …

Contextual Approach To Improve Problem Solving Skills In Ipas Subject At Elementary School: A Study Development Of Teaching Materials, Nur Hidayah, Sumarno Sumarno, Joko Siswanto

Jurnal Pendidikan Sains

The objective of this study is to assess the validity, practicality, and efficacy of instructional materials. We refer to this research as research and development, with a focus on the creation of teaching materials. The research design proposed by Borg and Gall consists of six steps: identification of potential and difficulties, data collecting, product design, design validation, design revision, and product trial. The utilized instruments comprise expert and practitioner validity sheets, teacher and student response surveys, and validation sheets for teaching materials and modules, as well as pretest and posttest questions. Experts performed the validity assessment, attaining a score of …

The Effort To Improve Students’ Problem-Solving Ability: Physics E-Modules For High School Students, Hidayatullah Hana Putra, Edi Supriana, Nasikhuddin Nasikhuddin, Annisa U. Yana, Suhailee Sohnui

Jurnal Pendidikan Sains

Physics teachers in Indonesia still face obstacles during learning, such as students who are less active and have difficulty in solving physics problems. The physics learning media used are also still not very interesting and are not based on authentic problem solving. Therefore, this study focuses on the development of PBL-based e-modules on work and energy to improve the physics problem-solving abilities of high school students. This research and development used the ADDIE design and was tested on 90 high school students in High School 1 Sumber Pucung Malang in the 2022/2023 academic year. The questionnaire instrument was used in …

Differentiated Teaching Module Using Problem Solving Model: Numerical Ability Of Elementary School Students, Risa Alifatin, Agus Sutono, Ida Dwijayanti

Jurnal Pendidikan Sains

This study aims to develop a differentiated teaching module using the problem-solving model that is valid, practical, and effective to improve students' numerical abilities. This study uses the ADDIE Model research and development approach. The sample in this study was class III of elementary school Tenggulangharjo as an experimental class totaling 22 students and class III of elementary school Karangtengah as a control class totaling 19 students. Data analysis used the t-test and N-Gain test. The study found that (1) the average validity score of the three parts of the Differentiated Teaching Module was 3.74, which is 93.62%, placing it …

Ethnoscience-Based Science Learning Through Composite Board Making Utilizing Eggshell Waste And Water Hyacinth Fiber (Eichornia Crassipes), Asep Khaidir Arpan, Yulia Sukmawardani, Pina Pitriana, Ade Yeti Nuryantini

Jurnal Pendidikan Sains

The demand for boards continues to increase every year, while overexploitation of wood leads to environmental degradation and forest loss. On the other hand, eggshell and water hyacinth waste continues to grow without optimal utilization. This research aims to make composite boards based on eggshell waste and water hyacinth fibers and analyze the potential of ethnoscience in science learning. This research used a qualitative descriptive method with a literature and documentation study approach. The materials used in this experiment are eggshell waste, water hyacinth fiber, and polyester resin. The composite board was made by mixing water hyacinth fiber and eggshell …

Analysis Of Students' Creative Thinking Skills In Learning Hydrocarbons By Using Daily Life-Based Practicum Method, Yenni Kurniawati, Laras Dyaz Handayani, Dea Ramadani, Nurhikmah Sari

Jurnal Pendidikan Sains

Creative thinking skill is a competence of the 21st century that is needed very much and needs to be increased by utilizing chemistry in life. This research aimed at analyzing student creative thinking skills in experimental and control groups and finding out the effect of the daily life-based practical work learning method on student creative thinking skills. This research was conducted in the eleventh grade at High School 1 Pekanbaru on the hydrocarbon lesson. The quasi-experimental method was used in this research with pretest-posttest and non-equivalent control group designs. The instruments used in this research were essay tests, observation, and …

Exploring Students’ Perceptions Of Science Laboratory Practices: A Comparative Study Between Rural And Urban Schools, Safrida Dwiningsih, Ina Lestari, Roma Ismi, Sri Wahyu Rahmadina, Masdalena Sinaga, M. Rahmad

Jurnal Pendidikan Sains

This study aims to analyze students' perceptions of the implementation of science laboratory practicums at public middle school 020 Pekanbaru and public middle school 7 Pangkalan Kuras, Riau Province. Using a quantitative survey method, this study involved 75 student respondents. The instrument used was a questionnaire consisting of 26 statements, analyzed descriptively. The results show that students' perceptions of the preparation, implementation, and conclusion stages of the practicum fall into the "good" category, with urban schools having a higher percentage. In conclusion, the implementation of practicums in urban schools is better than in rural schools, bringing attention to the need …

Digital Comic Learning Media (E-Comic) To Increase Student Learning Interest In Reaction Rate Material At High School, Berliana Afsohin Nabila, Achmad Lutfi

Jurnal Pendidikan Sains

This study aims to develop digital comic learning media that is effective in increasing students' interest in learning about reaction rate material, focusing on the media's validity, practicality, and overall effectiveness. This research utilizes the research and development method with the ADDIE model. Research instruments were used, including validity sheets to assess the media's validity, student activity observations, and student response questionnaires to evaluate the media's practicality, as well as student interest questionnaires and learning outcomes to measure the effectiveness of the learning media. The findings show that validity results showed a mode score of 4, indicating a very valid …

Teaching Materials Containing Kse To Support Character Education In Mathematics Subjects In Elementary Schools, Kunaenah Kunaenah, Rasiman Rasiman, Bagus Ardi Saputro

Jurnal Pendidikan Sains

The purpose of the study was to determine the validity, practicality, and effectiveness of teaching materials containing KSE to support character education in mathematics lesson content. This study employs a development research approach based on Borg and Gall's research design. The subjects of the study were in class V at public elementary school Kaliboyo. The data collection instruments used were validity sheets, response questionnaires, validation sheets, and observation sheets. The findings show that experts carried out the validity test, achieving a value of 93.30% in the very valid category. The practicality test results were derived from various sources: students' questionnaires, …

Development Of Differentiated Teaching Modules With A Scientific Approach To Improve Elementary School Students’ Science Literacy, Supriyanto Supriyanto, Joko Sulianto, Achmad Buchori

Jurnal Pendidikan Sains

The study aim is to determine the validity, practicality, and effectiveness of teaching materials. This type of research involves the development and creation of teaching module products. The research design used is ADDIE (Analysis, Design, Development, Implementation, Evaluation). The instruments used are validity sheets for experts and practitioners, teacher response questionnaires, teaching module validation sheets, and pretest and posttest questions. The findings show that experts conducted the validity test, achieving a score of 92.22 in the very valid category. The practicality test was obtained from the teacher questionnaire, which was stated as practical with an average value of 91.25, and …

Analysis Of Misconceptions In Learning Biology Mutation Material At High School, Fitri Hayati Kurnia, Tri Wahyu Agustina, Wahyuni Handayani

Jurnal Pendidikan Sains

This research aims to analyze student misconceptions regarding mutation material in class XII. The research method uses a descriptive approach with mixed methods, which combines qualitative and quantitative methods. Qualitative data was obtained through interviews with biology teachers, while quantitative data was obtained through questionnaires and essay tests on students. The research results indicate that the material that students like is growth and development, while the material they don't like is gene mutation and genetic material. Students' misconceptions occur due to preconception aspects, associative thinking, and a lack of understanding of genetic concepts. It was found that students' understanding of …

Regularity, Uniqueness And The Relative Size Of Small And Large Scales In Sqg Flows, Z. Akridge, Z. Bradshaw

Mathematical Sciences Faculty Publications and Presentations

The problems of regularity and uniqueness are open for the supercritically dissipative surface quasi-geostrophic equations in certain classes. In this note we examine the extent to which small or large scales are necessarily active both for the temperature in a hypothetical blow-up scenario and for the error in hypothetical non-uniqueness scenarios, the latter understood within the class of Marchand's solutions. This extends prior work for the 3D Navier-Stokes equations. The extension is complicated by the fact that mild solution techniques are unavailable for supercritical SQG. This forces us to develop a new approach using energy methods and Littlewood-Paley theory.

On Uses For And Constructions Of Differential Graded Algebras, Henry Potts-Rubin

Dissertations - ALL

This thesis is comprised of two projects (in reverse chronological order) with the unifying theme of differential graded (dg) algebras. The first is a collaborative effort with Hugh Geller and Desiree Martin, in which we completely classify the trees and cycles whose edge ideals are minimally resolved by dg algebras. To do this, we pull from discrete Morse theory and homological algebra to give descriptions of the dg algebra structures at play. We also use a "pruning" technique due to Boocher to give a combinatorial obstruction to the existence of dg algebra structure on minimal free resolutions of edge ideals …

Applications Of Contracting Self-Similar Groups To Cryptography And Scale Groups, Arsalan Akram Malik

USF Tampa Graduate Theses and Dissertations

Given their peculiar properties, self-similar groups are of great interest both from applications and theoretical standpoints. In this work we study the scope of their applications in post-quantum cryptography and in constructing scale groups via lifting maps.

We propose self-similar contracting groups as a platform for cryptographic schemes based on simultaneous conjugacy search problem (SCSP). This class of groups admits fast polynomial-time algorithms for the word problem and element multiplication that can be used for effective encryption and decryption of messages. It contains extraordinary examples like the Grigorchuk group, which is known to be non-linear, thus making some of existing …

On Some Hypergraph Coloring Algorithms, Boyoon Lee

USF Tampa Graduate Theses and Dissertations

Of a given bipartite graph G = (V, E), it is elementary to construct a bipartition in timeO(|V |+|E|). For a given k-graph H = H(k) with k ≥ 3 fixed, Lovász proved that deciding whether H is bipartite is NP-complete. In this thesis, we consider the average running time of this problem. For that, let B_n = (B^(k))_n be the collection (family) of all bipartite k-graphs H on the fixed vertex set [n] = {1, ...., n}. We construct, of a given H ∈ B_n, a bipartition in time averaging O(n^k) over the class B_n. We provide two proofs …

The Only Constant Is Change: The Role Of Genetic Diversification In Cancer And Beyond, Malgorzata Tyczynska Weh

USF Tampa Graduate Theses and Dissertations

Genetic diversification, the process by which genetic variation arises in a population, is fundamental to evolution by natural selection. Mutation, a central diversification process, fuels adaptation across species, including in cancer. Yet most new mutations are neutral or deleterious on cell fitness, raising the question of how mutation-driven adaptation persists. To explore this paradox, I developed a spatial agent-based model (ABM) in which population fitness emerges from individual cells acquiring mutations at varied rates and with diverse fitness effects. I evaluated model behavior across adaptive states, mutation rates, and distributions of fitness effects. The results show that high mutation rates …

Probabilities With Values In Scaled Hyperbolic Numbers, Daniel Alpay, Ilwoo Choo

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we introduce a notion of a probabilistic measure which takes values in t-scaled hyperbolic numbers for t ∈ R, with a system of axioms generalizing directly Kolmogorov’s axioms. i.e., we establish a suitable measure theory in the set Dt of all t-scaled hyperbolic numbers for arbitrarily fixed t ∈ R.

Machine Learning: Neural Networking With Relu And Optimization, Aidan Redmond Brownell

Undergraduate Theses, Capstones, and Recitals

At its core, learning is an algorithmic process: it begins with input data, undergoes a series of transformations or computations, and yields an output intended to solve a specific task. This output is then compared against a target or desired result, and the internal mechanisms are updated based on how well the output aligns with expectations. While this feedback-driven process occurs almost effortlessly in humans, it is a far more structured, deliberate, and computationally intensive undertaking for machines.