Applied Mathematics Commons^™

Graphsearchnet: Enhancing Gnns Via Capturing Global Dependencies For Semantic Code Search, Shangqing Liu, Xiaofei Xie, Jjingkai Siow, Lei Ma, Guozhu Meng, Yang Liu

Research Collection School Of Computing and Information Systems

Code search aims to retrieve accurate code snippets based on a natural language query to improve software productivity and quality. With the massive amount of available programs such as (on GitHub or Stack Overflow), identifying and localizing the precise code is critical for the software developers. In addition, Deep learning has recently been widely applied to different code-related scenarios, ., vulnerability detection, source code summarization. However, automated deep code search is still challenging since it requires a high-level semantic mapping between code and natural language queries. Most existing deep learning-based approaches for code search rely on the sequential text ., …

Data-Driven Learning Algorithm Via Densely-Defined Multiplication Operators And Occupation Kernels., John Kyei

USF Tampa Graduate Theses and Dissertations

Consider a nonautonomous nonlinear evolution $\dot{x}=f(x,t,\mu)$, where the vector $x(t) \in \mathbb{R}^n$ represents the state of the dynamical system at time $t$, $\mu$ contains system parameters, and $f(\cdot)$ represents a dynamic constraint. In most practical applications, the nonlinear dynamic constraint $f$ is unknown analytically. The problem of approximating $f$ directly from data measurements generated by the system is a main goal of this manuscript. In the postulates of the Nonlinear Autoregressive (NAR) framework, we show that the problem of approximating $f$ can be studied through symbols of densely defined multiplication operators over a Reproducing Kernel Hilbert Spaces (RKHS). In this …

Mathematical Modeling And Inverse Problems In Applications, Thanh T. Nguyen

College of Science & Mathematics Departmental Research

Mathematical models, based on ordinary or partial differential equations, are widely used to describe physical/chemical/biological processes and can be found in several applications: nondestructive testing, subsurface imaging, defense, medicine, environmental sciences, etc.

Using Physics-Informed Neural Networks For Multigrid In Time Coarse Grid Equations, Jonathan P. Gutierrez

Mathematics & Statistics ETDs

For parallel-in-time integration methods, the multigrid-reduction-in-time (MGRIT) method has shown promising results in both improved convergence and increased computational speeds when solving evolution problems. However, one problem the MGRIT algorithm currently faces is it struggles solving hyperbolic problems efficiently. In particular, hyperbolic problems are generally solved using explicit methods and this causes issues on the coarser multigrid levels, where larger (coarser) time step sizes can violate the stability condition. In this thesis, physics-informed neural networks (PINNs) are used to evaluate the coarse grid equations in the MGRIT algorithm with the goal to improve convergence for problems with hyperbolic behavior, as …

Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner

UNO Student Research and Creative Activity Fair

Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy …

Formal Conjugacy Growth In Graph Products I, Laura Ciobanu,, Susan Hermiller, Valentin Mercier

Department of Mathematics: Faculty Publications

In this paper we give a recursive formula for the conjugacy growth series of a graph product in terms of the conjugacy growth and standard growth series of subgraph products. We also show that the conjugacy and standard growth rates in a graph product are equal provided that this property holds for each vertex group. All results are obtained for the standard generating set consisting of the union of generating sets of the vertex groups.

Infinite-Dimensional Stochastic Transforms And Reproducing Kernel Hilbert Space, Myung-Sin Song, Palle Jorgensen, James Feng Tian

SIUE Faculty Research, Scholarship, and Creative Activity

By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new infinite-dimensional Fourier transform in a general setting of Gaussian processes. Our results serve to unify existing tools from infinite-dimensional analysis.

Chatgpt As Metamorphosis Designer For The Future Of Artificial Intelligence (Ai): A Conceptual Investigation, Amarjit Kumar Singh (Library Assistant), Dr. Pankaj Mathur (Deputy Librarian)

Library Philosophy and Practice (e-journal)

Abstract

Purpose: The purpose of this research paper is to explore ChatGPT’s potential as an innovative designer tool for the future development of artificial intelligence. Specifically, this conceptual investigation aims to analyze ChatGPT’s capabilities as a tool for designing and developing near about human intelligent systems for futuristic used and developed in the field of Artificial Intelligence (AI). Also with the helps of this paper, researchers are analyzed the strengths and weaknesses of ChatGPT as a tool, and identify possible areas for improvement in its development and implementation. This investigation focused on the various features and functions of ChatGPT that …

Evolution Of Coronal Magnetic Field Parameters During X5.4 Solar Flare, Seth H. Garland, Benjamin F. Akers, Vasyl B. Yurchyshyn, Robert D. Loper, Daniel J. Emmons

Faculty Publications

The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz| ≥ 300 G, areas of flare brightening seen …

Kegg_Pull: A Software Package For The Restful Access And Pulling From The Kyoto Encyclopedia Of Gene And Genomes, Erik D. Huckvale, Hunter N. B. Moseley

Markey Cancer Center Faculty Publications

Background: The Kyoto Encyclopedia of Genes and Genomes (KEGG) provides organized genomic, biomolecular, and metabolic information and knowledge that is reasonably current and highly useful for a wide range of analyses and modeling. KEGG follows the principles of data stewardship to be findable, accessible, interoperable, and reusable (FAIR) by providing RESTful access to their database entries via their web-accessible KEGG API. However, the overall FAIRness of KEGG is often limited by the library and software package support available in a given programming language. While R library support for KEGG is fairly strong, Python library support has been lacking. Moreover, there …

Student Performance In Traditional In-Person Vs. Online Sections Of An Introductory Graduate Mathematics Course, Lauran E. Kittle

Theses and Dissertations

The growth of technology impacts nearly every aspect of everyday life, to include education and learning. The availability of distance learning (online) classes has increased drastically in the last few decades, expanding access to education for millions of people. However, it is imperative to consider exactly how the growth of technology impacts education – whether it is a positive, negative, or neutral impact. Previous research comparing distance learning and in-residence (traditional) classes have widely mixed, disparate conclusions. This type of research, two-stage analysis, and modeling has yet to be conducted on a graduate school level. For this reason, a detailed …

Mathematical Models For Thalassemia, Hamda Mohammed Al Dhaheri

Theses

Thalassemia is a genetic blood disorder caused by gene mutation or deletion in a blood protein called hemoglobin. Treatment of thalassemia requires a life-long blood transfusion and removal of excessive iron in the blood stream, which usually causes a big pressure on health care systems. Various forms of thalassemia control measures have been used to reduce the prevalence of thalassemia major. This has resulted in a substantial reduction in the prevalence of thalassemia. However, the thalassemia carrier population remains high, which could lead to an increase in the thalassemia major population through carrier-to-carrier marriages. Thus, we developed two mathematical models …

Analysis Of The Accuracy Of The Solution Of The Integral Equation Of The Interpretation Problem, Majid Malikovich Karimov, Mirhusan Mirazizovich Sagatov

Chemical Technology, Control and Management

Intensive development and expansion of the field of application of modern observation systems are largely determined by the improvement of methods and means of interpreting the primary results recorded by the system. The high quality of the results of solving interpretation problems is achieved by improving such indicators as accuracy, resolution, speed. In the general case, the influence of the observation system on the result is naturally described by an integral equation, which is a general integral mathematical model for the problems of interpreting the results of observations. In the presented article, it is proposed to improve the accuracy of …

A Mathematical Algorithm Approach For Estimating Water-Based Paint Requirements For A Given Wall, Ismail W. R. Taifa Dr

Tanzania Journal of Engineering and Technology (TJET)

The research aimed to improve the accuracy of estimating water based paint requirements for a given wall using mathematical algorithms. The approach used in this study included a survey and document review to obtain details concerning paint. The study focused on water-based paints, including silk, weather guard, emulsion hi-cover and polyvinyl acetate (PVA) roof paint used in Tanzania’s building and construction industry. Data collected from the field study were analysed systematically. It was observed that there is a high level of familiarity in improving the accuracy of estimation of the required water-based paints, namely silk, weather guard, emulsion hi-cover and …

Bernstein-Sato Theory For Singular Rings In Positive Characteristic, Jack Jack, Luis Núñez-Betancourt, Eamon Quinlan-Gallego

Department of Mathematics: Faculty Publications

The Bernstein-Sato polynomial is an important invariant of an element or an ideal in a polynomial ring or power series ring of characteristic zero, with interesting connections to various algebraic and topological aspects of the singularities of the vanishing locus. Work of Mustaţă, later extended by Bitoun and the third author, provides an analogous Bernstein-Sato theory for regular rings of positive characteristic.

In this paper, we extend this theory to singular ambient rings in positive characteristic. We establish finiteness and rationality results for Bernstein-Sato roots for large classes of singular rings, and relate these roots to other classes of numerical …

Tri-Plane Diagrams For Simple Surfaces In S4, Manuel Aragón, Zack Dooley, Alexander Goldman, Yucong Lei, Isaiah Martinez, Nicholas Meyer, Devon Peters, Scott Warrander, Ana Wright, Alex Zupan

Department of Mathematics: Faculty Publications

Meier and Zupan proved that an orientable surface K in S⁴ admits a tri-plane diagram with zero crossings if and only if K is unknotted, so that the crossing number of K is zero. We determine the minimal crossing numbers of nonorientable unknotted surfaces in S⁴, proving that c(P^n,m) = max{1, |n−m|}, where P^n,m denotes the connected sum of n unknotted projective planes with normal Euler number +2 and m unknotted projective planes with normal Euler number −2. In addition, we convert Yoshikawa’s table of knotted surface ch-diagrams to tri-plane …

Session 12: Analysis Of State And Parameter Estimation Techniques Using Dynamic Perturbation Signals, Timothy M. Hansen

SDSU Data Science Symposium

The trend in electric power systems is the displacement of traditional synchronous generation (e.g., coal, natural gas) with renewable energy resources (e.g., wind, solar photovoltaic) and battery energy storage. These energy resources require power electronic converters (PECs) to interconnect to the grid and have different response characteristics and dynamic stability issues compared to conventional synchronous generators. As a result, there is a need for validated models to study and mitigate PEC-based stability issues, especially for converter dominated power systems (e.g., island power systems, remote microgrids).

This presentation will introduce methods related to dynamic state and parameter estimation via the design …

Decomposition Rate As An Emergent Property Of Optimal Microbial Foraging, Stefano Manzoni, Arjun Chakrawal, Glenn Ledder

Department of Mathematics: Faculty Publications

Decomposition kinetics are fundamental for quantifying carbon and nutrient cycling in terrestrial and aquatic ecosystems. Several theories have been proposed to construct process-based kinetics laws, but most of these theories do not consider that microbial decomposers can adapt to environmental conditions, thereby modulating decomposition. Starting from the assumption that a homogeneous microbial community maximizes its growth rate over the period of decomposition, we formalize decomposition as an optimal control problem where the decomposition rate is a control variable. When maintenance respiration is negligible, we find that the optimal decomposition kinetics scale as the square root of the substrate concentration, resulting …

A Statistical Analysis Of The Change In Age Distribution Of Spawning Hatchery Salmon, Rachel Macaulay, Emily Barrett, Grace Penunuri, Eli E. Goldwyn

Spora: A Journal of Biomathematics

Declines in salmon sizes have been reported primarily as a result of younger maturation rates. This change in age distribution poses serious threats to salmon-dependent peoples and ecological systems. We perform a statistical analysis to examine the change in age structure of spawning Alaskan chum salmon Oncorhynchus keta and Chinook salmon O. tshawytscha using 30 years of hatchery data. To highlight the impacts of this change, we investigate the average number of fry/smolt that each age of spawning chum/Chinook salmon produce. Our findings demonstrate an increase in younger hatchery salmon populations returning to spawn, and fewer amounts of fry produced …

Modeling And Analyzing Homogeneous Tumor Growth Under Virotherapy, Chayu Yang, Jin Wang

Department of Mathematics: Faculty Publications

We present a mathematical model based on ordinary differential equations to investigate the spatially homogeneous state of tumor growth under virotherapy. The model emphasizes the interaction among the tumor cells, the oncolytic viruses, and the host immune system that generates both innate and adaptive immune responses. We conduct a rigorous equilibrium analysis and derive threshold conditions that determine the growth or decay of the tumor under various scenarios. Numerical simulation results verify our analytical predictions and provide additional insight into the tumor growth dynamics.

A Dynamical System Model Of Dengue Transmission For Rio De Janeiro, Brazil, Gregory Schmidt, Benjamin Whipple, Vinodh Chellamuthu, Xiaoxia Xie

Spora: A Journal of Biomathematics

The dengue virus is a serious concern in many parts of the world, including Brazil. As data indicates, a prominent vector for dengue is the mosquito Aedes aegypti. By using the dengue incidence records from the Brazilian SINAN database, we estimate the population of A. aegypti within the city of Rio de Janeiro. Using historical climate data for Rio de Janeiro and the computed population estimates, we extend an existing model for the population dynamics of mosquitoes to incorporate precipitation in aquatic stages of development for A. aegypti.

Integrable Systems On Symmetric Spaces From A Quadratic Pencil Of Lax Operators, Rossen Ivanov

Conference papers

The article surveys the recent results on integrable systems arising from quadratic pencil of Lax operator L, with values in a Hermitian symmetric space. The counterpart operator M in the Lax pair defines positive, negative and rational flows. The results are illustrated with examples from the A.III symmetric space. The modeling aspect of the arising higher order nonlinear Schrödinger equations is briefly discussed.

A Path Planning Framework For Multi-Agent Robotic Systems Based On Multivariate Skew-Normal Distributions, Peter Estephan

Theses, Dissertations and Capstones

This thesis presents a path planning framework for a very-large-scale robotic (VLSR) system in an known obstacle environment, where the time-varying distributions of agents are applied to represent the multi-agent robotic system (MARS). A novel family of the multivariate skew-normal (MVSN) distributions is proposed based on the Bernoulli random field (BRF) referred to as the Bernoulli-random-field based skew-normal (BRF-SN) distribution. The proposed distributions are applied to model the agents’ distributions in an obstacle-deployed environment, where the obstacle effect is represented by a skew function and separated from the no-obstacle agents’ distributions. First, the obstacle layout is represented by a Hilbert …

Modeling Self-Diffusiophoretic Janus Particles In Fluid, Kausik Das

HMC Senior Theses

We explore spherical Janus particles in which a chemical reaction occurs on one face, depleting a substrate in the suspending fluid, while no reaction occurs on the other face. The steady state concentration field is governed by Laplace’s equation with mixed boundary conditions. We use the collocation method to obtain numerical solutions to the equation in spherical coordinates. The asymmetry of the reaction gives rise to a slip velocity that causes the particle to move spontaneously in the fluid through a process known as self-diffusiophoresis. Using the Lorentz reciprocal theorem, we obtain the swimming velocity of the particle. We extend …

Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, Emerson Mcmullen

HMC Senior Theses

Although women have made progress in entering positions in academia and
industry, they are still underrepresented at the highest levels of leadership.
Two factors that may contribute to this leaky pipeline are gender bias,
the tendency to treat individuals differently based on the person’s gender
identity, and homophily, the tendency of people to want to be around those
who are similar to themselves. Here, we present a multilayer network model
of gender representation in professional hierarchies that incorporates these
two factors. This model builds on previous work by Clifton et al. (2019), but
the multilayer network framework allows us to …

Graph-Based Acoustic Clustering And Classification, Justin Youngho Sunu

CGU Theses & Dissertations

The rapid growth of audio data collection in various domains necessitates advanced techniquesfor efficient analysis and classification. This dissertation proposes new approaches for categorizing acoustic data, using both unsupervised and semi-supervised learning methods. Starting with raw audio, we preprocess the signal to segment it into time windows, each of which we consider as an independent data point. We use the short-time Fourier transform to describe the signal in a given time window as a set of Fourier coefficients. We interpret the resulting frequency signature as a high-dimensional feature description of each data point. We then develop a graph-based approach for …

Application Of The Two-Variable Model To Simulate A Multisensory Reaction-Time Task, Rebecca Brady, John Butler

Academic Posters Collection

To navigate the world in an efficient manner, the brain seamlessly integrates signals received across multiple sensory modalities. Behavioral studies have suggested that multisensory processing is a winner-take-all sensory response mechanism to some optimal combination of sensory signals. In addition, multiple sensory cues are not always beneficial with some studies showing maladaptive multisensory processing as an identifier of older adults prone to falls from age matched healthy controls.

A stalwart of modelling sensory decision-making is the work by (Wong &Wang, 2006) but to date almost all of this research has been focused on unisensory tasks. We extend the reduced two-variable …

An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

This paper presents an alternate proof of the divergence of the unique maximizer sequence {𝑥∗ 𝑛} of a function sequence {𝐹𝑛(𝑥)} that is derived from an adaptive algorithm based on the now classic optimal stopping problem, known by many names but here ‘the secretary problem’. The alternate proof uses a result established by Nguyen, Xu, and Zhao (n.d.) regarding the uniqueness of maximizer points of a generalized function sequence {𝑆𝜇,𝜎 𝑛 } and relies on the strict monotonicity of 𝐹𝑛(𝑥) as 𝑛 increases in order to show divergence of {𝑥∗ 𝑛}. Towards this, limits of the exponentiated Gaussian CDF are …

Evaluating A Temperature-Dependent Mosquito Population Model, Morgan H. Jackson, Elizabet L. Estallo, Cheng Ly, Michael A. Robert

Graduate Research Posters

Dengue Virus causes over 390 million infections and around 40,000 deaths each year. This virus is primarily transmitted by the mosquito Aedes aegypti. The life cycle of these mosquitos is significantly impacted by temperature, however, temperature is often neglected in mechanistic models. Predictive models of mosquito populations thus require the inclusion of temperature and are valuable for helping medical officials plan for the impact of outbreaks. Using mosquito and climate data collected in Córdoba, Argentina from 2010-2013, we developed a non-autonomous ordinary differential equations model that includes temperature dependent parameters associated with mosquito life history. We performed local sensitivity …

The Power Of Supercomputing Applied To Fractal Image Generation, Charlin Me Duff

Mathematics Senior Capstones

This project looks into how parallelism benefits the runtime of generating large fractal images. First, it explains what the Julia and Mandelbrot Sets are, who discovered them, and how they are calculated. Following that is an introduction to supercomputers, parallel computing, and Cal Poly Humboldt’s very own supercomputer. Once groundwork is laid, I explain my process of adapting a fractal image generation program from serial computing to different levels of parallelism. After that, is an analysis of the effects of levels of parallelism on the runtime of large fractal image generation. This paper concludes with a reflection on the project …