Physical Sciences and Mathematics Commons^™

Target Control Of Networked Systems, Isaac S. Klickstein

Mechanical Engineering ETDs

The control of complex networks is an emerging field yet it has already garnered interest from across the scientific disciplines, from robotics to sociology. It has quickly been noticed that many of the classical techniques from controls engineering, while applicable, are not as illuminating as they were for single systems of relatively small dimension. Instead, properties borrowed from graph theory provide equivalent but more practical conditions to guarantee controllability, reachability, observability, and other typical properties of interest to the controls engineer when dealing with large networked systems. This manuscript covers three topics investigated in detail by the author: (i) the …

Symbolic Construction Of Matrix Functions In A Numerical Environment, Evan D. Butterworth

Honors College Theses

Within the field of Computational Science, the importance of programs and tools involving systems of differential equations cannot be overemphasized. Many industrial sites, such as nuclear power facilities, are unable to safely operate without these systems. This research explores and studies matrix differential equations and their applications to real computing structures. Through the use of software such as MatLab, I have constructed a toolbox, or collection, of programs that will allow any user to easily calculate a variety of matrix functions. The first tool in this collection is a program that computes the matrix exponential, famously studied and presented by …

Modeling Drought, Drought Teleconnection, And Its Effect On Groundwater Level Dynamics In The Biscayne Aquifer, Anteneh Z. Abiy

FIU Electronic Theses and Dissertations

Developing a self-sufficient water supply system in Southeast Florida is one input to the success of the ongoing restoration effort in the Everglades. Maintaining a high groundwater level in the urban side of the Biscayne Aquifer (BA) is important to sustain the urban water supply. However, the long-term groundwater table condition in the Biscayne Aquifer (BA) is threatened by a combination of drought, groundwater pumping, and sea-level rise. Further, the long-term drought pattern, drought drivers, and the aquifer’s response to drought and other stress conditions are not well known. As a result, options that would help to maintain a high …

A Study Of Addiction: The Opioid Epidemic, An Analysis At The State And County Level, Jamey Van Dyke

Undergraduate Theses

Addictive diseases such as those stemming from the use of alcohol, cocaine and opioids lead to serious negative consequences at both the individual and societal level. Over the last two decades, there has been a significant increase in opioid prescriptions and addiction. The potential for addiction is related to factors that include genetics, prescriber behavior, user behavior and characteristics, in addition to environmental and systemic determinants. One measure of the seriousness of the opioid epidemic is the number of overdose deaths. In 2017, drug overdoses killed over seventy thousand Americans, and overdose deaths are projected to increase in the future. …

Contraction Analysis Of Functional Competitive Lotka-Volterra Systems: Understanding Competition Between Modified Bacteria And Plasmodium Within Mosquitoes., Nickolas Goncharenko

Electronic Thesis and Dissertation Repository

We propose and analyze an extension to the classic Competitive Lotka-Volterra (CLV) model. The goal is to model competition between species, with a response from the environment. This response is a function of the population of all species and can represent numerous physical phenomena including resource limitation and immune response of a host due to infection. We name this new system a Functional Competitive Lotka-Volterra (FCLV) model. We mainly use the construction of contraction metrics, to determine global properties of the model. We use this result to analyze the competition between Plasmodium sp. and genetically engineered bacteria within the midgut …

483— Effectiveness Of Mmr Vaccination In Orthodox Jewish Neighborhoods, Meenu Mundackal

GREAT Day Posters

Measles is a highly contagious disease, where large outbreaks arise by direct contact between susceptible (unvaccinated) and infectious individuals. Many Orthodox Jewish neighborhoods were affected by measles from 2018-2019. To quantify the vaccination effort on this susceptible population, a retrospective analysis was used to study the NYC and Rockland County populations using a differential equations model. A subsequent model, known as a realistically-structured network model, studied only the NYC population, in relation to typical household size. Vaccination strategies were applied to three cohorts: unvaccinated family members, members with 1 prior MMR dose, and members with 2 prior MMR doses. The …

484— Modeling Social Distancing Methods And Their Effectiveness In Combating The Spread Of Ebola, Rachel Fair

GREAT Day Posters

Ebola Virus Disease (EVD) is a rare but severe disease that is transmitted among humans through direct-contact with, and close proximity to, infected bodily fluids. From 2014-16, West Africa experienced the largest Ebola outbreak ever recorded, infecting over 28,000 people, and killing over 11,000. Although the symptoms of EVD are treatable, the disease can be extremely deadly, with an average of 50% EVD cases resulting in fatality. In areas where healthcare is scarce and vaccinations are not readily available, the practices of social distancing and self-quarantining have been shown to be highly effective in combating the spread of EVD. To …

465— Modeling Vaccine Efficacy For Tuberculosis In A Prison Population, Kaitlyn Mundackal

GREAT Day Posters

Tuberculosis is a highly contagious disease and is particularly problematic in confined communities such as prisons. I simulated how Tuberculosis moves through a prison population and tested how much vaccination effort is needed to control its spread. To explore this, I tested adding ever increasing numbers of randomly placed edges in a network and determined the size of the largest component. Afterwards, I removed edges in the model using two different methods, one illustrating if the edges were removed randomly and the other starting with prisoners that had the most connections, to simulate the effect of vaccination. My results show …

358— Hybridization Of Particle Swam Optimization And Pattern Search Algorithms With Application, Eric Koessler

GREAT Day Posters

We test three methods of hybridizing Particle Swarm Optimization (PSO) and Pattern Search (PS) to improve the global minima, speed, and robustness. All methods let PSO run first followed by PS. The first method lets PSO use a large number of particles for a limited number of iterations. The second method lets PSO run normally until tolerance is reached. The third method lets PSO run normally until the average particle distance from the global best location is within a threshold. Numerical results using non-differentiable test functions reveal that all three methods improve the global minima and robustness versus PSO, while …

Modeling Fico Score And Loan Amount, Ashleigh Romer

Georgia College Student Research Events

In this research, we use Lending Club data from Kaggle to analyze FICO scores and loan amounts funded using multiple predictors. Lending Club is a US peer-to-peer lending company, headquartered in San Francisco, California. First, we cleaned our big data with 1,048,575 rows and 97 columns and then performed exploratory data analysis. We also used feature engineering and subset selection methods to build a linear model to predict FICO score and amount funded of customers loan requests. Overall, we found that FICO score is best modeled using backward regression which gives an exponential function with the predictors being grade, title, …

A Study Of Cholera Transmission, Urmi Ghosh-Dastidar

Open Educational Resources

A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a practical problem such as cholera transmission using various mathematical tools. Students will learn to develop a differential equation model based on practical scenarios, analyze the model using mathematics as well as numerical simulation, and finally describe the results in words that are understandable by the people who are not specialists in this …

The Dual Of The Compressed Shift, M. C. Câmara, William T. Ross

Department of Math & Statistics Faculty Publications

For an inner function u, we discuss the dual operator for the compressed shift P_uS∣_Ku, where K_u is the model space for u. We describe the unitary equivalence/similarity classes for these duals as well as their invariant subspaces.

Abelian Integral Method And Its Application, Xianbo Sun

Electronic Thesis and Dissertation Repository

Oscillation is a common natural phenomenon in real world problems. The most efficient mathematical models to describe these cyclic phenomena are based on dynamical systems. Exploring the periodic solutions is an important task in theoretical and practical studies of dynamical systems.

Abelian integral is an integral of a polynomial differential 1-form over the real ovals of a polynomial Hamiltonian, which is a basic tool in complex algebraic geometry. In dynamical system theory, it is generalized to be a continuous function as a tool to study the periodic solutions in planar dynamical systems. The zeros of Abelian integral and their distributions …

Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann

Mathematics & Statistics ETDs

This thesis uses a geometric approach to derive and solve nonlinear least squares minimization problems to geolocate a signal source in three dimensions using time differences of arrival at multiple sensor locations. There is no restriction on the maximum number of sensors used. Residual errors reach the numerical limits of machine precision. Symmetric sensor orientations are found that prevent closed form solutions of source locations lying within the null space. Maximum uncertainties in relative sensor positions and time difference of arrivals, required to locate a source within a maximum specified error, are found from these results. Examples illustrate potential requirements …

Modeling The Effects Of Passive Immunity In Birds For The Disease Dynamics Of West Nile Virus, Noelle West, Vinodh K. Chellamuthu

Spora: A Journal of Biomathematics

West Nile Virus (WNV) is a mosquito-borne virus that circulates among birds but also affects humans. Migrating birds carry these viruses from one place to another each year. WNV has spread rapidly across the continental United States resulting in numerous human infections and deaths. Several studies suggest that larval mosquito control measures should be taken as early as possible in a season to control the mosquito population size. Also, adult mosquito control measures are necessary to prevent the transmission of WNV from mosquitoes to birds and humans. To better understand the effective strategy for controlling affected larvae mosquito population, we …

Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …

Storage Management Strategy In Mobile Phones For Photo Crowdsensing, En Wang, Zhengdao Qu, Xinyao Liang, Xiangyu Meng, Yongjian Yang, Dawei Li, Weibin Meng

Department of Computer Science Faculty Scholarship and Creative Works

In mobile crowdsensing, some users jointly finish a sensing task through the sensors equipped in their intelligent terminals. In particular, the photo crowdsensing based on Mobile Edge Computing (MEC) collects pictures for some specific targets or events and uploads them to nearby edge servers, which leads to richer data content and more efficient data storage compared with the common mobile crowdsensing; hence, it has attracted an important amount of attention recently. However, the mobile users prefer uploading the photos through Wifi APs (PoIs) rather than cellular networks. Therefore, photos stored in mobile phones are exchanged among users, in order to …

Studies Of Oval Tube And Fin Heat Exchangers, Phillip Nielsen

Discovery Day - Prescott

Heating Ventilation and air-conditioning (HVAC) is a system which changes the temperature of the surroundings for the purposes of cooling or heating. This system requires energy to maintain a temperature difference from the outside temperature. This is important since minimized power is one of the requirements for the system to achieve a better efficiency. Optimizing the flow over the evaporator coils is one way to increase the cooling efficiency. This will reduce the power required to have a sustainable system. Optimizing the flow to increase the energy transfer between the fins and the incoming air could result in a greater …

Mitigating Safety Concerns And Profit/Production Losses For Chemical Process Control Systems Under Cyberattacks Via Design/Control Methods, Helen Durand, Matthew Wegener

Chemical Engineering and Materials Science Faculty Research Publications

One of the challenges for chemical processes today, from a safety and profit standpoint, is the potential that cyberattacks could be performed on components of process control systems. Safety issues could be catastrophic; however, because the nonlinear systems definition of a cyberattack has similarities to a nonlinear systems definition of faults, many processes have already been instrumented to handle various problematic input conditions. Also challenging is the question of how to design a system that is resilient to attacks attempting to impact the production volumes or profits of a company. In this work, we explore a process/equipment design framework for …

Redesign Of Math 1601 Modeling With Calculus, Dustin Grindstaff

Q2S Enhancing Pedagogy

This is the redesign of the course math 1601 - Modeling with Calculus. It includes a sample syllabus and tentative schedule of topics to be covered. The course must meet the Technological Literacy requirement so I have also included a list of potential GeoGebra activities, as well as, what a sample activity would look like.

Analysis Of An Ode Model For Sea Turtle Populations With Temperature-Dependent Sex Determination, Lindsey A. Ukishima

Student Publications

The sex of green sea turtles is determined by the temperature at which the eggs are incubated. Recent studies have shown that the sex ratios of sea turtle populations have changed over recent years, likely due to climate change, which has produced a more female-biased population. This paper finds the nonzero equilibrium point of the novel system developed by Herrera et a. (2019) and attempts to determine the stability of the population at that point.

Certain Mathieu-Type Series Pertaining To Incomplete H-Functions, Nidhi Jolly, Manish K. Bansal, Devendra Kumar, Jagdev Singh

Applications and Applied Mathematics: An International Journal (AAM)

In the present article, we derive closed integral form expressions for a family of convergent Mathieu type a-series along with its alternating variants, whose terms contain incomplete H-functions, which are a notable generalization of familiar H-function. The results established herewith are very general in nature and provide an exquisite generalization of closed integral form expressions of aforementioned series whose terms contain H-function and Fox-Wright function, respectively. Next, we present some new and interesting special cases of our main results.

Scale-Invariance Ideas Explain The Empirical Soil-Water Characteristic Curve, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

The prediction of the road's properties under the influence of water infiltration is important for pavement design and management. Traditionally, this prediction heavily relied on expert estimates. In the last decades, complex empirical formulas have been proposed to capture the expert's intuition in estimating the effect of water infiltration on the stiffness of the pavement's payers. Of special importance is the effect of water intrusion on the pavement's foundation -- known as subgrade soil. In this paper, we show that natural scale-invariance ideas lead to a theoretical explanation for an empirical formula describing the dependence between soil suction and water …

Non-Uniform Haar Wavelet Method For Solving Singularly Perturbed Differential Difference Equations Of Neuronal Variability, Akmal Raza, Arshad Khan

Applications and Applied Mathematics: An International Journal (AAM)

A non-uniform Haar wavelet method is proposed on specially designed non-uniform grid for the numerical treatment of singularly perturbed differential-difference equations arising in neuronal variability.We convert the delay and shift terms using Taylor series up to second order and then the problem with delay and shift is converted into a new problem without the delay and shift terms. Then it is solved by using non-uniform Haar wavelet. Two test examples have been demonstrated to show the accuracy of the non-uniform Haar wavelet method. The performance of the present method yield more accurate results on increasing the resolution level and converges …

Class Of Integrals Involving Generalized Hypergeometric Function, D. L. Suthar, Teklay Hailay, Hafte Amsalu, Jagdev Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we establish some definite integrals involving generalized hypergeometric function, product of algebraic functions, Jacobi function, Legendre function and general class of polynomials. Certain special cases of the main results are also pointed out.

Ruscheweyh-Goyal Derivative Of Fractional Order, Its Properties Pertaining To Pre-Starlike Type Functions And Applications, Ritu Agarwal, G. S. Paliwal

Applications and Applied Mathematics: An International Journal (AAM)

The study of the operators possessing convolution form and their properties is considered advantageous in geometric function theory. In 1975 Ruscheweyh defined operator for analytic functions using the technique of convolution. In 2005, Goyal and Goyal generalized the Ruscheweyh operator to fractional order (which we call here Ruscheweyh-Goyal differential operator) using Srivastava-Saigo fractional differential operator involving hypergeometric function. Inspired by these earlier efforts, we discuss the properties of the Ruscheweyh-Goyal derivative of arbitrary order. We define a class of pre-starlike type functions involving the Ruscheweyh-Goyal fractional derivative and obtain the inclusion relation. Further, we prove that Ruscheweyh-Goyal derivative operator preserve …

Finite And Infinite Integral Formulas Involving The Family Of Incomplete H-Functions, Manish K. Bansal, Devendra Kumar, Jagdev Singh, Kottakkaran Sooppy Nisar

Applications and Applied Mathematics: An International Journal (AAM)

Recent research focuses on the integral representations of the various type of special functions due to their potential applicability in different disciplines. In this line, we deal with several finite and infinite integrals involving the family of incomplete H-functions. Further, we point out some known and new special cases of these integrals. Finally, we establish the integral representation of incomplete H-functions.

Some Quadratic Transformations And Reduction Formulas Associated With Hypergeometric Functions, M. I. Qureshi, M. Kashif Khan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we construct four summation formulas for terminating Gauss’ hypergeometric series having argument “two" and with the help of our summation formulas. We establish two quadratic transformations for Gauss’ hypergeometric function in terms of finite summation of combination of two Clausen hypergeometric functions. Further, we have generalized our quadratic transformations in terms of general double series identities as well as in terms of reduction formulas for Kampé de Fériet’s double hypergeometric function. Some results of Rathie-Nagar, Kim et al. and Choi-Rathie are also obtained as special cases of our findings.

Existence And Stability Results Of Nonlinear Fractional Differential Equations With Nonlinear Integral Boundary Condition On Time Scales, Vipin Kumar, Muslim Malik

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we establish the existence and uniqueness of the solution to a nonlinear fractional differential equation with nonlinear integral boundary conditions on time scales.We used the fixed point theorems due to Banach, Schaefer’s, nonlinear alternative of Leray Schauder’s type and Krasnoselskii’s to establish these results. In addition, we study Ulam-Hyer’s (UH) type stability result. At the end, we present two examples to show the effectiveness of the obtained analytical results.

Wilson Sensor Footballs: Consistency Metric, Kenneth Eaton

Honors Capstone Enhancement Presentations

No abstract provided.