Applied Mathematics Commons^™

Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown

The Journal of Purdue Undergraduate Research

No abstract provided.

Compartmental Modeling For The Neophyte: An Application Of Berkeley Madonna, Olcay Akman, Siddharth Bhumpelli, Cody Cline, Christopher Hay-Jahans

Spora: A Journal of Biomathematics

Compartmental modeling serves as a necessary framework in many fields, especially biomathematics and ecology. This article introduces readers to a user-friendly approach to constructing compartmental models and solving the resulting systems of differential equations to simulate real-world applications. The platform used is Berkeley Madonna, a software package that has an intuitive graphical interface which empowers users—even those with limited mathematical and programming backgrounds—to focus on modeling concepts rather than mathematical or programming intricacies. This makes Berkeley Madonna an ideal platform for students, educators, and researchers.

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, Atallah El-Shenawy, Mohamed El-Gamel, Muhammad E. Anany

Mansoura Engineering Journal

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Efficient And Secure Digital Signature Algorithm (Dsa), Nissa Mehibel, M'Hamed Hamadouche

Emirates Journal for Engineering Research

The digital signature is used to ensure the integrity of messages as well as the authentication and non-repudiation of users. Today it has a very important role in information security. Digital signature is used in various fields such as e-commerce and e-voting, health, internet of things (IOT). Many digital signature schemes have been proposed, depending on the computational cost and security level. In this paper, we analyzed a recently proposed digital signature scheme based on the discrete logarithm problem (DLP). Our analysis shows that the scheme is not secure against the repeated random number attack to determine the secret keys …

Quantum Computing And Its Applications In Healthcare, Vu Giang

OUR Journal: ODU Undergraduate Research Journal

This paper serves as a review of the state of quantum computing and its application in healthcare. The various avenues for how quantum computing can be applied to healthcare is discussed here along with the conversation about the limitations of the technology. With more and more efforts put into the development of these computers, its future is promising with the endeavors of furthering healthcare and various other industries.

Swarm Intelligence For Solving Some Nonlinear Differential Equations, Ahmed Elzaghal, Mohammed Mohammed Elgamal, Ahmed H. Eltanboly

Mansoura Engineering Journal

The Euler method is a well-known numerical technique employed for solving initial value problems of ordinary differential equations. The solution obtained through Euler's method is subject to significant inaccuracies, which tend to amplify with each successive iteration. The Particle Swarm Optimization (PSO) algorithm is a highly effective method for finding optimal solutions to both linear and nonlinear optimization problems. In this particular investigation, the PSO technique was utilized to solve initial value problems associated with ordinary differential equations. The Euler method, on the other hand, employs equidistant grid points to approximate solutions, which can result in significant errors and a …

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 …

Computational Models To Detect Radiation In Urban Environments: An Application Of Signal Processing Techniques And Neural Networks To Radiation Data Analysis, Jose Nicolas Gachancipa

Beyond: Undergraduate Research Journal

Radioactive sources, such as uranium-235, are nuclides that emit ionizing radiation, and which can be used to build nuclear weapons. In public areas, the presence of a radioactive nuclide can present a risk to the population, and therefore, it is imperative that threats are identified by radiological search and response teams in a timely and effective manner. In urban environments, such as densely populated cities, radioactive sources may be more difficult to detect, since background radiation produced by surrounding objects and structures (e.g., buildings, cars) can hinder the effective detection of unnatural radioactive material. This article presents a computational model …

On Efficacy And Effectiveness Of Vaccines: A Mathematical Approach Based On Conditional Probability With Applications To The Covid-19 Context, Flavius Guias

Spora: A Journal of Biomathematics

This paper presents a mathematically formalized approach which points out the relation between efficacy and effectiveness of vaccines. The first term denotes the relative degree of protection in clinical trials or under ideal conditions, while the latter is based on observed real-life data. We define the efficacy by a similar formula to the effectiveness, but the probabilities involved in the relative risk are conditional with respect to the exposure to the virus. If exposure and vaccination status are independent, the two quantities are equal. Otherwise, the observed value of the effectiveness is a biased one, as it could be seen …

An Axiomatic And Contextual Review Of The Armitage And Doll Model Of Carcinogenesis, W. Zane Billings, Justin Clifton, Josh Hiller, Tommy Meek, Andrew Penland, Wesley Rogers, Gabriella Smokovich, Andrew Velasquez-Berroteran, Eleni Zamagias

Spora: A Journal of Biomathematics

In 1954, Armitage and Doll published one of the most influential papers in the history of mathematical epidemiology. However, when one examines the literature one finds that there are in fact at least three distinct mathematical models attributed to the 1954 paper. In this study, we examine this important paper and the mathematical derivation of their model. We find, very surprisingly, that no stochastic process can account for all the assumptions of the model and that many of the models in the literature use a consistent subset of the assumptions used in Armitage and Doll's paper.

Using Adaptive Research Design To Define The Proper Methodology To Use A Data Peek For Power: Step By Step Process, Tom Wasser

Advances in Clinical Medical Research and Healthcare Delivery

When planning or conducting research in the hospital setting, often termed Real-World Environment (RWE), therapeutic assumptions and outcomes are often different than in the Randomized Clinical Trial (RCT) where medications, devices and therapies are tested and developed. This is because RWE research has a lack of experimental control, additional confounding due to patient complications and comorbid conditions, lack of pure patient selection and compliance with therapy in the patients being treated and many other factors as well. However, when RWE experiments are conducted, sample size determination using data from the RCT is common because that is the only data that …

Fifth And Eleventh-Order Iterative Methods For Roots Of Nonlinear Equations, Hassan Mohammed Bawazir

Hadhramout University Journal of Natural & Applied Sciences

In this work, two iterative methods, based on Newton’s method, to obtain the numerical solutions of nonlinear equations have been constructed. We proved that our methods converge in fifth and eleventh orders. Analytical investigation has been established to show that our schemes have higher efficiency indexes than some recent methods. Numerical examples are experimented to investigate the performance of the proposed schemes. Moreover, the theoretical order of convergence is verified in the experiment work.

Empirical Fitting Of Periodically Repeating Environmental Data, Pavel Bělík, Andrew Hotchkiss, Brandon Perez, John Zobitz

Spora: A Journal of Biomathematics

We extend and generalize an approach to conduct fitting models of periodically repeating data. Our method first detrends the data from a baseline function and then fits the data to a periodic (trigonometric, polynomial, or piecewise linear) function. The polynomial and piecewise linear functions are developed from assumptions of continuity and differentiability across each time period. We apply this approach to different datasets in the environmental sciences in addition to a synthetic dataset. Overall the polynomial and piecewise linear approaches developed here performed as good (or better) compared to the trigonometric approach when evaluated using statistical measures (R^{2 …}

Crocheting Mathematics Through Covid-19, Beyza C. Aslan

Journal of Humanistic Mathematics

As it is often said, something good often comes out of most bad situations. The time I spent during COVID-19, at home and isolated with my two children, brought out one secret passion in me: crocheting. Not only did it help me pass the time in a sane and productive way, but also it gave me a new goal in life. It connected my math side with my artistic side. It gave me a new perspective to look at math, and helped me help others see math in a positive way.

A Family Of Householder Matrices, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

A Householder transformation, or Householder reflection, or Household matrix, is a reflection about a hyperplane with a unit normal vector. Not only have the Household matrices been used in QR decomposition efficiently but also implicitly and successfully applied in other areas. In the process of investigating a family of unitary filterbanks, a new family of Householder matrices are established. These matrices are produced when a matrix filter is required to preserve certain order of 2d digital polynomial signals. Naturally, they can be applied to image and signal processing among others.

Kleptoparasitic Hawk-Dove Games, Isabella H. Evans-Riester, Chasity T. Kay, Karina L. Ortiz-Suarez, Jan Rychtář, Dewey Taylor

Spora: A Journal of Biomathematics

The Hawk-Dove game is a classical game-theoretical model of potentially aggressive animal conflicts. In this paper, we apply game theory to a population of foraging animals that may engage in stealing food from one another. We assume that the population is composed of two types of individuals, Hawks and Doves. Hawks try to escalate encounters into aggressive contests while Doves engage in non-aggressive displays between themselves or concede to aggressive Hawks. The fitness of each type depends upon various natural parameters, such as food density, the mean handling time of a food item, as well as the mean times of …

A Quantitative Analysis On Bitmex Perpetual Inverse Futures Xbtusd Contract, Yue Wu

Undergraduate Economic Review

The perpetual inverse futures contract is a recent and most popularly traded cryptocurrency derivative over crypto derivatives exchanges. Exchanges implement a liquidation mechanism that terminates positions which no longer satisfy maintenance requirements. In this study, we use regression, stochastic calculus, and simulation methods to provide a quantitative description of the wealth/return process for holding an XBTUSD contract on BitMEX, examine the funding rate and index price properties, and relate liquidation to leverage as a stopping time problem. The results will help investors understand liquidation to optimize their trading strategy and researchers in studying the design of crypto derivatives.

National Numeracy Network Officers And Board Of Directors, Milo Schield

Numeracy

National Numeracy Network Officers and Board of Directors in the year 2020.

Emergency Communications Deficiency Locator, Austin Collins

Undergraduate Journal of Mathematical Modeling: One + Two

The Bi-Directional Amplifier (BDA) is the newest edition to Life Safety in the state of Florida. The Florida Fire Prevention Code (NFPA 1) section 11.10.1 states that “In all new and existing buildings, minimum radio signal strength for fire department communications shall be maintained at a level determined by the authority having jurisdiction (Committee NFPA 1: Fire Code 2018). That authority having jurisdiction for our local Tampa Bay area is the Hillsborough County Fire Rescue department and they have posted their own requirements along with the Florida Senate for emergency communication standards. All existing “Hi-rise” buildings, 75 feet tall …

Is Technological Progress A Random Walk? Examining Data From Space Travel, Michael Howell, Daniel Berleant, Hyacinthe Aboudja, Richard Segall, Peng-Hung Tsai

Journal of the Arkansas Academy of Science

Improvement in a variety of technologies can often be successful modeled using a general version of Moore’s law (i.e. exponential improvements over time). Another successful approach is Wright’s law, which models increases in technological capability as a function of an effort variable such as production. While these methods are useful, they do not provide prediction distributions, which would enable a better understanding of forecast quality

Farmer and Lafond (2016) developed a forecasting method which produces forecast distributions and is applicable to many kinds of technology. A fundamental assumption of their method is that technological progress can be modeled as a …

Algorithm And Application For Iot Based Real Time Patient Monitoring System, Hakimjon Zaynidinov, Sarvar Maxmudjonov, Ruzikulov R.A.

Bulletin of TUIT: Management and Communication Technologies

Among the applications that Internet of Things (IoT) facilitated to the world, Healthcare applications are most important. In general, IoT has been widely used to interconnect the advanced medical resources and to offer smart and effective healthcare services to the people. The advanced sensors can be either worn or be embedded into the body of the patients, so as to continuously monitor their health. The information collected in such manner, can be analyzed, aggregated and mined to do the early prediction of diseases. The processing algorithms assist the physicians for the personalization of treatment and it helps to make the …

Explicit Formulas For Solutions Of Maxwell’S Equations In Conducting Media, Valery Yakhno

Applications and Applied Mathematics: An International Journal (AAM)

A new explicit presentation of the fundamental solution of the time-dependent Maxwell’s equations in conducting isotropic media is derived by Hadamard techniques through the fundamental solution of the telegraph operator. This presentation is used to obtain explicit formulas for generalized solutions of the initial value problem for Maxwell’s equations. A new explicit Kirchhoff’s formula for the classical solution of the initial value problem for the Maxwell equations in conducting media is derived. The obtained explicit formulas can be used in the boundary integral method, Green’s functions method and for computation of electric and magnetic fields in conducting media and materials.

Stability Of Modified Host-Parasitoid Model With Allee Effect, Özlem A. Gümüs, A. G. Maria Selvam, R. Janagaraj

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with a host-parasitoid model subject to Allee effect and its dynamical behavior. Steady state points of the proposed host-parasitoid model are computed. Stability properties are analyzed with eigen values of Jacobian matrix which are determined at the steady states. Theoretical findings are supported by numerical illustrations and enhanced by pictorial representations such as bifurcation diagrams, phase portraits and local amplifications for different parameter values. Existence of chaotic behavior in the system is established via bifurcation and sensitivity analysis of the system at the initial conditions. Various phase portraits are simulated for a better understanding of the qualitative …

A Mathematical Model Of Avian Influenza For Poultry Farm And Its Stability Analysis, Abdul Malek, Ashabul Hoque

Applications and Applied Mathematics: An International Journal (AAM)

This paper aims to estimate the basic reproduction number for Avian Influenza outbreak in local and global poultry industries. In this concern, we apply the SEIAVR compartmental model which is developed based on the well-known SEIR model. The SEIAVR model provides the mathematical formulations of the basic reproduction number, final size relationship and a relationship between these two phenomena. The developed model Equations are solved numerically with the help of Range-Kutta method and the values of initial parameters are taken from the several literatures and reports. The calculated result of basic reproduction number shows that it is locally and globally …

Impulse Effect On The Food-Limited Population Model With Piecewise Constant Argument, Fatma Karakoç

Applications and Applied Mathematics: An International Journal (AAM)

The qualitative study of mathematical models is an important area in applied mathematics. In this paper, a version of the food-limited population model with piecewise constant argument under impulse effect is investigated. Differential equations with piecewise constant arguments are related to difference equations. First, a representation for the solutions of the food-limited population model is stated in terms of the solutions of corresponding difference equation. Then using linearized oscillation theory for difference equations, a sufficient condition for the oscillation of the solutions about positive equilibrium point is obtained. Moreover, asymptotic behavior of the non-oscillatory solutions are investigated. Later, applying the …

On The Construction And Mathematical Analysis Of The Wavelet Transform And Its Matricial Properties, Diego Sejas Viscarra

Rose-Hulman Undergraduate Mathematics Journal

We study the properties of computational methods for the Wavelet Transform and its Inverse from the point of view of Linear Algebra. We present a characterization of such methods as matrix products, proving in particular that each iteration corresponds to the multiplication of an adequate unitary matrix. From that point we prove that some important properties of the Continuous Wavelet Transform, such as linearity, distributivity over matrix multiplication, isometry, etc., are inherited by these discrete methods.

This work is divided into four sections. The first section corresponds to the classical theoretical foundation of harmonic analysis with wavelets; it is used …

Dna Self-Assembly Design For Gear Graphs, Chiara Mattamira

Rose-Hulman Undergraduate Mathematics Journal

Application of graph theory to the well-known complementary properties of DNA strands has resulted in new insights about more efficient ways to form DNA nanostructures, which have been discovered as useful tools for drug delivery, biomolecular computing, and biosensors. The key concept underlying DNA nanotechnology is the formation of complete DNA complexes out of a given collection of branched junction molecules. These molecules can be modeled in the abstract as portions of graphs made up of vertices and half-edges, where complete edges are representations of double-stranded DNA pieces that have joined together. For efficiency, one aim is to minimize the …

Hamming Codes, Steve Mwangi, Sterling Quinn

Access*: Interdisciplinary Journal of Student Research and Scholarship

We will be looking into the application of Matrix Algebra in forming Hamming Codes. Hamming Codes are essential not just in the detection of errors, but also in the linear concurrent correction of these errors. The matrices we will use, will have entries that are binary units. Binary units are mathematically convenient, and their simplicity permits the representation of many open and closed circuits used in communication systems. The entries in the matrices will represent a message that is meant for transmission or reception, akin to the contemporary application of Hamming Codes in wireless communication. We will use Hamming (7,4) …

Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman

Access*: Interdisciplinary Journal of Student Research and Scholarship

The history of wagering predictions and their impact on wide reaching disciplines such as statistics and economics dates to at least the 1700’s, if not before. Predicting the outcomes of sports is a multibillion-dollar business that capitalizes on these tools but is in constant development with the addition of big data analytics methods. Sportsline.com, a popular website for fantasy sports leagues, provides odds predictions in multiple sports, produces proprietary computer models of both winning and losing teams, and provides specific point estimates. To test likely candidates for inclusion in these prediction algorithms, the authors developed a computer model, and test …