Mathematics Commons^™

Invited Article By M. Gidea Extreme Events And Emergency Scales, Veniamin Smirnov, Zhuanzhuan Ma, Dimitri Volchenkov

School of Mathematical & Statistical Sciences Faculty Publications

An event is extreme if its magnitude exceeds the threshold. A choice of a threshold is subject to uncertainty caused by a method, the size of available data, a hypothesis on statistics, etc. We assess the degree of uncertainty by the Shannon's entropy calculated on the probability that the threshold changes at any given time. If the amount of data is not sufficient, an observer is in the state of Lewis Carroll's Red Queen who said "When you say hill, I could show you hills, in comparison with which you'd call that a valley". If we have enough data, the …

Impact Of Concept-Based Mathematics Instructional Strategies On Seventh Grade Student Achievement, Katherine Annette Lawley Ellsworth

Doctoral Dissertations and Projects

In a nation with declining enrollment in college math courses, it is important to examine how mathematics is being taught in the K-12 education system and to identify best practices. The purpose of this study was to examine the impact concept-based instructional strategies has on middle school student achievement in mathematics when integrated into the traditional mathematics curriculum. Participants included 424 seventh grade students from two middle schools. Students Measures of Academic Progress (MAP) Fall-to-Winter data 2018 prior to implementation was used a covariate and Fall-to-Winter data 2019 data during the implementation of concept-based instructional strategies integrated into the traditional …

Quotient-Transitivity And Cyclic Subgroup-Transitivity, Brendan Goldsmith, Ketao Gong

Articles

We introduce two new notions of transitivity for Abelian 𝑝-groups based on isomorphism of quotients rather than the classical use of equality of height sequences associated with Abelian 𝑝-group theory. Unlike the classical theory where “most” groups are transitive, these new notions lead to much smaller classes, but even these classes are sufficiently large to be interesting.

Contact Graphs Of Ball Packings, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

A contact graph of a packing of closed balls is a graph with balls as vertices and pairs of tangent balls as edges. We prove that the average degree of the contact graph of a packing of balls (with possibly different radii) in R3 is not greater than 13.955. We also find new upper bounds for the average degree of contact graphs in R4 and R5.

Stochastic Delay Differential Equations With Applications In Ecology And Epidemics, Hebatallah Jamil Alsakaji

Dissertations

Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and predictions in various areas of life sciences, such as population dynamics, epidemiology, immunology, physiology, and neural networks. The memory or time-delays, in these models, are related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period, and so on. In ordinary differential equations (ODEs), the unknown state and its derivatives are evaluated at the same time instant. In DDEs, however, the …

Legendre G-Array Pairs And The Theoretical Unification Of Several G-Array Families, K. T. Arasu, Dursun A. Bulutoglu, J. R. Hollon

Faculty Publications

We investigate how Legendre G-array pairs are related to several different perfect binary G-array families. In particular we study the relations between Legendre G-array pairs, Sidelnikov-Lempel-Cohn-Eastman ℤ_q−1-arrays, Yamada-Pott G-array pairs, Ding-Helleseth-Martinsen ℤ₂×ℤ^m_p-arrays, Yamada ℤ_(q−1)/2-arrays, Szekeres ℤ^m_p-array pairs, Paley ℤ^m_p-array pairs, and Baumert ℤ^m1_p1×ℤ^m2_p2-array pairs. Our work also solves one of the two open problems posed in Ding~[J. Combin. Des. 16 (2008), 164-171]. Moreover, we provide several computer search based existence and non-existence results regarding Legendre ℤ_n-array pairs. …

Twitter Reveals Human Mobility Dynamics During The Covid-19 Pandemic, Xiao Huang, Zhenlong Li, Yuqin Jiang, Xiaoming Li, Dwayne Porter

Geosciences Faculty Publications and Presentations

The current COVID-19 pandemic raises concerns worldwide, leading to serious health, economic, and social challenges. The rapid spread of the virus at a global scale highlights the need for a more harmonized, less privacy-concerning, easily accessible approach to monitoring the human mobility that has proven to be associated with viral transmission. In this study, we analyzed over 580 million tweets worldwide to see how global collaborative efforts in reducing human mobility are reflected from the user-generated information at the global, country, and U.S. state scale. Considering the multifaceted nature of mobility, we propose two types of distance: the single-day distance …

Oer Indoor Ellipse Multicultural (Easter Island) Activity, Cynthia Huffman Ph.D.

Faculty Submissions

This activity would fit in with a secondary or college algebra class studying conic sections, in particular ellipses, and gives students a multicultural hands-on application of the definition of an ellipse, while tracing out a scale model of the foundation of a hare paenga (boat house) from prehistoric Easter Island (Rapa Nui)..

Oer Outdoor Ellipse Multicultural (Easter Island) Activity, Cynthia Huffman Ph.D.

Faculty Submissions

This activity would fit in with a secondary or college algebra class studying conic sections, in particular ellipses, and gives students a multicultural hands-on application of the definition of an ellipse, while tracing out a full-scale model of the foundation of a hare paenga (boat house) from prehistoric Easter Island (Rapa Nui)..

Security Model For Tracking Creation Of Mobile Money Using Transport Layer Security Protocol, Sigsbert Rwiza, Mussa Kissaka, Kosmas Kapis

Tanzania Journal of Science

Mobile Network Operator (MNO) financial service model has security vulnerabilities in addressing verification of cash and mobile money. For instance, monthly returns are transferred in plain text from banks and MNOs to financial regulators. This may result to failure of financial regulators in detecting creation of fake mobile money. This study was conducted to develop a security model for tracking creation of mobile money using Transport Layer security protocol as a way of protecting returns in transit from banks and MNOs to financial regulators. The proposed model was developed using insights from literature, function decomposition and composition techniques and was …

Total And Available Fluoride Content In Toothpastes Sold In Dar Es Salaam, Tanzania, Monica Mbaraka Ndoile

Tanzania Journal of Science

A total of eleven (11) different toothpaste brands (imported and manufactured in Tanzania) sold in Dar es Salaam were evaluated for Total Fluoride (TF) and Total Soluble Fluoride (TSF) concentrations. To protect the subject’s identity, the samples were coded. Four selected toothpastes were analyzed for potentially bioavailable fluoride by examining the relationship between TSF in tooth brushing residues and in that of the toothpaste. The results indicated that measured TF of the toothpaste samples coded as TPSA, TPSC and TPSH were consistent to the one declared by the manufacturers. On the other hand, samples coded as TPSB, TPSD, TPSE, TPSF, …

Verification Of Depth Dose Curves Derived On Beeswax, Paraffin And Water Phantoms Using Fluka Monte Carlo Code, Khamis O. Amour, Peane P. Maleka, Khamza Maunda, Mohammed S. Mazunga, Peter K. Msaki

Tanzania Journal of Science

This study aimed on the investigation of depth dose curves from beeswax, water and paraffin phantoms using FLUKA Monte Carlo code. In order to test the validity of FLUKA code, computational values of depth doses in water, beeswax and paraffin have been obtained using this code. The relative average coefficient of variation of percentage depth dose was observed to be less than 0.38% between beeswax and water, below 0.2% between water and paraffin and 0.98% between beeswax and British Journal of Radiology supplement 25 data. The deviations of percentage depth doses within the beeswax phantom material were also calculated and …

A Hybrid Agent-Based And Equation Based Model For The Spread Of Infectious Diseases, Elizabeth Hunter, Brian Mac Namee, John D. Kelleher

Articles

Both agent-based models and equation-based models can be used to model the spread of an infectious disease. Equation-based models have been shown to capture the overall dynamics of a disease outbreak while agent-based models are able to capture heterogeneous characteristics of agents that drive the spread of an outbreak. However, agent-based models are computationally intensive. To capture the advantages of both the equation-based and agent-based models, we create a hybrid model where the disease component of the hybrid model switches between agent-based and equation-based. The switch is determined using the number of agents infected. We first test the model at …

Quaternions And Matrices Of Quaternions, Fuzhen Zhang

Mathematics Colloquium Series

Quaternions comprise a noncommutative division algebra (skew field). As part of contemporary mathematics, they find uses not only in theoretical and applied mathematics but also in computer graphics, control theory, signal processing, physics, and mechanics. Speaker, N S U Professor, Fuzhen Zhang reviews basic theory on quaternions and matrices of quaternions, presents important results, proposes open questions, and surveys recent developments in the area.

Perceiving Mathematics And Art, Edmund Harriss

Mic Lectures

Mathematics and art provide powerful lenses to perceive and understand the world, part of an ancient tradition whether it starts in the South Pacific with tapa cloth and wave maps for navigation or in Iceland with knitting patterns and sunstones. Edmund Harriss, an artist and assistant clinical professor of mathematics in the Fulbright College of Arts and Sciences, explores these connections in his Honors College Mic lecture.

Essays On Environmental And Health Economics., Prachi Singh Dr.

Doctoral Theses

This thesis consists of three empirical essays that investigate issues in environmental and health economics. The main focus of this thesis is to study how environmental degradation or interventions in this domain can affect demographic and health outcomes of the population in developing countries. The first chapter explores the effect of an information campaign about arsenic contamination in Bangladesh on marriage market outcomes. This study finds that providing information about negative effects of arsenic consumption had an unintended consequence in the marriage market. Specifically, information about lower fertility, skin lesions, cancers and higher mortality related to arsenic exposure induced individuals …

Provable Security Of Symmetric-Key Cryptographic Schemes., Ashwin Jha Dr.

Doctoral Theses

In this thesis, we provide quantitative and/or qualitative improvements in the provable security of several symmetric-key schemes, encompassing major information security goals, viz. data authentication, encryption, and authenticated encryption.AUTHENTICATION AND INTEGRITY: Among authentication schemes, we analyze the CBC-MAC family and counter-based MACs (XMACC, XMACR, PCS, LightMAC etc.), referred as the XMAC family. First, we revisit the security proofs for CBC-MAC and EMAC, and identify a critical flaw in the state-of-the-art results. We revise the security proofs and obtain significantly better bounds in case of EMAC, ECBC and FCBC. Second, we study the security of CBC-MAC family, when the underlying primitive …

Controlling Aircraft Yaw Movement By Interval Type-2 Fuzzy Logic, Yamama Shafeek, Laith Majeed, Rasha Naji

Emirates Journal for Engineering Research

Aircraft yaw movement is essential in maneuvering; it has been controlled by some methods which achieved tracking but not fast enough. This paper performs the dynamic modeling of aircraft yaw movement and develops PI and PI-like interval type-2 fuzzy logic controller for the model. The mathematical model is derived by inserting the parameters values of single-engine Navion aircraft into standard equations. Using Matlab/ Simulink platform, the controllers' effectivity is tested and verified in two different cases; system without disturbance and when system is disturbed by some wind gust to investigate the system robustness. Simulation results show that PI controller response …

World Statistics Day: Malaria And Its Effects On The World: A Statistical Look, Aysha Nuhuman, Pola Naguib

Mathematics Colloquium Series

As October 20, 2020 is designated United Nations World Statistics Day, we look at an important statistical problem using a data set collected by researchers from the United Nations. We have all heard about Malaria and seen the effects it could have on friends and family. Still, while we ponder on the who and why this could have occurred, we are here to tell you about the what and how. The severity of this disease can be seen throughout the world. In this presentation, we will look at the number of reported cases of Malaria worldwide and how they affected …

Weaving Mathematics, Ma. Louise Antonette N. De Las Peñas

Magisterial Lectures

In this lecture, Dr. De las Peñas talks about the intersection of mathematics and Philippine indigenous weaving.

Speaker:

Ma. Louise Antonette N. De Las Peñas is a Professor at the Department of Mathematics and currently the Associate Dean for Research and Creative Work, Loyola Schools, Ateneo De Manila University, Philippines. Her research interests are discrete geometry, mathematical crystallography, group theory, and technology in mathematics education.

She is a recipient of several research awards including the National Research Council of the Philippines (NRCP) Achievement Award in the Mathematical Sciences and the Philippine Commission on Higher Education Republica National Research Award. She …

Finite-Time State Estimation For An Inverted Pendulum Under Input-Multiplicative Uncertainty, William Mackunis, Sergey V. Drakunov, Anu Kossery Jayaprakash, Krishna Bhavithavya Kidambi, Mahmut Reyhanoglu

Publications

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous …

Espade: An Efficient And Semantically Secure Shortest Path Discovery For Outsourced Location-Based Services, Bharath K. Samanthula, Divyadharshini Karthikeyan, Boxiang Dong, K. Anitha Kumari

Department of Computer Science Faculty Scholarship and Creative Works

With the rapid growth of smart devices and technological advancements in tracking geospatial data, the demand for Location-Based Services (LBS) is facing a constant rise in several domains, including military, healthcare and transportation. It is a natural step to migrate LBS to a cloud environment to achieve on-demand scalability and increased resiliency. Nonetheless, outsourcing sensitive location data to a third-party cloud provider raises a host of privacy concerns as the data owners have reduced visibility and control over the outsourced data. In this paper, we consider outsourced LBS where users want to retrieve map directions without disclosing their location information. …

Cross-Shelf Transport Through The Interaction Among A Coastal Jet, A Topographic Wave, And Tides, Helga Huntley, Charles W. Mcmahon, Joseph J. Kuehl, A. D. Kirwan Jr.

College of Science & Mathematics Departmental Research

Shelf break flows are often characterized by along-isobath jets with cross-shelf currents associated with tides and waves guided by variable topography. Here, we address the question: Can a superposition of such flows produce significant aperiodic cross-shelf transport? To answer this question, we use a barotropic analytic model for the jet based on a similarity solution of the shallow water equations over variable topography, a wave disturbance determined by the topography, and a diurnal tidal disturbance. We use standard Lagrangian methods to assess the cross-shelf transport, presenting the results, however, in a Eulerian frame, so as to be amenable to oceanographic …

Dupin Submanifolds In Lie Sphere Geometry (Updated Version), Thomas E. Cecil, Shiing-Shen Chern

Mathematics and Computer Science Department Faculty Scholarship

A hypersurface M^n-1 in Euclidean space Eⁿ is proper Dupin if the number of distinct principal curvatures is constant on M^n-1, and each principal curvature function is constant along each leaf of its principal foliation. This paper was originally published in 1989 (see Comments below), and it develops a method for the local study of proper Dupin hypersurfaces in the context of Lie sphere geometry using moving frames. This method has been effective in obtaining several classification theorems of proper Dupin hypersurfaces since that time. This updated version of the paper contains the original exposition together …

Phyllotaxis As Geometric Canalization During Plant Development, Christophe Godin, Christophe Golé, Stéphane Douady

Mathematics Sciences: Faculty Publications

Why living forms develop in a relatively robust manner, despite various sources of internal or external variability, is a fundamental question in developmental biology. Part of the answer relies on the notion of developmental constraints: at any stage of ontogenesis, morphogenetic processes are constrained to operate within the context of the current organism being built. One such universal constraint is the shape of the organism itself, which progressively channels the development of the organism toward its final shape. Here, we illustrate this notion with plants, where strikingly symmetric patterns (phyllotaxis) are formed by lateral organs. This Hypothesis article aims first …

Optimal Control Of An Hiv Model With Gene Therapy And Latency Reversing Agents, Andrew B. Grant, Paul Hazelton

S.U.R.E Posters

In this project, we study the dynamics of HIV under gene therapy and latency reversing agents. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of the basic reproductive ratio. We then consider time dependent controls and formulate an associated optimal control problem that emphasizes reduction of the latent reservoir. Characterizations for the optimal control profiles are found using Pontryagin's Maximum Principle. We perform numerical simulations of the optimal control model using the fourth-order Runge-Kutta forward-backward sweep method. We conclude with findings that suggest a combination treatment of gene therapy …

A Nonlinear Multi-Population Behavioral Model To Assess The Roles Of Education Campaigns, Random Supply Of Aids, And Delayed Art Treatment In Hiv/Aids Epidemics, Divine Wanduku

Mathematical Sciences: Faculty Publications

The successful reduction in prevalence rates of HIV in many countries is attributed to control measures such as information and education campaigns (IEC), antiretroviral therapy (ART), and national, multinational and multilateral support providing offcial developmental assistance (ODAs) to combat HIV. However, control of HIV epidemics can be interrupted by limited random supply of ODAs, high poverty rates and low living standards. This study presents a stochastic HIV/AIDS model with treatment assessing the roles of IEC, the supply of ODAs and early treatment in HIV epidemics. The supply of ODAs is assessed via the availability of medical and financial resources leading …

Period Estimation And Noise In A Neutrally Stable Stochastic Oscillator, Kevin R. Sanft, Ben F. M. Intoy

Spora: A Journal of Biomathematics

The periods of the orbits for the well-mixed cyclic three-species Lotka-Volterra model far away from the fixed point are studied. For finite system sizes, a discrete stochastic approach is employed and periods are found via wavelet analysis. As the system size is increased, a hierarchy of approximations ranging from Poisson noise to Gaussian noise to deterministic models are utilized. Based on the deterministic equations, a mathematical relationship between a conserved quantity of the model and the period of the population oscillations is found. Exploiting this property we then study the deterministic conserved quantity and period noise in finite size systems.

Guide To Geometry, Maddison Webb

Electronic Theses & Dissertations

Euclid’s Postulates--Polygons--Fundamentals of Euclidean Geometry--Similar Figures--Trigonometry--Tessellations--Non-Euclidean Geometry.

Intrinsic Curvature For Schemes, Pat Lank

Mathematics & Statistics ETDs

This thesis develops an algebraic analog of psuedo-Riemannian geometry for relative schemes whose cotangent sheaf is finite locally free. It is a generalization of the algebraic differential calculus proposed by Dr. Ernst Kunz in an unpublished manuscript to the non-affine case. These analogs include the psuedo-Riemannian metric, Levi-Civit´a connection, curvature, and various existence theorems.