Applied Mathematics Commons^™

Asymptotic Estimate Of Variance With Applications To Stochastic Differential Equations Arises In Mathematical Neuroscience, Mahbubur Rahman 6203748

Showcase of Faculty Scholarly & Creative Activity

Approximation of stochastic differential equations (SDEs) with parametric noise plays an important role in a range of application areas, including engineering, mechanics, epidemiology, and neuroscience. A complete understanding of SDE theory with perturbed noise requires familiarity with advanced probability and stochastic processes. In this paper, we derive an asymptotic estimate of variance, and it is shown that numerical method gives a useful step toward solving SDEs with perturbed noise. Our goal is to diffuse the results to an audience not entirely familiar with functional notations or semi-group theory, but who might nonetheless be interested in the practical simulation of dynamical …

Stability Of Solitary And Cnoidal Traveling Wave Solutions For A Fifth Order Korteweg-De Vries Equation, Ronald Adams, S.C. Mancas

Publications

We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally) stable.

Essentials Of Structural Equation Modeling, Mustafa Emre Civelek

Zea E-Books Collection

Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. However, since many universities do not include this method in the curriculum of undergraduate and graduate courses, students and scholars try to solve the problems they encounter by using various books and internet resources.

This book aims to guide the researcher who wants to use this method in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling …

Short-Time Expansions For Call Options On Leveraged Etfs Under Exponential Lévy Models With Local Volatility, José E. Figueroa-López, Ruoting Gong, Matthew Lorig

Mathematics Faculty Research

In this article, we consider the small-time asymptotics of options on a leveraged exchange-traded fund (LETF) when the underlying exchange-traded fund (ETF) exhibits both local volatility and jumps of either finite or infinite activity. We show that leverage modifies the drift, volatility, jump intensity, and jump distribution of a LETF in addition to inducing the possibility of default, even when the underlying ETF price remains strictly positive. Our main results are closed-form expressions for the leading-order terms of off-the-money European call and put LETF option prices near expiration, with explicit error bounds. These results show that the price of an …

P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing

Honors Scholars & Undergraduate Research Poster Symposium Programs

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise.

Mathemagics, Arthur Benjamin

Dalrymple Lecture Series

Dr. Arthur Benjamin is the Smallwood Family Professor of Mathematics at Harvey Mudd College in Claremont, California. He is also a professional magician, and in his entertaining and fast-paced performance, Dr. Benjamin will demonstrate how to mentally add and multiply numbers faster than a calculator, how to figure out the day of the week of any date in history, and other amazing feats of mind.

Quasi-Static Nonlinear Analysis Of A Celestial Icosahedron Shaped Vacuum Lighter Than Air Vehicle, Kyle D. Moore

Theses and Dissertations

Due to the many drawbacks associated with a traditional lighter than air vehicle (LTAV), there is a desire for a LTAV which generates lift from an internal vacuum. To date, two feasible designs (the icosahedron and the hexakis icosahedron) for this so called vacuum lighter than air vehicle (VLTAV) have been studied at the Air Force Institute of Technology (AFIT). This research looks to show the feasibility of a new design for a VLTAV, the celestial icosahedron. This research includes a boundary condition study which proves the symmetric nature of the celestial icosahedron's frame with laterally constrained and unconstrained vertices. …

Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski

Publications

Dynamic materials are artificially constructed in such a way that they may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (non-mechanical) field, or through a phase transition. In principle, all materials change their properties with time, but very slowly and smoothly. Changes in properties of dynamic materials should be realized in a short or quasi-nil time lapse and over a sufficiently large material region. Wave propagation is a characteristic feature for dynamic materials because it is also …

Screening Algorithm Based On The Color Halftone Fluorescent Printing And Its Application In Packaging Design, Hu Yaojian, Liu Juan, Wang Ruojing, Zhong Yunfei

Journal of Applied Packaging Research

Abstract：This paper analyzed the characteristics of colorless fluorescent ink and the existing color separation theory, so that colored additive method should be used in printing color pattern with colorless fluorescent ink as well as three-color screening separation type (red, green and blue). Considering the exhibition of the tone, this paper selected dot parallel screening method. At the same time, through comparing the properties of different dots, this paper adopted a special method of AM screening, using regular triangle as the basic dot model to a threshold matrix of AM screening. Finally, designing a screening algorithm which best suit the …

Indicators For Early Assessment Of Palliative Care In Lung Cancer Patients: A Population Study Using Linked Health Data, Maria Kelly, Katie M. O'Brien, Michael Lucey, Kerri Clough-Gorr, Ailish Hannigan

Department of Mathematics Publications

Analysing linked, routinely collected data may be useful to identify characteristics of patients with suspected lung cancer who could benefit from early assessment for palliative care. The aim of this study was to compare characteristics of newly diagnosed lung cancer patients dying within 30 days of diagnosis (short term survivors) with those surviving more than 30 days. To identify indicators for early palliative care assessment we distinguished between characteristics available at diagnosis (age, gender, smoking status, marital status, comorbid disease, admission type, tumour stage and histology) from those available post diagnosis. A second aim was to examine the association between …

Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, Q. Zhong, Demetrios N. Christodoulides, M. Khajavikhan, K. G. Makris, Ramy El-Ganainy

Department of Physics Publications

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time (PT) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other …

Examples Of Finite Free Complexes Of Small Rank And Small Homology, Srikanth B. Iyengar, Mark E. Walker

Department of Mathematics: Faculty Publications

In this paper we construct counterexamples to five related conjectures concerning the rank an homology of finite free complexes over commuatitive noetherian rings, and, in particular, over group algebras of elementary abelian groups.

Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier

Electronic Theses and Dissertations

Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …

Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right halfplane, and the other moves to the left half-plane. When the parameters move into the …

Ns-Cross Entropy-Based Magdm Under Single-Valued Neutrosophic Set Environment, Florentin Smarandache, Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy

Branch Mathematics and Statistics Faculty and Staff Publications

A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is …

Summary Of The Special Issue “Neutrosophic Information Theory And Applications” At “Information” Journal, Florentin Smarandache, Jun Ye

Branch Mathematics and Statistics Faculty and Staff Publications

Over a period of seven months (August 2017–February 2018), the Special Issue dedicated to “Neutrosophic Information Theory and Applications” by the “Information” journal (ISSN 2078-2489), located in Basel, Switzerland, was a success. The Guest Editors, Prof. Dr. Florentin Smarandache from the University of New Mexico (USA) and Prof. Dr. Jun Ye from the Shaoxing University (China), were happy to select—helped by a team of neutrosophic reviewers from around the world, and by the “Information” journal editors themselves—and publish twelve important neutrosophic papers, authored by 27 authors and coauthors. There were a variety of neutrosophic topics studied and used by the …

Neutrosophic Soft Rough Graphs With Application, Florentin Smarandache, Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In …

Nn-Harmonic Mean Aggregation Operators-Based Mcgdm Strategy In A Neutrosophic Number Environment, Florentin Smarandache, Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

Branch Mathematics and Statistics Faculty and Staff Publications

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and …

Progenitors Involving Simple Groups, Nicholas R. Andujo

Electronic Theses, Projects, and Dissertations

I will be going over writing representations of both permutation and monomial progenitors, which include 2^{*4} : D_4, 2^(*7) :L_2 (7) as permutation progenitors, and monomial progenitors 7^(*2) :_m S_3 \times 2, 11^{*2} :_m (5:2)^{*}5, 11^{*3} :_m (25:3), 11^{*4} :_m (4 : 5)^{*}5. Also, the images of these different progenitors at both lower and higher fields and orders. \\ We will also do the double coset enumeration of S5 over D6, S6 over 5 : 4, A_5 x A_5 over (5:2)^{*}5, and go on to also do the double coset enumeration over maximal subgroups for larger constructions. We will also …

Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood

Journal of Humanistic Mathematics

In Andy Weir’s novel The Martian, the characters encounter high-stakes, life-or-death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have different reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book.

Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

Publications and Research

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic …

Numerical Approximation Of Diffusive Capture Rates By Planar And Spherical Surfaces With Absorbing Pores, Andrew J. Bernoff, Alan E. Lindsay

All HMC Faculty Publications and Research

In 1977 Berg and Purcell published a landmark paper entitled Physics of Chemore- ception, which examined how a bacterium can sense a chemical attractant in the fluid surrounding it [H. C. Berg and E. M. Purcell, Biophys J, 20 (1977), pp. 193–219]. At small scales the attrac- tant molecules move by Brownian motion and diffusive processes dominate. This example is the archetype of diffusive signaling problems where an agent moves via a random walk until it either strikes or eludes a target. Berg and Purcell modeled the target as a sphere with a set of small circular targets (pores) that …

Analytical Approaches To Improve Accuracy In Solving The Protein Topology Problem, Kamal Al Nasr, Feras Yousef, Ruba Jebril, Christopher Jones

Computer Science Faculty Research

To take advantage of recent advances in genomics and proteomics it is critical that the three-dimensional physical structure of biological macromolecules be determined. Cryo-Electron Microscopy (cryo-EM) is a promising and improving method for obtaining this data, however resolution is often not sufficient to directly determine the atomic scale structure. Despite this, information for secondary structure locations is detectable. De novo modeling is a computational approach to modeling these macromolecular structures based on cryo-EM derived data. During de novo modeling a mapping between detected secondary structures and the underlying amino acid sequence must be identified. DP-TOSS (Dynamic Programming for determining the …

Truancy In High School, Itzel Ruiz, Jason Mink, Xochitl Aleman

SPACE: Student Perspectives About Civic Engagement

The main focus of this project is to analyze students’ poor attendance in order to understand the applicable factors as to why upperclassmen tend to miss more school than students in younger grades. We will be focusing on how students relationships with parents and teachers affect upperclassmen attendance. An anonymous ten question survey was given to five Junior and Senior Civics and U.S. History classes at Steinmetz College Prep high school. The questions were geared towards the students days absent during the school year, and their relationship with teachers and parents. Majority of the students surveyed missed more than 20 …

Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John M. Zobitz

Spora: A Journal of Biomathematics

We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model development …

The Entrance Times Of Feigenbaum's Map, Akhtam Dzhalilov, Khamza Kudratov

Acta of Turin Polytechnic University in Tashkent

It is well known that the Feigenbaum's map ϕ plays main role in theory of universality. The map ϕ is unimodal, even, analitic map of the interval [-1; 1] with one critical point. It is important that the Feigenbaum's map ϕ have infinitely many unstable periodic points and an attractor K of "Cantor type". In present work we investigate the behaviour of entrance times to the set F:

Uniform Distribution For Piecewise-Linear Herman's Maps With Two Breaks, Akhtam Dzhalilov, Khamza Tashkulov

Acta of Turin Polytechnic University in Tashkent

Let h be a piecewise-linear (PL) circle homeomorphism with two break points a0 , c0 and irrational rotation number ρh . Denote by qn , n ≥ 1 the first return times of h and 000(0)():(0)hhaahaσ′−=′+ the jump of h at the point a0 . We prove that for every 1xS∈ the sequence 01log()mod1,1log()nqhDhxnaσ≥ is uniformly distributed on [0,1].

Communication Based Control For Dc Microgrids, Mahmoud S. Saleh, Yusef Esa, Ahmed Mohamed

Publications and Research

Centralized communication-based control is one of the main methods that can be implemented to achieve autonomous advanced energy management capabilities in DC microgrids. However, its major limitation is the fact that communication bandwidth and computation resources are limited in practical applications. This can be often improved by avoiding redundant communications and complex computations. In this paper, an autonomous communication-based hybrid state/event driven control scheme is proposed. This control scheme is hierarchical and heuristic, such that on the primary control level, it encompasses state-driven local controllers, and on the secondary control level, an event-driven MG centralized controller (MGCC) is used. This …

Quasi-Symmetric Distribution Function Of Invariant Measure Of Circle Homeomorphisms With Singularities, U.A. Safarov

Acta of Turin Polytechnic University in Tashkent

Let f be a circle homeomorphism with single critical point of non-integer order, that is, 1()()||()dcrcrcrfxxxxxfx−=−−+, 2d>, for some δ-neighborhood ()crUxδ. We prove that, if the homeomorphism f is P-homeomorphism on the set 1\()crSUxδ with irrational rotation numberfρ, then f is topologically conjugate to the pure rotation fρ . Moreover, ϕ is quasi-symmetric if and only if fρ is of bounded type.

Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John Zobitz

Faculty Authored Articles

We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model development …