Applied Mathematics Commons^™

Are Terrorist Networks Just Glorified Criminal Cells?, Elie Alhajjar, Ryan Fameli, Shane Warren

Northeast Journal of Complex Systems (NEJCS)

The notions of organized crime and terrorism have an old and rich history around the globe. Researchers and practitioners have been studying events and phenomena related to these notions for a long time. There are pointers in the literature in which it is misleading to see the unfair comparison between terrorist and criminal networks with the argument that all actors involved in these networks are simply evil individuals. In this paper, we conduct a systematic study of the operational structure of such networks from a network science perspective. We highlight some of the major differences between them and support our …

Computational Modelling Enables Robust Multidimensional Nanoscopy, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

The following sections are included:

• Present State of Computational Modelling in Fluorescence Nanoscopy

• Recent Contributions to Computational Modelling in Fluorescence Nanoscopy

• Outlook on Computational Modelling in Fluorescence Nanoscopy

• Acknowledgments

• References

Modeling And Analysis Of Affiliation Networks With Subsumption, Alexey Nikolaev

Dissertations, Theses, and Capstone Projects

An affiliation (or two-mode) network is an abstraction commonly used for representing systems with group interactions. It consists of a set of nodes and a set of their groupings called affiliations. We introduce the notion of affiliation network with subsumption, in which no affiliation can be a subset of another. A network with this property can be modeled by an abstract simplicial complex whose facets are the affiliations of the network.

We introduce a new model for generating affiliation networks with and without subsumption (represented as simplicial complexes and hypergraphs, respectively). In this model, at each iteration, a constant number …

Numerical Integration Through Concavity Analysis, Daniel J. Pietz

Rose-Hulman Undergraduate Mathematics Journal

We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.

Numerical Reconstruction Of Spalled Particle Trajectories In An Arc-Jet Environment, Raghava S. C. Davuluri, Sean C. C. Bailey, Kaveh A. Tagavi, Alexandre Martin

Mechanical Engineering Faculty Publications

To evaluate the effects of spallation on ablative material, it is necessary to evaluate the mass loss. To do so, a Lagrangian particle trajectory code is used to reconstruct trajectories that match the experimental data for all kinematic parameters. The results from spallation experiments conducted at the NASA HYMETS facility over a wedge sample were used. A data-driven adaptive methodology was used to adapts the ejection parameters until the numerical trajectory matches the experimental data. The preliminary reconstruction results show that the size of the particles seemed to be correlated with the location of the ejection event. The size of …

Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes

HMC Senior Theses

Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.

Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands, Miguel Velez

HMC Senior Theses

Many biological systems form structured swarms, for instance in locusts, whose swarms are known as hopper bands. There is growing interest in applying mathematical models to understand the emergence and dynamics of these biological and social systems. We model the locusts of a hopper band as point particles interacting through repulsive and attractive social "forces" on a one dimensional periodic domain. The primary goal of this work is to modify this well studied modelling framework to be more biological by restricting repulsion to act locally between near neighbors, while attraction acts globally between all individuals. This is a biologically motivated …

Common Unit Conversions For Irrigation, Dean E. Eisenhauer, Derrel L. Martin, Derek M. Heeren, Glenn J. Hoffman

Open Learning Resources, General/Selected

A fact sheet that includes common unit conversions for irrigation in international system of units (SI) and United States customary system of units (USCS).

Includes units for: length, area, volume, flow, weight and mass, pressure, crop yield, temperature, and the United States public land survey system.

Arnold Transformations As Applied To Data Encryption, Haley N. Anderson

College of Graduate Studies: Theses & Dissertations

As our world becomes increasingly digital, data security becomes key. Data must be encrypted such that it can be easily encrypted only by the intended recipient. Arnold Transformations are a useful tool in this because of its unpredictable periodicity. Our goal is to outline a method for choosing an Arnold Transformation that is both secure and easy to implement. We find the necessary and sufficient condition that a key matrix has periodicity. The chosen key matrix has a random structure, and it has a periodicity that is sufficiently high. We apply this method to several image and data string examples …

Five-Wave Resonances In Deep Water Gravity Waves: Integrability, Numerical Simulations And Experiments, Dan Lucas, Marc Perlin, Dian-Yong Liu, Shane Walsh, Rossen Ivanov, Miguel D. Bustamante

Articles

In this work we consider the problem of finding the simplest arrangement of resonant deep water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wave vectors K₁ + K₂ = K₃ (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wave packets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction …

Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman

Pitzer Senior Theses

This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …

A Mathematical Analysis Of The Wind Triangle Problem And An Inquiry Of True Airspeed Calculations In Supersonic Flight, Leonard T. Huang, Lisa I. Cummings

International Journal of Aviation, Aeronautics, and Aerospace

In the first half of this paper, we present a fresh perspective toward the Wind Triangle Problem in aerial navigation by deriving necessary and sufficient conditions, which we call "go/no-go conditions", for the existence/non-existence of a solution of the problem. Although our derivation is based on simple trigonometry and basic properties of quadratic functions, it is mathematically rigorous. We also offer examples to demonstrate how easy it is to check these conditions graphically. In the second half of this paper, we use function theory to re-examine another problem in aerial navigation, namely, that of computing true airspeed — even in …

Development Of Synthetic Coal Char Simulant For Microwave Conversion Studies: A Computationally-Driven Approach, Kevin A. Hager

Graduate Theses, Dissertations, and Problem Reports (ETD)

Recent experimental demonstration of new reaction windows for coal char/methane reactions that are less energy-intensive, provides innovation for modular reactors. However, the correlation of the exact mechanism for the enhancement of these reaction windows is not certain. This study investigates the simplification of these experimental studies by developing a well-characterized coal char simulant. The approach involves using a computational approach to screen macroscopic composition to replicate the dielectric and compositional response of actual char. This study is focused on PRB coal char. A discrete element method (DEM) technique was used to simulate the packing of coal chars to give the …

Buckling Loads Of A Graphene Layer Interacting With Rigid Substrates, Bradley Beckwith

Williams Honors College, Honors Research Projects

The goal of this project is to formulate a model that can predict the buckling of a graphene layer between two rigid substrates. The model will predict the buckling of the graphene layer when it is parallel to the substrates and an edge load is applied to the ends of the layer. Our main focus is to use the model to predict buckling loads given different assumptions for interaction forces between the graphene layer and the substrates. For this project continuum modeling will be used to create a model for the graphene buckling problem. This modeling leads to a total …

Inference Of Surface Velocities From Oblique Time Lapse Photos And Terrestrial Based Lidar At The Helheim Glacier, Franklyn T. Dunbar Ii

Graduate Student Theses, Dissertations, & Professional Papers

Using time dependent observations derived from terrestrial LiDAR and oblique
time-lapse imagery, we demonstrate that a Bayesian approach to glacial motion es-
timation provides a concise way to incorporate multiple data products into a single
motion estimation procedure effectively producing surface velocity estimates with
an associated uncertainty. This approach brings both improved computational effi-
ciency, and greater scalability across observational time-frames when compared to
existing methods. To gauge efficacy, we apply these methods to a set of observa-
tions from the Helheim Glacier, a critical actor in contemporary mass loss trends
observed in the Greenland Ice Sheet. We find that …

Design Project: Smart Headband, John Michel, Jack Durkin, Noah Lewis

Williams Honors College, Honors Research Projects

Concussion in sports is a prevalent medical issue. It can be difficult for medical professionals to diagnose concussions. With the fast pace nature of many sports, and the damaging effects of concussions, it is important that any concussion risks are assessed immediately. There is a growing trend of wearable technology that collects data such as steps and provides the wearer with in-depth information regarding their performance. The Smart Headband project created a wearable that can record impact data and provide the wearer with a detailed analysis on their risk of sustaining a concussion. The Smart Headband uses accelerometers and gyroscopes …

Improving The Temporal Accuracy Of Turbulence Models And Resolving The Implementation Issues Of Fluid Flow Modeling, Kyle J. Schwiebert

Dissertations, Master's Theses and Master's Reports

A sizeable proportion of the work in this thesis focuses on a new turbulence model, dubbed ADC (the approximate deconvolution model with defect correction). The ADC is improved upon using spectral deferred correction, a means of constructing a higher order ODE solver. Since both the ADC and SDC are based on a predictor-corrector approach, SDC is incorporated with essentially no additional computational cost. We will show theoretically and using numerical tests that the new scheme is indeed higher order in time than the original, and that the benefits of defect correction, on which the ADC is based, are preserved.

The …

Deterministic And Statistical Methods For Inverse Problems With Partial Data, Yanfang Liu

Dissertations, Master's Theses and Master's Reports

Inverse problems with partial data have many applications in science and engineering. They are more challenging than the complete data cases since the lack of data increases ill-posedness and nonlinearity. The use of only deterministic or statistical methods might not provide satisfactory results. We propose to combine the deterministic and statistical methods to treat such inverse problems. The thesis is organized as follows.

In Chapter 1, we briefly introduce the inverse problems and their applications. The classical deterministic methods and Bayesian inversion are discussed. The chapter is concluded with a summary of contributions.

Chapter 2 considers the reconstruction of the …

Implementing A Neural Network For Supervised Learning With A Random Configuration Of Layers And Nodes, Kane A. Phillips

College of Graduate Studies: Theses & Dissertations

Deep learning has a substantial amount of real-life applications, making it an increasingly popular subset of artificial intelligence over the last decade. These applications come to fruition due to the tireless research and implementation of neural networks. This paper goes into detail on the implementation of supervised learning neural networks utilizing MATLAB, with the purpose being to generate a neural network based on specifications given by a user. Such specifications involve how many layers are in the network, and how many nodes are in each layer. The neural network is then trained based on known sample values of a function …

Multigrid For The Nonlinear Power Flow Equations, Enrique Pereira Batista

Mathematics Theses and Dissertations

The continuously changing structure of power systems and the inclusion of renewable
energy sources are leading to changes in the dynamics of modern power grid,
which have brought renewed attention to the solution of the AC power flow equations.
In particular, development of fast and robust solvers for the power flow problem
continues to be actively investigated. A novel multigrid technique for coarse-graining
dynamic power grid models has been developed recently. This technique uses an
algebraic multigrid (AMG) coarsening strategy applied to the weighted
graph Laplacian that arises from the power network's topology for the construction
of coarse-grain approximations to …

Uncertainty Quantification Of Nonreflecting Boundary Schemes, Brian Citty

Mathematics Theses and Dissertations

Numerical methods have been developed to solve partial differential equations involving the far-field radiation of waves. In addition, there has been recent interest in uncertainty quantification- a burgeoning field involving solving PDEs where random variables are used to model uncertainty in the data. In this thesis we will apply uncertainty quantification methodology to the 1D and 2D wave equation with nonreflecting boundary. We first derive a boundary condition for the 1D wave equation assuming several models of the random wave speed. Later we use our result to compare to an asymptotic SDE approach, and finally we repeat our analysis for …

The Revised Nim For Solving The Non-Linear System Variant Boussinesq Equations And Comparison With Nim, Oday Ahmed Jasim

Karbala International Journal of Modern Science

This research aims to guide researchers to use a new method, and it is the Revised New Iterative Method (RNIM) to solve partial differential equation systems and apply them to solve problems in various disciplines such as chemistry, physics, engineering and medicine. In this paper, the numerical solutions of the nonlinear Variable Boussinesq Equation System (VBE) were obtained using a new modified iterative method (RNIM); this was planned by (Bhaleker and Datterder-Gejj). A numerical solution to the Variable Boussinesq Equation System (VBE) was also found using a widely known method, a new iterative method (NIM). By comparing the numerical solutions …

Using Statistical Analysis To Examine Weather Variability In New York City, Ryan Chen, Yuhuang Wang, Jiehao Huang

Publications and Research

As the overall temperature of Earth continues to warm, atmospheric hazards (e.g. heatwaves, cyclones) may be driving increases in climatological trends. This study examines the daily precipitation and temperature record of the greater New York City region during the 1979-2014 period. Daily station observations from three greater New York City airports: John F. Kennedy (JFK), LaGuardia (LGA) and Newark (EWR), are used in this study. Climatological & statistical analyses are performed for the weather variability of New York City metro area to understand the impacts of climate change.The temperature climatology reveals a distinct seasonal cycle, while the precipitation climatology exhibits …

Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, Bailey Rester

Master's Theses

Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale effectively to higher spatial resolution. This thesis will present a stability analysis of a first-order KSS method applied to the wave equation in inhomogeneous media.

Development Of An Effect Size To Classify The Magnitude Of Dif In Dichotomous And Polytomous Items, James D. Weese

Graduate Theses and Dissertations

A standardized effect size for the SIBTEST/POLYSIBTEST procedure is proposed, allowing for Differential Item Functioning (DIF) to be classified with a single set of DIF heuristics regardless of whether data are dichotomous or polytomous. This proposed standardized effect size accounts for both variability in responses and whether participants are included in the SIBTEST/POLYSIBTEST calculations. First, a new set of unstandardized effect size heuristics are established for dichotomous data that are more aligned with Educational Testing Service (ETS) standards using two and three parameter logistic (2PL and 3PL) models. Second, a standardized effect size is proposed and compared to other DIF …

Diagonalization Of 1-D Schrodinger Operators With Piecewise Constant Potentials, Sarah Wright

Master's Theses

In today's world our lives are very layered. My research is meant to adapt current inefficient numerical methods to more accurately model the complex situations we encounter. This project focuses on a specific equation that is used to model sound speed in the ocean. As depth increases, the sound speed changes. This means the variable related to the sound speed is not constant. We will modify this variable so that it is piecewise constant. The specific operator in this equation also makes current time-stepping methods not practical. The method used here will apply an eigenfunction expansion technique used in previous …

Replenishment Policy For Pareto Type Deteriorating Items With Quadratic Demand Under Partial Backlogging And Delay In Payments, Ganesh Kumar, Ramesh Inaniyan, Sunita -

Applications and Applied Mathematics: An International Journal (AAM)

The present model develops a replenishment policy in which the demand rate is quadratic polynomial-time function. Deterioration rate is a Pareto type function. Shortages are partial backlogging and delay in payments are allowed. Holding cost is a linear function of time. The backlogging rate varies with the waiting duration for the next replenishment. The present paper determines the optimal policy for the individual by minimizing the total cost. The optimization procedure has been explained by a numerical example and a detailed sensitivity analysis of the optimal solution has been carried out to display the effect of various parameters.

Impatient Customers In An Markovian Queue With Bernoulli Schedule Working Vacation Interruption And Setup Time, P. Manoharan, T. Jeeva

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, using probability generating function method, Impatient customers in an Markovian queue with Bernoulli schedule working vacation interruption and setup time is discussed. Customers impatience is due to the servers vacation. During the working vacation period, if there are customers in the queue, the vacation can be interrupted at a service completion instant and the server begins a regular service period with probability (1 - b) or continues the vacation with probability b. We obtain the probability generating functions of the stationary state probabilities, performance measures, sojourn time of a customer and stochastic decomposition of the queue length, …

On A Multiserver Queueing System With Customers’ Impatience Until The End Of Service Under Single And Multiple Vacation Policies, Mokhtar Kadi, Amina A. Bouchentouf, Lahcene Yahiaoui

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with a multiserver queueing system with Bernoulli feedback and impatient customers (balking and reneging) under synchronous multiple and single vacation policies. Reneged customers may be retained in the system. Using probability generating functions (PGFs) technique, we formally obtain the steady-state solution of the proposed queueing system. Further, important performance measures and cost model are derived. Finally, numerical examples are presented.

Accurate Spectral Algorithms For Solving Variable-Order Fractional Percolation Equations, M. A. Abdelkawy

Applications and Applied Mathematics: An International Journal (AAM)

A high accurate spectral algorithm for one-dimensional variable-order fractional percolation equations (VO-FPEs) is considered.We propose a shifted Legendre Gauss-Lobatto collocation (SL-GLC) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the proposed problem. Firstly, the solution and its space fractional derivatives are expanded as shifted Legendre polynomials series. Then, we determine the expansion coefficients by reducing the VO-FPEs and its conditions to a system of ordinary differential equations (SODEs) in time. The numerical approximation of SODEs is achieved by means of the SC-GR-C method. The under-study’s problem subjected to the Dirichlet or non-local boundary conditions is presented …