Applied Mathematics Commons^™

A Literature Review On Combining Heuristics And Exact Algorithms In Combinatorial Optimization, Hesamoddin Tahami, Hengameh Fakhravar

Engineering Management & Systems Engineering Faculty Publications

There are several approaches for solving hard optimization problems. Mathematical programming techniques such as (integer) linear programming-based methods and metaheuristic approaches are two extremely effective streams for combinatorial problems. Different research streams, more or less in isolation from one another, created these two. Only several years ago, many scholars noticed the advantages and enormous potential of building hybrids of combining mathematical programming methodologies and metaheuristics. In reality, many problems can be solved much better by exploiting synergies between these approaches than by “pure” classical algorithms. The key question is how to integrate mathematical programming methods and metaheuristics to achieve such …

Camouflaged Poisoning Attack On Graph Neural Networks, Chao Jiang, Yi He, Richard Chapman, Hongyi Wu

Computer Science Faculty Publications

Graph neural networks (GNNs) have enabled the automation of many web applications that entail node classification on graphs, such as scam detection in social media and event prediction in service networks. Nevertheless, recent studies revealed that the GNNs are vulnerable to adversarial attacks, where feeding GNNs with poisoned data at training time can lead them to yield catastrophically devastative test accuracy. This finding heats up the frontier of attacks and defenses against GNNs. However, the prior studies mainly posit that the adversaries can enjoy free access to manipulate the original graph, while obtaining such access could be too costly in …

Drop In The Bucket?, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Horizontal Air Mass: Solutions For Fermi Questions, November 2022, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Real-Time Cavity Fault Prediction In Cebaf Using Deep Learning, Md. M. Rahman, K. Iftekharuddin, A. Carptenter, T. Mcguckin, C. Tennant, L. Vidyaratne, Sandra Biedron (Ed.), Evgenya Simakov (Ed.), Stephen Milton (Ed.), Petr M. Anisimov (Ed.), Volker R.W. Schaa (Ed.)

Electrical & Computer Engineering Faculty Publications

Data-driven prediction of future faults is a major research area for many industrial applications. In this work, we present a new procedure of real-time fault prediction for superconducting radio-frequency (SRF) cavities at the Continuous Electron Beam Accelerator Facility (CEBAF) using deep learning. CEBAF has been afflicted by frequent downtime caused by SRF cavity faults. We perform fault prediction using pre-fault RF signals from C100-type cryomodules. Using the pre-fault signal information, the new algorithm predicts the type of cavity fault before the actual onset. The early prediction may enable potential mitigation strategies to prevent the fault. In our work, we apply …

On The P-Inner Functions Of ℓPA, James G. Dragas

Mathematics & Statistics Theses & Dissertations

Define ℓ^p_A as the space of all functions holomorphic over the unit disk whose Taylor coefficients are p-summable. Despite their classical origins and simple definition, these spaces are not as well understood as one might expect. This is particularly true when compared with the Hardy spaces, which provide a useful road map for the types of questions we might consider reasonable. In this work we examine the zero sets of ℓ^p_A, p ∈ (1;∞), as well as a notion of inner function that is consistent with the approach taken on numerous other function spaces. …

High-Order Positivity-Preserving L2-Stable Spectral Collocation Schemes For The 3-D Compressible Navier-Stokes Equations, Johnathon Keith Upperman

Mathematics & Statistics Theses & Dissertations

High-order entropy stable schemes are a popular method used in simulations with the compressible Euler and Navier-Stokes equations. The strength of these methods is that they formally satisfy a discrete entropy inequality which can be used to guarantee L₂ stability of the numerical solution. However, a fundamental assumption that is explicitly or implicitly used in all entropy stability proofs available in the literature for the compressible Euler and Navier-Stokes equations is that the thermodynamic variables (e.g., density and temperature) are strictly positive in the entire space{time domain considered. Without this assumption, any entropy stability proof for a numerical scheme …

Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis

Mathematics & Statistics Theses & Dissertations

Volterra integral equations arise in a variety of applications in modern physics and engineering, namely in interactions that contain a memory term. Classical formulations of these problems are largely inflexible when considering non-homogeneous media, which can be problematic when considering long term interactions of real-world applications. The use of fractional derivative and integral terms naturally relax these restrictions in a natural way to consider these problems in a more general setting. One major drawback to the use of fractional derivatives and integrals in modeling is the regularity requirement for functions, where we can no longer assume that functions are as …

Electrohydrodynamic Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Scheme, Charles Leland Armstrong

Mathematics & Statistics Theses & Dissertations

Capsules are fluid-filled, elastic membranes that serve as a useful model for synthetic and biological membranes. One prominent application of capsules is their use in modeling the response of red blood cells to external forces. These models can be used to study the cell’s material properties and can also assist in the development of diagnostic equipment. In this work we develop a three dimensional model for numerical simulations of red blood cells under the combined influence of hydrodynamic and electrical forces. The red blood cell is modeled as a biconcave-shaped capsule suspended in an ambient fluid domain. Cell deformation occurs …

A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Gamage, Yan Peng

College of Sciences Posters

Interface problems have many applications in fluid dynamics, molecular biology, electromagnetism, material science, heat distribution in engines, and hyperthermia treatment of cancer. Mathematically, interface problems commonly lead to partial differential equations (PDE) whose in- put data are discontinuous or singular across the interfaces in the solution domain. Many standard numerical methods designed for smooth solutions poorly work for interface problems as solutions of the interface problems are mostly non-smoothness or discontinuous. Moving interface problems depends on the accuracy of the gradient of the solution at the interface. Therefore, it became essential to derive a method for interface problems that gives …

End-To-End Physics Event Generator, Yasir Alanazi, N. Sato, Tianbo Liu, W. Melnitchouk, Michelle P. Kuchera, Evan Pritchard, Michael Robertson, Ryan Strauss, Luisa Velasco, Yaohang Li

College of Sciences Posters

We apply generative adversarial network (GAN) technology to build an event generator that simulates particle production in electron-proton scattering that is free of theoretical assumptions about underlying particle dynamics. The difficulty of efficiently training a GAN event simulator lies in learning the complicated pat- terns of the distributions of the particles physical properties. We develop a GAN that selects a set of transformed features from particle momenta that can be generated easily by the generator, and uses these to produce a set of augmented features that improve the sensitivity of the discriminator. The new Feature-Augmented and Transformed GAN (FAT-GAN) is …

Undetermined Coefficients: A Fully Generalized Approach, Taylor Powell

Undergraduate Research Symposium

In this presentation, I outline the development of a fully-generalized solution of linear, non-homogeneous differential equations with constant coefficients and whose non-homogeneous function is any product of sinusoidal, exponential, and polynomial functions. This particular method does not require the reader to work with annihilator operators or additional related ODEs, and only requires an understanding of summation notation, matrix multiplication, and calculus. Additionally, this method provides a straightforward way to develop a program to implement the technique, and potentially reduces the time-complexity for solutions with comparisons to other methods.

Fixed-Point Proximity Minimization: A Theoretical Review And Numerical Study, Daniel Weddle, Jianfeng Guo

OUR Journal: ODU Undergraduate Research Journal

This study examines the relatively recent development of a “fixed-point proximity” approach to one type of minimization problem, considers its application to image denoising, and explores convergence and divergence of the iterative algorithm beyond a (previously supplied) theoretically guaranteed convergence bound on one of the parameters (𝜆). While reviewing the fixed-point proximity approach and its application to image denoising, we aim to communicate the concepts and details in a way that will facilitate understanding for undergraduates and for scholars from other subfields. In the latter portion of our study, the numerical experiment provides thought-provoking data on the effects that parameters …

Conical Orbital Mechanics: A Rework Of Classic Orbit Transfer Mechanics, Cian Anthony Branco

Mechanical & Aerospace Engineering Theses & Dissertations

Simple orbital maneuvers obeying Kepler’s Laws, when taken with respect to Newton’s framework, require considerable time and effort to interpret and understand. Instead of a purely mathematical approach relying on the governing relations, a graphical geometric conceptual representation provides a useful alternative to the physical realities of orbits. Conic sections utilized within the full scope of a modified cone (frustum) were employed to demonstrate and develop a geometric approach to elliptical orbit transformations. The geometric model in-question utilizes the rotation of a plane intersecting the orbital frustum at some angle β (and the change in this angle) in a novel …

Inference And Estimation In Change Point Models For Censored Data, Kristine Gierz

Mathematics & Statistics Theses & Dissertations

In general, the change point problem considers inference of a change in distribution for a set of time-ordered observations. This has applications in a large variety of fields and can also apply to survival data. With improvements to medical diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time-ordered observations, potentially under censoring or truncation.

In this dissertation, we first propose a sequential testing approach for detecting multiple change …

D-Vine Copula Model For Dependent Binary Data, Huihui Lin, N. Rao Chaganty

College of Sciences Posters

High-dimensional dependent binary data are prevalent in a wide range of scientific disciplines. A popular method for analyzing such data is the Multivariate Probit (MP) model. But the MP model sometimes fails even within a feasible range of binary correlations, because the underlying correlation matrix of the latent variables may not be positive definite. In this research, we proposed pair copula models, assuming the dependence between the binary variables is first order autoregressive (AR(1))or equicorrelated structure. Also, when Archimediean copula is used, most paper converted Kendall Tau to corresponding copula parameter, there is no explicit function of Pearson’s correlation coefficient …

Investigating The Feasibility And Stability For Modeling Acoustic Wave Scattering Using A Time-Domain Boundary Integral Equation With Impedance Boundary Condition, Michelle E. Rodio

Mathematics & Statistics Theses & Dissertations

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet and environmentally friendly aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction and are characterized by a frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners

This work considers using either an impedance or an admittance (inverse …

Certified Functions For Mesh Generation, Andrey N. Chernikov

Chemistry & Biochemistry Faculty Publications

Formal methods allow for building correct-by-construction software with provable guarantees. The formal development presented here resulted in certified executable functions for mesh generation. The term certified means that their correctness is established via an artifact, or certificate, which is a statement of these functions in a formal language along with the proofs of their correctness. The term is meaningful only when qualified by a specific set of properties that are proven. This manuscript elaborates on the precise statements of the properties being proven and their role in an implementation of a version of the Isosurface Stuffing algorithm by Labelle and …

Multiplicative Noise Removal: Nonlocal Low-Rank Model And It's Proximal Alternating Reweighted Minimization Algorithm, Xiaoxia Liu, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Mathematics & Statistics Faculty Publications

The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to multiplicative noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex …

Mesoscopic Methods In Engineering And Science, Christian Jansen, Manfred Krafczyk, Li-Shi Luo

Mathematics & Statistics Faculty Publications

(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the …

Boundary Vortex Formation In Polarization-Modulated Orthogonal Smectic Liquid Crystals, Carlos J. García-Cervera, Tiziana Giorgi, Sookyung Joo

Mathematics & Statistics Faculty Publications

We investigate the relaxation of an energy functional originated in the physics literature to study the bistability of polarization modulated orthogonal smectic phases (SmAP_Fmod) of bent-core molecules liquid crystals. We show that the interplay between the mixed boundary conditions and the shape of the sample results in boundary defects. We also analyze the bistable switching due to an applied electric field via gradient flow numerical simulations. Our computations reveal a novel dynamic scenario, where switching is achieved by the formation of two internal vortices.

Electrohydrodynamic Simulations Of The Deformation Of Liquid-Filled Capsules, Pai Song

Mathematics & Statistics Theses & Dissertations

A comprehensive two- and three-dimensional framework for the electrohydrodynamic simulation of deformable capsules is provided. The role of a direct current (DC) electric field on the deformation and orientation of a liquid-filled capsule is thoroughly considered numerically. This framework is based on lattice Boltzmann method for the fluid, finite element method for the membrane structure of the capsule, fast immersed interface method for the electric field and immersed boundary method being used to consider the fluid-structure-electric interaction. Under the effect of electric field, two different types of equilibrium states, prolate or oblate are obtained. The numerical algorithm is also applied …

Computational Analysis Of Antipode Algorithms For The Output Feedback Hopf Algebra, Lance Berlin

Electrical & Computer Engineering Theses & Dissertations

The feedback interconnection of two systems written in terms of Chen-Fliess series can be described explicitly in terms of the antipode of the output feedback Hopf algebra. At present, there are three known computational approaches to calculating this antipode: the left coproduct method, the right coproduct method, and the derivation method. Each of these algorithms is defined recursively, and thus becomes computationally expensive quite quickly. This motivates the need for a more complete understanding of the algorithmic complexity of these methods, as well as the development of new approaches for determining the Hopf algebra antipode. The main goals of this …

Dynamic Attribute-Level Best Worst Discrete Choice Experiments, Amanda Working, Mohammed Alqawba, Norou Diawara

Mathematics & Statistics Faculty Publications

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are …

On Analytic Nonlinear Input-Output Systems: Expanded Global Convergence And System Interconnections, Irina M. Winter Arboleda

Electrical & Computer Engineering Theses & Dissertations

Functional series representations of nonlinear systems first appeared in engineering in the early 1950’s. One common representation of a nonlinear input-output system are Chen-Fliess series or Fliess operators. Such operators are described by functional series indexed by words over a noncommutative alphabet. They can be viewed as a noncommutative generalization of a Taylor series. A Fliess operator is said to be globally convergent when its radius of convergence is infinite, in other words, when there is no a priori upper bound on both the L1-norm of an admissible input and the length of time over which the corresponding output is …

Resilience For Asynchronous Iterative Methods For Sparse Linear Systems, Evan Coleman

Computational Modeling & Simulation Engineering Theses & Dissertations

Large scale simulations are used in a variety of application areas in science and engineering to help forward the progress of innovation. Many spend the vast majority of their computational time attempting to solve large systems of linear equations; typically arising from discretizations of partial differential equations that are used to mathematically model various phenomena. The algorithms used to solve these problems are typically iterative in nature, and making efficient use of computational time on High Performance Computing (HPC) clusters involves constantly improving these iterative algorithms. Future HPC platforms are expected to encounter three main problem areas: scalability of code, …

Solutions For Fermi Questions, November 2019: Question 1: Cell Phones Make Me Boil; Question 2: Charging The Phone, Larry Weinstein

Physics Faculty Publications

Answers to the Fermi questions:

How much water can you boil with the energy stored in a cell phone battery?

How much does the electrical energy for a cell phone cost each year?

Reliability Estimation Of Reciprocating Seals Based On Multivariate Dependence Analysis And It's Experimental Validation, Chao Zhang, Rentong Chen, Shaoping Wang, Yujie Qian, Mileta M. Tomovic

Engineering Technology Faculty Publications

Accurate reliability estimation for reciprocating seals is of great significance due to their wide use in numerous engineering applications. This work proposes a reliability estimation method for reciprocating seals based on multivariate dependence analysis of different performance indicators. Degradation behavior corresponding to each performance indicator is first described by the Wiener process. Dependence among different performance indicators is then captured using D-vine copula, and a weight-based copula selection method is utilized to determine the optimal bivariate copula for each dependence relationship. A two-stage Bayesian method is used to estimate the parameters in the proposed model. Finally, a reciprocating seal degradation …

Extended Poisson Models For Count Data With Inflated Frequencies, Monika Arora

Mathematics & Statistics Theses & Dissertations

Count data often exhibits inflated counts for zero. There are numerous papers in the literature that show how to fit Poisson regression models that account for the zero inflation. However, in many situations the frequencies of zero and of some other value k tends to be higher than the Poisson model can fit appropriately. Recently, Sheth-Chandra (2011), Lin and Tsai (2012) introduced a mixture model to account for the inflated frequencies of zero and k. In this dissertation, we study basic properties of this mixture model and parameter estimation for grouped and ungrouped data. Using stochastic representation we show …

Power Corrections To Tmd Factorization For Z-Boson Production, I. Balitsky, A. Tatasov

Physics Faculty Publications

A typical factorization formula for production of a particle with a small transverse momentum in hadron-hadron collisions is given by a convolution of two TMD parton densities with cross section of production of the final particle by the two partons. For practical applications at a given transverse momentum, though, one should estimate at what momenta the power corrections to the TMD factorization formula become essential. In this paper we calculate the first power corrections to TMD factorization formula for Z-boson production and Drell-Yan process in high-energy hadron-hadron collisions. At the leading order in N_c power corrections are expressed in …