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Articles 1 - 30 of 54
Full-Text Articles in Physical Sciences and Mathematics
Accurate Covariance Estimation For Pose Data From Iterative Closest Point Algorithm, Rick H. Yuan, Clark N. Taylor, Scott L. Nykl
Accurate Covariance Estimation For Pose Data From Iterative Closest Point Algorithm, Rick H. Yuan, Clark N. Taylor, Scott L. Nykl
Faculty Publications
One of the fundamental problems of robotics and navigation is the estimation of the relative pose of an external object with respect to the observer. A common method for computing the relative pose is the iterative closest point (ICP) algorithm, where a reference point cloud of a known object is registered against a sensed point cloud to determine relative pose. To use this computed pose information in downstream processing algorithms, it is necessary to estimate the uncertainty of the ICP output, typically represented as a covariance matrix. In this paper, a novel method for estimating uncertainty from sensed data is …
A Predator-Prey Biological Model With Combined Birth Rates, Self-Limitation And Competition Terms, Joon Hyuk Kang, Lucinda Ford
A Predator-Prey Biological Model With Combined Birth Rates, Self-Limitation And Competition Terms, Joon Hyuk Kang, Lucinda Ford
Faculty Publications
The purpose of this paper is to give sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in Rn. Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive …
Evolution Of Coronal Magnetic Field Parameters During X5.4 Solar Flare, Seth H. Garland, Benjamin F. Akers, Vasyl B. Yurchyshyn, Robert D. Loper, Daniel J. Emmons
Evolution Of Coronal Magnetic Field Parameters During X5.4 Solar Flare, Seth H. Garland, Benjamin F. Akers, Vasyl B. Yurchyshyn, Robert D. Loper, Daniel J. Emmons
Faculty Publications
The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz| ≥ 300 G, areas of flare brightening seen …
Uniqueness Of Steady State Positive Solutions To A General Elliptic System With Dirichlet Boundary Conditions, Joon Hyuk Kang
Uniqueness Of Steady State Positive Solutions To A General Elliptic System With Dirichlet Boundary Conditions, Joon Hyuk Kang
Faculty Publications
The purpose of this paper is to give conditions for the uniqueness of positive solution to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in Rn. Also considered are the effects of perturbations on the coexistence state and uniqueness.
Obstructions To Shake Sliceness For Links, Anthony Bosman
Obstructions To Shake Sliceness For Links, Anthony Bosman
Faculty Publications
Shake slice generalizes the notion of a slice link, naturally extending the notion of shake slice knots to links. There is also a relative version, shake concordance, that generalizes link concordance. We show that if two links are shake concordant, then their zero surgery manifolds are homology cobordant. Then we give several obstructions to a link being shake slice; for instance, the Arf invariants vanish for both the link and each component. Finally we show that a shake slice link bounds disjoint disks in a homology 4-ball and hence each component is algebraically slice.
Robust Error Estimation Based On Factor-Graph Models For Non-Line-Of-Sight Localization, O. Arda Vanli, Clark N. Taylor
Robust Error Estimation Based On Factor-Graph Models For Non-Line-Of-Sight Localization, O. Arda Vanli, Clark N. Taylor
Faculty Publications
This paper presents a method to estimate the covariances of the inputs in a factor-graph formulation for localization under non-line-of-sight conditions. A general solution based on covariance estimation and M-estimators in linear regression problems, is presented that is shown to give unbiased estimators of multiple variances and are robust against outliers. An iteratively re-weighted least squares algorithm is proposed to jointly compute the proposed variance estimators and the state estimates for the nonlinear factor graph optimization. The efficacy of the method is illustrated in a simulation study using a robot localization problem under various process and measurement models and measurement …
Survivals Of Two Cooperating Species Of Animals, Joon Hyuk Kang
Survivals Of Two Cooperating Species Of Animals, Joon Hyuk Kang
Faculty Publications
The purpose of this paper is to give conditions for the existence and uniqueness of positive solution to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">Ω in Rn" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: …
Extending Critical Infrastructure Element Longevity Using Constellation-Based Id Verification, Christopher M. Rondeau, Michael A. Temple, J. Addison Betances, Christine M. Schubert Kabban
Extending Critical Infrastructure Element Longevity Using Constellation-Based Id Verification, Christopher M. Rondeau, Michael A. Temple, J. Addison Betances, Christine M. Schubert Kabban
Faculty Publications
This work supports a technical cradle-to-grave protection strategy aimed at extending the useful lifespan of Critical Infrastructure (CI) elements. This is done by improving mid-life operational protection measures through integration of reliable physical (PHY) layer security mechanisms. The goal is to improve existing protection that is heavily reliant on higher-layer mechanisms that are commonly targeted by cyberattack. Relative to prior device ID discrimination works, results herein reinforce the exploitability of constellation-based PHY layer features and the ability for those features to be practically implemented to enhance CI security. Prior work is extended by formalizing a device ID verification process that …
A Learning Curve Model Accounting For The Flattening Effect In Production Cycles, Evan R. Boone, John J. Elshaw, Clay M. Koschnick, Jonathan D. Ritschel, Adedeji B. Badiru
A Learning Curve Model Accounting For The Flattening Effect In Production Cycles, Evan R. Boone, John J. Elshaw, Clay M. Koschnick, Jonathan D. Ritschel, Adedeji B. Badiru
Faculty Publications
We investigate production cost estimates to identify and model modifications to a prescribed learning curve. Our new model examines the learning rate as a decreasing function over time as opposed to a constant rate that is frequently used. The purpose of this research is to determine whether a new learning curve model could be implemented to reduce the error in cost estimates for production processes. A new model was created that mathematically allows for a “flattening effect,” which typically occurs later in the production process. This model was then compared to Wright’s learning curve, which is a popular method used …
Modeling And Simulation Techniques Used In High Strain Rate Projectile Impact, Derek G. Spear, Anthony N. Palazotto, Ryan A. Kemnitz
Modeling And Simulation Techniques Used In High Strain Rate Projectile Impact, Derek G. Spear, Anthony N. Palazotto, Ryan A. Kemnitz
Faculty Publications
A series of computational models and simulations were conducted for determining the dynamic responses of a solid metal projectile impacting a target under a prescribed high strain rate loading scenario in three-dimensional space. The focus of this study was placed on two different modeling techniques within finite element analysis available in the Abaqus software suite. The first analysis technique relied heavily on more traditional Lagrangian analysis methods utilizing a fixed mesh, while still taking advantage of the finite difference integration present under the explicit analysis approach. A symmetry reduced model using the Lagrangian coordinate system was also developed for comparison …
On Subdiagonal Rational Pade Approximations And The Brenner-Thomee Approximation Theorem For Operator Semigroups, Frank Neubrander, Koray Ozer, Lee Windsperger
On Subdiagonal Rational Pade Approximations And The Brenner-Thomee Approximation Theorem For Operator Semigroups, Frank Neubrander, Koray Ozer, Lee Windsperger
Faculty Publications
The computational powers of Mathematica are used to prove polynomial identities that are essential to obtain growth estimates for subdiagonal rational Pade approximations of the exponential function and to obtain new estimates of the constants of the Brenner-Thomee Approximation Theorem of Semigroup Theory.
Through-The-Wall Radar Detection Using Machine Learning, Aihua W. Wood, Ryan Wood, Matthew Charnley
Through-The-Wall Radar Detection Using Machine Learning, Aihua W. Wood, Ryan Wood, Matthew Charnley
Faculty Publications
This paper explores the through-the-wall inverse scattering problem via machine learning. The reconstruction method seeks to discover the shape, location, and type of hidden objects behind walls, as well as identifying certain material properties of the targets. We simulate RF sources and receivers placed outside the room to generate observation data with objects randomly placed inside the room. We experiment with two types of neural networks and use an 80-20 train-test split for reconstruction and classification.
An Ultra-Sparse Approximation Of Kinetic Solutions To Spatially Homogeneous Flows Of Non-Continuum Gas, Alexander Alekseenko, Amy Grandilli, Aihua W. Wood
An Ultra-Sparse Approximation Of Kinetic Solutions To Spatially Homogeneous Flows Of Non-Continuum Gas, Alexander Alekseenko, Amy Grandilli, Aihua W. Wood
Faculty Publications
We consider a compact approximation of the kinetic velocity distribution function by a sum of isotropic Gaussian densities in the problem of spatially homogeneous relaxation. Derivatives of the macroscopic parameters of the approximating Gaussians are obtained as solutions to a linear least squares problem derived from the Boltzmann equation with full collision integral. Our model performs well for flows obtained by mixing upstream and downstream conditions of normal shock wave with Mach number 3. The model was applied to explore the process of approaching equilibrium in a spatially homogeneous flow of gas. Convergence of solutions with respect to the model …
A Sequential Partial Information Bomber‐Defender Shooting Problem, Krishna Kalyanam, David W. Casbeer, Meir Pachter
A Sequential Partial Information Bomber‐Defender Shooting Problem, Krishna Kalyanam, David W. Casbeer, Meir Pachter
Faculty Publications
No abstract provided.
A Comparison Of The Trojan Y Chromosome Strategy To Harvesting Models For Eradication Of Non-Native Species, Jingjing Lyu, Pamela J. Schofield, Kristen M. Reaver, Matthew Beauregard, Rana D. Parshad
A Comparison Of The Trojan Y Chromosome Strategy To Harvesting Models For Eradication Of Non-Native Species, Jingjing Lyu, Pamela J. Schofield, Kristen M. Reaver, Matthew Beauregard, Rana D. Parshad
Faculty Publications
The Trojan Y Chromosome Strategy (TYC) is a promising eradication method for biological control of non-native species. The strategy works by manipulating the sex ratio of a population through the introduction of supermales that guarantee male offspring. In the current manuscript, we compare the TYC method with a pure harvesting strategy. We also analyze a hybrid harvesting model that mirrors the TYC strategy. The dynamic analysis leads to results on stability of solutions and bifurcations of the model. Several conclusions about the different strategies are established via optimal control methods. In particular, the results affirm that either a pure harvesting …
Large And Small Data Blow-Up Solutions In The Trojan Y Chromosome Model, Rana D. Parshad, Matthew Beauregard, Eric M. Takyi, Thomas Griffin, Landrey Bobo
Large And Small Data Blow-Up Solutions In The Trojan Y Chromosome Model, Rana D. Parshad, Matthew Beauregard, Eric M. Takyi, Thomas Griffin, Landrey Bobo
Faculty Publications
The Trojan Y Chromosome Strategy (TYC) is an extremely well investigated biological control method for controlling invasive populations with an XX-XY sex determinism. In [35, 36] various dynamical properties of the system are analyzed, including well posedness, boundedness of solutions, and conditions for extinction or recovery. These results are derived under the assumption of positive solutions. In the current manuscript, we show that if the introduction rate of trojan fish is zero, under certain large data assumptions, negative solutions are possible for the male population, which in turn can lead to finite time blow-up in the female and male populations. …
Quenching Estimates For A Non-Newtonian Filtration Equation With Singular Boundary Conditions, Matthew Beauregard, Burhan Selcuk
Quenching Estimates For A Non-Newtonian Filtration Equation With Singular Boundary Conditions, Matthew Beauregard, Burhan Selcuk
Faculty Publications
In this paper, the quenching behavior of the non-Newtonian filtration equation (φ(u))t = (|ux| r−2 ux)x with singular boundary conditions, ux (0, t) = u −p (0, t), ux (a, t) = (1 − u(a, t))−q is investigated. Various conditions on the initial condition are shown to guarantee quenching at either the left or right boundary. Theoretical quenching rates and lower bounds to the quenching time are determined when φ(u) = u and r = 2. Numerical experiments are provided to illustrate and provide additional validation of the theoretical estimates to the quenching rates and times.
Ergodicity For The 3d Stochastic Navier-Stokes Equations Perturbed By Lévy Noise, Manil T. Mohan, K. Sakthivel, Sivaguru S. Sritharan
Ergodicity For The 3d Stochastic Navier-Stokes Equations Perturbed By Lévy Noise, Manil T. Mohan, K. Sakthivel, Sivaguru S. Sritharan
Faculty Publications
In this work we construct a Markov family of martingale solutions for 3D stochastic Navier–Stokes equations (SNSE) perturbed by Lévy noise with periodic boundary conditions. Using the Kolmogorov equations of integrodifferential type associated with the SNSE perturbed by Lévy noise, we construct a transition semigroup and establish the existence of a unique invariant measure. We also show that it is ergodic and strongly mixing.
Abstract © Wiley.
A Variable Nonlinear Splitting Algorithm For Reaction Diffusion Systems With Self- And Cross-Diffusion, Matthew Beauregard, Joshua L. Padgett
A Variable Nonlinear Splitting Algorithm For Reaction Diffusion Systems With Self- And Cross-Diffusion, Matthew Beauregard, Joshua L. Padgett
Faculty Publications
Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response of one species in light of the concentration of another. In this paper, a novel nonlinear operator splitting method is presented that directly incorporates both self- and cross-diffusion into a computational efficient design. The numerical analysis guarantees the accuracy and demonstrates appropriate criteria for stability. Numerical experiments display its efficiency and accuracy
Cross-Participant Eeg-Based Assessment Of Cognitive Workload Using Multi-Path Convolutional Recurrent Neural Networks, Ryan G. Hefron, Brett J. Borghetti, Christine M. Schubert Kabban, James Christensen, Justin Estep
Cross-Participant Eeg-Based Assessment Of Cognitive Workload Using Multi-Path Convolutional Recurrent Neural Networks, Ryan G. Hefron, Brett J. Borghetti, Christine M. Schubert Kabban, James Christensen, Justin Estep
Faculty Publications
Applying deep learning methods to electroencephalograph (EEG) data for cognitive state assessment has yielded improvements over previous modeling methods. However, research focused on cross-participant cognitive workload modeling using these techniques is underrepresented. We study the problem of cross-participant state estimation in a non-stimulus-locked task environment, where a trained model is used to make workload estimates on a new participant who is not represented in the training set. Using experimental data from the Multi-Attribute Task Battery (MATB) environment, a variety of deep neural network models are evaluated in the trade-space of computational efficiency, model accuracy, variance and temporal specificity yielding three …
Uncertainty Evaluation In The Design Of Structural Health Monitoring Systems For Damage Detection, Christine M. Schubert Kabban, Richard P. Uber, Kevin J. Lin, Bin Lin, M. Bhuiyan, Victor Giurgiutiu
Uncertainty Evaluation In The Design Of Structural Health Monitoring Systems For Damage Detection, Christine M. Schubert Kabban, Richard P. Uber, Kevin J. Lin, Bin Lin, M. Bhuiyan, Victor Giurgiutiu
Faculty Publications
The validation of structural health monitoring (SHM) systems for aircraft is complicated by the extent and number of factors that the SHM system must demonstrate for robust performance. Therefore, a time- and cost-efficient method for examining all of the sensitive factors must be conducted. In this paper, we demonstrate the utility of using the simulation modeling environment to determine the SHM sensitive factors that must be considered for subsequent experiments, in order to enable the SHM validation. We demonstrate this concept by examining the effect of SHM system configuration and flaw characteristics on the response of a signal from a …
Modeling The Disappearance Of The Neanderthals Using Concepts Of Population Dynamics And Ecology, Michael F. Roberts, Stephen E. Bricher
Modeling The Disappearance Of The Neanderthals Using Concepts Of Population Dynamics And Ecology, Michael F. Roberts, Stephen E. Bricher
Faculty Publications
Current hypotheses regarding the disappearance of Neanderthals (NEA) in Europe fall into two main categories: climate change, and competition. Here we review current research and existing mathematical models that deal with this question, and we propose an approach that incorporates and permits the investigation of the current hypotheses. We have developed a set of differential equations that model population dynamics of anatomically modern humans (AMH) and NEA, their ecological relations to prey species, and their mutual interactions. The model allows investigators to explore each of the two main categories or combinations of both, as well as various forms of competition …
Wavelet Anova Bisection Method For Identifying Simulation Model Bias, Andrew D. Atkinson, Raymond R. Hill, Joseph J. Pignatiello Jr., G. Geoffrey Vining, Edward D. White, Eric Chicken
Wavelet Anova Bisection Method For Identifying Simulation Model Bias, Andrew D. Atkinson, Raymond R. Hill, Joseph J. Pignatiello Jr., G. Geoffrey Vining, Edward D. White, Eric Chicken
Faculty Publications
High-resolution computer models can simulate complex systems and processes in order to evaluate a solution quickly and inexpensively. Many simulation models produce dynamic functional output, such as a set of time-series data generated during a process. These computer models require verification and validation (V&V) to assess the correctness of these simulations. In particular, the model validation effort evaluates if the model is an appropriate representation of the real-world system that it is meant to simulate. However, when assessing a model capable of generating functional output, it is useful to learn more than simply whether the model is valid or invalid. …
Homogenization Techniques For Population Dynamics In Strongly Heterogeneous Landscapes, Brian P. Yurk, Christina A. Cobbold
Homogenization Techniques For Population Dynamics In Strongly Heterogeneous Landscapes, Brian P. Yurk, Christina A. Cobbold
Faculty Publications
An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction–diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic …
Stochastic Quasilinear Evolution Equations In Umd Banach Spaces, Manil T. Mohan, Sivaguru S. Sritharan
Stochastic Quasilinear Evolution Equations In Umd Banach Spaces, Manil T. Mohan, Sivaguru S. Sritharan
Faculty Publications
In this work we prove the existence and uniqueness up to a stopping time for the stochastic counterpart of Tosio Kato's quasilinear evolutions in UMD Banach spaces. These class of evolutions are known to cover a large class of physically important nonlinear partial differential equations. Existence of a unique maximal solution as well as an estimate on the probability of positivity of stopping time is obtained. An example of stochastic Euler and Navier–Stokes equation is also given as an application of abstract theory to concrete models.
Measuring The Reflection Matrix Of A Rough Surface, Kenneth W. Burgi, Michael A. Marciniak, Mark E. Oxley, Stephen E. Nauyoks
Measuring The Reflection Matrix Of A Rough Surface, Kenneth W. Burgi, Michael A. Marciniak, Mark E. Oxley, Stephen E. Nauyoks
Faculty Publications
Phase modulation methods for imaging around corners with reflectively scattered light required illumination of the occluded scene with a light source either in the scene or with direct line of sight to the scene. The RM (reflection matrix) allows control and refocusing of light after reflection, which could provide a means of illuminating an occluded scene without access or line of sight. Two optical arrangements, one focal-plane, the other an imaging system, were used to measure the RM of five different rough-surface reflectors. Intensity enhancement values of up to 24 were achieved. Surface roughness, correlation length, and slope were examined …
Time Lags Associated With Effects Of Oceanic Conditions On Seabird Breeding In The Salish Sea Region Of The Northern California Current System, Rashida S. Smith, Lynelle M. Weldon, James L. Hayward, Shandelle M. Henson
Time Lags Associated With Effects Of Oceanic Conditions On Seabird Breeding In The Salish Sea Region Of The Northern California Current System, Rashida S. Smith, Lynelle M. Weldon, James L. Hayward, Shandelle M. Henson
Faculty Publications
No abstract provided.
Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh
Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh
Faculty Publications
The notions of rectifying subspaces and of rectifying submanifolds were introduced in [B.-Y. Chen, Int. Electron. J. Geom 9 (2016), no. 2, 1–8]. More precisely, a submanifold in a Euclidean m-space Em is called a rectifying submanifold if its position vector field always lies in its rectifying subspace. Several fundamental properties and classification of rectifying submanifolds in Euclidean space were obtained in [B.-Y. Chen, op. cit.]. In this present article, we extend the results in [B.-Y. Chen, op. cit.] to rectifying space- like submanifolds in a pseudo-Euclidean space with arbitrary codimension. In particular, we completely classify all rectifying space-like submanifolds …
Estimates Of Life Span Of Solutions Of A Cauchy Problem, Joon Hyuk Kang
Estimates Of Life Span Of Solutions Of A Cauchy Problem, Joon Hyuk Kang
Faculty Publications
In this paper we get estimates of life span of a Cauchy problem ut(x, t) = ∆ u(x, t) +u(x, t)p, x∈Rn, t >0,u(x,0) =λφ(x), x∈Rn in terms of the positive constant parameterλ whenφ(x)∈Lq is a nonnegative bounded continuous function in Rn but not identically zero, where q is large enough. The technique we used in this paper is the Comparison Principle.
Characterization Of Rectifying And Sphere Curves In R^3, Yun Myung Oh, Julie Logan
Characterization Of Rectifying And Sphere Curves In R^3, Yun Myung Oh, Julie Logan
Faculty Publications
Studies of curves in 3D-space have been developed by many geometers and it is known that any regular curve in 3D space is completely determined by its curvature and torsion, up to position. Many results have been found to characterize various types of space curves in terms of conditions on the ratio of torsion to curvature. Under an extracondition on the constant curvature, Y.L. Seo and Y. M. Oh found the series solution when the ratio of torsion to curvature is a linear function. Furthermore, this solution is known to be a rectifying curve by B. Y. Chen’s work. This …