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Articles 1 - 30 of 104
Full-Text Articles in Applied Mathematics
Transfer Learning In The Era Of Foundational Models: Application To Diagnosis In Rheumatology, Prashant Shekhar
Transfer Learning In The Era Of Foundational Models: Application To Diagnosis In Rheumatology, Prashant Shekhar
Math Department Colloquium Series
Problems with current synovitis grading procedures
- There has been a lack of reliability in grading these images in the medical community due to a lack of universally accepted diagnostic criteria [Momtazmanesh et al., 2022]
- The human/machine variability creates an additional challenge in an efficient automated scoring system [Ranganath et al., 2022]
- There is a lack of consistency between doctors in grading these images [Momtazmanesh et al., 2022]
Understanding Collective Performance: Human Factors And Team Science, Joseph Keebler
Understanding Collective Performance: Human Factors And Team Science, Joseph Keebler
Math Department Colloquium Series
This talk will focus on modern issues with team science. Joe will discuss a variety of projects he's been involved with aimed at improving teamwork in complex sociotechnical systems including military, aviation, and healthcare. He will discuss major theoretical facets of teamwork and provide evidence-based best practices that were utilized to improve teams in applied settings.
Modeling And Estimation Of A Continuous Flexible Structure Using The Theory Of Functional Connections, Riccardo Bevilacqua
Modeling And Estimation Of A Continuous Flexible Structure Using The Theory Of Functional Connections, Riccardo Bevilacqua
Math Department Colloquium Series
This talk presents a novel method for modeling and estimating the dynamics of a continuous structure based on a limited number of noisy measurements. The goal is reached using a Kalman filter in synergy with the recently developed mathematical framework known as the Theory of Functional Connections (TFC). The TFC allows to derive a functional expression capable of representing the entire space of the functions that satisfy a given set of linear and, in some cases, nonlinear constraints. The proposed approach exploits the possibilities offered by the TFC to derive an approximated dynamical model for the flexible system using the …
Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, Brennan S. Mccann
Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, Brennan S. Mccann
Doctoral Dissertations and Master's Theses
Rigid body motion requires formulations where rotational and translational motion are accounted for appropriately. Two Lie groups, the special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and attitude, the special Euclidean group SE(3) and the space of dual quaternions DH are frequently utilized. All these groups are Lie groups and Riemannian manifolds, and these identifications have profound implications for dynamics and controls. The trajectory optimization and optimal control problem on Riemannian manifolds presents significant opportunities for theoretical development. Riemannian optimization is an attractive …
Privacy-Preserving Federated Learning, Dumindu Samaraweera
Privacy-Preserving Federated Learning, Dumindu Samaraweera
Math Department Colloquium Series
AI's applicability across diverse fields is hindered by data sensitivity, privacy concerns, and limited training data availability. Federated Learning (FL) addresses this challenge by enabling collaborative machine learning while preserving data privacy. FL allows clients to engage in model training with their local data, avoiding centralized storage. However, even with FL, security threats persist, jeopardizing model integrity and client data privacy. In this presentation, we will explore our latest findings in this area of research, safeguarding sensitive data from attacks through techniques like secure multiparty computation, homomorphic encryption, and differential privacy within the FL framework, enhancing data protection, and expanding …
A Low-Complexity Algorithm To Determine Spacecraft Trajectories, Sirani Perera
A Low-Complexity Algorithm To Determine Spacecraft Trajectories, Sirani Perera
Math Department Colloquium Series
The growing traffic within the Cislunar region has created a need for computationally effective methods to obtain the trajectories of spacecraft in the Cislunar region. By developing algorithms with low time and arithmetic complexities, we can effectively address these needs.
In this talk, we will present a mathematical model that uses interpolation and boundary conditions to obtain trajectories for satellites based on the principles of three-body dynamics. Following the model, we propose a low- complexity algorithm to generate satellite trajectories. Once the algorithm is proposed, we will apply it to the relevant periodic orbits in the Cislunar region. Finally, we …
Response Of Planetary Waves And Tides To The 2019 Southern Hemisphere Ssw And Q2dw Enhancement In Jan-Feb 2020 Observed By Condor Meteor Radar In Chile And Adelaide Meteor Radar In Australia, Alan Liu, Zishun Qiao, Iain Reid, Javier Fuentes, Chris Adami
Response Of Planetary Waves And Tides To The 2019 Southern Hemisphere Ssw And Q2dw Enhancement In Jan-Feb 2020 Observed By Condor Meteor Radar In Chile And Adelaide Meteor Radar In Australia, Alan Liu, Zishun Qiao, Iain Reid, Javier Fuentes, Chris Adami
Publications
A new multi-static meteor radar (CONDOR) has recently been installed in northern Chile. This CONDOR meteor radar (30.3°S, 70.7°W) and the Adelaide meteor radar (35°S, 138°E) have provided longitudinally spaced observations of the mean winds, tides and planetary waves of the PW-tides interaction cases we present here. We have observed a Quasi-6-Day Wave (Q6DW) enhancement in MLT winds at the middle latitudes (30.3°S, 35°S) during the unusual minor South Hemisphere SSW 2019 by the ground-based meteor radars. Tidal analysis also indicates modulation of the Q6DW w/ amplitude ~15 [m/s] and diurnal tides w/ amplitude ~60 [m/s]. Another case we present …
Manufacturability And Analysis Of Topologically Optimized Continuous Fiber Reinforced Composites, Jesus A. Ferrand
Manufacturability And Analysis Of Topologically Optimized Continuous Fiber Reinforced Composites, Jesus A. Ferrand
Doctoral Dissertations and Master's Theses
Researchers are unlocking the potential of Continuous Fiber Reinforced Composites for producing components with greater strength-to-weight ratios than state of the art metal alloys and unidirectional composites. The key is the emerging technology of topology optimization and advances in additive manufacturing. Topology optimization can fine tune component geometry and fiber placement all while satisfying stress constraints. However, the technology cannot yet robustly guarantee manufacturability. For this reason, substantial post-processing of an optimized design consisting of manual fiber replacement and subsequent Finite Element Analysis (FEA) is still required.
To automate this post-processing in two dimensions, two (2) algorithms were developed. The …
A Data Driven Modeling Approach For Store Distributed Load And Trajectory Prediction, Nicholas Peters
A Data Driven Modeling Approach For Store Distributed Load And Trajectory Prediction, Nicholas Peters
Doctoral Dissertations and Master's Theses
The task of achieving successful store separation from aircraft and spacecraft has historically been and continues to be, a critical issue for the aerospace industry. Whether it be from store-on-store wake interactions, store-parent body interactions or free stream turbulence, a failed case of store separation poses a serious risk to aircraft operators. Cases of failed store separation do not simply imply missing an intended target, but also bring the risk of collision with, and destruction of, the parent body vehicle. Given this risk, numerous well-tested procedures have been developed to help analyze store separation within the safe confines of wind …
Computational Models To Detect Radiation In Urban Environments: An Application Of Signal Processing Techniques And Neural Networks To Radiation Data Analysis, Jose Nicolas Gachancipa
Computational Models To Detect Radiation In Urban Environments: An Application Of Signal Processing Techniques And Neural Networks To Radiation Data Analysis, Jose Nicolas Gachancipa
Beyond: Undergraduate Research Journal
Radioactive sources, such as uranium-235, are nuclides that emit ionizing radiation, and which can be used to build nuclear weapons. In public areas, the presence of a radioactive nuclide can present a risk to the population, and therefore, it is imperative that threats are identified by radiological search and response teams in a timely and effective manner. In urban environments, such as densely populated cities, radioactive sources may be more difficult to detect, since background radiation produced by surrounding objects and structures (e.g., buildings, cars) can hinder the effective detection of unnatural radioactive material. This article presents a computational model …
Statistical Characteristics Of High-Frequency Gravity Waves Observed By An Airglow Imager At Andes Lidar Observatory, Alan Z. Liu, Bing Cao
Statistical Characteristics Of High-Frequency Gravity Waves Observed By An Airglow Imager At Andes Lidar Observatory, Alan Z. Liu, Bing Cao
Publications
The long-term statistical characteristics of high-frequency quasi-monochromatic gravity waves are presented using multi-year airglow images observed at Andes Lidar Observatory (ALO, 30.3° S, 70.7° W) in northern Chile. The distribution of primary gravity wave parameters including horizontal wavelength, vertical wavelength, intrinsic wave speed, and intrinsic wave period are obtained and are in the ranges of 20–30 km, 15–25 km, 50–100 m s−1, and 5–10 min, respectively. The duration of persistent gravity wave events captured by the imager approximately follows an exponential distribution with an average duration of 7–9 min. The waves tend to propagate against the local background winds and …
Vertical Take-Off And Landing Control Via Dual-Quaternions And Sliding Mode, Joshua Sonderegger
Vertical Take-Off And Landing Control Via Dual-Quaternions And Sliding Mode, Joshua Sonderegger
Doctoral Dissertations and Master's Theses
The landing and reusability of space vehicles is one of the driving forces into renewed interest in space utilization. For missions to planetary surfaces, this soft landing has been most commonly accomplished with parachutes. However, in spite of their simplicity, they are susceptible to parachute drift. This parachute drift makes it very difficult to predict where the vehicle will land, especially in a dense and windy atmosphere such as Earth. Instead, recent focus has been put into developing a powered landing through gimbaled thrust. This gimbaled thrust output is dependent on robust path planning and controls algorithms. Being able to …
A Meshless Approach To Computational Pharmacokinetics, Anthony Matthew Khoury
A Meshless Approach To Computational Pharmacokinetics, Anthony Matthew Khoury
Doctoral Dissertations and Master's Theses
The meshless method is an incredibly powerful technique for solving a variety of problems with unparalleled accuracy and efficiency. The pharmacokinetic problem of transdermal drug delivery (TDDD) is one such topic and is of significant complexity. The locally collocated meshless method (LCMM) is developed in solution to this topic. First, the meshless method is formulated to model this transport phenomenon and is then validated against an analytical solution of a pharmacokinetic problem set, to demonstrate this accuracy and efficiency. The analytical solution provides a locus by which convergence behavior are evaluated, demonstrating the super convergence of the locally collocated meshless …
A Mathematical Analysis Of The Wind Triangle Problem And An Inquiry Of True Airspeed Calculations In Supersonic Flight, Leonard T. Huang, Lisa I. Cummings
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 …
Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski
Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski
Publications
The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples.
2n-Dimensional Canonical Systems And Applications, Andrei Ludu, Keshav Baj Acharya
2n-Dimensional Canonical Systems And Applications, Andrei Ludu, Keshav Baj Acharya
Publications
We study the 2N-dimensional canonical systems and discuss some properties of its fundamental solution. We then discuss the Floquet theory of periodic canonical systems and observe the asymptotic behavior of its solution. Some important physical applications of the systems are also discussed: linear stability of periodic Hamiltonian systems, position-dependent effective mass, pseudo-periodic nonlinear water waves, and Dirac systems.
Studies Of Oval Tube And Fin Heat Exchangers, Phillip Nielsen
Studies Of Oval Tube And Fin Heat Exchangers, Phillip Nielsen
Discovery Day - Prescott
Heating Ventilation and air-conditioning (HVAC) is a system which changes the temperature of the surroundings for the purposes of cooling or heating. This system requires energy to maintain a temperature difference from the outside temperature. This is important since minimized power is one of the requirements for the system to achieve a better efficiency. Optimizing the flow over the evaporator coils is one way to increase the cooling efficiency. This will reduce the power required to have a sustainable system. Optimizing the flow to increase the energy transfer between the fins and the incoming air could result in a greater …
Meshless Modeling Of Flow Dispersion And Progressive Piping In Poroelastic Levees, Anthony Khoury, Eduardo Divo, Alain J. Kassab, Sai Kakuturu, Lakshmi Reddi
Meshless Modeling Of Flow Dispersion And Progressive Piping In Poroelastic Levees, Anthony Khoury, Eduardo Divo, Alain J. Kassab, Sai Kakuturu, Lakshmi Reddi
Publications
Performance data on earth dams and levees continue to indicate that piping is one of the major causes of failure. Current criteria for prevention of piping in earth dams and levees have remained largely empirical. This paper aims at developing a mechanistic understanding of the conditions necessary to prevent piping and to enhance the likelihood of self-healing of cracks in levees subjected to hydrodynamic loading from astronomical and meteorological (including hurricane storm surge-induced) forces. Systematic experimental investigations are performed to evaluate erosion in finite-length cracks as a result of transient hydrodynamic loading. Here, a novel application of the localized collocation …
Nonlocal Symmetries For Time-Dependent Order Differential Equations, Andrei Ludu
Nonlocal Symmetries For Time-Dependent Order Differential Equations, Andrei Ludu
Publications
A new type of ordinary differential equation is introduced and discussed: time-dependent order ordinary differential equations. These equations are solved via fractional calculus by transforming them into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equation represent deformations of the solutions of the classical (integer order) differential equations, mapping them into one-another as limiting cases. This equation can also move, remove or generate singularities without involving variable coefficients. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers is observed.
Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, V. Adamek
Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, V. Adamek
Publications
In the paper, the finite element method and the finite volume method are used in parallel for the simulation of a pulse propagation in periodically layered composites beyond the validity of homogenization methods. The direct numerical integration of a pulse propagation demonstrates dispersion effects and dynamic stress redistribution in physical space on example of a one-dimensional layered bar. Results of numerical simulations are compared with analytical solution constructed specifically for the considered problem. Analytical solution as well as numerical computations show the strong influence of the composition of constituents on the dispersion of a pulse in a heterogeneous bar and …
Patient-Specific Multiscale Computational Fluid Dynamics Assessment Of Embolization Rates In The Hybrid Norwood: Effects Of Size And Placement Of The Reverse Blalock–Taussig Shunt, Ray Prather, John Seligson, Marcus Ni, Eduardo Divo, Alain J. Kassab, William Decampli
Patient-Specific Multiscale Computational Fluid Dynamics Assessment Of Embolization Rates In The Hybrid Norwood: Effects Of Size And Placement Of The Reverse Blalock–Taussig Shunt, Ray Prather, John Seligson, Marcus Ni, Eduardo Divo, Alain J. Kassab, William Decampli
Publications
The hybrid Norwood operation is performed to treat hypoplastic left heart syndrome. Distal arch obstruction may compromise flow to the brain. In a variant of this procedure, a synthetic graft (reverse Blalock–Taussig shunt) is placed between the pulmonary trunk and innominate artery to improve upper torso blood flow. Thrombi originating in the graft may embolize to the brain. In this study, we used computational fluid dynamics and particle tracking to investigate the patterns of particle embolization as a function of the anatomic position of the reverse Blalock–Taussig shunt. The degree of distal arch obstruction and position of particle origin influence …
Godunov-Type Upwind Flux Schemes Of The Two-Dimensional Finite Volume Discrete Boltzmann Method, Leitao Chen, Laura Schaefer
Godunov-Type Upwind Flux Schemes Of The Two-Dimensional Finite Volume Discrete Boltzmann Method, Leitao Chen, Laura Schaefer
Publications
A simple unified Godunov-type upwind approach that does not need Riemann solvers for the flux calculation is developed for the finite volume discrete Boltzmann method (FVDBM) on an unstructured cell-centered triangular mesh. With piecewise-constant (PC), piecewise-linear (PL) and piecewise-parabolic (PP) reconstructions, three Godunov-type upwind flux schemes with different orders of accuracy are subsequently derived. After developing both a semi-implicit time marching scheme tailored for the developed flux schemes, and a versatile boundary treatment that is compatible with all of the flux schemes presented in this paper, numerical tests are conducted on spatial accuracy for several single-phase flow problems. Four major …
Stability Of Solitary And Cnoidal Traveling Wave Solutions For A Fifth Order Korteweg-De Vries Equation, Ronald Adams, S.C. Mancas
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.
Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski
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 …
Differential Equations Of Dynamical Order, Andrei Ludu, Harihar Khanal
Differential Equations Of Dynamical Order, Andrei Ludu, Harihar Khanal
Publications
No abstract provided.
A Regression Model To Predict Stock Market Mega Movements And/Or Volatility Using Both Macroeconomic Indicators & Fed Bank Variables, Timothy A. Smith, Alcuin Rajan
A Regression Model To Predict Stock Market Mega Movements And/Or Volatility Using Both Macroeconomic Indicators & Fed Bank Variables, Timothy A. Smith, Alcuin Rajan
Publications
In finance, regression models or time series moving averages can be used to determine the value of an asset based on its underlying traits. In prior work we built a regression model to predict the value of the S&P 500 based on macroeconomic indicators such as gross domestic product, money supply, produce price and consumer price indices. In this present work this model is updated both with more data and an adjustment in the input variables to improve the coefficient of determination. A scheme is also laid out to alternately define volatility rather than using common tools such as the …
Traveling Wave Solutions To Kawahara And Related Equations, S.C. Mancas
Traveling Wave Solutions To Kawahara And Related Equations, S.C. Mancas
Publications
Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the tanh-method. The method works by assuming that a polynomial ansatz satisfies a Weierstrass equation, and has two advantages: first, it reduces the number of terms in the ansatz by an order of two, and second, it uses Weierstrass functions which satisfy an elliptic equation for the dependent variable instead of the hyperbolic tangent functions which only satisfy the Riccati equation with constant coefficients. When the polynomial ansatz in the traveling wave …
Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, S.C. Mancas
Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, S.C. Mancas
Publications
A one-parameter family of Emden-Fowler equations defined by Lampariello’s parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.
A Coupled Localized Rbf Meshless/Drbem Formulation For Accurate Modeling Of Incompressible Fluid Flows, Leonardo Bueno, Eduardo Divo, Alain J. Kassab
A Coupled Localized Rbf Meshless/Drbem Formulation For Accurate Modeling Of Incompressible Fluid Flows, Leonardo Bueno, Eduardo Divo, Alain J. Kassab
Publications
Velocity-pressure coupling schemes for the solution of incompressible fluid flow problems in Computational Fluid Dynamics (CFD) rely on the formulation of Poisson-like equations through projection methods. The solution of these Poisson-like equations represent the pressure correction and the velocity correction to ensure proper satisfaction of the conservation of mass equation at each step of a time-marching scheme or at each level of an iteration process. Inaccurate solutions of these Poisson-like equations result in meaningless instantaneous or intermediate approximations that do not represent the proper time-accurate behavior of the flow. The fact that these equations must be solved to convergence at …
An Rbf Interpolation Blending Scheme For Effective Shock-Capturing, M. Harris, Eduardo Divo, Alain J. Kassab
An Rbf Interpolation Blending Scheme For Effective Shock-Capturing, M. Harris, Eduardo Divo, Alain J. Kassab
Publications
In recent years significant focus has been given to the study of Radial basis functions (RBF), especially in their use on solving partial differential equations (PDE). RBF have an impressive capability of inter- polating scattered data, even when this data presents localized discontinuities. However, for infinitely smooth RBF such as the Multiquadrics, inverse Multiquadrics, and Gaussian, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary significantly depending on the field, particularly in locations of steep gradients, shocks, or discontinuities. Typically, the shape parameter is chosen …