Mathematics Commons^™

Multiple Imputation For Robust Cluster Analysis To Address Missingness In Medical Data, Arnold Harder, Gayla R. Olbricht, Godwin Ekuma, Daniel B. Hier, Tayo Obafemi-Ajayi

Mathematics and Statistics Faculty Research & Creative Works

Cluster Analysis Has Been Applied To A Wide Range Of Problems As An Exploratory Tool To Enhance Knowledge Discovery. Clustering Aids Disease Subtyping, I.e. Identifying Homogeneous Patient Subgroups, In Medical Data. Missing Data Is A Common Problem In Medical Research And Could Bias Clustering Results If Not Properly Handled. Yet, Multiple Imputation Has Been Under-Utilized To Address Missingness, When Clustering Medical Data. Its Limited Integration In Clustering Of Medical Data, Despite The Known Advantages And Benefits Of Multiple Imputation, Could Be Attributed To Many Factors. This Includes Methodological Complexity, Difficulties In Pooling Results To Obtain A Consensus Clustering, Uncertainty Regarding …

Kinetic Particle Simulations Of Plasma Charging At Lunar Craters Under Severe Conditions, David Lund, Xiaoming He, Daoru Frank Han

Mathematics and Statistics Faculty Research & Creative Works

This paper presents fully kinetic particle simulations of plasma charging at lunar craters with the presence of lunar lander modules using the recently developed Parallel Immersed-Finite-Element Particle-in-Cell (PIFE-PIC) code. The computation model explicitly includes the lunar regolith layer on top of the lunar bedrock, taking into account the regolith layer thickness and permittivity as well as the lunar lander module in the simulation domain, resolving a nontrivial surface terrain or lunar lander configuration. Simulations were carried out to study the lunar surface and lunar lander module charging near craters at the lunar terminator region under mean and severe plasma environments. …

Fabrications And Applications Of Micro/Nanofluidics In Oil And Gas Recovery: A Comprehensive Review, Junchen Liu, Yandong Zhang, Mingzhen Wei, Xiaoming He, Baojun Bai

Geosciences and Geological and Petroleum Engineering Faculty Research & Creative Works

Understanding fluid flow characteristics in porous medium, which determines the development of oil and gas oilfields, has been a significant research subject for decades. Although using core samples is still essential, micro/nanofluidics have been attracting increasing attention in oil recovery fields since it offers direct visualization and quantification of fluid flow at the pore level. This work provides the latest techniques and development history of micro/nanofluidics in oil and gas recovery by summarizing and discussing the fabrication methods, materials and corresponding applications. Compared with other reviews of micro/nanofluidics, this comprehensive review is in the perspective of solving specific issues in …

Error Estimate Of A Decoupled Numerical Scheme For The Cahn-Hilliard-Stokes-Darcy System, Wenbin Chen, Shufen Wang, Yichao Zhang, Daozhi Han, Cheng Wang, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We analyze a fully discrete finite element numerical scheme for the Cahn-Hilliard-Stokes-Darcy system that models two-phase flows in coupled free flow and porous media. To avoid a well-known difficulty associated with the coupling between the Cahn-Hilliard equation and the fluid motion, we make use of the operator-splitting in the numerical scheme, so that these two solvers are decoupled, which in turn would greatly improve the computational efficiency. The unique solvability and the energy stability have been proved in Chen et al. (2017, Uniquely solvable and energy stable decoupled numerical schemes for the Cahn-Hilliard-Stokes-Darcy system for two-phase flows in karstic geometry. …

Maintenance Optimization In A Digital Twin For Industry 4.0, Abhijit Gosavi, Vy Khoi Le

Engineering Management and Systems Engineering Faculty Research & Creative Works

The advent of Internet of Things and artificial intelligence in the era of Industry 4.0 has transformed decision-making within production systems. In particular, many decisions that previously required significant human activity are now made automatically with minimal human intervention via so-called digital twins (DTs). In the context of maintenance and reliability modeling, this naturally calls for new paradigms that can be seamlessly integrated within DTs for decision-making. The input data for time to failure needed in reliability computations are directly collected from the work center in a digital setting and often do not satisfy a known distribution. A neural network …

Three-Dimensional Rotation Of Paramagnetic And Ferromagnetic Prolate Spheroids In Simple Shear And Uniform Magnetic Field, Christopher A. Sobecki, Yanzhi Zhang, Cheng Wang

Mathematics and Statistics Faculty Research & Creative Works

We examine a time-dependent, three-dimensional rotation of magnetic ellipsoidal particles in a two-dimensional, simple shear flow and a uniform magnetic field. We consider that the particles have paramagnetic and ferromagnetic properties, and we compare their rotational dynamics due to the strengths and directions of the applied uniform magnetic field. We determine the critical magnetic field strength that can pin the particles' rotations. Above the critical field strength, the particles' stable steady angles were determined. In a weak magnetic regime (below the critical field strength), a paramagnetic particle's polar angle will oscillate toward the magnetic field plane while its azimuthal angle …

A Framework Of Integrating Manufacturing Plants In Smart Grid Operation: Manufacturing Flexible Load Identification, Md. Monirul Islam, Zeyi Sun, Wenqing Hu, Cihan H. Dagli

Engineering Management and Systems Engineering Faculty Research & Creative Works

In the deregulated electricity markets run by Independent System Operator (ISO), a two-settlement (day-ahead and real-time) process is typically used to determine the electricity price to the end-use customers at different buses. In the day-ahead settlement, the demand is predicted at each bus based on the previous consumption behavior of the consumers and thus, Locational Marginal Price (LMP) can be determined and shared to the consumers. A significant gap is usually observed between the planned and real-time demands due to the uncertainties of the weather (temperature, wind-speed etc.), the intensity of business, and everyday activities. Therefore, a large price variation …

Joint Manufacturing And Onsite Microgrid System Control Using Markov Decision Process And Neural Network Integrated Reinforcement Learning, Wenqing Hu, Zeyi Sun, Y. Zhang, Y. Li

Mathematics and Statistics Faculty Research & Creative Works

Onsite microgrid generation systems with renewable sources are considered a promising complementary energy supply system for manufacturing plant, especially when outage occurs during which the energy supplied from the grid is not available. Compared to the widely recognized benefits in terms of the resilience improvement when it is used as a backup energy system, the operation along with the electricity grid to support the manufacturing operations in non-emergent mode has been less investigated. In this paper, we propose a joint dynamic decision-making model for the optimal control for both manufacturing system and onsite generation system. Markov Decision Process (MDP) is …

Pressure Versus Impulse Graph For Blast-Induced Traumatic Brain Injury And Correlation To Observable Blast Injuries, Barbara Rutter

Doctoral Dissertations

"With the increased use of explosive devices in combat, blast induced traumatic brain injury (bTBI) has become one of the signature wounds in current conflicts. Animal studies have been conducted to understand the mechanisms in the brain and a pressure versus time graph has been produced. However, the role of impulse in bTBIs has not been thoroughly investigated for animals or human beings.

This research proposes a new method of presenting bTBI data by using a pressure versus impulse (P-I) graph. P-I graphs have been found useful in presenting lung lethality regions and building damage thresholds. To present the animal …

A Multi-Step Nonlinear Dimension-Reduction Approach With Applications To Bigdata, R. Krishnan, V. A. Samaranayake, Jagannathan Sarangapani

Mathematics and Statistics Faculty Research & Creative Works

In this paper, a multi-step dimension-reduction approach is proposed for addressing nonlinear relationships within attributes. In this work, the attributes in the data are first organized into groups. In each group, the dimensions are reduced via a parametric mapping that takes into account nonlinear relationships. Mapping parameters are estimated using a low rank singular value decomposition (SVD) of distance covariance. Subsequently, the attributes are reorganized into groups based on the magnitude of their respective singular values. The group-wise organization and the subsequent reduction process is performed for multiple steps until a singular value-based user-defined criterion is satisfied. Simulation analysis is …

Direct Error Driven Learning For Deep Neural Networks With Applications To Bigdata, R. Krishnan, Jagannathan Sarangapani, V. A. Samaranayake

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, generalization error for traditional learning regimes-based classification is demonstrated to increase in the presence of bigdata challenges such as noise and heterogeneity. To reduce this error while mitigating vanishing gradients, a deep neural network (NN)-based framework with a direct error-driven learning scheme is proposed. To reduce the impact of heterogeneity, an overall cost comprised of the learning error and approximate generalization error is defined where two NNs are utilized to estimate the costs respectively. To mitigate the issue of vanishing gradients, a direct error-driven learning regime is proposed where the error is directly utilized for learning. It …

Phytoforensics: Trees As Bioindicators Of Potential Indoor Exposure Via Vapor Intrusion, Jordan L. Wilson, V. A. Samaranayake, Matt A. Limmer, Joel Gerard Burken

Mathematics and Statistics Faculty Research & Creative Works

Human exposure to volatile organic compounds (VOCs) via vapor intrusion (VI) is an emerging public health concern with notable detrimental impacts on public health. Phytoforensics, plant sampling to semi-quantitatively delineate subsurface contamination, provides a potential non-invasive screening approach to detect VI potential, and plant sampling is effective and also time- and cost-efficient. Existing VI assessment methods are time- and resource-intensive, invasive, and require access into residential and commercial buildings to drill holes through basement slabs to install sampling ports or require substantial equipment to install groundwater or soil vapor sampling outside the home. Tree-core samples collected in 2 days at …

Numerical Modeling Of Capillary-Driven Flow In Open Microchannels: An Implication Of Optimized Wicking Fabric Design, Mehrad Gholizadeh Ansari

Masters Theses

"The use of microfluidics to transfer fluids without applying any exterior energy source is a promising technology in different fields of science and engineering due to their compactness, simplicity and cost-effective design. In geotechnical engineering, to increase the soil's strength, hydrophilic wicking fibers as type of microfluidics have been employed to transport and drain water out of soil spontaneously by taking advantage of natural capillary force without using any pumps or other auxiliary devices. The objective of this study is to understand the scientific mechanisms of the capability for wicking fiber to drain both gravity and capillary water out of …

Magnetic Control Of Lateral Migration Of Ellipsoidal Microparticles In Microscale Flows, R. Zhou, C. A. Sobecki, J. Zhang, Yanzhi Zhang, Cheng Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Programming Problems On Time Scales: Theory And Computation, Rasheed Basheer Al-Salih

Doctoral Dissertations

"In this dissertation, novel formulations for several classes of programming problems are derived and proved using the time scales technique. The new formulations unify the discrete and continuous programming models and extend them to other cases "in between." Moreover, the new formulations yield the exact optimal solution for the programming problems on arbitrary isolated time scales, which solve an important open problem. Throughout this dissertation, six distinct classes of programming problems are presented as follows. First, the primal as well as the dual time scales linear programming models on arbitrary time scales are formulated. Second, separated linear programming primal and …

A Linear Matrix Inequality-Based Approach For The Computation Of Actuator Bandwidth Limits In Adaptive Control, Daniel Robert Wagner

Masters Theses

"Linear matrix inequalities and convex optimization techniques have become popular tools to solve nontrivial problems in the field of adaptive control. Specifically, the stability of adaptive control laws in the presence of actuator dynamics remains as an important open control problem. In this thesis, we present a linear matrix inequalities-based hedging approach and evaluate it for model reference adaptive control of an uncertain dynamical system in the presence of actuator dynamics. The ideal reference dynamics are modified such that the hedging approach allows the correct adaptation without being hindered by the presence of actuator dynamics. The hedging approach is first …

Boundary Control Of Parabolic Pde Using Adaptive Dynamic Programming, Behzad Talaei

Doctoral Dissertations

"In this dissertation, novel adaptive/approximate dynamic programming (ADP) based state and output feedback control methods are presented for distributed parameter systems (DPS) which are expressed as uncertain parabolic partial differential equations (PDEs) in one and two dimensional domains. In the first step, the output feedback control design using an early lumping method is introduced after model reduction. Subsequently controllers were developed in four stages; Unlike current approaches in the literature, state and output feedback approaches were designed without utilizing model reduction for uncertain linear, coupled nonlinear and two-dimensional parabolic PDEs, respectively. In all of these techniques, the infinite horizon cost …

Generation And Validation Of Optimal Topologies For Solid Freeform Fabrication, Purnajyoti Bhaumik

Masters Theses

"The study of fabricating topologically optimized parts is presented hereafter. The mapping of topology optimization results for Standard Tessellation Language (STL) writing would enable the solid freeform fabrication of lightweight mechanisms. Aerospace leaders such as NASA, Boeing, Airbus, European Aeronautic Defense And Space Company (EADS), and GE Aero invest in topology optimization research for the production of lightweight materials. Certain concepts such as microstructural homogenization, discretization, and mapping are reviewed and presented in the context of topology optimization. Future biomedical applications of solid freeform fabrication such as organ printing stand to save millions of lives through the robust development of …

Decoupling The Stationary Navier-Stokes-Darcy System With The Beavers-Joseph-Saffman Interface Condition, Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

Effective Use Of Process Capability Indices For Supplier Management, Elizabeth A. Cudney, David Drain

Engineering Management and Systems Engineering Faculty Research & Creative Works

Process capability indices were originally invented to enable an organization to make economically sound decisions for process management. Process capability is a comparison of the voice of the process with the voice of the customer. Current practice is to use Cp and Cpk regardless of the validity of the underlying assumptions necessary for their use. Even if all necessary assumptions are satisfied, important problems can be missed if these indices are the sole process evaluation examined. Customer-supplier axioms are introduced to motivate more useful process evaluations and foster long-term harmonious relationships. This paper explores the alternative capability indices Cpm, Cpmk, …

2nd Annual Undergraduate Research Conference Abstract Book, University Of Missouri--Rolla

Undergraduate Research Conference at Missouri S&T

No abstract provided.

Multiple Lebesgue Integration On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.

Statistical Analysis Of A Compound Power-Law Model For Repairable Systems, Max Engelhardt, Lee J. Bain

Geosciences and Geological and Petroleum Engineering Faculty Research & Creative Works

Conclusions - A compound (mixed) Poisson distribution is sometimes used as an alternative to the Poisson distribution for count data. Such a compound distribution, which has a negative binomial form, occurs when the population consists of Poisson distributed individuals, but with intensities which have a gamma distribution. A similar situation can occur with a repairable system when failure intensities of each system are different. A more general situation is considered where the system failures are distributed according to nonhomogeneous Poisson processes having Power Law intensity functions with gamma distributed intensity parameter. If the failures of each system in a population …

On The Mean Time Between Failures For Repairable Systems, Max Engelhardt, Lee J. Bain

Geosciences and Geological and Petroleum Engineering Faculty Research & Creative Works

Much of the recent work on modeling repairable systems involves Poisson processes with nonconstant intensity functions, viz, nonhomogeneous Poisson processes. Since times between failures are not identically distributed when the process is nonhomogeneous, it is not clear what concept should take the place of the mean time between failures in assessing the reliability of a repairable system. A number of alternate concepts can be found in the literature. We investigate the relationship between two of the most frequently considered alternatives: the reciprocal of the intensity function, and the mean waiting time from t until the next failure. Theorem 1 states …

Approximate Tolerance Limits And Confidence Limits On Reliability For The Gamma Distribution, Lee J. Bain, Max Engelhardt, Wei Kei Shiue

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Sequential Probability Ratio Tests For The Shape Parameter Of A Nonhomogeneous Poisson Process, Lee J. Bain, Max Engelhardt

Mathematics and Statistics Faculty Research & Creative Works

Sequential probability ratio tests for the shape parameter of one or more nonhomogeneous Poisson processes, with power intensity functions, are provided. The tests can be performed when the scale parameter is an unknown nuisance parameter; the effective loss of not knowing the scale parameter is one observation per process. The resulting tests can be expressed in terms of the maximum likelihood estimators of the shape parameters for the usual fixed sample procedure. A further advantage of the present approach is that the scale parameters for different processes, in the multiple sample procedures, need not be equal. Approximations for the operating …

Handlos And Baron Model: Short Contact Times, J. Patel, Robert M. Wellek

Chemical and Biochemical Engineering Faculty Research & Creative Works

No abstract provided.