Physical Sciences and Mathematics Commons^™

Post-Pareto Optimality Methods For The Analysis Of Large Pareto Sets In Multi-Objective Optimization, Victor Manuel Carrillo

Open Access Theses & Dissertations

Multiple objective optimization involves the simultaneous optimization of more than one, possibly conflicting, objectives. Multiple objective optimization problems arise in a variety of real-world applications. In general, the main difference between single and multi-objective optimization is that in multi-objective optimization there is usually no single optimal solution, but a set of equally good alternatives with different trade-offs, also known as Pareto-optimal solutions. There are two general approaches to solve multiple objective optimization problems: mathematical methods and meta-heuristic methods. The first approach involves the aggregation of the attributes into a linear combination of the objective functions, also known as scalarization. The …

Functional Data Analysis To Guide A Conditional Likelihood Regression In A Case-Crossover Study Investigating Whether Social Characteristics Modify The Health Effects Of Air Pollution, Juana Maribel Herrera Hernandez

Open Access Theses & Dissertations

In this study we are focused on exploring whether social characteristics modify the relationship between air pollution and hospitalizations due to asthma or chronic pulmonary obstructive disease (COPD) in El Paso, Tx. The case-crossover design with conditional regression analysis was used, here the controls and the case are the same subject at different

times and has the advantage of removing confounding by permanently confounding factors. Social characteristics are included in the models as interactions with the pollutants, variables included are age, sex, ethnicity and insurance status as indicator for the socio-economic status. The pollutant's lags were chosen using the historical …

Reduced-Order Modeling Using Orthogonal And Bi-Orthogonal Wavelet Transforms, Miguel Hernandez Iv

Open Access Theses & Dissertations

It is well known that model reduction methods borrow techniques typically found in data compression, and current state-of-the-art techniques for data compression are based on the wavelet transform. Given these facts, it is surprising that model reduction using wavelets has not received much attention and has not been adequately addressed in the literature. This research seeks to determine if wavelets can be used for model reduction and if wavelet model reduction is a viable alternative to existing model reduction methods.

In this work we propose a novel method for model reduction using wavelets. Specifically, we introduce techniques for deriving wavelet …

Automatic Elucidation Of Gpi Molecular Structures With Grid Computing Technology, Juan Clemente Aguilar Bonavides

Open Access Theses & Dissertations

Glycosylphosphatidylinositol (GPI)-anchored proteins are involved in many biological processes and are of medical importance. The identification and analysis of the entire collection of free and protein-linked GPIs within an organism (i.e., GPIomics) requires highly sensitive instruments. At present, liquid chromatography-tandem mass spectrometry (LC-MS/MS or -MSⁿ) is the most efficient laboratory technique for these tasks. As a typical MSⁿ experiment produces hundreds of thousands of spectra, the data analysis creates a major bottleneck in high-throughput GPIomic projects. Yet, no computational tool for characterizing the chemical structures of GPI is available to date. We propose a library-search algorithm to …

Modeling The Human Gait Phases Using Granular Computing, Melaku Ayenew Bogale

Open Access Theses & Dissertations

Gait analysis is applied for the provision of diagnosis, evaluation, and for the design of therapeutic intervention for subjects suffering from neurological disorders. The benefits accruing from gait analysis are well established. People with neurological disorders like mild traumatic brain injury, Cerebral Palsy and Multiple Sclerosis, suffer associated functional gait problems. The symptoms and sign of these gait deficits are different from subject to subject and even for the same subject at different stage of the disease. Identifying these gait related abnormalities helps in the treatment planning and rehabilitation process.

The dynamic behavior of gait parameters is cyclic and the …

A Block Operator Splitting Method For Heterogeneous Multiscale Poroelasticity, Paul M. Delgado

Open Access Theses & Dissertations

Traditional models of poroelastic deformation in porous media assume relatively homogeneous material properties such that macroscopic constitutive relations lead to accurate results. Many realistic applications involve heterogeneous material properties whose oscillatory nature require multiscale methods to balance accuracy and efficiency in computation.

The current study develops a multiscale method for poroelastic deformation based on a fixed point iteration based operator splitting method and a heterogeneous multiscale method using finite volume and direct stiffness methods. To characterize the convergence

of the operator splitting method, we use a numerical root finding algorithm to determine a threshold surface in a non-dimensional parameter space …

Constrained Optimal Control For A Multi-Group Discrete Time Influenza Model, Paula Andrea Gonzalez Parra

Open Access Theses & Dissertations

During the last decades, mathematical epidemiological models have been used to understand the dynamics of infectious diseases and guide public health policy. In particular, several continuous models have been considered to study single in uenza outbreaks and the impact of dierent control policies. In this dissertation, a discrete time model is introduced in order to study optimal control strategies for in uenza transmission; since epidemiological data is collected on discrete units of time, a discrete formulation is more ecient. From a mathematical point of view, continuous time model are easier to analyze, however, the numerical solution of discrete-time models is …

Granular Computing For Assessment Of Mild Traumatic Brain Injury, Melaku Ayenew Bogale

Open Access Theses & Dissertations

Mild traumatic brain injury (mTBI) is one of the most common neurological disorders. It is a serious public health problem in the United States. Although, penetrating (open) brain injuries that result in extended period of loss of consciousness (LOC) usually gets attention and well taken care of by the emergency departments, mild traumatic brain injury with no visible sign of damage, may be undetected or misdiagnosed. The clinical assessments and evaluations are mostly based on subjective cognitive and behavioral tests. Many people after suffering mTBI complain about decreased balance, coordination and stability even though the clinical evaluations show no sign …

Constrained Optimization Schemes For Geophysical Inversion Of Seismic Data, Uram Anibal Sosa Aguirre

Open Access Theses & Dissertations

Many experimental techniques in geophysics advance the understanding of Earth processes by estimating and interpreting Earth structure (e.g., velocity and/or density structure). These techniques use dierent types of geophysical data which can be collected and analyzed separately, sometimes resulting in inconsistent models of the Earth depending on data quality, methods and assumptions made. This dissertation presents two approaches for geophysical inversion of seismic data based on constrained optimization. In one approach we expand a one dimensional (1-D) joint inversion least-squares (LSQ) algorithm by introducing a constrained optimization methodology. Then we use the 1-D inversion results to produce 3-D Earth velocity …

Development Of New Mathematical Methods For Post-Pareto Optimality, Victor Manuel Carrillo

Open Access Theses & Dissertations

Many real-world applications of multi-objective optimization involve a large number of objectives. A multi-objective optimization task involving multiple conflicting objectives ideally demands finding a multi-dimensional Pareto-optimal front. Although the classical methods have dealt with finding one preferred solution with the help of a decision-maker, evolutionary multi-objective optimization (EMO) methods have been attempted to find a representative set of solutions in the Pareto-optimal front. Multiple objective evolutionary algorithms (MOEAs), which are biologically-inspired optimization methods, have become popular approaches to solve problems with multiple objective functions. With the use of MOEAs, multiple objective optimization becomes a two-part problem. First, the multiple objective …

Analytical And Numerical Solution To The Partial Differential Equation Arising In Financial Modeling, Pavel Bezdek

Open Access Theses & Dissertations

In this work we will present a self-contained introduction to the option pricing problem. We will introduce some basic ideas from the probability theory and stochastic differential equations. Later we will move to the partial differential equations since the option pricing problem arising in financial mathematics when asset is driven by a stochastic volatility process and assumed presence of transaction cost leads to solving non-linear partial dif- ferential equation. We will also present the complete process from deriving the desired partial differential equation to the proof of existence of a solution and also the numerical simulations. Using techniques form stochastic …

Software Development For A Three-Dimensional Gravity Inversion And Application To Study Of The Border Ranges Fault System, South-Central Alaska, Rolando Cardenas

Open Access Theses & Dissertations

The Border Ranges Fault System (BRFS) bounds the Cook Inlet and Susitna Basins, an important petroleum province within south-central Alaska. A primary goal in the research is to test several plausible models of structure along the Border Ranges Fault System using a novel three-dimensional inversion utilizing gravity and magnetic data, constrained with other geophysical, borehole and surface geological information. This research involves the development of inversion modeling software using a Borland C++ compiler as part of the Rapid Application Development (RAD) Studio. The novel inversion approach directly models known geology, and "a priori" uncertainties on the geologic model to allow …

Solving The Partial Differential Equation Of Vibrations With Interval Parameters Using The Interval Finite Difference Method, Brenda G. Medina

Open Access Theses & Dissertations

Accuracy and efficiency are among the main factors that drive today's innovative disciplines. As technology rapidly advances, efficiency takes on new meanings but what about accuracy? How accurate is accurate? Human error, uncertainties in measurement, and rounding errors are just some causes of inaccuracy. Interval Computations is an area that allows for such issues to be taken into account; for each measurement attained (for example), an interval can be built by considering the error associated with the measurement, and such an interval can be utilized in the mathematical computations of interest.

We consider the partial differential equation (PDE) of vibrations …

Digital Image Processing Based On Sparse Representation And Convex Programming, Carlos Andres Ramirez

Open Access Theses & Dissertations

Sparse representation models have been of central interest in recent years due to important achievements in computational harmonic analysis, such as wavelet transformations, and the most recent sampling theory, compressed sensing. Numerous applications based on sparse models have been studied in the last decade leading to promising results. These applications include areas in seismology, image processing, wireless sensor networks, computed tomography and magnetic resonance imaging just to mention a few.

In this work, we propose to extend such applications in the area of image processing, particularly for the image segmentation problem, and examine algorithms involved in sparse modeling from both …

A Sparse Representation Technique For Classification Problems, Reinaldo Sanchez Arias

Open Access Theses & Dissertations

In pattern recognition and machine learning, a classification problem refers to finding an algorithm for assigning a given input data into one of several categories. Many natural signals are sparse or compressible in the sense that they have short representations when expressed in a suitable basis. Motivated by the recent successful development of algorithms for sparse signal recovery, we apply the selective nature of sparse representation to perform classification. In order to find such sparse linear representation, we implement an l₁-minimization algorithm. This methodology overcomes the lack of robustness with respect to outliers. In contrast to other classification …

On Constrained Optimization Schemes For Joint Inversion Of Geophysical Datasets, Uram Anibal Sosa Aguirre

Open Access Theses & Dissertations

In the area of geological sciences, there exist several experimental techniques used to advance in the understanding of the Earth. We implement a joint inversion least-squares (LSQ) algorithm to characterize one dimensional Earth's structure by using seismic shear wave velocities as a model parameter. We use two geophysical datasets sensitive to shear velocities, namely Receiver Function and Surface Wave dispersion velocity observations, with a choice of an optimization method: Truncated Singular Value Decomposition (TSVD) or Primal-Dual Interior-Point (PDIP). The TSVD and the PDIP methods solve a regularized unconstrained and a constrained minimization problem, respectively. Both techniques include bounds into the …

Multi-Objective Network Reliability Optimization Using Evolutionary Algorithms, Franciso Oswaldo Aguirre

Open Access Theses & Dissertations

This work presents a new multiple objective evolutionary algorithm to solve three well known network reliability allocation problems considering different conflicting objectives to be optimized simultaneously. The new algorithm is applied in the design of a telecommunication network that is formed for several stations or nodes interconnected by telecommunication links or paths. The problem presented in this work involves finding which links to activate in order to obtain connectivity in the nodes. The number of nodes that need to be connected depends of the case that is being evaluated. The three network reliability problems considered are: all-terminal, k-terminal, and two-terminal. …