Matching Items (11)

132421-Thumbnail Image.png

Predicting Mechanical Failure of Vacuum Pumps Using Accelerometer Data

Description

The objective of this paper is to find and describe trends in the fast Fourier transformed accelerometer data that can be used to predict the mechanical failure of large vacuum pumps used in industrial settings, such as providing drinking water.

The objective of this paper is to find and describe trends in the fast Fourier transformed accelerometer data that can be used to predict the mechanical failure of large vacuum pumps used in industrial settings, such as providing drinking water. Using three-dimensional plots of the data, this paper suggests how a model can be developed to predict the mechanical failure of vacuum pumps.

Contributors

Agent

Created

Date Created
2019-05

162238-Thumbnail Image.png

Network Based Models of Opinion Formation: Consensus and Beyond

Description

Understanding the evolution of opinions is a delicate task as the dynamics of how one changes their opinion based on their interactions with others are unclear.

Contributors

Agent

Created

Date Created
2021

157026-Thumbnail Image.png

Bootstrapped information-theoretic model selection with error control (BITSEC)

Description

Statistical model selection using the Akaike Information Criterion (AIC) and similar criteria is a useful tool for comparing multiple and non-nested models without the specification of a null model, which has made it increasingly popular in the natural and social

Statistical model selection using the Akaike Information Criterion (AIC) and similar criteria is a useful tool for comparing multiple and non-nested models without the specification of a null model, which has made it increasingly popular in the natural and social sciences. De- spite their common usage, model selection methods are not driven by a notion of statistical confidence, so their results entail an unknown de- gree of uncertainty. This paper introduces a general framework which extends notions of Type-I and Type-II error to model selection. A theo- retical method for controlling Type-I error using Difference of Goodness of Fit (DGOF) distributions is given, along with a bootstrap approach that approximates the procedure. Results are presented for simulated experiments using normal distributions, random walk models, nested linear regression, and nonnested regression including nonlinear mod- els. Tests are performed using an R package developed by the author which will be made publicly available on journal publication of research results.

Contributors

Agent

Created

Date Created
2018

156576-Thumbnail Image.png

Three essays on shrinkage estimation and model selection of linear and nonlinear time series models

Description

The primary objective in time series analysis is forecasting. Raw data often exhibits nonstationary behavior: trends, seasonal cycles, and heteroskedasticity. After data is transformed to a weakly stationary process, autoregressive moving average (ARMA) models may capture the remaining temporal

The primary objective in time series analysis is forecasting. Raw data often exhibits nonstationary behavior: trends, seasonal cycles, and heteroskedasticity. After data is transformed to a weakly stationary process, autoregressive moving average (ARMA) models may capture the remaining temporal dynamics to improve forecasting. Estimation of ARMA can be performed through regressing current values on previous realizations and proxy innovations. The classic paradigm fails when dynamics are nonlinear; in this case, parametric, regime-switching specifications model changes in level, ARMA dynamics, and volatility, using a finite number of latent states. If the states can be identified using past endogenous or exogenous information, a threshold autoregressive (TAR) or logistic smooth transition autoregressive (LSTAR) model may simplify complex nonlinear associations to conditional weakly stationary processes. For ARMA, TAR, and STAR, order parameters quantify the extent past information is associated with the future. Unfortunately, even if model orders are known a priori, the possibility of over-fitting can lead to sub-optimal forecasting performance. By intentionally overestimating these orders, a linear representation of the full model is exploited and Bayesian regularization can be used to achieve sparsity. Global-local shrinkage priors for AR, MA, and exogenous coefficients are adopted to pull posterior means toward 0 without over-shrinking relevant effects. This dissertation introduces, evaluates, and compares Bayesian techniques that automatically perform model selection and coefficient estimation of ARMA, TAR, and STAR models. Multiple Monte Carlo experiments illustrate the accuracy of these methods in finding the "true" data generating process. Practical applications demonstrate their efficacy in forecasting.

Contributors

Agent

Created

Date Created
2018

157719-Thumbnail Image.png

Experimental design issues in functional brain imaging with high temporal resolution

Description

Functional brain imaging experiments are widely conducted in many fields for study- ing the underlying brain activity in response to mental stimuli. For such experiments, it is crucial to select a good sequence of mental stimuli that allow researchers to

Functional brain imaging experiments are widely conducted in many fields for study- ing the underlying brain activity in response to mental stimuli. For such experiments, it is crucial to select a good sequence of mental stimuli that allow researchers to collect informative data for making precise and valid statistical inferences at minimum cost. In contrast to most existing studies, the aim of this study is to obtain optimal designs for brain mapping technology with an ultra-high temporal resolution with respect to some common statistical optimality criteria. The first topic of this work is on finding optimal designs when the primary interest is in estimating the Hemodynamic Response Function (HRF), a function of time describing the effect of a mental stimulus to the brain. A major challenge here is that the design matrix of the statistical model is greatly enlarged. As a result, it is very difficult, if not infeasible, to compute and compare the statistical efficiencies of competing designs. For tackling this issue, an efficient approach is built on subsampling the design matrix and the use of an efficient computer algorithm is proposed. It is demonstrated through the analytical and simulation results that the proposed approach can outperform the existing methods in terms of computing time, and the quality of the obtained designs. The second topic of this work is to find optimal designs when another set of popularly used basis functions is considered for modeling the HRF, e.g., to detect brain activations. Although the statistical model for analyzing the data remains linear, the parametric functions of interest under this setting are often nonlinear. The quality of the de- sign will then depend on the true value of some unknown parameters. To address this issue, the maximin approach is considered to identify designs that maximize the relative efficiencies over the parameter space. As shown in the case studies, these maximin designs yield high performance for detecting brain activation compared to the traditional designs that are widely used in practice.

Contributors

Agent

Created

Date Created
2019

Single-Focus Confocal Data Analysis with Bayesian Nonparametrics

Description

The cell is a dense environment composes of proteins, nucleic acids, as well as other small molecules, which are constantly bombarding each other and interacting. These interactions and the diffusive motions are driven by internal thermal fluctuations. Upon collision, molecules

The cell is a dense environment composes of proteins, nucleic acids, as well as other small molecules, which are constantly bombarding each other and interacting. These interactions and the diffusive motions are driven by internal thermal fluctuations. Upon collision, molecules can interact and form complexes. It is of interest to learn kinetic parameters such as reaction rates of one molecule converting to different species or two molecules colliding and form a new species as well as to learn diffusion coefficients.

Several experimental measurements can probe diffusion coefficients at the single-molecule and bulk level. The target of this thesis is on single-molecule methods, which can assess diffusion coefficients at the individual molecular level. For instance, super resolution methods like stochastic optical reconstruction microscopy (STORM) and photo activated localization microscopy (PALM), have a high spatial resolution with the cost of lower temporal resolution. Also, there is a different group of methods, such as MINFLUX, multi-detector tracking, which can track a single molecule with high spatio-temporal resolution. The problem with these methods is that they are only applicable to very diluted samples since they need to ensure existence of a single molecule in the region of interest (ROI).

In this thesis, the goal is to have the best of both worlds by achieving high spatio-temporal resolutions without being limited to a few molecules. To do so, one needs to refocus on fluorescence correlation spectroscopy (FCS) as a method that applies to both in vivo and in vitro systems with a high temporal resolution and relies on multiple molecules traversing a confocal volume for an extended period of time. The difficulty here is that the interpretation of the signal leads to different estimates for the kinetic parameters such as diffusion coefficients based on a different number of molecules we consider in the model. It is for this reason that the focus of this thesis is now on using Bayesian nonparametrics (BNPs) as a way to solve this model selection problem and extract kinetic parameters such as diffusion coefficients at the single-molecule level from a few photons, and thus with the highest temporal resolution as possible.

Contributors

Agent

Created

Date Created
2020

158674-Thumbnail Image.png

Modeling and Analyzing the Progression of Retinitis Pigmentosa

Description

Patients suffering from Retinitis Pigmentosa (RP), the most common type of inherited retinal degeneration, experience irreversible vision loss due to photoreceptor degeneration. The preservation of cone photoreceptors has been deemed medically relevant as a therapy aimed at preventing blindness in

Patients suffering from Retinitis Pigmentosa (RP), the most common type of inherited retinal degeneration, experience irreversible vision loss due to photoreceptor degeneration. The preservation of cone photoreceptors has been deemed medically relevant as a therapy aimed at preventing blindness in patients with RP. Cones rely on aerobic glycolysis to supply the metabolites necessary for outer segment (OS) renewal and maintenance. The rod-derived cone viability factor (RdCVF), a protein secreted by the rod photoreceptors that preserves the cones, accelerates the flow of glucose into the cone cell stimulating aerobic glycolysis. This dissertation presents and analyzes ordinary differential equation (ODE) models of cellular and molecular level photoreceptor interactions in health and disease to examine mechanisms leading to blindness in patients with RP.

First, a mathematical model composed of four ODEs is formulated to investigate the progression of RP, accounting for the new understanding of RdCVF’s role in enhancing cone survival. A mathematical analysis is performed, and stability and bifurcation analyses are used to explore various pathways to blindness. Experimental data are used for parameter estimation and model validation. The numerical results are framed in terms of four stages in the progression of RP. Sensitivity analysis is used to determine mechanisms that have a significant affect on the cones at each stage of RP. Utilizing a non-dimensional form of the RP model, a numerical bifurcation analysis via MATCONT revealed the existence of stable limit cycles at two stages of RP.

Next, a novel eleven dimensional ODE model of molecular and cellular level interactions is described. The subsequent analysis is used to uncover mechanisms that affect cone photoreceptor functionality and vitality. Preliminary simulations show the existence of oscillatory behavior which is anticipated when all processes are functioning properly. Additional simulations are carried out to explore the impact of a reduction in the concentration of RdCVF coupled with disruption in the metabolism associated with cone OS shedding, and confirms cone-on-rod reliance. The simulation results are compared with experimental data. Finally, four cases are considered, and a sensitivity analysis is performed to reveal mechanisms that significantly impact the cones in each case.

Contributors

Agent

Created

Date Created
2020

158338-Thumbnail Image.png

Simultaneous Material Microstructure Classification and Discovery using Acoustic Emission Signals

Description

Acoustic emission (AE) signals have been widely employed for tracking material properties and structural characteristics. In this study, the aim is to analyze the AE signals gathered during a scanning probe lithography process to classify the known microstructure types and

Acoustic emission (AE) signals have been widely employed for tracking material properties and structural characteristics. In this study, the aim is to analyze the AE signals gathered during a scanning probe lithography process to classify the known microstructure types and discover unknown surface microstructures/anomalies. To achieve this, a Hidden Markov Model is developed to consider the temporal dependency of the high-resolution AE data. Furthermore, the posterior classification probability and the negative likelihood score for microstructure classification and discovery are computed. Subsequently, a diagnostic procedure to identify the dominant AE frequencies that were used to track the microstructural characteristics is presented. In addition, machine learning methods such as KNN, Naive Bayes, and Logistic Regression classifiers are applied. Finally, the proposed approach applied to identify the surface microstructures of additively manufactured Ti-6Al-4V and show that it not only achieved a high classification accuracy (e.g., more than 90\%) but also correctly identified the microstructural anomalies that may be subjected to further investigation to discover new material phases/properties.

Contributors

Agent

Created

Date Created
2020

158484-Thumbnail Image.png

Cancer Invasion in Time and Space

Description

Cancer is a disease involving abnormal growth of cells. Its growth dynamics is perplexing. Mathematical modeling is a way to shed light on this progress and its medical treatments. This dissertation is to study cancer invasion in time and space

Cancer is a disease involving abnormal growth of cells. Its growth dynamics is perplexing. Mathematical modeling is a way to shed light on this progress and its medical treatments. This dissertation is to study cancer invasion in time and space using a mathematical approach. Chapter 1 presents a detailed review of literature on cancer modeling.

Chapter 2 focuses sorely on time where the escape of a generic cancer out of immune control is described by stochastic delayed differential equations (SDDEs). Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and stochasticity in the tumor proliferation rate are studied by including delay and noise in the model. Stability, persistence and extinction of the tumor are analyzed. The result shows that both time delay and noise can induce the transition from low tumor burden equilibrium to high tumor equilibrium. The aforementioned work has been published (Han et al., 2019b).

In Chapter 3, Glioblastoma multiforme (GBM) is studied using a partial differential equation (PDE) model. GBM is an aggressive brain cancer with a grim prognosis. A mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. A novel method is developed to approximate key characteristics of the wave profile, which can be compared with MRI data. Several test cases of MRI data of GBM patients are used to yield personalized parameterizations of the model. The aforementioned work has been published (Han et al., 2019a).

Chapter 4 presents an innovative way of forecasting spatial cancer invasion. Most mathematical models, including the ones described in previous chapters, are formulated based on strong assumptions, which are hard, if not impossible, to verify due to complexity of biological processes and lack of quality data. Instead, a nonparametric forecasting method using Gaussian processes is proposed. By exploiting the local nature of the spatio-temporal process, sparse (in terms of time) data is sufficient for forecasting. Desirable properties of Gaussian processes facilitate selection of the size of the local neighborhood and computationally efficient propagation of uncertainty. The method is tested on synthetic data and demonstrates promising results.

Contributors

Agent

Created

Date Created
2020

158520-Thumbnail Image.png

Contributions to Optimal Experimental Design and Strategic Subdata Selection for Big Data

Description

In this dissertation two research questions in the field of applied experimental design were explored. First, methods for augmenting the three-level screening designs called Definitive Screening Designs (DSDs) were investigated. Second, schemes for strategic subdata selection for nonparametric

In this dissertation two research questions in the field of applied experimental design were explored. First, methods for augmenting the three-level screening designs called Definitive Screening Designs (DSDs) were investigated. Second, schemes for strategic subdata selection for nonparametric predictive modeling with big data were developed.

Under sparsity, the structure of DSDs can allow for the screening and optimization of a system in one step, but in non-sparse situations estimation of second-order models requires augmentation of the DSD. In this work, augmentation strategies for DSDs were considered, given the assumption that the correct form of the model for the response of interest is quadratic. Series of augmented designs were constructed and explored, and power calculations, model-robustness criteria, model-discrimination criteria, and simulation study results were used to identify the number of augmented runs necessary for (1) effectively identifying active model effects, and (2) precisely predicting a response of interest. When the goal is identification of active effects, it is shown that supersaturated designs are sufficient; when the goal is prediction, it is shown that little is gained by augmenting beyond the design that is saturated for the full quadratic model. Surprisingly, augmentation strategies based on the I-optimality criterion do not lead to better predictions than strategies based on the D-optimality criterion.

Computational limitations can render standard statistical methods infeasible in the face of massive datasets, necessitating subsampling strategies. In the big data context, the primary objective is often prediction but the correct form of the model for the response of interest is likely unknown. Here, two new methods of subdata selection were proposed. The first is based on clustering, the second is based on space-filling designs, and both are free from model assumptions. The performance of the proposed methods was explored visually via low-dimensional simulated examples; via real data applications; and via large simulation studies. In all cases the proposed methods were compared to existing, widely used subdata selection methods. The conditions under which the proposed methods provide advantages over standard subdata selection strategies were identified.

Contributors

Agent

Created

Date Created
2020