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- Creators: Prokofiev, Sergey, 1891-1953
Description
The main objective of this research is to develop an integrated method to study emergent behavior and consequences of evolution and adaptation in engineered complex adaptive systems (ECASs). A multi-layer conceptual framework and modeling approach including behavioral and structural aspects is provided to describe the structure of a class of engineered complex systems and predict their future adaptive patterns. The approach allows the examination of complexity in the structure and the behavior of components as a result of their connections and in relation to their environment. This research describes and uses the major differences of natural complex adaptive systems (CASs) with artificial/engineered CASs to build a framework and platform for ECAS. While this framework focuses on the critical factors of an engineered system, it also enables one to synthetically employ engineering and mathematical models to analyze and measure complexity in such systems. In this way concepts of complex systems science are adapted to management science and system of systems engineering. In particular an integrated consumer-based optimization and agent-based modeling (ABM) platform is presented that enables managers to predict and partially control patterns of behaviors in ECASs. Demonstrated on the U.S. electricity markets, ABM is integrated with normative and subjective decision behavior recommended by the U.S. Department of Energy (DOE) and Federal Energy Regulatory Commission (FERC). The approach integrates social networks, social science, complexity theory, and diffusion theory. Furthermore, it has unique and significant contribution in exploring and representing concrete managerial insights for ECASs and offering new optimized actions and modeling paradigms in agent-based simulation.
ContributorsHaghnevis, Moeed (Author) / Askin, Ronald G. (Thesis advisor) / Armbruster, Dieter (Thesis advisor) / Mirchandani, Pitu (Committee member) / Wu, Tong (Committee member) / Hedman, Kory (Committee member) / Arizona State University (Publisher)
Created2013
Description
This thesis presents a model for the buying behavior of consumers in a technology market. In this model, a potential consumer is not perfectly rational, but exhibits bounded rationality following the axioms of prospect theory: reference dependence, diminishing returns and loss sensitivity. To evaluate the products on different criteria, the analytic hierarchy process is used, which allows for relative comparisons. The analytic hierarchy process proposes that when making a choice between several alternatives, one should measure the products by comparing them relative to each other. This allows the user to put numbers to subjective criteria. Additionally, evidence suggests that a consumer will often consider not only their own evaluation of a product, but also the choices of other consumers. Thus, the model in this paper applies prospect theory to products with multiple attributes using word of mouth as a criteria in the evaluation.
ContributorsElkholy, Alexander (Author) / Armbruster, Dieter (Thesis advisor) / Kempf, Karl (Committee member) / Li, Hongmin (Committee member) / Arizona State University (Publisher)
Created2014
Description
Pre-Exposure Prophylaxis (PrEP) is any medical or public health procedure used before exposure to the disease causing agent, its purpose is to prevent, rather than treat or cure a disease. Most commonly, PrEP refers to an experimental HIV-prevention strategy that would use antiretrovirals to protect HIV-negative people from HIV infection. A deterministic mathematical model of HIV transmission is developed to evaluate the public-health impact of oral PrEP interventions, and to compare PrEP effectiveness with respect to different evaluation methods. The effects of demographic, behavioral, and epidemic parameters on the PrEP impact are studied in a multivariate sensitivity analysis. Most of the published models on HIV intervention impact assume that the number of individuals joining the sexually active population per year is constant or proportional to the total population. In the second part of this study, three models are presented and analyzed to study the PrEP intervention, with constant, linear, and logistic recruitment rates. How different demographic assumptions can affect the evaluation of PrEP is studied. When provided with data, often least square fitting or similar approaches can be used to determine a single set of approximated parameter values that make the model fit the data best. However, least square fitting only provides point estimates and does not provide information on how strongly the data supports these particular estimates. Therefore, in the third part of this study, Bayesian parameter estimation is applied on fitting ODE model to the related HIV data. Starting with a set of prior distributions for the parameters as initial guess, Bayes' formula can be applied to obtain a set of posterior distributions for the parameters which makes the model fit the observed data best. Evaluating the posterior distribution often requires the integration of high-dimensional functions, which is usually difficult to calculate numerically. Therefore, the Markov chain Monte Carlo (MCMC) method is used to approximate the posterior distribution.
ContributorsZhao, Yuqin (Author) / Kuang, Yang (Thesis advisor) / Taylor, Jesse (Committee member) / Armbruster, Dieter (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
Bacteriophage (phage) are viruses that infect bacteria. Typical laboratory experiments show that in a chemostat containing phage and susceptible bacteria species, a mutant bacteria species will evolve. This mutant species is usually resistant to the phage infection and less competitive compared to the susceptible bacteria species. In some experiments, both susceptible and resistant bacteria species, as well as phage, can coexist at an equilibrium for hundreds of hours. The current research is inspired by these observations, and the goal is to establish a mathematical model and explore sufficient and necessary conditions for the coexistence. In this dissertation a model with infinite distributed delay terms based on some existing work is established. A rigorous analysis of the well-posedness of this model is provided, and it is proved that the susceptible bacteria persist. To study the persistence of phage species, a "Phage Reproduction Number" (PRN) is defined. The mathematical analysis shows phage persist if PRN > 1 and vanish if PRN < 1. A sufficient condition and a necessary condition for persistence of resistant bacteria are given. The persistence of the phage is essential for the persistence of resistant bacteria. Also, the resistant bacteria persist if its fitness is the same as the susceptible bacteria and if PRN > 1. A special case of the general model leads to a system of ordinary differential equations, for which numerical simulation results are presented.
ContributorsHan, Zhun (Author) / Smith, Hal (Thesis advisor) / Armbruster, Dieter (Committee member) / Kawski, Matthias (Committee member) / Kuang, Yang (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2012
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
Factory production is stochastic in nature with time varying input and output processes that are non-stationary stochastic processes. Hence, the principle quantities of interest are random variables. Typical modeling of such behavior involves numerical simulation and statistical analysis. A deterministic closure model leading to a second order model for the product density and product speed has previously been proposed. The resulting partial differential equations (PDE) are compared to discrete event simulations (DES) that simulate factory production as a time dependent M/M/1 queuing system. Three fundamental scenarios for the time dependent influx are studied: An instant step up/down of the mean arrival rate; an exponential step up/down of the mean arrival rate; and periodic variation of the mean arrival rate. It is shown that the second order model, in general, yields significant improvement over current first order models. Specifically, the agreement between the DES and the PDE for the step up and for periodic forcing that is not too rapid is very good. Adding diffusion to the PDE further improves the agreement. The analysis also points to fundamental open issues regarding the deterministic modeling of low signal-to-noise ratio for some stochastic processes and the possibility of resonance in deterministic models that is not present in the original stochastic process.
ContributorsWienke, Matthew (Author) / Armbruster, Dieter (Thesis advisor) / Jones, Donald (Committee member) / Platte, Rodrigo (Committee member) / Gardner, Carl (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2015
Description
Though the likelihood is a useful tool for obtaining estimates of regression parameters, it is not readily available in the fit of hierarchical binary data models. The correlated observations negate the opportunity to have a joint likelihood when fitting hierarchical logistic regression models. Through conditional likelihood, inferences for the regression and covariance parameters as well as the intraclass correlation coefficients are usually obtained. In those cases, I have resorted to use of Laplace approximation and large sample theory approach for point and interval estimates such as Wald-type confidence intervals and profile likelihood confidence intervals. These methods rely on distributional assumptions and large sample theory. However, when dealing with small hierarchical datasets they often result in severe bias or non-convergence. I present a generalized quasi-likelihood approach and a generalized method of moments approach; both do not rely on any distributional assumptions but only moments of response. As an alternative to the typical large sample theory approach, I present bootstrapping hierarchical logistic regression models which provides more accurate interval estimates for small binary hierarchical data. These models substitute computations as an alternative to the traditional Wald-type and profile likelihood confidence intervals. I use a latent variable approach with a new split bootstrap method for estimating intraclass correlation coefficients when analyzing binary data obtained from a three-level hierarchical structure. It is especially useful with small sample size and easily expanded to multilevel. Comparisons are made to existing approaches through both theoretical justification and simulation studies. Further, I demonstrate my findings through an analysis of three numerical examples, one based on cancer in remission data, one related to the China’s antibiotic abuse study, and a third related to teacher effectiveness in schools from a state of southwest US.
ContributorsWang, Bei (Author) / Wilson, Jeffrey R (Thesis advisor) / Kamarianakis, Ioannis (Committee member) / Reiser, Mark R. (Committee member) / St Louis, Robert (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2017
Description
Correlation is common in many types of data, including those collected through longitudinal studies or in a hierarchical structure. In the case of clustering, or repeated measurements, there is inherent correlation between observations within the same group, or between observations obtained on the same subject. Longitudinal studies also introduce association between the covariates and the outcomes across time. When multiple outcomes are of interest, association may exist between the various models. These correlations can lead to issues in model fitting and inference if not properly accounted for. This dissertation presents three papers discussing appropriate methods to properly consider different types of association. The first paper introduces an ANOVA based measure of intraclass correlation for three level hierarchical data with binary outcomes, and corresponding properties. This measure is useful for evaluating when the correlation due to clustering warrants a more complex model. This measure is used to investigate AIDS knowledge in a clustered study conducted in Bangladesh. The second paper develops the Partitioned generalized method of moments (Partitioned GMM) model for longitudinal studies. This model utilizes valid moment conditions to separately estimate the varying effects of each time-dependent covariate on the outcome over time using multiple coefficients. The model is fit to data from the National Longitudinal Study of Adolescent to Adult Health (Add Health) to investigate risk factors of childhood obesity. In the third paper, the Partitioned GMM model is extended to jointly estimate regression models for multiple outcomes of interest. Thus, this approach takes into account both the correlation between the multivariate outcomes, as well as the correlation due to time-dependency in longitudinal studies. The model utilizes an expanded weight matrix and objective function composed of valid moment conditions to simultaneously estimate optimal regression coefficients. This approach is applied to Add Health data to simultaneously study drivers of outcomes including smoking, social alcohol usage, and obesity in children.
ContributorsIrimata, Kyle (Author) / Wilson, Jeffrey R (Thesis advisor) / Broatch, Jennifer (Committee member) / Kamarianakis, Ioannis (Committee member) / Kao, Ming-Hung (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2018
Description
The Kuramoto model is an archetypal model for studying synchronization in groups
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
ContributorsGilg, Brady (Author) / Armbruster, Dieter (Thesis advisor) / Mittelmann, Hans (Committee member) / Scaglione, Anna (Committee member) / Strogatz, Steven (Committee member) / Welfert, Bruno (Committee member) / Arizona State University (Publisher)
Created2018
Description
Generalized Linear Models (GLMs) are widely used for modeling responses with non-normal error distributions. When the values of the covariates in such models are controllable, finding an optimal (or at least efficient) design could greatly facilitate the work of collecting and analyzing data. In fact, many theoretical results are obtained on a case-by-case basis, while in other situations, researchers also rely heavily on computational tools for design selection.
Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem.
Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem.
ContributorsWang, Zhongsheng (Author) / Stufken, John (Thesis advisor) / Kamarianakis, Ioannis (Committee member) / Kao, Ming-Hung (Committee member) / Reiser, Mark R. (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2018