Physical Sciences and Mathematics Commons^™

Essays On Environmental And Health Economics., Prachi Singh Dr.

Doctoral Theses

This thesis consists of three empirical essays that investigate issues in environmental and health economics. The main focus of this thesis is to study how environmental degradation or interventions in this domain can affect demographic and health outcomes of the population in developing countries. The first chapter explores the effect of an information campaign about arsenic contamination in Bangladesh on marriage market outcomes. This study finds that providing information about negative effects of arsenic consumption had an unintended consequence in the marriage market. Specifically, information about lower fertility, skin lesions, cancers and higher mortality related to arsenic exposure induced individuals …

A Mathematical Model Of The Opioid Epidemic In The State Of Maine, Cole Butler

Honors College

For the past two decades the United States has been embroiled in a prescription drug epidemic that has since grown in magnitude and complexity. The ripples of this epidemic have been especially apparent in the state of Maine, which has fought hard to mitigate the damage caused by addiction to pharmaceutical and illicit opioids. Us- ing data from state and federal sources, we construct a mathematical model capturing the dynamics of the opioid epidemic in the state of Maine, specifically as it pertains to pharmaceutical opioids and heroin. Parameter fitting is performed followed by an uncertainty analysis to quantify potential …

Sensitivity Analysis In Parametric Vector Optimization In Banach Spaces Via ${\Tau}^W$-Contingent Derivatives, Thanh Tung Le, Thanh Hung Pham

Turkish Journal of Mathematics

This paper is concerned with sensitivity analysis in parametric vector optimization problems via ${\tau}^w$-contingent derivatives. Firstly, relationships between the ${\tau}^w$-contingent derivative of the Borwein proper perturbation map and the ${\tau}^w$-contingent derivative of feasible map in objective space are considered. Then, the formulas for estimating the ${\tau}^w$-contingent derivative of the Borwein proper perturbation map via the ${\tau}^w$-contingent of the constraint map and the Hadamard derivative of the objective map are obtained.

New Flexible Regression Models Generated By Gamma Random Variables With Censored Data, Elizabeth M. Hashimoto, Gauss M. Cordeiro, Edwin M. M. Ortega, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking …

Services Sector And Non-Balanced Growth., Anuradha Saha Dr.

Doctoral Theses

No abstract provided.

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

Three Essays On The Impact Of Global Warming In India., Eshita Gupta Dr.

Doctoral Theses

This dissertation consists of three chapters. The Örst chapter studies the impact of climate change on electricity demand in Delhi using daily data on electricity demand and apparent temperature for the period 2000-09. It estimates a semi-parametric variable coe¢ - cient model that allows for a non-linear relationship between temperature and electricity to shift over time, a feature that is necessary to incorporate given the rapid economic growth in India. As evident from previous studies, electricity demand is a U-shaped function of temperature. Three results from our analysis have important implications for electricityclimate policy: Firstly, the rising part of the …

Mathematical Modeling Of Immune Responses To Hepatitis C Virus Infection, Ivan Ramirez

Electronic Theses and Dissertations

An existing mathematical model of ordinary differential equations was studied to better understand the interactions between hepatitis C virus (HCV) and the immune system cells in the human body. Three possible qualitative scenarios were explored: dominant CTL response, dominant antibody response, and coexistence. Additionally, a sensitivity analysis was carried out to rank model parameters for each of these scenarios. Therapy was addressed as an optimal control problem. Numerical solutions of optimal controls were computed using a forward-backward sweep scheme for each scenario. Model parameters were estimated using ordinary least squares fitting from longitudinal data (serum HCV RNA measurements) given in …

Parametric Sensitivity Analysis For Biochemical Reaction Networks Based On Pathwise Information Theory, Yannis Pantazis, Markos Katsoulakis, Dionisios G. Vlachos

Markos Katsoulakis

Background: Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space. …

Parametric Sensitivity Analysis For Stochastic Molecular Systems Using Information Theoretic Metrics, Anastasios Tsourtis, Yannis Pantazis, Markos Katsoulakis, Vagelis Harmandaris

Markos Katsoulakis

Background Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space. …

A Relative Entropy Rate Method For Path Space Sensitivity Analysis Of Stationary Complex Stochastic Dynamics, Yannis Pantazis, Markos Katsoulakis

Markos Katsoulakis

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the relative entropy rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the relative entropy rate and the corresponding Fisher information matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-Gaussian stationary probability …

An Epidemiological Model Of Rift Valley Fever With Spatial Dynamics, Tianchan Niu, Holly D. Gaff, Yiannis E. Papelis, David M. Hartley

Biological Sciences Faculty Publications

As a category A agent in the Center for Disease Control bioterrorism list, Rift Valley fever (RVF) is considered a major threat to the United States (USA). Should the pathogen be intentionally or unintentionally introduced to the continental USA, there is tremendous potential for economic damages due to loss of livestock, trade restrictions, and subsequent food supply chain disruptions. We have incorporated the effects of space into a mathematical model of RVF in order to study the dynamics of the pathogen spread as affected by the movement of humans, livestock, and mosquitoes. The model accounts for the horizontal transmission of …

Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho

Mathematics Research Reports

This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more difficult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do not to a large extent differ from those known for the conventional problem. It has been already well recognized in the literature that for optimality conditions of the usual optimistic bilevel program …

Public Policy, Long Run Growth And Economic Transition From Agriculture To Industrial Mass Production., Rudrani Bhattacharya Dr.

Doctoral Theses

It has been recognized that the heart of the development process lies on the transformation of an economy from traditional activities in agriculture to industrial activities. As emphasized by Lewis (1954), the movement of labor from primary sector to industry is conducive to the rise of economy’s savings and investment rate and thus fostering economic growth. The core of this paradigm is the historically observed rapid growth in today’s developed countries associated with expansion of industrial activities.It is well-documented by now that at least over a few centuries leading up to 1800 AD there was little change in the world …

Variational Analysis In Parametric Optimization, Yen Nhi Nguyen Thi

Wayne State University Dissertations

The dissertation is devoted to the development of variational analysis and generalized differentiation in infinite dimensions. We derive new calculus rules for both first-order partial subdifferentials and second-order partial subdifferentials in the framework of general Banach spaces as well as more developed rules in the framework of Asplund spaces. This calculus is applied in the study of sensitivity analysis for solution maps to the parameterized generalized equations in Asplund spaces, where both bases and fields are parameter-dependent multifunctions. We analyze the parametric sensitivity of either stationary points or stationary point multiplier multifunctions associated with parameterized optimization problems under consideration. The …

Slippage And Change Point Problem With Directional Data., Arnab Kumar Laha Dr.

Doctoral Theses

In this thesis we develop statistical methods for dealing with two problems namely (1) THE SLIPPAGE PROBLEM and (2) THE CHANGE POINT PROB- LEM in the set-up of directional data. In this chapter, we provide an intro- duction to these problems and discuss the importance of the present work. The slippage problem is basically a problem to detect whether any unspecified observation in a given random sample comes from a distribution different from that for all the other remaining observations. This can also be viewed as a problem of outlier detection or that of spuriosity. This problem assumes great importance …

Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim

All HMC Faculty Publications and Research

Highly Active Anti-Retroviral Therapy (HAART) of HIV infection has significantly reduced morbidity and mortality in developed countries. However, since these treatments can cause side effects and require strict adherence to treatment protocol, questions about whether or not treatment can be interrupted or discontinued with control of infection maintained by the host immune system remain to be answered. We present sensitivity analysis of a compartmental model for HIV infection that allows for treatment interruptions, including the sensitivity of the compartments themselves to our parameters as well as the sensitivity of the cost function used in parameter estimation. Recommendations are made about …