A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^

The non-linear acousto-mechanical and thermodynamic response of spherical absorbers to laser pulses of various temporal profiles

This study is to theoretically investigate shockwave and microbubble formation due to laser absorption by microparticles and nanoparticles. The initial motivation for this research was to understand the underlying physical mechanisms responsible for laser damage to the retina, as well as the predict threshold levels for damage for laser pulses with of progressively shorter durations. The strongest absorbers in the retina are micron size melanosomes, and their absorption of laser light causes them to accrue very high energy density. I theoretically investigate how this absorbed energy is transferred to the surrounding medium. For a wide range of conditions I calculate shockwave generation and bubble growth as a function of the three parameters; fluence, pulse duration and pulse shape. In order to develop a rigorous physical treatment, the governing equations for the behavior of an absorber and for the surrounding medium are derived. Shockwave theory is investigated and the conclusion is that a shock pressure explanation is likely to be the underlying physical cause of retinal damage at threshold fluences for sub-nanosecond pulses. The same effects are also expected for non-biological micro and nano absorbers. ^

Nonlinear dynamics and chaos simulation system analysis for improved design

Small errors proved catastrophic. Our purpose to remark that a very small cause which escapes our notice determined a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. Small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. When dealing with any kind of electrical device specification, it is important to note that there exists a pair of test conditions that define a test: the forcing function and the limit. Forcing functions define the external operating constraints placed upon the device tested. The actual test defines how well the device responds to these constraints. Forcing inputs to threshold for example, represents the most difficult testing because this put those inputs as close as possible to the actual switching critical points and guarantees that the device will meet the Input-Output specifications. ^ Prediction becomes impossible by classical analytical analysis bounded by Newton and Euclides. We have found that non linear dynamics characteristics is the natural state of being in all circuits and devices. Opportunities exist for effective error detection in a nonlinear dynamics and chaos environment. ^ Nowadays there are a set of linear limits established around every aspect of a digital or analog circuits out of which devices are consider bad after failing the test. Deterministic chaos circuit is a fact not a possibility as it has been revived by our Ph.D. research. In practice for linear standard informational methodologies, this chaotic data product is usually undesirable and we are educated to be interested in obtaining a more regular stream of output data. ^ This Ph.D. research explored the possibilities of taking the foundation of a very well known simulation and modeling methodology, introducing nonlinear dynamics and chaos precepts, to produce a new error detector instrument able to put together streams of data scattered in space and time. Therefore, mastering deterministic chaos and changing the bad reputation of chaotic data as a potential risk for practical system status determination. ^

Crack tip stress study for elastic-perfectly plastic materials with some applications

The problems of plasticity and non-linear fracture mechanics have been generally recognized as the most difficult problems of solid mechanics. The present dissertation is devoted to some problems on the intersection of both plasticity and non-linear fracture mechanics. The crack tip is responsible for the crack growth and therefore is the focus of fracture science. The problem of crack has been studied by an army of outstanding scholars and engineers in this century, but has not, as yet, been solved for many important practical situations. The aim of this investigation is to provide an analytical solution to the problem of plasticity at the crack tip for elastic-perfectly plastic materials and to apply the solution to a classical problem of the mechanics of composite materials.^ In this work, the stresses inside the plastic region near the crack tip in a composite material made of two different elastic-perfectly plastic materials are studied. The problems of an interface crack, a crack impinging an interface at the right angle and at arbitrary angles are examined. The constituent materials are assumed to obey the Huber-Mises yielding condition criterion. The theory of slip lines for plane strain is utilized. For the particular homogeneous case these problems have two solutions: the continuous solution found earlier by Prandtl and modified by Hill and Sokolovsky, and the discontinuous solution found later by Cherepanov. The same type of solutions were discovered in the inhomogeneous problems of the present study. Some reasons to prefer the discontinuous solution are provided. The method is also applied to the analysis of a contact problem and a push-in/pull-out problem to determine the critical load for plasticity in these classical problems of the mechanics of composite materials.^ The results of this dissertation published in three journal articles (two of which are under revision) will also be presented in the Invited Lecture at the 7$\rm\sp{th}$ International Conference on Plasticity (Cancun, Mexico, January 1999). ^

Hybrid multi-objective optimization and hybridized self-organizing response surface method

Numerical optimization is a technique where a computer is used to explore design parameter combinations to find extremes in performance factors. In multi-objective optimization several performance factors can be optimized simultaneously. The solution to multi-objective optimization problems is not a single design, but a family of optimized designs referred to as the Pareto frontier. The Pareto frontier is a trade-off curve in the objective function space composed of solutions where performance in one objective function is traded for performance in others. A Multi-Objective Hybridized Optimizer (MOHO) was created for the purpose of solving multi-objective optimization problems by utilizing a set of constituent optimization algorithms. MOHO tracks the progress of the Pareto frontier approximation development and automatically switches amongst those constituent evolutionary optimization algorithms to speed the formation of an accurate Pareto frontier approximation. Aerodynamic shape optimization is one of the oldest applications of numerical optimization. MOHO was used to perform shape optimization on a 0.5-inch ballistic penetrator traveling at Mach number 2.5. Two objectives were simultaneously optimized: minimize aerodynamic drag and maximize penetrator volume. This problem was solved twice. The first time the problem was solved by using Modified Newton Impact Theory (MNIT) to determine the pressure drag on the penetrator. In the second solution, a Parabolized Navier-Stokes (PNS) solver that includes viscosity was used to evaluate the drag on the penetrator. The studies show the difference in the optimized penetrator shapes when viscosity is absent and present in the optimization. In modern optimization problems, objective function evaluations may require many hours on a computer cluster to perform these types of analysis. One solution is to create a response surface that models the behavior of the objective function. Once enough data about the behavior of the objective function has been collected, a response surface can be used to represent the actual objective function in the optimization process. The Hybrid Self-Organizing Response Surface Method (HYBSORSM) algorithm was developed and used to make response surfaces of objective functions. HYBSORSM was evaluated using a suite of 295 non-linear functions. These functions involve from 2 to 100 variables demonstrating robustness and accuracy of HYBSORSM.

Hybrid power system intelligent operation and protection involving distributed architectures and pulsed loads

Efficient and reliable techniques for power delivery and utilization are needed to account for the increased penetration of renewable energy sources in electric power systems. Such methods are also required for current and future demands of plug-in electric vehicles and high-power electronic loads. Distributed control and optimal power network architectures will lead to viable solutions to the energy management issue with high level of reliability and security. This dissertation is aimed at developing and verifying new techniques for distributed control by deploying DC microgrids, involving distributed renewable generation and energy storage, through the operating AC power system. To achieve the findings of this dissertation, an energy system architecture was developed involving AC and DC networks, both with distributed generations and demands. The various components of the DC microgrid were designed and built including DC-DC converters, voltage source inverters (VSI) and AC-DC rectifiers featuring novel designs developed by the candidate. New control techniques were developed and implemented to maximize the operating range of the power conditioning units used for integrating renewable energy into the DC bus. The control and operation of the DC microgrids in the hybrid AC/DC system involve intelligent energy management. Real-time energy management algorithms were developed and experimentally verified. These algorithms are based on intelligent decision-making elements along with an optimization process. This was aimed at enhancing the overall performance of the power system and mitigating the effect of heavy non-linear loads with variable intensity and duration. The developed algorithms were also used for managing the charging/discharging process of plug-in electric vehicle emulators. The protection of the proposed hybrid AC/DC power system was studied. Fault analysis and protection scheme and coordination, in addition to ideas on how to retrofit currently available protection concepts and devices for AC systems in a DC network, were presented. A study was also conducted on the effect of changing the distribution architecture and distributing the storage assets on the various zones of the network on the system's dynamic security and stability. A practical shipboard power system was studied as an example of a hybrid AC/DC power system involving pulsed loads. Generally, the proposed hybrid AC/DC power system, besides most of the ideas, controls and algorithms presented in this dissertation, were experimentally verified at the Smart Grid Testbed, Energy Systems Research Laboratory. All the developments in this dissertation were experimentally verified at the Smart Grid Testbed.

Investigation of escape and negative student behaviors related to Florida state high stakes test preparation in Miami-Dade County Public High Schools

The purpose of this study was to determine whether there was a relationship between pressure to perform on state mandated, high-stakes tests and the rate of student escape behavior defined as the number of school suspensions and absences. The state assigned grade of a school was used as a surrogate measure of pressure with the assumption that pressure increased as the school grade decreased. Student attendance and suspension data were gathered from all 33 of the regular public high schools in Miami-Dade County Public Schools. The research questions were: Is the number of suspensions highest in the third quarter, when most FCAT preparation takes place for each of the 3 school years 2007-08 through 2009-10? How accurately does the high school's grade predict the number of suspensions and number of absences during each of the 4 school years 2005-06 through 2008-09? The research questions were answered using repeated measures analysis of variance for research question #1 and non-linear multiple regression for research question #2. No significant difference could be found between the numbers of suspensions in each of the grading periods nor was there a relationship between the number of suspensions and school grade. A statistically significant relationship was found between student attendance and school grade. When plotted, this relationship was found to be quadratic in nature and formed a loose inverted U for each of the four years during which data were collected. This indicated that students in very high and very low performing schools had low levels of absences while those in the midlevel of the distribution of school performance (C schools) had the greatest rates of absence. Identifying a relationship between the pressures associated with high stakes testing and student escape behavior suggests that it might be useful for building administrators to reevaluate test preparation activities and procedures being used in their building and to include anxiety reducing strategies. As a relationship was found, it sets the foundation for future studies to identify whether testing related activities are impacting some students emotionally and are causing unintended consequences of testing mandates.

Land Use and Climate Change Impacts on the Hydrology of the Upper Mara River Basin, Kenya: Results of a Modeling Study to Support Better Resource Management

Some of the most valued natural and cultural landscapes on Earth lie in river basins that are poorly gauged and have incomplete historical climate and runoff records. The Mara River Basin of East Africa is such a basin. It hosts the internationally renowned Mara-Serengeti landscape as well as a rich mixture of indigenous cultures. The Mara River is the sole source of surface water to the landscape during the dry season and periods of drought. During recent years, the flow of the Mara River has become increasingly erratic, especially in the upper reaches, and resource managers are hampered by a lack of understanding of the relative influence of different sources of flow alteration. Uncertainties about the impacts of future climate change compound the challenges. We applied the Soil Water Assessment Tool (SWAT) to investigate the response of the headwater hydrology of the Mara River to scenarios of continued land use change and projected climate change. Under the data-scarce conditions of the basin, model performance was improved using satellite-based estimated rainfall data, which may also improve the usefulness of runoff models in other parts of East Africa. The results of the analysis indicate that any further conversion of forests to agriculture and grassland in the basin headwaters is likely to reduce dry season flows and increase peak flows, leading to greater water scarcity at critical times of the year and exacerbating erosion on hillslopes. Most climate change projections for the region call for modest and seasonally variable increases in precipitation (5–10 %) accompanied by increases in temperature (2.5–3.5 °C). Simulated runoff responses to climate change scenarios were non-linear and suggest the basin is highly vulnerable under low (−3 %) and high (+25 %) extremes of projected precipitation changes, but under median projections (+7 %) there is little impact on annual water yields or mean discharge. Modest increases in precipitation are partitioned largely to increased evapotranspiration. Overall, model results support the existing efforts of Mara water resource managers to protect headwater forests and indicate that additional emphasis should be placed on improving land management practices that enhance infiltration and aquifer recharge as part of a wider program of climate change adaptation.

Hybrid Power System Intelligent Operation and Protection Involving Distributed Architectures and Pulsed Loads

Efficient and reliable techniques for power delivery and utilization are needed to account for the increased penetration of renewable energy sources in electric power systems. Such methods are also required for current and future demands of plug-in electric vehicles and high-power electronic loads. Distributed control and optimal power network architectures will lead to viable solutions to the energy management issue with high level of reliability and security. This dissertation is aimed at developing and verifying new techniques for distributed control by deploying DC microgrids, involving distributed renewable generation and energy storage, through the operating AC power system. To achieve the findings of this dissertation, an energy system architecture was developed involving AC and DC networks, both with distributed generations and demands. The various components of the DC microgrid were designed and built including DC-DC converters, voltage source inverters (VSI) and AC-DC rectifiers featuring novel designs developed by the candidate. New control techniques were developed and implemented to maximize the operating range of the power conditioning units used for integrating renewable energy into the DC bus. The control and operation of the DC microgrids in the hybrid AC/DC system involve intelligent energy management. Real-time energy management algorithms were developed and experimentally verified. These algorithms are based on intelligent decision-making elements along with an optimization process. This was aimed at enhancing the overall performance of the power system and mitigating the effect of heavy non-linear loads with variable intensity and duration. The developed algorithms were also used for managing the charging/discharging process of plug-in electric vehicle emulators. The protection of the proposed hybrid AC/DC power system was studied. Fault analysis and protection scheme and coordination, in addition to ideas on how to retrofit currently available protection concepts and devices for AC systems in a DC network, were presented. A study was also conducted on the effect of changing the distribution architecture and distributing the storage assets on the various zones of the network on the system’s dynamic security and stability. A practical shipboard power system was studied as an example of a hybrid AC/DC power system involving pulsed loads. Generally, the proposed hybrid AC/DC power system, besides most of the ideas, controls and algorithms presented in this dissertation, were experimentally verified at the Smart Grid Testbed, Energy Systems Research Laboratory. All the developments in this dissertation were experimentally verified at the Smart Grid Testbed.

Investigation of Escape and Negative Student Behaviors Related to Florida State High Stakes Test Preparation in Miami-Dade County Public High Schools, having been approved in respect to style and intellectual content, is referred to you for judgment

The purpose of this study was to determine whether there was a relationship between pressure to perform on state mandated, high-stakes tests and the rate of student escape behavior defined as the number of school suspensions and absences. The state assigned grade of a school was used as a surrogate measure of pressure with the assumption that pressure increased as the school grade decreased. Student attendance and suspension data were gathered from all 33 of the regular public high schools in Miami-Dade County Public Schools. The research questions were: Is the number of suspensions highest in the third quarter, when most FCAT preparation takes place for each of the 3 school years 2007-08 through 2009-10? How accurately does the high school’s grade predict the number of suspensions and number of absences during each of the 4 school years 2005-06 through 2008-09? The research questions were answered using repeated measures analysis of variance for research question #1 and non-linear multiple regression for research question #2. No significant difference could be found between the numbers of suspensions in each of the grading periods nor was there a relationship between the number of suspensions and school grade. A statistically significant relationship was found between student attendance and school grade. When plotted, this relationship was found to be quadratic in nature and formed a loose inverted U for each of the four years during which data were collected. This indicated that students in very high and very low performing schools had low levels of absences while those in the midlevel of the distribution of school performance (C schools) had the greatest rates of absence. Identifying a relationship between the pressures associated with high stakes testing and student escape behavior suggests that it might be useful for building administrators to reevaluate test preparation activities and procedures being used in their building and to include anxiety reducing strategies. As a relationship was found, it sets the foundation for future studies to identify whether testing related activities are impacting some students emotionally and are causing unintended consequences of testing mandates.