A comparisation of methods for the optimisation of a non-linear function subject to non-linear constraints

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A mixed methods investigation of parental factors in non-attendance at general paediatric hospital outpatient appointments

Non-attendance at paediatric outpatient appointments results in delayed diagnosis and treatment, putting children at risk of avoidable ill health, and incurring considerable health service costs. Links between missed appointments and clinical, socio-demographic, and access-related factors have been indicated, but parental cognitions associated with non-attendance have yet to be investigated. The aims of this project were to evaluate the effectiveness and theoretical bases of existing interventions designed to reduce non-attendance; to consider the ways in which missed appointments are managed by healthcare providers; to explore parents’ beliefs and experiences of attending and missing appointments; and to investigate the factors underlying these beliefs. A systematic literature review focusing on non-attendance interventions was conducted Within a mixed methods framework, interviews were conducted with healthcare professionals, subsequent interviews were conducted with parents who had attended or missed a General Paediatric outpatient appointment, and a cross-sectional questionnaire study of parents’ beliefs was implemented. The systematic review revealed that text message appointment reminders are effective at reducing non-attendance rates, but that no interventions have thus far been developed using theories of behaviour. Healthcare professionals recognised both barriers and parents’ beliefs as influences on attendance, but also believed there were ‘types’ of families who miss appointments. Healthcare professionals disagreed somewhat about how non-attendance should best be managed. The parent interview study found six themes. The findings reflect parents’ perceptions about the importance of attending and of their ability to attend. The results of the questionnaire study corroborate this structure of beliefs as the analysis produced two factors, the perceived ‘worth’ of attending and anticipated ‘worry’ when attending. This thesis demonstrates an original approach to investigating non-attendance at children’s outpatient appointments, using mixed methods and adopting a psychological rather than service-use perspective. The findings contribute to Health Psychology theory and offer recommendations for healthcare providers.

Greedy Approximation with Regard to Bases and General Minimal Systems

*This research was supported by the National Science Foundation Grant DMS 0200187 and by ONR Grant N00014-96-1-1003

Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

Általános egyensúlyi modellek alkalmazása gazdaságpolitikai elemzésekre (Application of general equilibrium models to economic policy analyses)

A szerző az alkalmazott többszektoros modellezés területén a lineáris programozási modellektől a számszerűsített általános egyensúlyi modellekig végbement változásokat tekinti át. Egy rövid történeti visszapillantás után a lineáris programozás módszereire épülő nemzetgazdasági szintű modellekkel összevetve mutatja be az általános egyensúlyi modellek közös, illetve eltérő jellemzőit. Egyidejűleg azt is érzékelteti, hogyan lehet az általános egyensúlyi modelleket a gazdaságpolitikai célok konzisztenciájának, a célok közötti átváltási lehetőségek elemzésére és általában a gazdaságpolitikai elképzelések érzékenységi vizsgálatára felhasználni. A szerző az elméleti-módszertani kérdések taglalását számszerűsített általános egyensúlyi modell segítségével illusztrálja. _______ The author surveys the changes having taken place in the field of multi-sector modeling, from the linear programming models to the quantified general equilibrium models. After a brief historical retrospection he presents the common and different characteristic features of the general equilibrium models by comparing them with the national economic level models based on the methods of linear programming. He also makes clear how the general equilibrium models can be used for analysing the consistency of economic policy targets, for the investigation of trade-off possibilities among the targets and, in general, for sensitivity analyses of economic policy targets. The discussion of theoretical and methodological quuestions is illustrated by the author with the aid of a quantified general equilibrium model.

Reliability analysis of encapsulation methods for lead -based paint through an accelerated life testing

The adverse health effects of long-term exposure to lead are well established, with major uptake into the human body occurring mainly through oral ingestion by young children. Lead-based paint was frequently used in homes built before 1978, particularly in inner-city areas. Minority populations experience the effects of lead poisoning disproportionately. ^ Lead-based paint abatement is costly. In the United States, residents of about 400,000 homes, occupied by 900,000 young children, lack the means to correct lead-based paint hazards. The magnitude of this problem demands research on affordable methods of hazard control. One method is encapsulation, defined as any covering or coating that acts as a permanent barrier between the lead-based paint surface and the environment. ^ Two encapsulants were tested for reliability and effective life span through an accelerated lifetime experiment that applied stresses exceeding those encountered under normal use conditions. The resulting time-to-failure data were used to extrapolate the failure time under conditions of normal use. Statistical analysis and models of the test data allow forecasting of long-term reliability relative to the 20-year encapsulation requirement. Typical housing material specimens simulating walls and doors coated with lead-based paint were overstressed before encapsulation. A second, un-aged set was also tested. Specimens were monitored after the stress test with a surface chemical testing pad to identify the presence of lead breaking through the encapsulant. ^ Graphical analysis proposed by Shapiro and Meeker and the general log-linear model developed by Cox were used to obtain results. Findings for the 80% reliability time to failure varied, with close to 21 years of life under normal use conditions for encapsulant A. The application of product A on the aged gypsum and aged wood substrates yielded slightly lower times. Encapsulant B had an 80% reliable life of 19.78 years. ^ This study reveals that encapsulation technologies can offer safe and effective control of lead-based paint hazards and may be less expensive than other options. The U.S. Department of Health and Human Services and the CDC are committed to eliminating childhood lead poisoning by 2010. This ambitious target is feasible, provided there is an efficient application of innovative technology, a goal to which this study aims to contribute. ^

RELIBILITY ANALYSIS OF SIMPLE SLOPES AND SOIL-STRUCTURES WITH LINEAR LIMIT STATES

The first objective of this research was to develop closed-form and numerical probabilistic methods of analysis that can be applied to otherwise conventional methods of unreinforced and geosynthetic reinforced slopes and walls. These probabilistic methods explicitly include random variability of soil and reinforcement, spatial variability of the soil, and cross-correlation between soil input parameters on probability of failure. The quantitative impact of simultaneously considering the influence of random and/or spatial variability in soil properties in combination with cross-correlation in soil properties is investigated for the first time in the research literature. Depending on the magnitude of these statistical descriptors, margins of safety based on conventional notions of safety may be very different from margins of safety expressed in terms of probability of failure (or reliability index). The thesis work also shows that intuitive notions of margin of safety using conventional factor of safety and probability of failure can be brought into alignment when cross-correlation between soil properties is considered in a rigorous manner. The second objective of this thesis work was to develop a general closed-form solution to compute the true probability of failure (or reliability index) of a simple linear limit state function with one load term and one resistance term expressed first in general probabilistic terms and then migrated to a LRFD format for the purpose of LRFD calibration. The formulation considers contributions to probability of failure due to model type, uncertainty in bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety (OFS). Bias is defined as the ratio of measured to predicted value. Parametric analyses were carried out to show that ignoring possible correlations between random variables can lead to conservative (safe) values of resistance factor in some cases and in other cases to non-conservative (unsafe) values. Example LRFD calibrations were carried out using different load and resistance models for the pullout internal stability limit state of steel strip and geosynthetic reinforced soil walls together with matching bias data reported in the literature.

STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.

Therapeutic commitment for general nurses in dealing with mental health problems of People Living with HIV/AIDS in Blantyre, Malawi

Introduction Therapeutic commitment of general nurses influences their provision of mental health care to clients. It is the general nurses’ predisposition for working therapeutically with clients who have mental health problems (MHPs). In Malawi, general nurses are the majority of health care professionals who care for people living with HIV/AIDS (PLWHA) and they are expected to deal with the mental health problems of these patients. The provision of mental health care to PLWHA is vital because apart from the physical illnesses associated with the virus, these people are also affected by mental health problems. However, most general nurses, feel neither confident nor competent when dealing with the mental health problems of their clients in Malawi. This may negatively influence their therapeutic commitment in dealing with mental health problems of PLWHA. However, therapeutic commitment of general nurses in providing mental health care to PLWHA in Malawi remains unknown. Materials and Methods The study used a quantitative descriptive survey design. a convenient sample comprising of 136 general nurses was used and data was collected using Mental Health Problems Perception Questionnaire. Permission to use the tool in this study was granted by Prof. Lauder. Ethical approval to conduct the study was granted by Ethics Committees at University of KwaZulu Natal and University of Malawi. Data were analysed using Statistical Package for Social Sciences version 15.0. Results The study findings revealed that there is a linear relationship between general nurses’ levels of knowledge and skills and their therapeutic commitment (r=.40, n=136, p<.05) to provide mental health care of PLWHA. Conclusion This study suggests general nurses’ levels of therapeutic commitment in dealing with MHPs of PLWHA vary and their levels of knowledge and skill to deal with MHPs influence their willingness to provide mental health care to PLWHA.

Physical activity assessment in the general population; validated self-report methods.

Los cuestionarios auto-administrados han sido comúnmente utilizados en los estudios con grandes cohortes con el fin de evaluar la actividad física de sus participantes. Como consecuencia de ello, existe una considerable cantidad de evidencias científicas sobre el efecto protector de la actividad física sobre la salud. Sin embargo, los estudios de validación que utilizan métodos objetivos para la cuantificación de la actividad física o el gasto energético (el agua doblemente marcada, los acelerómetros, los podómetros, etc.) indican que la precisión de los cuestionarios es limitada. Los cuestionarios de actividad física pueden fallar especialmente al estimar la actividad física no vigorosa, y suelen centrarse de forma desproporcionada en los tipos de ejercicios planificados (ir en bicicleta, correr, andar,…), mientras que no suelen recoger las actividades de la vida diaria y movimientos de intensidad más moderada no planificada. La estimación del gasto energético a partir de estos datos no es recomendable. Por otro lado, y a pesar de que los métodos objetivos deberían de ser la primera elección a la hora de evaluar la actividad física, los cuestionarios se mantienen como herramientas válidas y con muchas ventajas, una de ellas, el bajo coste. Este tipo de instrumentos están específicamente diseñados y validados para diferentes grupos de edad y proporcionan información valiosa e importante, sobre todo, del patrón de actividad física. Los futuros estudios requieren de más precisión a la hora de medir la actividad física respecto a la que proporcionan los cuestionarios. Podemos concluir que probablemente un método mixto que combine los métodos objetivos y subjetivos y que incluya nuevos sistemas y registros electrónicos sería lo recomendable.

Physical activity assessment in the general population; instrumental methods and new technologies.

La medición objetiva del movimiento humano y la cuantificación del gasto energético debido a la actividad física es una necesidad identificada tanto en investigación como en clínica. Los métodos de referencia validados y bien definidos (el agua doblemente marcada, la calorimetría directa, la calorimetría indirecta) son caros y prácticamente se limitan a la investigación en el laboratorio. Por lo tanto, en los últimos años, se han desarrollado diferentes dispositivos de medición objetiva que son apropiados para los estudios de campo y clínicos. No hay ningún estándar de oro entre ellos, ya que todos tienen limitaciones. Los podómetros son ligeros, poco costosos, cuentan los pasos y aportan información sobre la actividad física total, pero no sobre el comportamiento y los patrones de actividad física. Los acelerómetros son caros, aportan información sobre patrón, frecuencia e intensidad de la actividad física, pero no sobre el tipo de actividad física. Los podómetros y acelerómetros únicamente recogen información sobre el movimiento del movimiento corporal, pero la validez en la estimación del gasto energético es limitada. La monitorización de la frecuencia cardíaca relaciona intensidad del ejercicio con gasto de energía, pero no aporta información sobre la actividad física. Los dispositivos GPS son portátiles, relativamente asequibles, no invasivos y recogen distancia, velocidad y elevación con hora y lugar exactos, pero quizás estén limitados para la evaluación de movimientos cortos de alta intensidad y elevado gasto energético. Los dispositivos de última generación combinan acelerometría con la medición de variables fisiológicas, comparten las ventajas de los dispositivos individuales y son más precisos. Para el cálculo del gasto energético se aplican algoritmos específicos de la actividad incluidos en el software del fabricante que pueden afectar a los resultados. La mayoría de los dispositivos estiman con mayor precisión el gasto energético a intensidades ligeras y moderadas, pero subestiman el gasto a intensidades muy ligeras y de mayor intensidad.

Integer Linear Programming for Sequence Problems: A general approach to reduce the problem size

Sequence problems belong to the most challenging interdisciplinary topics of the actuality. They are ubiquitous in science and daily life and occur, for example, in form of DNA sequences encoding all information of an organism, as a text (natural or formal) or in form of a computer program. Therefore, sequence problems occur in many variations in computational biology (drug development), coding theory, data compression, quantitative and computational linguistics (e.g. machine translation). In recent years appeared some proposals to formulate sequence problems like the closest string problem (CSP) and the farthest string problem (FSP) as an Integer Linear Programming Problem (ILPP). In the present talk we present a general novel approach to reduce the size of the ILPP by grouping isomorphous columns of the string matrix together. The approach is of practical use, since the solution of sequence problems is very time consuming, in particular when the sequences are long.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.