Main focus is to extend the analysis of the ruin related quantities, such as the surplus immediately prior to ruin, the deficit at ruin or the ruin probability, to the delayed renewal risk models. First, the background for the delayed renewal risk model is introduced and two important equations that are used as frameworks are derived. These equations are extended from the ordinary renewal risk model to the delayed renewal risk model. The first equation is obtained by conditioning on the first drop below the initial surplus level, and the second equation by conditioning on the amount and the time of the first claim. Then, we consider the deficit at ruin in particular among many random variables associated with ruin and six main results are derived. We also explore how the Gerber-Shiu expected discounted penalty function can be expressed in closed form when distributional assumptions are given for claim sizes or the time until the first claim. Lastly, we consider a model that has premium rate reduced when the surplus level is above a certain threshold value until it falls below the threshold value. The amount of the reduction in the premium rate can also be viewed as a dividend rate paid out from the original premium rate when the surplus level is above some threshold value. The constant barrier model is considered as a special case where the premium rate is reduced to $0$ when the surplus level reaches a certain threshold value. The dividend amount paid out during the life of the surplus process until ruin, discounted to the beginning of the process, is also considered.

The purpose of this study was to describe and analyze youth community service in the Kalmar municipality. Our focus was on juvenile offenders and predecessor of public authorities. The juvenile offenders in our study have completed youth community service. A qualitative study was undertaken which include seven interviews. Our empirical data were compared and analyzed with previous research data. This was used in combination with two theoretical perspectives relevant to this study’s purpose and questions. Results of our empirical data showed that the experience of youth community service was an appropriate/good penalty method.  Even though the juveniles viewed it as an appropriate/good method, they did not consider it an effective method to prevent them from committing additional crimes. The study also showed that the adolescents’ viewed the experience very differently when the treatment came from the predecessors of public authorities. The juveniles in the study thought the police had a bad attitude but considered the social service to be very helpful and active listeners. The predecessors of public authorities thought the cooperation between them to be good and important.

Main focus is to extend the analysis of the ruin related quantities, such as the surplus immediately prior to ruin, the deficit at ruin or the ruin probability, to the delayed renewal risk models. First, the background for the delayed renewal risk model is introduced and two important equations that are used as frameworks are derived. These equations are extended from the ordinary renewal risk model to the delayed renewal risk model. The first equation is obtained by conditioning on the first drop below the initial surplus level, and the second equation by conditioning on the amount and the time of the first claim. Then, we consider the deficit at ruin in particular among many random variables associated with ruin and six main results are derived. We also explore how the Gerber-Shiu expected discounted penalty function can be expressed in closed form when distributional assumptions are given for claim sizes or the time until the first claim. Lastly, we consider a model that has premium rate reduced when the surplus level is above a certain threshold value until it falls below the threshold value. The amount of the reduction in the premium rate can also be viewed as a dividend rate paid out from the original premium rate when the surplus level is above some threshold value. The constant barrier model is considered as a special case where the premium rate is reduced to $0$ when the surplus level reaches a certain threshold value. The dividend amount paid out during the life of the surplus process until ruin, discounted to the beginning of the process, is also considered.

This thesis describes the research conducted on the use of historical performance data in assessing the financial risk for a power distribution utility in a performance based regulation (PBR) regime. The historical utility data used in this research are taken from the Canadian Electrical Association (CEA) annual reports. The individual utility data in these reports are confidential and only provided to the participating utilities. Thirteen utilities that participate in the CEA data reporting activity agreed to provide their individual utility data for the research described in this thesis. These utilities are anonymous and are referred to by numerical designations in accordance with the CEA protocol. This research could not have been conducted without the support of these utilities. The objectives of the research described in this thesis are to examine and analyze the variations in the annual performance indices of the thirteen participating utilities and the aggregated systems including the overall indices and the cause code contributions, and to examine the possible utilization of historic utility reliability indices to create suitable reward/penalty structures in a PBR protocol. The potential financial risk and actual financial payment analyses for these selected utilities are conducted using their historical performance data imposed on a number of possible reward/penalty structures developed in this thesis. An approach to recognize adverse utility performance in the form of Major Outage Years (MOY) is developed and the influence of the MOY performance in PBR decision making is examined.

This thesis develops approximate dynamic programming (ADP) strategies suitable for process control problems aimed at overcoming the limitations of MPC, which are the potentially exorbitant on-line computational requirement and the inability to consider the future interplay between uncertainty and estimation in the optimal control calculation. The suggested approach solves the DP only for the state points visited by closed-loop simulations with judiciously chosen control policies. The approach helps us combat a well-known problem of the traditional DP called 'curse-of-dimensionality,' while it allows the user to derive an improved control policy from the initial ones. The critical issue of the suggested method is a proper choice and design of function approximator. A local averager with a penalty term is proposed to guarantee a stably learned control policy as well as acceptable on-line performance. The thesis also demonstrates versatility of the proposed ADP strategy with difficult process control problems. First, a stochastic adaptive control problem is presented. In this application an ADP-based control policy shows an "active" probing property to reduce uncertainties, leading to a better control performance. The second example is a dual-mode controller, which is a supervisory scheme that actively prevents the progression of abnormal situations under a local controller at their onset. Finally, two ADP strategies for controlling nonlinear processes based on input-output data are suggested. They are model-based and model-free approaches, and have the advantage of conveniently incorporating the knowledge of identification data distribution into the control calculation with performance improvement.

In this research, least-squares based finite element formulations and their applications in fluid mechanics are presented. Least-squares formulations offer several computational and theoretical advantages for Newtonian as well as non-Newtonian fluid flows. Most notably, these formulations circumvent the inf-sup condition of Ladyzhenskaya-Babuska- Brezzi (LBB) such that the choice of approximating space is not subject to any compatibility condition. Also, the resulting coefficient matrix is symmetric and positive-definite. It has been observed that pressure and velocities are not strongly coupled in traditional leastsquares based finite element formulations. Penalty based least-squares formulations that fix the pressure-velocity coupling problem are proposed, implemented in a computational scheme, and evaluated in this study. The continuity equation is treated as a constraint on the velocity field and the constraint is enforced using the penalty method. These penalty based formulations produce accurate results for even low penalty parameters (in the range of 10-50 penalty parameter). A stress based least-squares formulation is also being proposed to couple pressure and velocities. Stress components are introduced as independent variables to make the system first order. The continuity equation is eliminated from the system with suitable modifications. Least-squares formulations are also developed for viscoelastic flows and moving boundary flows. All the formulations developed in this study are tested using several benchmark problems. All of the finite element models developed in this study performed well in all cases. A method to exploit orthogonality of modal bases to avoid numerical integration and have a fast computation is also developed during this study. The entries of the coefficient matrix are calculated analytically. The properties of Jacobi polynomials are used and most of the entries of the coefficient matrix are recast so that they can be evaluated analytically.

In this thesis, least-squares based finite element models (LSFEM) for the Poisson equation and Navier-Stokes equation are presented. The least-squares method is simple, general and reliable. Least-squares formulations offer several computational and theoretical advantages. The resulting coefficient matrix is symmetric and positive-definite. Using these formulations, the choice of approximating space is not subject to any compatibility condition. The Poisson equation is cast as a set of first order equations involving gradient of the primary variable as auxiliary variables for the mixed least-square finite element model. Equal order C0 continuous approximation functions is used for primary and auxiliary variables. Least-squares principle was directly applied to develop another model which requires C1continous approximation functions for the primary variable. Each developed model is compared with the conventional model to verify its performance. Penalty based least-squares formulation was implemented to develop a finite element for the Navier Stokes equations. The continuity equation is treated as a constraint on the velocity field and the constraint is enforced using the penalty method. Velocity gradients are introduced as auxiliary variables to get the first order equivalent system. Both the primary and auxiliary variables are interpolated using equal order C0 continuous, p-version approximation functions. Numerical examples are presented to demonstrate the convergence characteristics and accuracy of the method.

In recent years Boolean Networks (BN) and Probabilistic Boolean Networks (PBN) have become popular paradigms for modeling gene regulation. A PBN is a collection of BNs in which the gene state vector transitions according to the rules of one of the constituent BNs, and the network choice is governed by a selection distribution. Intervention in the context of PBNs was first proposed with an objective of avoid- ing undesirable states, such as those associated with a disease. The early methods of intervention were ad hoc, using concepts like mean first passage time and alteration of rule based structure. Since then, the problem has been recognized and posed as one of optimal control of a Markov Network, where the objective is to find optimal strategies for manipulating external control variables to guide the network away from the set of undesirable states towards the set of desirable states. This development made it possible to use the elegant theory of Markov decision processes (MDP) to solve an array of problems in the area of control in gene regulatory networks, the main theme of this work. We first introduce the optimal control problem in the context of PBN models and review our solution using the dynamic programming approach. We next discuss a case in which the network state is not observable but for which measurements that are probabilistically related to the underlying state are available. We then address the issue of terminal penalty assignment, considering long term prospective behavior and the special attractor structure of these networks. We finally discuss our recent work on optimal intervention for the case of a family of BNs. Here we consider simultaneously controlling a set of Boolean Models that satisfy the constraints imposed by the underlying biology and the data. This situation arises in a case where the data is assumed to arise by sampling the steady state of the real biological network.

This study analyzed case and sentencing data from 632 capital cases involving Black and White defendants and victims, processed in North Carolina from May 1990 through December 2002. Logistic regression analysis of all cases and race-specific data allowed assessment of the variable effects of jury acceptance of statutory aggravating and mitigating factors on capital sentencing outcomes (death versus life). The purpose was to evaluate the role race plays in shaping jury use of legally defined factors in capital sentencing. Significant variance in the effect of jury acceptance of aggravators was observed between Black and White defendants. Black defendants pay a higher premium in terms of the risk of a death sentence than do White defendants whose crimes are comparably aggravated. There was no overall disparity in the effect of jury acceptance of mitigatory factors observed, although certain mitigators reduced the risk of a death sentence significantly more for Black or White. Overall, the aggravators had a statistically significantly stronger effect on sentencing outcomes than did the mitigators, regardless of race, and on cases involving Black defendants, regardless of victim race. Racial invariance was not shown.

Disparities in the administration of capital punishment are a prominent social and political issue. While the focus of death penalty disparity research initially lay with the defendant and how the defendant’s race or ethnicity affects sentencing outcomes, only marginal support for offender effects has been found. A consistent finding, however, is that victim race has a significant effect on capital sentencing outcomes. Recent examinations of the joint effects of victim characteristics indicate that victim gender also has some influence in capital sentencing decisions. While these prior studies have examined the interactive effects of victim gender and victim race the current study proposes that victim-related variables other than race may be important components in understanding the female victim effect. This analysis is focused on understanding the joint effects of victim gender in terms of identifying an “innocent female victim” effect. Based on prior studies and theoretical perspectives, three hypotheses are proposed and tested here using a sub-population of capital cases in North Carolina between the years 1990 and 2007: 1. Cases with a female victim and male defendant will be more likely to result in the death penalty than other defendant-victim gender dyads, 2. Cases with a female victim and stranger defendant will be more likely to result in the death penalty than other dyads, and 3. Cases with a female victim who was not involved in illegal activity at the time of her victimization will be more likely to result in the death penalty than other dyads. The results indicate that victim conduct (illegal activity) and victim gender both play a role in jury sentencing recommendations, but regardless of victim conduct, cases with a female victim are the most likely to result in the death penalty. Therefore, this study finds marginal support for an “innocent female victim” effect in jury decisions to recommend the death penalty, but consistent support for a “female victim” effect. Conclusions and implications of the findings are discussed.