In this paper, we prove that the simulation method for interval-censored data proposed by Fay (1999) is consistent in the sense that if we select a sample, then the estimate obtained from Turnbulls (1974) EM algorithm will converge to the true parameter when the sample size tends to infinity. We also propose a non-parametric rank test for interval-censored data to determine whether two populations come from the same distribution. Simulation result shows that the proposed test statistics performs pretty satisfactory.

A t-spanner of a graph G is a subgraph H of G, which the distance between any two vertices in H is at most t times their distance in G. A tree t-spanner of G is a t-spanner which is a tree. In this dissertation, we discuss the t-spanners on trapezoid, permutation, and interval graphs. We first introduce an O(n) algorithm for finding a tree 4-spanner on trapezoid graphs. Then, give an O(n)algorithm for finding a tree 3-spanner on permutation graphs, improving the existed O(n + m) algorithm. Since the class of permutation graphs is a subclass of trapezoid graphs, we can apply the algorithm on permutation graphs to find the approximation of a tree 3-spanner on trapezoid graphs in O(n) time with edge bound 2n. Finally, we show that not all interval graphs have a tree 2-spanner.

Many construction companies today utilize webcams on their jobsites to monitor and record construction operations. Jobsite monitoring is often limited to outdoor construction operations due to lack of mobility of wired webcams. A wireless webcam may help monitor indoor construction operations with enhanced mobility. The transfer time of sending a photograph from the wireless webcam, however, is slower than that of a wired webcam. It is expected that professionals may have to analyze indoor construction operations with longer interval time-lapse photographs if they want to use a wireless webcam. This research aimed to determine the maximum time interval for time-lapse photos that enables professionals to interpret construction operations and productivity. In order to accomplish the research goal, brickwork of five different construction sites was videotaped. Various interval time-lapse photographs were generated from each video. Worker?s activity in these photographs was examined and graded. The grades in one-second interval photographs were compared with the grades of the same in longer time interval photographs. Error rates in observing longer time-lapse photographs were then obtained and analyzed to find the maximum time interval of time-lapse photography for monitoring construction operations. Research has discovered that the observation error rate increased rapidly until the 60-second interval and its increasing ratio remained constant. This finding can be used to predict a reasonable amount of error rate when observing time-lapse photographs less than 60-second interval. The observation error rate with longer than 60-second interval did not show a constant trend. Thus, the 60-second interval could be considered as the maximum time interval for professionals to interpret construction operations and productivity.

Two types of fuzzy linear programming i.e. fuzzy number linear programming and interval number linear programming are used for optimization problems. In interval form of linear programming we convert the inequalities from the feasible region, containing intervals as coefficients, to two groups of inequalities characterized by real, exact coefficients values. Then classical programming has been used to achieve an optimal solution in the feasible region. In fuzzy number linear programming, α‐cuts and LR forms of fuzzy numbers as coefficients have been used to find optimal solution in the feasible region. Finally the numerical examples and their solutions are attached to provide explanations of procedures.

Analyzing the twelve-tone compositions of Shostakovich often requires the application of various analytical procedures. This study examines Shostakovich's Suite for Voice and Piano, Op. 143, focusing on the two twelve-tone songs in the Suite. While the songs exhibit some traditional treatment of twelve-tone rows, the study focuses on Shostakovich's unique manipulations and the integration of tonal elements and chromaticism. An innovative analytical tool developed by Dr. Stephen Brown (NAU) is utilized in the study, as it provides clarity and strengthens otherwise weak associations. Along with the application of Brown's dual interval space, the study includes twelve-tone analysis and traditional harmonic analysis to provide a more comprehensive analysis of the Suite.

published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

The study and contemplation of the natural world was a significant impetus for the stylistic development of Maurice Ohana's (1913-1992) music. More than any other source, it was the sounds, textures, and patterns of the natural world that served as his compositional model, inspiring a unique approach to form and sound. Using the metaphor of a coral reef, Ohana sought to imbue his compositions with a process of development that organically generated musical form. His mature musical style is defined by an organic development of traits inherent within the motivic beginning of a work to produce unique musical structures that are intrinsically connected with their musical substance. Ohana's final work for piano solo, the Études d'interprétation (1983/6), demonstrate the process of organic development. Complementing Claude Debussy's (1862-1918) Études, Ohana's interval etudes 'Secondes,' 'Quintes,' 'Septiemes,' and 'Neuvièmes' illustrate the stylistic variety generated by his unique, sound-driven approach to form. The following analyses address the thematic development of each work, connecting melodic, harmonic, and textural material to the opening, and developmentally central, `germ' each composition begins with. By examining the comprehensive process of organic development within Ohana's four interval etudes it may be possible to gain a greater understanding of his unique musical language

A failure recovery methodology based on decomposing the platform task space into the major and secondary subtasks is proposed which enables the manipulator to minimize the least-squares error of the major subtasks and to optimize the secondary criterion. A methodology for wrench recovery of parallel manipulators is proposed so that the platform task is divided into the recoverable and non-recoverable subtasks based on the number and type of actuator failures, manipulator configuration and task/application purposes. It is investigated that when the Jacobian matrix of the manipulator is of full row-rank and the minimum 2-norm of the joint velocity vector satisfies the velocity limits of the joints, the full recovery of the platform twist will be provided. If the full recovery of the platform twist cannot be achieved, the optimization method followed by the partitioned Jacobian matrix is used to deal with the failure recovery. It is verified that the optimization method recovers as many as possible components of the platform velocity vector when the objective function, 2-norm of the overall velocity vector of the healthy joints, is minimized. To model uncertainty in the kinematic parameters, the interval analysis is proposed. Different interval-based algorithms to enclose the solution set to the interval linear systems are applied and the solution sets are compared. A novel approach in characterizing the exact solution of the interval linear system is proposed to deal with the failure recovery of parallel manipulators with velocity limits of the joints and uncertainty in the kinematic parameters. Simulation results show how the solution sets of the joint velocity vector are characterized by introducing uncertainties in the kinematic parameters. The calculation of the exact solution takes more computation time compared to the interval-based algorithms. However, the interval-based algorithms give the wider solution box with less computation time. The effect of variations and/or uncertainties in design parameters on the workspace of wire-actuated parallel manipulators without and with gravity is investigated. Simulation results show how the workspace size and shape are changed under variations in design parameters. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2014-03-09 16:18:12.74

Diagnostic tests are central in the field of modern medicine. One of the main factors for interpreting a diagnostic test is the discriminatory accuracy. For a continuous-scale diagnostic test, the area under the receiver operating characteristic (ROC) curve, AUC, is a useful one-number summary index for the diagnostic accuracy of the test. When only a particular region of the ROC curve would be of interest, the partial AUC (pAUC) is a more appropriate index for the diagnostic accuracy. In this thesis, we develop seven confidence intervals for the pAUC under the semi-parametric models for the diseased and non-diseased populations by using the normal approximation, bootstrap and empirical likelihood methods. In addition, we conduct simulation studies to compare the finite sample performance of the proposed confidence intervals for the pAUC. A real example is also used to illustrate the application of the recommended intervals.

In this thesis, we study two independent samples under right censoring. Using a smoothed empirical likelihood method, we investigate the difference of quantiles in the two samples and construct the pointwise confidence intervals from it as well. The empirical log-likelihood ratio is proposed and its asymptotic limit is shown as a chi-squared distribution. In the simulation studies, in terms of coverage accuracy and average length of confidence intervals, we compare the empirical likelihood and the normal approximation method. It is concluded that the empirical likelihood method has a better performance. At last, a real clinical trial data is used for the purpose of illustration. Numerical examples to illustrate the efficacy of the method are presented.