The main object of study in this thesis is branching Brownian motion, in which each particle moves like a Brownian motion and gives birth to new particles at some rate. In particular we are interested in where particles are located in this model at large times T : so, for a function f up to time T , we want to know how many particles have paths that look like f. Additive spine martingales are central to the study, and we also investigate some simple general properties of changes of measure related to such martingales.

by Li Jian Lin. / "November 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 85-90) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Lo Yiu Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 89-90). / Abstract also in Chinese. / Abstract --- p.iii / Acknowledgements --- p.iv / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Main Idea --- p.5 / Chapter 1.2. --- Organization --- p.8 / Chapter Chapter 2. --- Geometric and Analytic Preliminaries --- p.9 / Chapter 2.1. --- A Review on Measure Theory --- p.9 / Chapter 2.2. --- Submanifolds in Rn --- p.11 / Chapter 2.3. --- Several Results from PDEs --- p.17 / Chapter 2.4. --- Biharmonic Comparison Lemma --- p.20 / Chapter Chapter 3. --- Approximate Graphical Decomposition --- p.24 / Chapter 3.1. --- Some Preliminaries --- p.24 / Chapter 3.2. --- Approximate Graphical Decomposition --- p.30 / Chapter Chapter 4. --- Existence & Regularity of Measure-theoretic Limits of Minimizing Sequence --- p.41 / Chapter 4.1. --- Willmore Functional and Area --- p.41 / Chapter 4.2. --- Existence of Measure-theoretic Limit of Minimizing Sequence --- p.45 / Chapter 4.3. --- Higher Regularity at Good Points --- p.54 / Chapter 4.4. --- Convergence in Hausdorff Distance Sense --- p.62 / Chapter 4.5. --- Regularity near Bad Points --- p.64 / Chapter Chapter 5. --- Existence of Genus 1 Minimizers in Rn --- p.83 / References --- p.89

Patients who are treated empathically tend to be more satisfied and have better health outcomes. Many instruments for measuring empathy in different health contexts have been developed for postgraduate and to a lesser extent undergraduate health professional use. This thesis presents the results of three studies. The first is a systematic review of the literature describing empathy measures for use in the health professional context. The review was conducted to find the best measure specifically designed for and evaluated in the clinical context that assessed empathy reliably and preferably from a patient perspective. The Consultation and Relational Empathy (CARE) measure was selected from the 12 potential empathy measures available. This instrument was developed and tested in general practice consultations in Scotland, and its usefulness for assessing physicians’ empathy has been demonstrated. The second study, which forms the main research component of the thesis, is an evaluation of the utility of the CARE measure in assessing medical undergraduates on general practice placements. This study aimed to establish whether the CARE measure offers a reliable, valid, and practical means of assessing certain aspects of senior clinical medical students’ consultation skills. Fifth-year students who performed a two- or three-month GP attachment in academic years 2009–2010, 2010–2011, and 2011– 2012 were invited to participate. In 2011 participation in the study became a course requirement. Consulted patients were invited to complete a modified CARE questionnaire ‘on the student’. The form initially included 11 questions answered on a five -point scale; from the academic year 2010–2011, the form also included a free-text comment option. Patients completed questionnaires anonymously. Forms were collated xvi and forwarded to the principle investigator. A minimum of 25 forms were required for each student in order to minimise potential selection bias in the analysis. In the first year of the study the response rate was 56 %. During the next two academic years, this rate improved to over 95%. The total number of the CARE measure forms returned was 2,145, with 1,808 adequately completed. The average score of the students recruited was 4.57 (standard deviation = 0.19), which is higher than average scores for general practitioners. Generalisability theory calculations showed that the CARE measure had high internal consistency, with 25 patients per student delivering an overall reliability coefficient of 0.74. Using the CARE measure with students significantly correlated at a moderate level with relevant outcome assessments such as the mini-Clinical Evaluation Exercise (mini-CEX), Objective Structured Clinical Examination (OSCE) at the end of the GP block, and tutor scores (r = 0.38, r = 0.33, r = 0.33, respectively; P < 0.05). The findings suggest that the CARE measure is a useful tool for assessing senior medical students’ consultation skills, at least in the context of extended general practice attachments. In addition, the measure provides students with valuable and authentic patient feedback for their training. The third study was a ‘mapping exercise’ designed to establish the role of current assessment tools at the University of Dundee in relation to Tomorrow’s Doctors outcomes, and specifically where/how CARE might fit in. Dundee medical faculty staff, block leaders, undergraduate medical educators, and others who engaged directly with assessments and with experience of the existing exams were invited to ‘map’ the value of each aspect of the medical school’s 11 assessment tools against General Medical Council (GMC) attributes. Data was collected electronically from 17 staff xvii members. The results of the exercise revealed both gaps in assessment and over-testing of specific GMC attributes. These findings offer Dundee Medical School an opportunity to optimise their approach to assessment and achieve a broader coverage of GMC outcomes. Thus, the CARE measure offers a logical extension to aspects of the OSCE assessment. The results show that the CARE measure is a feasible, acceptable, reliable, and valid measure for the assessment of students. In addition, as it incorporates authentic patient feedback into training, this measure can offer unique utility to the medical school’s curriculum and assessment as it incorporates the rarely employed patient voice.

Lai, Chun Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 83-87). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Spectral sets in Rd --- p.11 / Chapter 2.1 --- Preliminaries --- p.11 / Chapter 2.2 --- Fundamental domains and convex sets in Rd --- p.15 / Chapter 2.3 --- Finite union of cubes --- p.20 / Chapter 3 --- Spectral theory on discrete groups --- p.27 / Chapter 3.1 --- Finite groups and Zd --- p.28 / Chapter 3.2 --- Rational spectrums and tiling sets --- p.32 / Chapter 3.3 --- Fuglede´ةs Problem in R1 --- p.37 / Chapter 3.4 --- "Failure of Fuglede´ةs Conjecture in Rd, d >3" --- p.42 / Chapter 4 --- Self-similar tiles in R1 --- p.49 / Chapter 4.1 --- Basics of self-similar tiles --- p.49 / Chapter 4.2 --- Self-similar tile digit sets and spectral problem --- p.52 / Chapter 4.3 --- Kenyon criterion --- p.55 / Chapter 5 --- Spectral self-similar measures --- p.66 / Chapter 5.1 --- Spectral self-similar measures --- p.66 / Chapter 5.2 --- One-dimensional self-similar measures --- p.72 / Chapter 5.3 --- General properties of spectral measures --- p.80 / Bibliography --- p.83

In this thesis we compute an explicit Plancherel fromula for PGL_2(F) where F is a non-archimedean local field. Let G be connected reductive group over a non-archimedean local field F. We show that we can obtain types and covers as defined by Kutzko and Bushnell for G/Z coming from types and covers of G in a very explicit way. We then compute those types and covers for GL_2(F ) which give rise to all types and covers for PGL_2(F) that are in the principal series. The Hecke algebra is a Hilbert algebra and has a measure associated to it called Plancherel measure of the Hecke algebra. We have that computing the Plancherel measure for PGL_2(F) essentially reduces to computing the Plancherel measure for the Hecke algebra for every type. We get that the Hacke algebras come in two flavors; they are either the group ring of the integers or they are a free algebra in two generators s_1, s_2 subject to the relations s_1^2=1 and s_2^2=(q^{-1/2}-q^{-1/2})s_2+1, where q is the order of the residue field. The Plancherel measure for both algebras are known, as a result we obtain the Plancherel measure for PGL_2(F).

An attitude is a mental state that influences the way an individual responds to relevant objects and situations. Attitudes toward the elderly have a potential impact on all Americans, as the population is growing older. These attitudes constitute an important area of study because their nature is unclear and their impact extensive. The Kogan Attitudes Toward Old People Scale (OP) was examined to establish reliability and validity estimates. A questionnaire, consisting of this scale and four others, was administered to a sample of adults. Factor analysis of the OP revealed two factors, which were somewhat ambiguous. Internal consistency estimates for these factors and the total OP ranged from .72 to .92. Validity estimates were in the expected direction and ranged from -.13 to .36. Gender, age, education level, and degree of tolerance for others immerged as predictive variables for reported attitudes toward the elderly. It was concluded that the use of the OP is of questionable utility. If one must use it, the total OP score or only the items from Factors 1 and 2 should be utilized, as long as the discussed weaknesses, such as the sampling and validation procedures, are taken into account

For my senior thesis, I am planning to blend my mathematical studies with my second field of study, psychology. In particular, to develop and test various scoring methods for a multidimensional, psychometric measure of social skills/competence. I would work with the Social Skills Inventory (see below) and an existing data set, using statistical modelling to design a more representative total score measure. The current total score measure does not appear to take into account balances and value weights of the six inventory items.

Research indicates that relational aggression, social aggression, and indirect aggression are important predictors and outcomes of social development (Archer & Coyne, 2005). Socially, indirectly, and relationally aggressive behaviors are utilized in order to harm an individual's social status, relationships, and/or social resources (Archer, & Coyne, 2005), but scholars disagree about the extent of the similarities and differences between these subtypes. Previous efforts to understand the distinction between these subtypes of aggression have been limited by how these behaviors have been operationalized and studied. The primary aim of the current study was to develop a self-report measure of these aggressive behaviors for emerging adults by utilizing factor analytic techniques to examine existing and newly created items. A series of five stages was used to code all items into existing theoretical categories of behavior (e.g., social aggression), establish the factor structure of the items, select the best items to measure each factor, test measurement invariance across subgroups (e.g., men and women), ensure strong psychometric properties, and relate the final factor structure to relevant developmental correlates (e.g., depressive symptoms). Three independent samples of emerging adults aged 18 - 29 years (49.51% - 52.33% women; Mage= 25.71 - 26.26) were recruited online through Amazon's Mechanical Turk (sample 1 N = 299; sample 2 N = 299; sample 3 N = 119). Indirect, social, and relational aggression items were selected and adapted from existing self-report measures of these constructs for adults and several new items were created from qualitative interviews with emerging adults. Through a rigorous theoretical, methodological, and statistical approach, the Relational/Social Aggression in Adulthood Measure (RSAAM) was developed. The final factor structure consisted of three factors: Ignoring, Gossip, and Relational Manipulation. The three factors demonstrated measurement invariance across gender and educational groups and strong internal consistency and test-retest reliability. Purely relationally manipulative behaviors were distinct from other, related behaviors (i.e., ignoring, gossip) and were also differentially related to developmental correlates. Findings suggest that it may be advantageous for researchers to move beyond broad theoretical definitions of relational and social aggression and instead focus on the specific aggressive behaviors being enacted.

Research indicates that relational aggression, social aggression, and indirect aggression are important predictors and outcomes of social development (Archer & Coyne, 2005). Socially, indirectly, and relationally aggressive behaviors are utilized in order to harm an individual’s social status, relationships, and/or social resources (Archer, & Coyne, 2005), but scholars disagree about the extent of the similarities and differences between these subtypes. Previous efforts to understand the distinction between these subtypes of aggression have been limited by how these behaviors have been operationalized and studied. The primary aim of the current study was to develop a self-report measure of these aggressive behaviors for emerging adults by utilizing factor analytic techniques to examine existing and newly created items. A series of five stages was used to code all items into existing theoretical categories of behavior (e.g., social aggression), establish the factor structure of the items, select the best items to measure each factor, test measurement invariance across subgroups (e.g., men and women), ensure strong psychometric properties, and relate the final factor structure to relevant developmental correlates (e.g., depressive symptoms). Three independent samples of emerging adults aged 18 – 29 years (49.51% –52.33% women; Mage= 25.71 - 26.26) were recruited online through Amazon’s Mechanical Turk (sample 1 N = 299; sample 2 N = 299; sample 3 N = 119). Indirect, social, and relational aggression items were selected and adapted from existing self-report measures of these constructs for adults and several new items were created from qualitative interviews with emerging adults. Through a rigorous theoretical, methodological, and statistical approach, the Relational/Social Aggression in Adulthood Measure (RSAAM) was developed. The final factor structure consisted of three factors: Ignoring, Gossip, and Relational Manipulation. The three factors demonstrated measurement invariance across gender and educational groups and strong internal consistency and test-retest reliability. Purely relationally manipulative behaviors were distinct from other, related behaviors (i.e., ignoring, gossip) and were also differentially related to developmental correlates. Findings suggest that it may be advantageous for researchers to move beyond broad theoretical definitions of relational and social aggression and instead focus on the specific aggressive behaviors being enacted.