A Generalized Typicality for Abstract Alphabets

A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including conditional typicality lemma, joint typicality lemma, and packing and covering lemmas, which are fundamental tools for deriving many inner bounds of various multi-terminal coding problems, are obtained in terms of the proposed notion. This enables us to directly generalize lots of results on finite alphabet problems to general problems involving abstract alphabets, without any complicated additional arguments. For instance, quantization procedure is no longer necessary to achieve such generalizations. Another fundamental lemma, Markov lemma, is also obtained but its scope of application is quite limited compared to others. Yet, an alternative theory of typical sets for Gaussian measures, free from this limitation, is also developed. Some remarks on a possibility to generalize the proposed notion for sources with memory are also given.Comment: 44 pages; submitted to IEEE Transactions on Information Theor

Subjectivity and health for Korean "goose mothers" in New Zealand : a thesis presented in partial fulfillment of the requirements for the degree of Master of Arts in Psychology at Massey University, Albany, New Zealand

The number of Korean goose mothers living in New Zealand with their children, while their husbands remain in their home country, is rapidly increasing. This particular form of Asian migration to Western countries is a new phenomenon, and brings with it new forms of family life. Existing research does not tell us much about how these mothers adjust to, and manage their health in, such different circumstances. This research explores how these Korean goose mothers experience their subjectivities in the new country and how these subjectivities relate to their health practice. Drawing on a critical perspective, I suggest that multiple subjectivities form through the different cultural discourses that are available to the mothers in their new context. Discourses around gender, health and ethnicity provide relevance to the Korean women, through constructing meanings of what it is to be a good mother, a Korean as well as a member of an ethnic minority group while in New Zealand. These constructions position the women in asymmetrical relationships: between men and women, between western health practitioners and Korean patients, and between the host society and the ethnic minority group. These multiple and simultaneous relationships complicate the Korean women's subjectivities, which are constantly renegotiated in response to these relationships. By both complying with and resisting positionings caused by these asymmetrical relationships, the women reinterpret and reformulate their subjectivities. They experience changes in their health, because their health practice relates so closely to their multiple subjectivities in New Zealand as mothers, Koreans, and members of an ethnic minority group. These findings provide further possibilities for understanding, and for intervening with Korean goose mothers' adjustment and health, if we attend to these multiple and contingent subjectivities which are complicated by gender and ethnicity in their new context. [From Introduction

Understanding Teacher Reflection as a Significant Tool for Bringing Reform-Based Teaching to College Mathematics

This paper describes a senior mathematics professor’s effort to change his teaching practice in a mathematical analysis course for secondary pre-service teachers in alignment with the current reform movement. Data include semester-long observations and interviews with the professor and his students. The data were analyzed by the use of reflection as the most significant tool for examining his experience of bringing about change. The reflection was used as a bridge from theory to practice by serving as a significant point for the professor to experience the process of professional development in a real sense. Discussions include the role of teacher reflection, teacher beliefs about good teaching and their manifestation in practice, the role of students in a reform-based classroom and the professor\u27s effort for changing pedagogy of the mathematics course and his search for continuing the effort. The researcher includes her own reflection of the processes of understanding the change process. Her views on inconsistency between the professors beliefs and his practice, the role of reflection as a hallmark of professionalism, and the importance of environment and support for the change to be sustainable are addressed