Closed Choice and a Uniform Low Basis Theorem

We study closed choice principles for different spaces. Given information about what does not constitute a solution, closed choice determines a solution. We show that with closed choice one can characterize several models of hypercomputation in a uniform framework using Weihrauch reducibility. The classes of functions which are reducible to closed choice of the singleton space, of the natural numbers, of Cantor space and of Baire space correspond to the class of computable functions, of functions computable with finitely many mind changes, of weakly computable functions and of effectively Borel measurable functions, respectively. We also prove that all these classes correspond to classes of non-deterministically computable functions with the respective spaces as advice spaces. Moreover, we prove that closed choice on Euclidean space can be considered as "locally compact choice" and it is obtained as product of closed choice on the natural numbers and on Cantor space. We also prove a Quotient Theorem for compact choice which shows that single-valued functions can be "divided" by compact choice in a certain sense. Another result is the Independent Choice Theorem, which provides a uniform proof that many choice principles are closed under composition. Finally, we also study the related class of low computable functions, which contains the class of weakly computable functions as well as the class of functions computable with finitely many mind changes. As one main result we prove a uniform version of the Low Basis Theorem that states that closed choice on Cantor space (and the Euclidean space) is low computable. We close with some related observations on the Turing jump operation and its initial topology

Completion of Choice

We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal role in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the Weihrauch lattice. On the other hand, choice problems also characterize several natural classes of computable problems, such as finite mind change computable problems, non-deterministically computable problems, Las Vegas computable problems and effectively Borel measurable functions. The closure operator of completion generates the concept of total Weihrauch reducibility, which is a variant of Weihrauch reducibility with total realizers. Logically speaking, the completion of a problem is a version of the problem that is independent of its premise. Hence, studying the completion of choice problems allows us to study simultaneously choice problems in the total Weihrauch lattice, as well as the question which choice problems can be made independent of their premises in the usual Weihrauch lattice. The outcome shows that many important choice problems that are related to compact spaces are complete, whereas choice problems for unbounded spaces or closed sets of positive measure are typically not complete.Comment: 30 page

Family Classes: Rethinking Contraceptive Choice

The political attention paid to moral values - in the context of the high profile fights over abortion, homosexuality, and abstinence education - has developed over the past quarter century in ideological terms as though race and class no longer existed. In fact, the changing understandings that attend family formation reflect a long term shift in the pathways to middle class life which has created a new technocratic elite - an elite that invests heavily in both men and women’s advanced degrees, and has remade family life to its advantage. The success of the new model, which we call the “blue family paradigm,” and the sexual revolution at its core undermines what had once been consensus support for traditional values (which we will call “the red family paradigm”), and for the structure of family life following from abstinence to courtship to marriage. The result of the tensions between these family ideals has been a moral backlash. In this Article, we highlight the tensions between the two family models, focusing on contraception, and critique the class-based nature of the results. We argue that the politicization of family issues has produced its own “vicious cycle” of moral concern, draconian changes that disproportionately affect the poorest and most vulnerable Americans, and a new round of moral panic justifying further punitive measures, as the initial restrictions (such as closing abortion clinics and slashing family planning funds) make matters worse. We conclude that the “culture wars” are very much about class, and yet they are framed as a fight between two relatively privileged groups, in which class implications of the struggle disappear from sight. This Article argues that only by making these class implications visible - for low income, middle class, and wealthy individuals - can we design more effective interventions that can break the cycle

Family Classes: Rethinking Contraceptive Choice

The political attention paid to moral values - in the context of the high profile fights over abortion, homosexuality, and abstinence education - has developed over the past quarter century in ideological terms as though race and class no longer existed. In fact, the changing understandings that attend family formation reflect a long term shift in the pathways to middle class life which has created a new technocratic elite - an elite that invests heavily in both men and women’s advanced degrees, and has remade family life to its advantage. The success of the new model, which we call the “blue family paradigm,” and the sexual revolution at its core undermines what had once been consensus support for traditional values (which we will call “the red family paradigm”), and for the structure of family life following from abstinence to courtship to marriage. The result of the tensions between these family ideals has been a moral backlash. In this Article, we highlight the tensions between the two family models, focusing on contraception, and critique the class-based nature of the results. We argue that the politicization of family issues has produced its own “vicious cycle” of moral concern, draconian changes that disproportionately affect the poorest and most vulnerable Americans, and a new round of moral panic justifying further punitive measures, as the initial restrictions (such as closing abortion clinics and slashing family planning funds) make matters worse. We conclude that the “culture wars” are very much about class, and yet they are framed as a fight between two relatively privileged groups, in which class implications of the struggle disappear from sight. This Article argues that only by making these class implications visible - for low income, middle class, and wealthy individuals - can we design more effective interventions that can break the cycle

Data driven rank tests for classes of tail alternatives

Tail alternatives describe the frequent occurrence of a non-constant shift in the two-sample problem with a shift function increasing in the tail. The classes of shift functions can be built up using Legendre polynomials. It is important to rightly choose the number of polynomials involved. Here this choice is based on the data, using a modification of Schwarz's selection rule. Given the data driven choice of the model, appropriate rank tests are applied. Simulations show that the new data driven rank tests work very well. While other tests for detecting shift alternatives as Wilcoxon's test may completely break down for important classes of tail alternatives, the new tests have high and stable power. The new tests have also higher power than data driven rank tests for the unconstrained two-sample problem. Theoretical support is obtained by proving consistency of the new tests against very large classes of alternatives, including all common tail alternatives. A simple but accurate approximation of the null distribution makes application of the new tests easy

The interactive sum choice number of graphs

We introduce a variant of the well-studied sum choice number of graphs, which we call the interactive sum choice number. In this variant, we request colours to be added to the vertices' colour-lists one at a time, and so we are able to make use of information about the colours assigned so far to determine our future choices. The interactive sum choice number cannot exceed the sum choice number and we conjecture that, except in the case of complete graphs, the interactive sum choice number is always strictly smaller than the sum choice number. In this paper we provide evidence in support of this conjecture, demonstrating that it holds for a number of graph classes, and indeed that in many cases the difference between the two quantities grows as a linear function of the number of vertices

High School students' participation and the provision of choice

Tesis (Profesor de Inglés para la Enseñanza Básica y Media y al grado académico de Licenciado en Educación)Participation has been studied by many researchers during the last years. Researchers and important authorities related to the educational field highlight the importance of having students who actively participate inside the classrooms. Participation promotes interaction, which is a key element in the acquisition of a new language, and for this reason, when it comes to English classes, participation becomes even more important. Even though many researchers have been focusing their studies on analyzing in-class participation, there is a lack of studies in which students’ perceptions about their own participation are considered. Due to the importance of participation, many people have tried to come out with ideas, class methodologies and techniques that could enhance participation. Little is known about the provision of choice within classes however, studies on the topic have shown that the provision of choice, when offered in an appropriate way, could be beneficial for the creation of a sense of autonomy on students, and more specifically on adolescents. For the aim of the current study to be fulfill, the provision of choice will be considered as the opportunity for the meaningful realization of the individual’s desires or preferences related to class materials. The purpose of the current study is to understand high school students’ classroom participation views, and explore whether the provision of choice could somehow influence their perceptions about participation. An explanatory study using a mixed-method research design was used. A survey, a quantitative instrument, was utilized at the beginning of this investigation in order to select 5 out of 41 students from a ninth grade of a subsidized school. Classes in the school selected for this study were focused mainly on grammar and the participation rate inside the classroom was low therefore, it was considered a perfect scenario for the current study. After the survey, a first interview was done to the five participant of this study with the purpose of knowing students’ perceptions about participation and the concept of choice. Then, an intervention in which the provision of choice was given to the students with the use of class material took place. Finally, another interview was held in order to know if students’ perceptions about participation and choice had changed after the intervention. Results showed that in general students considered participation as an important factor inside the classroom; however, they did not feel comfortable participating orally in class. Finally, the results demonstrated that the provision of choice influenced students’ perceptions about participation within English sessions