Black box tests for algorithmic stability

Algorithmic stability is a concept from learning theory that expresses the degree to which changes to the input data (e.g., removal of a single data point) may affect the outputs of a regression algorithm. Knowing an algorithm's stability properties is often useful for many downstream applications -- for example, stability is known to lead to desirable generalization properties and predictive inference guarantees. However, many modern algorithms currently used in practice are too complex for a theoretical analysis of their stability properties, and thus we can only attempt to establish these properties through an empirical exploration of the algorithm's behavior on various data sets. In this work, we lay out a formal statistical framework for this kind of "black box testing" without any assumptions on the algorithm or the data distribution, and establish fundamental bounds on the ability of any black box test to identify algorithmic stability.Comment: 26 pages. Updates to Section 2.1.1 and Sections B.1 & B.

South Korean elementary teachers' knowledge for teaching mathematics

Thesis advisor: Lillie Richardson AlbertThe purpose of this research is to identify the categories of South Korean elementary teachers' knowledge for teaching mathematics. Operating under the assumption that elementary teachers' knowledge for teaching affects students' learning, eleven South Korean elementary teachers volunteered to participate in this study. Emerging from the data collected and the subsequent analysis are five categories of South Korean elementary teachers' knowledge for teaching mathematics: Mathematics Curriculum Knowledge, Mathematics Learner Knowledge, Fundamental Mathematics Conceptual Knowledge, Mathematics Pedagogical Content Knowledge, and Mathematics Pedagogical Procedural Knowledge. The first three categories of knowledge play a significant role in mathematics instruction as an integrated form within Mathematics Pedagogical Content Knowledge. A notable conclusion of this study is that Pedagogical Content Knowledge might not be the sum of the other categories of knowledge for teaching mathematics. These findings may be connected to results from relevant studies in terms of the significant role of teachers' knowledge in their mathematics instruction. This study contributes to the existing literature in that it provides empirical bases for understanding teachers' knowledge for teaching mathematics and reveals the relationship among categories of knowledge for teaching mathematics.Thesis (PhD) — Boston College, 2014.Submitted to: Boston College. Lynch School of Education.Discipline: Teacher Education, Special Education, Curriculum and Instruction

Elementary Teachers’ Knowledge for Teaching Mathematics: A Review

The objective of this review is to provide a clear interpretation and implication of the research for policymakers and researchers who are interested in elementary teachers’ knowledge for teaching mathematics. Based on the objectives, I examine 20 empirical studies in the area of elementary teachers’ knowledge for teaching mathematics. The fundamental criterion for grouping studies is their research questions. The studies’ research questions are related to each other to a greater or lesser detail. Thus, the research questions are categorized into four groups. The four groups are (a) how can we define elementary teachers’ knowledge for teaching mathematics? (b) How can instruments for measuring elementary teachers’ knowledge for teaching mathematics be developed? (c) What factors are to be related to elementary teachers’ knowledge for teaching mathematics? And (d) what are international studies saying about elementary knowledge for teaching mathematics? For each group, description of all relevant studies and findings and interpretations are presented. The analysis of studies demonstrates that expanding the field of researchers will provide new ways of examining elementary teachers’ knowledge for teaching mathematics and at the same time may provide critical information about affects and factors of knowledge for teaching mathematics. DOI: 10.5901/mjss.2014.v5n9p42

From the mouths of social media users: A focus group study exploring the social casino gaming–online gambling link

Background and aims The potential link between social casino gaming and online gambling has raised considerable concerns among clinicians, researchers and policy makers. Unfortunately, however, there is a paucity of research examining this potential link, especially among young adults. This represents a significant gap given young adults are frequently exposed to and are players of social casino games. Methods To better understand the potential link between social casino games and online gambling, we conducted three focus groups (N = 30) at two large Canadian Universities with college students who were avid social media users (who are regularly exposed to social casino games). Results Many participants spontaneously mentioned that social casino games were a great opportunity to build gambling skills before playing for real money. Importantly, some participants expressed a belief that there is a direct progression from social casino gaming to online gambling. Conversely, others believed the transition to online gambling depended on a person’s personality, rather than mere exposure to social casino games. While many young adults in our focus groups felt immune to the effects of social casino games, there was a general consensus that social casino games may facilitate the transition to online gambling among younger teenagers (i.e., 12–14 yr olds), due to the ease of accessibility and early exposure. Discussion The results of the present research point to the need for more study on the effects of social casino gambling as well as a discussion concerning regulation of social casino games in order to minimize their potential risks

Cinchonine Prevents High-Fat-Diet-Induced Obesity through Downregulation of Adipogenesis and Adipose Inflammation

Cinchonine (C19H22N2O) is a natural compound of Cinchona bark. Although cinchonine's antiplatelet effect has been reported in the previous study, antiobesity effect of cinchonine has never been studied. The main objective of this study was to investigate whether cinchonine reduces high-fat-diet- (HFD-) induced adipogenesis and inflammation in the epididymal fat tissues of mice and to explore the underlying mechanisms involved in these reductions. HFD-fed mice treated with 0.05% dietary cinchonine for 10 weeks had reduced body weight gain (−38%), visceral fat-pad weights (−26%), and plasma levels of triglyceride, free fatty acids, total cholesterol, and glucose compared with mice fed with the HFD. Moreover, cinchonine significantly reversed HFD-induced downregulations of WNT10b and galanin-mediated signaling molecules and key adipogenic genes in the epididymal adipose tissues of mice. Cinchonine also attenuated the HFD-induced upregulation of proinflammatory cytokines by inhibiting toll-like-receptor-2- (TLR2-) and TLR4-mediated signaling cascades in the adipose tissue of mice. Our findings suggest that dietary cinchonine with its effects on adipogenesis and inflammation may have a potential benefit in preventing obesity

Macrophage inflammatory protein-related protein-2, a novel CC chemokine, can regulate preadipocyte migration and adipocyte differentiation

AbstractAdipocytes not only store energy, but also secrete biologically active molecules called adipocytokines, which play a pivotal role in adipocyte-related pathological processes such as diabetes and cardiovascular disease. Recent studies have shown that preadipocyte/adipocyte expresses chemokines (e.g. monocyte chemoattractant protein-1, macrophage inflammatory protein-1 alpha) which alter adipocyte function, indicating the involvement of chemokines in adipocyte-related pathologies. The current study investigated the potential of macrophage inflammatory protein-related protein-2 (MRP-2), a novel CC chemokine, to modulate preadipocyte trafficking and adipocyte differentiation. MRP-2 and its receptors were highly expressed in preadipocytes and differentiated adipocytes as well as in the mouse fat pad. Chemotaxis assays revealed that MRP-2 was a specific chemotactic regulator in preadipocyte migration. The levels of MRP-2 expression in adipose tissue were enhanced in obese mice compared to lean mice. MRP-2 secretion by preadipocytes was suppressed during differentiation. MRP-2 suppressed the expression of adipocyte differentiation markers such as adipocyte fatty acid-binding protein and glycerol-3 phosphate dehydrogenase. Taken together, our data suggest that MRP-2 plays a role in the regulation of preadipocyte migration and adipocyte differentiation during adipose tissue development. MRP-2 may be another adipocytokine, which can be involved in the adipocyte-related pathological process

The History of Base-Ten-Blocks: Why and Who Made Base-Ten-Blocks?

The purpose of this study is to present evidence of how base-ten-blocks have been developed and emphasized as a tool for learning in mathematics education. After an introduction of the theme, we discuss the theoretical and epistemological perspectives that provide the basis for our analysis of the literature. Then, we illustrate how base-ten-blocks have historically been associated with the numeral concepts from the prehistoric era to today. We also review studies about different manipulatives that focus on numerical concepts (e.g., Cuisenaire rods). This discussion will broaden our understanding regarding how perspectives toward mathematics instruction have changed with the introduction of base-ten-blocks. The intent was not to understand the process of developing base-ten-blocks but rather to suggest that teachers must consider the underlying mathematical concepts and structures of base-ten-blocks when they use them. In summary, this study revealed that base-ten-blocks as concrete materials seems to have been presented as different isomorphic numeral concepts for various educational purposes throughout its developmental process. DOI: 10.5901/mjss.2014.v5n9p35