Central Limit Results for Jump-Diffusions with Mean Field Interaction and a Common Factor

A system of $N$ weakly interacting particles whose dynamics is given in terms of jump-diffusions with a common factor is considered. The common factor is described through another jump-diffusion and the coefficients of the evolution equation for each particle depend, in addition to its own state value, on the empirical measure of the states of the $N$ particles and the common factor. A Central Limit Theorem, as $N \to \infty$, is established. The limit law is described in terms of a certain Gaussian mixture. An application to models in Mathematical Finance of self-excited correlated defaults is described

Building Classroom Communities In A Pbis World: Voices Of Teacher Candidates As They Transition Into First-Year Teachers

For both beginning and veteran teachers, classroom management consistently ranks as one of their primary areas of concern (Hoy & Woolfolk, 1990; Martin, Yin, & Mayall, 2006; Oakes, Lipton, Anderson, & Stillman, 2013; Veenman, 1983), and this concern is magnified in the early childhood years because these teachers are often the first service providers to interact with children exhibiting challenging behaviors (Powell, Fixsen, Dunlap, Smith, & Fox, 2007; Tillery, Varjas, Meyers, & Collins, 2010). Mixed messages in early childhood teacher preparation regarding the role of democracy and community in the classroom and the more behavioristic settings of field placements and first-year settings, such as in schools using the framework of Positive Behavior Interventions & Supports (Sugai & Horner, 2002), can contribute to this concern. Therefore, this qualitative study focused on exploring the perceptions and actions of early childhood teachers regarding their classroom management while teaching in schools using the PBIS frameworks, and as they graduated and became first-year teachers. Using a collective case study (Stake, 1995; 2010) with ethnomethodological techniques (Garfinkel, 1967) design, 11 early childhood teachers were interviewed upon their graduation, and three were followed over their first year of teaching. Findings from this year-long study revealed a lack of classroom management preparation, feelings of unpreparedness, concerns of challenging student behavior, an overall mismatch in beliefs and experiences, and a persistent tension between classroom management practices, including PBIS, and feelings of community in early childhood classrooms. Findings also include yearlong impacts of school-wide attitudes and practices contextual factors, including administrative support, mentorship, and teacher self-efficacy on new teachers’ ability to build classroom communities and establish strong classroom management practices

Socially Marginalized Youths\u27 Experiences with Social Media and its Impact on their Relationships

Social media use is prevalent among adolescents and young adults. However, little is known about the role and function of social media in the lives of youth who have experienced social marginalization. These youth face different challenges than their mainstream peers when it comes to the development, maintenance and outcomes of their friendships and relationships. It is unknown whether findings on social media and relationships accurately represent the experiences of youth who have experienced social marginalization, given the different challenges they face in achieving belonging and intimacy. Semi-structured interviews with youth regarding their social media use and its impact on their relationships took place at local youth-serving community agencies in a central Canadian city. A content analysis of 11 interview transcripts was performed and 6 themes emerged. Themes included: Prevalence & Preferences; Typical Activities; Negative Influences; Awareness of Risks; Positive Insights and Suggestions; and Break-Ups. Conclusions provide an understanding about how youth experiencing marginalization are using social media, and how programming can be developed to suit their specific mental health needs and concerns

Sudoku Variants on the Torus

This paper examines the mathematical properties of Sudoku puzzles defined on a Torus. We seek to answer the questions for these variants that have been explored for the traditional Sudoku. We do this process with two such embeddings. The end result of this paper is a deeper mathematical understanding of logic puzzles of this type, as well as a fun new puzzle which could be played

The Many Hats of Sonic Hedgehog Signaling in Nervous System Development and Disease.

Sonic hedgehog (Shh) signaling occurs concurrently with the many processes that constitute nervous system development. Although Shh is mostly known for its proliferative and morphogenic action through its effects on neural stem cells and progenitors, it also contributes to neuronal differentiation, axonal pathfinding and synapse formation and function. To participate in these diverse events, Shh signaling manifests differently depending on the maturational state of the responsive cell, on the other signaling pathways regulating neural cell function and the environmental cues that surround target cells. Shh signaling is particularly dynamic in the nervous system, ranging from canonical transcription-dependent, to non-canonical and localized to axonal growth cones. Here, we review the variety of Shh functions in the developing nervous system and their consequences for neurodevelopmental diseases and neural regeneration, with particular emphasis on the signaling mechanisms underlying Shh action