Randomness and differentiability in higher dimensions

We present two theorems concerned with algorithmic randomness and differentiability of functions of several variables. Firstly, we prove an effective form of the Rademacher's Theorem: we show that computable randomness implies differentiability of computable Lipschitz functions of several variables. Secondly, we show that weak 2-randomness is equivalent to differentiability of computable a.e. differentiable functions of several variables.Comment: 19 page

Responsible Fatherhood and Healthy Families Act of 2007

This brief on legislation outlines the provisions of the proposed Responsible Fatherhood and Health Families Act of 2007

Social (network) psychology: How networks shape performance, persistence, and access to information

Social psychologists have long been interested in understanding behavior as a function of both individuals and the social structures in which they are embedded. However, since the cognitive revolution of the 1960s, processes internal to individuals have received greater attention than structural influences. This dissertation examines how networks may shape important real-world outcomes beyond intrapsychic phenomena across three studies in varied contexts. In doing so, this work suggests that the networks to which people belong—whether networks of social ties or networks of information—provide both affordances and constraints that affect behavior and outcomes. Chapter I provides a brief introduction to social network analysis as a set of theoretical, methodological, and analytical tools. Chapter II examines the gender gap in negotiation performance. Findings suggest that disparities between male and female MBA students in class social network positions predict this gap more strongly than intrapsychic mechanisms more commonly studied, such as apprehension about negotiating and stereotype threat. Chapter III examines how students’ social networks promote persistence over time in a high-stress science, technology, engineering, and math (STEM) setting. This chapter pulls social network analysis into an experimental context by examining the effects of a randomly assigned social psychological intervention on students’ social networks and subsequent persistence in the biosciences. Chapter IV approaches networks from a different angle, examining how online news media are organized into network structures that may contribute to selective exposure to homogenous information. Finally, Chapter V discusses implications of these three studies. Specifically, I discuss implications for education research, intervention science, and the growing area of social network psychology