Modified linear programming and class 0 bounds for graph pebbling

Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move removes two pebbles from some vertex and places one pebble on an adjacent vertex. The pebbling number of a graph G is the smallest integer k such that for each vertex v and each configuration of k pebbles on G there is a sequence of pebbling moves that places at least one pebble on v. First, we improve on results of Hurlbert, who introduced a linear optimization technique for graph pebbling. In particular, we use a different set of weight functions, based on graphs more general than trees. We apply this new idea to some graphs from Hurlbert’s paper to give improved bounds on their pebbling numbers. Second, we investigate the structure of Class 0 graphs with few edges. We show that every n-vertex Class 0 graph has at least \(\frac{5}{3}n - \frac{11}{3}\) edges. This disproves a conjecture of Blasiak et al. For diameter 2 graphs, we strengthen this lower bound to \(2n - 5\), which is best possible. Further, we characterize the graphs where the bound holds with equality and extend the argument to obtain an identical bound for diameter 2 graphs with no cut-vertex.     

Infant Perception of Surface Texture and Relative Height as Distance Information: A Preferential‐Reaching Study

Two preferential‐reaching experiments explored 5‐ and 7‐month‐olds’ sensitivity to pictorial depth cues. In the first experiment, infants viewed a display in which texture gradients, linear perspective of the surface contours, and relative height in the visual field provided information that two objects were at different distances. Five‐ and 7‐month‐old infants reached preferentially for the apparently nearer object under monocular but not binocular viewing conditions, indicating that infants in both age groups respond to pictorial depth cues. In the second experiment, texture gradients and linear perspective of the surface contours were eliminated from the experimental display, making relative height the sole pictorial depth cue. Seven‐month‐olds again reached more often for the apparently nearer object under monocular, but not binocular viewing conditions. By contrast, the 5‐month‐olds’ reaching behavior did not differ between viewing conditions. These results indicate that 7‐month‐olds respond to the depth cue of relative height but provide no evidence of responsiveness to relative height in 5‐month‐olds. Both age groups responded more consistently to pictorial depth in Experiment 1 than in Experiment 2.     

Eight Motivational Forces and Voluntary Turnover: A Theoretical Synthesis with Implications for Research

In this study, we synthesize, from the attitude and turnover literatures, a framework of eight (8) distinctive motives, or “Forces”. We then illustrate how the “8 Forces” framework can be utilized by turnover researchers as clarification of reported reasons for turnover, as causal mediators of turnover predictors, and as factors related to the type of turnover decision process. Finally, we discuss further implications of this framework.     

Stressful neighborhoods and depression: a prospective study of the impact of neighborhood disorder

Quantitative and qualitative research suggests that urban disadvantaged environments may be highly stressful to their inhabitants. Social disorganization may be deleterious to both physical and mental health. The relationships among perceptions of one's neighborhood, measures of social support and social integration, and level of subsequent depressive symptoms was examined with a community sample of 818 individuals screened for an HIV prevention intervention, most of whom were current or former drug users. After adjusting for baseline levels of depressive symptoms, perceptions of neighborhood characteristics (vandalism, litter or trash, vacant housing, teenagers hanging out, burglary, drug selling, and robbery) predicted depressive symptoms at a 9-month follow-up interview. Measures of social support and social integration, entered as interactions with neighborhood perceptions, did not buffer the effect of neighborhood perceptions. However, CES-D scores at follow-up for frequent church attendees were lower. The data support theories of social disorganization and social stress and suggest the need for structural intervention.     

Fear and expectations: differences among female victims of domestic violence who come to the attention of the police

This study investigated a broad range of female victims of domestic partner abuse who came to the attention of the police. Ninety-five consecutive victims were interviewed by officers in a police department's domestic violence unit. Twenty-two percent of the victims matched expectations of women who were both afraid of their abusers and expected future abuse. Surprisingly, 46% of the victims were unafraid of their offenders and believed that future abuse was unlikely. A consistent pattern of findings supports the conclusion that a much broader range of victims than expected comes to the attention of the police. These results suggest exploring alternative police responses for different types of victims.     

Individual and ecological assets and positive developmental trajectories among gang and community-based organization youth

The Search Institute framework for conceptualizing developmental assets was used in a longitudinal study of African American male youth involved in gangs or in community-based organizations (CBOs) serving youth. Analyses of intraindividual change indicated that individual and ecological assets are linked to positive developmental trajectories among these youth.