Lemma 2.2. It suffices to find disjoint L,R ∈ V such that they are (1) Large in Ω(n), or more formally stated, |L||R| ≥ α(n). (2) ∆-separated for ∆ = Ω( 1 logn) Let us define what ∆-separated means so that we can formalize this notion of “farness”. Recall that a distance from a vertex i to a set S is defined as d(i, S) = minj∈S d(i, j) (distance to the closest point in the set) and a distance f...

This article presents a case study of play therapy with an emotionally disturbed abused child. The article discusses the intuitive and individualized approach to the world of the abused child (conceptualized as a "cultured of one") in which the nurse therapist's role is to develop a trusting relationship with the child. Distance between the nurse's world and that of the abused child can be brid...

We study a class of geometric stabbing/covering problems for sets of line segments, rays, and lines in the plane. While we demonstrate that the problems on sets of horizontal/vertical line segments are NP-complete, we show that versions involving (parallel) rays or lines are polynomially solvable.

Consider the symmetric group Sn equipped with the Hamming metric dH . Packing and covering problems in the finite metric space (Sn, dH) are surveyed, including a combination of both.

Finding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(n logn) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum)...

The reduction of coercive or inadequate parenting is essential if the mental health status of Australian children and adolescents is to be improved. Of the available approaches that address parenting practices, behavioural family interventions have the strongest empirical support and are effective in reducing parenting practices that contribute to the development of behavioural and emotional pr...

We investigated the long-term effects of parental divorce in childhood on demographic outcomes in young adulthood, using a British longitudinal national survey of children. Our analyses control for predisruption characteristics of the child and the family, including emotional problems, cognitive achievement, and socioeconomic status. The results show that by age 23, those whose parents divorced...

BACKGROUND Preschool language and neurodevelopmental problems often persist and impede learning. The aims of the current study are to assess the uptake of a new universal 30 month health visitor contact and to quantify the prevalence of language delay and social/emotional difficulties. METHODS All families of 30 month old children in four Glasgow localities were offered a visit from their hea...

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