Prognosis of learning disability.

This article reviews earlier and recent studies about the long-term and adult outcomes of children with learning disabilities (LDs). Although some results are contradictory or inconclusive because of the many methodological problems in the conduct of such studies, there is agreement that LDs persist into adulthood to some degree. Outcome is dependent on the severity of the LD at school age, on intelligence, on the socioeconomic status of parents, and on the presence or absence of neurological impairment. Intervention has not been clearly related to improved outcome. Some evidence has suggested that a language-deficit subtype of LD may show poorer outcome. The prognosis of outcome in the strict sense is limited at this time and has little validity for the individual child. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Parallel computation of disease transforms

Distance transforms are an important computational tool for the processing of binary images. For ann ×n image, distance transforms can be computed in time (n) on a mesh-connected computer and in polylogarithmic time on hypercube related structures. We investigate the possibilities of computing distance transforms in polylogarithmic time on the pyramid computer and the mesh of trees. For the pyramid, we obtain a polynomial lower bound using a result by Miller and Stout, so we turn our attention to the mesh of trees. We give a very simple (logn) algorithm for the distance transform with respect to theL ₁-metric, an (log² n) algorithm for the transform with respect to theL -metric, and find that the Euclidean metric is much more difficult. Based on evidence from number theory, we conjecture the impossibility of computing the Euclidean distance transform in polylogarithmic time on a mesh of trees. Instead, we approximate the distance transform up to a given error. This works for anyL _k -metric and takes time (log³ n).This research was supported by the Deutsche Forschungsgemeinschaft under Grant Al 253/1-1, Schwerpunktprogramm Datenstrukturen und effiziente Algorithmen.     

A Generalization of the Convex Kakeya Problem

Given a set of line segments in the plane, not necessarily finite, what is a convex region of smallest area that contains a translate of each input segment? This question can be seen as a generalization of Kakeya’s problem of finding a convex region of smallest area such that a needle can be rotated through 360 degrees within this region. We show that there is always an optimal region that is a triangle, and we give an optimal Θ(nlogn)-time algorithm to compute such a triangle for a given set of n segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then placing the segments with their midpoint at the origin and taking their convex hull results in an optimal solution. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of every rotated copy of G.     

Implications of test revisions for research.

Test revisions are increasingly common in psychology and neuropsychology in particular. However, such revisions may alter in complex ways the kind of information obtained, and they may assess traits, abilities, and conditions in ways different from earlier versions. This article outlines some of the problems associated with the revision of tests facing clinicians and researchers. Three broad classes of revision are considered. Part I considers the aging of tests, part 2 concerns the aging of participants, and part 3 considers changes in test format. Although the article focuses largely on measures of intelligence and personality, the issues addressed in the article apply to other tests and assessment domains as well. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Reaching a goal with directional uncertainty

We study two problems related to planar motion planning for robots with imperfect control, where, if the robot starts a linear movement in a certain commanded direction, we only know that its actual movement will be confined in a cone of angle centered around the specified direction.

First, we consider a single goal region, namely the “region at infinity”, and a set of polygonal obstacles, modeled as a set S of n line segments. We are interested in the region from where we can reach infinity with a directional uncertainty of . We prove that the maximum complexity of is O(n/⁵). Second, we consider a collection of k polygonal goal regions of total complexity m, but without any obstacles. Here we prove an O(k³m) bound on the complexity of the region from where we can reach a goal region with a directional uncertainty of . For both situations we also prove lower bounds on the maximum complexity, and we give efficient algorithms for computing the regions.