A metric d on a finite set X is called a Kalmanson metric if there exists a circular ordering of points of X , such that d(y; u) + d(z; v) > d(y; z) + d(u; v) for all crossing pairs yu and zv of . We prove that any Kalmanson metric d is an l1-metric, i.e. d can be written as a nonnegative linear combination of split metrics. The splits in the decomposition of d can be selected to form a circula...

Neuroimaging and lesion studies have provided insights into the neural mechanisms underlying numerical processing, yet the roles of the right and left hemispheres have not been systematically investigated within a single study. To address this issue, we investigated subitizing and magnitude comparison abilities in a split-brain patient. The first experiment examined the two hemispheres' abiliti...

Studies are reviewed that examine how perceptual and attentional systems operate in the cortically disconnected human. The data indicate that even though both simple and complex perceptual information associated with the cognitive activities of each disconnected half brain show virtually no interactions, the attentional system remains largely integrated in the split-brain patient. It also appea...

Converging lines of evidence from diverse research domains suggest that the left and right hemispheres play distinct, yet complementary, roles in inferential reasoning. Here, we review research on split-brain patients, brain-damaged patients, delusional patients, and healthy individuals that suggests that the left hemisphere tends to create explanations, make inferences, and bridge gaps in info...

The split-coloring problem is a generalized vertex coloring problem where we partition the vertices into a minimum number of split graphs. In this paper, we study some notions which are extensively studied for the usual vertex coloring and the cocoloring problem from the point of view of split-coloring, such as criticality and the uniqueness of the minimum split-coloring. We discuss some proper...