Drawing Phylogenetic Trees

We present linear-time algorithms for drawing phylogenetic trees in radial and circular representations. In radial drawings given edge lengths (representing evolutionary distances) are preserved, but labels (names of taxons represented in the leaves) need to be adjusted, whereas in circular drawings labels are perfectly spread out, but edge lengths adjusted. Our algorithms produce drawings that are unique solutions to reasonable criteria and assign to each subtree a wedge of its own. The linear running time is particularly interesting in the circular case, because our approach is a special case of Tutte s barycentric layout algorithm involving the solution of a system of linear equations

The mechanisms and boundary conditions of the Einstellung effect in chess: Evidence from eye movements

In a wide range of problem-solving settings, the presence of a familiar solution can block the discovery of better solutions (i.e., the Einstellung effect). To investigate this effect, we monitored the eye movements of expert and novice chess players while they solved chess problems that contained a familiar move (i.e., the Einstellung move), as well as an optimal move that was located in a different region of the board. When the Einstellung move was an advantageous (but suboptimal) move, both the expert and novice chess players who chose the Einstellung move continued to look at this move throughout the trial, whereas the subset of expert players who chose the optimal move were able to gradually disengage their attention from the Einstellung move. However, when the Einstellung move was a blunder, all of the experts and the majority of the novices were able to avoid selecting the Einstellung move, and both the experts and novices gradually disengaged their attention from the Einstellung move. These findings shed light on the boundary conditions of the Einstellung effect, and provide convergent evidence for Bilali?, McLeod, & Gobet (2008)’s conclusion that the Einstellung effect operates by biasing attention towards problem features that are associated with the familiar solution rather than the optimal solution

Levels of processing influences both recollection and familiarity: Evidence from a modified remember–know paradigm

A modified Remember/Know (RK) paradigm was used to investigate reported subjective awareness during retrieval. Levels of processing (shallow vs. deep) was manipulated at study. Word pairs (old/new or new/new) were presented during test trials, and participants were instructed to respond “remember” if they recollected one of the two words, “know” if the word was familiar in the absence of recollection, or “new” if they judged both words to be new. Participants were then required to indicate which of the 2 words was old (2AFC recognition). With the standard RK proportions, deeper processing at study increased remember proportions and decreased know proportions, but this dissociation was not shown with the 2AFC proportion correct measure which instead demonstrated robust LOP effects for both remember and know trials, suggesting that the know proportion measure severely distorts the nature of LOP effects on familiarity.<br/

Recurrence relations based on minimization and maximization

AbstractExplicit and asymptotic solutions are presented to the recurrence M(1) = g(1), M(n + 1) = g(n + 1) + min1 ⩽ t ⩽ n(αM(t) + βM(n + 1 − t)) for the cases (1) α + β < 1, log2αlog2β is rational, and g(n) = δnI. (2) α + β > 1, min(α, β) > 1, log2αlog2β is rational, and (a) g(n) = δn1, (b) g(n) = 1. The general form of this recurrence was studied extensively by Fredman and Knuth [J. Math. Anal. Appl. 48 (1974), 534–559], who showed, without actually solving the recurrence, that in the above cases M(n) = Ω(n1 + 1γ), where γ is defined by α−γ + β−γ = 1, and that limn → ∞ M(n)n1 + γ does not exist. Using similar techniques, the recurrence M(1) = g(1), M(n + 1) = g(n + 1) + max1 ⩽ t ⩽ n(αM(t) + βM(n + 1 − t)) is also investigated for the special case α = β < 1 and g(n) = 1 if n is odd = 0 if n is even

Aspects of insertion in random trees

A method formulated by Yao and used by Brown has yielded bounds on the fraction of nodes with specified properties in trees bult by a sequence of random internal nodes in a random tree built by binary search and insertion, and show that in such a tree about bounds better than those now known. We then apply these methods to weight-balanced trees and to a type of “weakly balanced” trees. We determine the distribution of the weight-balance factors of the internal nodes in a random tree built by binary search and insertion and show that in such a tree about 72% of all internal nodes have weight balance factors lying between 1−2√/2 and 2√/2