On a Subposet of the Tamari Lattice

We explore some of the properties of a subposet of the Tamari lattice introduced by Pallo, which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial order on the symmetric group studied by Edelman.Comment: 21 page

Effects of Upright and Recumbent Cycling on Executive Function and Prefrontal Cortex Oxygenation in Young Healthy Men

Background: The purpose of this study was to assess the acute effects of posture (upright vs. recumbent) during moderate-intensity cycle exercise on executive function and prefrontal cortex oxygenation, in young healthy adults. Methods: Seventeen physically active men (24.6 ± 4.3y) completed two 30-minute submaximal, exercise tests (Conditions: upright and recumbent cycle ergometry). Executive function was assessed using the ‘colour’ and ‘word’ Stroop task, pre- (resting) and post-exercise. Regional oxygen saturation (rSO2) to the prefrontal cortex was continuously monitored using near-infrared spectroscopy. Results: Significant improvements in executive function (Stroop colour and word tasks) were observed following 30 minutes of exercise, for both upright and recumbent cycling (P < .05). However, there were no differences in executive function between cycling Conditions (P > .05). A significant increase in rSO2 was recorded immediately post-exercise compared to pre-exercise for both Conditions (P < .05), with a trend (P = .06) for higher peak rSO2 following recumbent cycling compared to upright cycling (81.9 ± 6.5 cf. 79.7 ± 9.3%, respectively). Conclusions: Although submaximal cycling exercise acutely improves cognitive performance and prefrontal oxygenation, changes in cognition are not perceived to be dependent on body posture in young, healthy men

Exploring the Complexity of the HIV-1 Fitness Landscape

Although fitness landscapes are central to evolutionary theory, so far no biologically realistic examples for large-scale fitness landscapes have been described. Most currently available biological examples are restricted to very few loci or alleles and therefore do not capture the high dimensionality characteristic of real fitness landscapes. Here we analyze large-scale fitness landscapes that are based on predictive models for in vitro replicative fitness of HIV-1. We find that these landscapes are characterized by large correlation lengths, considerable neutrality, and high ruggedness and that these properties depend only weakly on whether fitness is measured in the absence or presence of different antiretrovirals. Accordingly, adaptive processes on these landscapes depend sensitively on the initial conditions. While the relative extent to which mutations affect fitness on their own (main effects) or in combination with other mutations (epistasis) is a strong determinant of these properties, the fitness landscape of HIV-1 is considerably less rugged, less neutral, and more correlated than expected from the distribution of main effects and epistatic interactions alone. Overall this study confirms theoretical conjectures about the complexity of biological fitness landscapes and the importance of the high dimensionality of the genetic space in which adaptation takes place

Predicting the Evolution of Sex on Complex Fitness Landscapes

Most population genetic theories on the evolution of sex or recombination are based on fairly restrictive assumptions about the nature of the underlying fitness landscapes. Here we use computer simulations to study the evolution of sex on fitness landscapes with different degrees of complexity and epistasis. We evaluate predictors of the evolution of sex, which are derived from the conditions established in the population genetic literature for the evolution of sex on simpler fitness landscapes. These predictors are based on quantities such as the variance of Hamming distance, mean fitness, additive genetic variance, and epistasis. We show that for complex fitness landscapes all the predictors generally perform poorly. Interestingly, while the simplest predictor, ΔVarHD, also suffers from a lack of accuracy, it turns out to be the most robust across different types of fitness landscapes. ΔVarHD is based on the change in Hamming distance variance induced by recombination and thus does not require individual fitness measurements. The presence of loci that are not under selection can, however, severely diminish predictor accuracy. Our study thus highlights the difficulty of establishing reliable criteria for the evolution of sex on complex fitness landscapes and illustrates the challenge for both theoretical and experimental research on the origin and maintenance of sexual reproduction

Comparative Oncogenomic Analysis of Copy Number Alterations in Human and Zebrafish Tumors Enables Cancer Driver Discovery

The identification of cancer drivers is a major goal of current cancer research. Finding driver genes within large chromosomal events is especially challenging because such alterations encompass many genes. Previously, we demonstrated that zebrafish malignant peripheral nerve sheath tumors (MPNSTs) are highly aneuploid, much like human tumors. In this study, we examined 147 zebrafish MPNSTs by massively parallel sequencing and identified both large and focal copy number alterations (CNAs). Given the low degree of conserved synteny between fish and mammals, we reasoned that comparative analyses of CNAs from fish versus human MPNSTs would enable elimination of a large proportion of passenger mutations, especially on large CNAs. We established a list of orthologous genes between human and zebrafish, which includes approximately two-thirds of human protein-coding genes. For the subset of these genes found in human MPNST CNAs, only one quarter of their orthologues were co-gained or co-lost in zebrafish, dramatically narrowing the list of candidate cancer drivers for both focal and large CNAs. We conclude that zebrafish-human comparative analysis represents a powerful, and broadly applicable, tool to enrich for evolutionarily conserved cancer drivers.Kathy and Curt Marble Cancer Research FundArthur C. MerrillNational Institutes of Health (U.S.) (Grant CA106416)National Institutes of Health (U.S.) (Grant ROI RR020833)National Institutes of Health (U.S.) (Grant 1F32GM095213-01