Metaheuristic approaches for the quartet method of hierarchical clustering

Given a set of objects and their pairwise distances, we wish to determine a visual representation of the data. We use the quartet paradigm to compute a hierarchy of clusters of the objects. The method is based on an NP-hard graph optimization problem called the Minimum Quartet Tree Cost problem. This paper presents and compares several metaheuristic approaches to approximate the optimal hierarchy. The performance of the algorithms is tested through extensive computational experiments and it is shown that the Reduced Variable Neighbourhood Search metaheuristic is the most effective approach to the problem, obtaining high quality solutions in short computational running times

Sweeps in time:Leveraging the joint distribution of branch lengths

Current methods of identifying positively selected regions in the genome are limited in two key ways: the underlying models cannot account for the timing of adaptive events and the comparison between models of selective sweeps and sequence data is generally made via simple summaries of genetic diversity. Here, we develop a tractable method of describing the effect of positive selection on the genealogical histories in the surrounding genome, explicitly modeling both the timing and context of an adaptive event. In addition, our framework allows us to go beyond analyzing polymorphism data via the site frequency spectrum or summaries thereof and instead leverage information contained in patterns of linked variants. Tests on both simulations and a human data example, as well as a comparison to SweepFinder2, show that even with very small sample sizes, our analytic framework has higher power to identify old selective sweeps and to correctly infer both the time and strength of selection. Finally, we derived the marginal distribution of genealogical branch lengths at a locus affected by selection acting at a linked site. This provides a much-needed link between our analytic understanding of the effects of sweeps on sequence variation and recent advances in simulation and heuristic inference procedures that allow researchers to examine the sequence of genealogical histories along the genome

Numerical Loop-Tree Duality: contour deformation and subtraction

We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour deformation automatically satisfies all constraints without the need for fine-tuning. We demonstrate that our construction is systematic and efficient by applying it to more than 100 examples of finite scalar integrals featuring up to six loops. We also showcase a first step towards handling non-integrable singularities by applying our work to one-loop infrared divergent scalar integrals and to the one-loop amplitude for the ordered production of two and three photons. This requires the combination of our contour deformation with local counterterms that regulate soft, collinear and ultraviolet divergences. This work is an important step towards computing higher-order corrections to relevant scattering cross-sections in a fully numerical fashion.Comment: 87 page

Analysis of 142 genes resolves the rapid diversification of the rice genus

The relationships among all diploid genome types of the rice genus were clarified using 142 single-copy gene

On Pairwise λ-Open Soft Sets and Pairwise Locally Closed Soft Sets

Kandil and his colleagues [10], introduced the notion of -closed soft set by involving -soft set and -closed soft set. In this paper, we give some additional properties of -closed soft sets. We also introduce and study a related new class of -spaces which lies between  and  . Moreover, we show that there exists a very important relation between the notion of -closed soft sets and the  property, ,  , . In addition, we offer the notion of -locally closed soft sets and we investigate a related new pairwise soft separation axiom  which is independent from . The relationships between the -closed soft sets and the -locally closed soft sets are obtained. Furthermore, we introduce the notion of -open soft sets and we construct supra soft topology associated with the class of -open soft sets and we present pairwise soft separation axioms related to such soft sets, namely . We provide some illustrative examples to support the results

Trajectory-based differential expression analysis for single-cell sequencing data

Trajectory inference has radically enhanced single-cell RNA-seq research by enabling the study of dynamic changes in gene expression. Downstream of trajectory inference, it is vital to discover genes that are (i) associated with the lineages in the trajectory, or (ii) differentially expressed between lineages, to illuminate the underlying biological processes. Current data analysis procedures, however, either fail to exploit the continuous resolution provided by trajectory inference, or fail to pinpoint the exact types of differential expression. We introduce tradeSeq, a powerful generalized additive model framework based on the negative binomial distribution that allows flexible inference of both within-lineage and between-lineage differential expression. By incorporating observation-level weights, the model additionally allows to account for zero inflation. We evaluate the method on simulated datasets and on real datasets from droplet-based and full-length protocols, and show that it yields biological insights through a clear interpretation of the data. Downstream of trajectory inference for cell lineages based on scRNA-seq data, differential expression analysis yields insight into biological processes. Here, Van den Berge et al. develop tradeSeq, a framework for the inference of within and between-lineage differential expression, based on negative binomial generalized additive models