Resolving Prime Modules: The Structure of Pseudo-cographs and Galled-Tree Explainable Graphs

The modular decomposition of a graph $G$ is a natural construction to capture key features of $G$ in terms of a labeled tree $(T,t)$ whose vertices are labeled as "series" ($1$), "parallel" ($0$) or "prime". However, full information of $G$ is provided by its modular decomposition tree $(T,t)$ only, if $G$ is a cograph, i.e., $G$ does not contain prime modules. In this case, $(T,t)$ explains $G$, i.e., $\{x,y\}\in E(G)$ if and only if the lowest common ancestor $\mathrm{lca}_T(x,y)$ of $x$ and $y$ has label "$1$". Pseudo-cographs, or, more general, GaTEx graphs $G$ are graphs that can be explained by labeled galled-trees, i.e., labeled networks $(N,t)$ that are obtained from the modular decomposition tree $(T,t)$ of $G$ by replacing the prime vertices in $T$ by simple labeled cycles. GaTEx graphs can be recognized and labeled galled-trees that explain these graphs can be constructed in linear time. In this contribution, we provide a novel characterization of GaTEx graphs in terms of a set $\mathfrak{F}_{\mathrm{GT}}$ of 25 forbidden induced subgraphs. This characterization, in turn, allows us to show that GaTEx graphs are closely related to many other well-known graph classes such as $P_4$-sparse and $P_4$-reducible graphs, weakly-chordal graphs, perfect graphs with perfect order, comparability and permutation graphs, murky graphs as well as interval graphs, Meyniel graphs or very strongly-perfect and brittle graphs. Moreover, we show that every GaTEx graph as twin-width at most 1.Comment: 18 pages, 3 figure

Uprooted Phylogenetic Networks

The need for structures capable of accommodating complex evolutionary signals such as those found in, for example, wheat has fueled research into phylogenetic networks. Such structures generalize the standard model of a phylogenetic tree by also allowing for cycles and have been introduced in rooted and unrooted form. In contrast to phylogenetic trees or their unrooted versions, rooted phylogenetic networks are notoriously difficult to understand. To help alleviate this, recent work on them has also centered on their “uprooted” versions. By focusing on such graphs and the combinatorial concept of a split system which underpins an unrooted phylogenetic network, we show that not only can a so-called (uprooted) 1-nested network N be obtained from the Buneman graph (sometimes also called a median network) associated with the split system  Σ(N)Σ(N)  induced on the set of leaves of N but also that that graph is, in a well-defined sense, optimal. Along the way, we establish the 1-nested analogue of the fundamental “splits equivalence theorem” for phylogenetic trees and characterize maximal circular split systems

Phylogenetic networks that are their own fold-ups

Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted directed acyclic graphs whose leaves are labelled by, for example, species. A number of mathematically interesting classes of phylogenetic networks are known. These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain "fold-up" and "un-fold" operations that link them with concepts arising within the theory of, for example, graph fibrations. Despite this exciting link, the structural complexity of stable phylogenetic networks is still relatively poorly understood. Employing the popular tree-based, reticulation-visible, and tree-child properties which allow one to gauge this complexity in one way or another, we provide novel characterizations for when a stable phylogenetic network satisfies either one of these three properties

OSF-Builder: A new tool for constructing and representing evolutionary histories involving introgression

Introgression is an evolutionary process which provides an important source of innovation for evolution. Although various methods have been used to detect introgression, very few methods are currently available for constructing evolutionary histories involving introgression. In this paper we propose a new method for constructing such evolutionary histories whose starting point is a species forest (consisting of a collection of lineage trees, usually arising as a collection of clades or monophyletic groups in a species tree), and a gene tree for a specific allele of interest, or allele tree for short. Our method is based on representing introgression in terms of a certain 'overlay' of the allele tree over the lineage trees, called an overlaid species forest (OSF). OSFs are similar to phylogenetic networks although a key difference is that they typically have multiple roots because each monophyletic group in the species tree has a different point of origin. Employing a new model for introgression, we derive an efficient algorithm for building OSFs called OSF-Builder that is guaranteed to return an optimal OSF in the sense that the number of potential introgression events is minimized. As well as using simulations to assess the performance of OSF-Builder, we illustrate its use on a butterfly dataset in which introgression has been previously inferred. The OSF-Builder software is available for download from https://www.uea.ac.uk/computing/software/OSF-Builde

Rheology of a confined granular material

We study the rheology of a granular material slowly driven in a confined geometry. The motion is characterized by a steady sliding with a resistance force increasing with the driving velocity and the surrounding relative humidity. For lower driving velocities a transition to stick-slip motion occurs, exhibiting a blocking enhancement whith decreasing velocity. We propose a model to explain this behavior pointing out the leading role of friction properties between the grains and the container's boundary.Comment: 9 pages, 3 .eps figures, submitted to PR

Three-way symbolic tree-maps and ultrametrics

Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance between any three objects. Such maps have applications in cluster analysis and have been used in areas such as psychology and phylogenetics, where three-way data tables can arise. Special examples of such dissimilarities are three-way tree-metrics and ultrametrics, which arise from leaf-labelled trees with edges labelled by positive real numbers. Here we consider three-way maps which arise from leaf-labelled trees where instead the interior vertices are labelled by an arbitrary set of values. For unrooted trees, we call such maps three-way symbolic tree-maps; for rooted trees, we call them three-way symbolic ultrametrics since they can be considered as a generalization of the (two-way) symbolic ultrametrics of Bocker and Dress. We show that, as with two- and three-way tree-metrics and ultrametrics, three-way symbolic tree-maps and ultrametrics can be characterized via certain k-point conditions. In the unrooted case, our characterization is mathematically equivalent to one presented by Gurvich for a certain class of edge-labelled hypergraphs. We also show that it can be decided whether or not an arbitrary three-way symbolic map is a tree-map or a symbolic ultrametric using a triplet-based approach that relies on the so-called BUILD algorithm for deciding when a set of 3-leaved trees or triplets can be displayed by a single tree. We envisage that our results will be useful in developing new approaches and algorithms for understanding 3-way data, especially within the area of phylogenetics

BrAPI-an application programming interface for plant breeding applications

Motivation: Modern genomic breeding methods rely heavily on very large amounts of phenotyping and genotyping data, presenting new challenges in effective data management and integration. Recently, the size and complexity of datasets have increased significantly, with the result that data are often stored on multiple systems. As analyses of interest increasingly require aggregation of datasets from diverse sources, data exchange between disparate systems becomes a challenge. Results: To facilitate interoperability among breeding applications, we present the public plant Breeding Application Programming Interface (BrAPI). BrAPI is a standardized web service API specification. The development of BrAPI is a collaborative, community-based initiative involving a growing global community of over a hundred participants representing several dozen institutions and companies. Development of such a standard is recognized as critical to a number of important large breeding system initiatives as a foundational technology. The focus of the first version of the API is on providing services for connecting systems and retrieving basic breeding data including germplasm, study, observation, and marker data. A number of BrAPI-enabled applications, termed BrAPPs, have been written, that take advantage of the emerging support of BrAPI by many databases

Survival of newly formed particles in haze conditions

Intense new particle formation events are regularly observed under highly polluted conditions, despite the high loss rates of nucleated clusters. Higher than expected cluster survival probability implies either ineffective scavenging by pre-existing particles or missing growth mechanisms. Here we present experiments performed in the CLOUD chamber at CERN showing particle formation from a mixture of anthropogenic vapours, under condensation sinks typical of haze conditions, up to 0.1 s(-1). We find that new particle formation rates substantially decrease at higher concentrations of pre-existing particles, demonstrating experimentally for the first time that molecular clusters are efficiently scavenged by larger sized particles. Additionally, we demonstrate that in the presence of supersaturated gas-phase nitric acid (HNO3) and ammonia (NH3), freshly nucleated particles can grow extremely rapidly, maintaining a high particle number concentration, even in the presence of a high condensation sink. Such high growth rates may explain the high survival probability of freshly formed particles under haze conditions. We identify under what typical urban conditions HNO3 and NH3 can be expected to contribute to particle survival during haze.Peer reviewe