Representing Partitions on Trees

In evolutionary biology, biologists often face the problem of constructing a phylogenetic tree on a set X of species from a multiset Π of partitions corresponding to various attributes of these species. One approach that is used to solve this problem is to try instead to associate a tree (or even a network) to the multiset ΣΠ consisting of all those bipartitions {A,X − A} with A a part of some partition in Π. The rational behind this approach is that a phylogenetic tree with leaf set X can be uniquely represented by the set of bipartitions of X induced by its edges. Motivated by these considerations, given a multiset Σ of bipartitions corresponding to a phylogenetic tree on X, in this paper we introduce and study the set P(Σ) consisting of those multisets of partitions Π of X with ΣΠ = Σ. More specifically, we characterize when P(Σ) is non-empty, and also identify some partitions in P(Σ) that are of maximum and minimum size. We also show that it is NP-complete to decide when P(Σ) is non-empty in case Σ is an arbitrary multiset of bipartitions of X. Ultimately, we hope that by gaining a better understanding of the mapping that takes an arbitrary partition system Π to the multiset ΣΠ, we will obtain new insights into the use of median networks and, more generally, split-networks to visualize sets of partitions

Carbon nanomaterials in clean and contaminated soils: environmental implications and applications

The exceptional sorptive ability of carbon nanomaterials (CNMs) for hydrophobic organic contaminants (HOCs) is driven by their characteristically large reactive surface areas and highly hydrophobic nature. Given these properties, it is possible for CNMs to impact on the persistence, mobility and bioavailability of contaminants within soils, either favourably through sorption and sequestration, hence reducing their bioavailability, or unfavourably through increasing contaminant dispersal. This review considers the complex and dynamic nature of both soil and CNM physicochemical properties to determine their fate and behaviour, together with their interaction with contaminants and the soil microflora. It is argued that assessment of CNMs within soil should be conducted on a case-by-case basis and further work to assess the long-term stability and toxicity of sorbed contaminants, as well as the toxicity of CNMs themselves, is required before their sorptive abilities can be applied to remedy environmental issues

Folding and unfolding phylogenetic trees and networks

Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network $N$ can be "unfolded" to obtain a MUL-tree $U(N)$ and, conversely, a MUL-tree $T$ can in certain circumstances be "folded" to obtain a phylogenetic network $F(T)$ that exhibits $T$. In this paper, we study properties of the operations $U$ and $F$ in more detail. In particular, we introduce the class of stable networks, phylogenetic networks $N$ for which $F(U(N))$ is isomorphic to $N$, characterise such networks, and show that they are related to the well-known class of tree-sibling networks.We also explore how the concept of displaying a tree in a network $N$ can be related to displaying the tree in the MUL-tree $U(N)$. To do this, we develop a phylogenetic analogue of graph fibrations. This allows us to view $U(N)$ as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in $U(N)$ and reconcilingphylogenetic trees with networks

Reconstructing pedigrees: some identifiability questions for a recombination-mutation model

Pedigrees are directed acyclic graphs that represent ancestral relationships between individuals in a population. Based on a schematic recombination process, we describe two simple Markov models for sequences evolving on pedigrees - Model R (recombinations without mutations) and Model RM (recombinations with mutations). For these models, we ask an identifiability question: is it possible to construct a pedigree from the joint probability distribution of extant sequences? We present partial identifiability results for general pedigrees: we show that when the crossover probabilities are sufficiently small, certain spanning subgraph sequences can be counted from the joint distribution of extant sequences. We demonstrate how pedigrees that earlier seemed difficult to distinguish are distinguished by counting their spanning subgraph sequences.Comment: 40 pages, 9 figure

Recovering a phylogenetic tree using pairwise closure operations

A fundamental task in evolutionary biology is the amalgamation of a collection P of leaf-labelled trees into a single parent tree. A desirable feature of any such amalgamation is that the resulting tree preserves all of the relationships described by the trees in P. For unrooted trees, deciding if there is such a tree is NP-complete. However, two polynomial-time approaches that sometimes provide a solution to this problem involve the computation of the semi-dyadic closure and split closure of a set of quartets that underlies P. In this paper we show that if a leaf-labelled tree T can be recovered from the semi-dyadic closure of some set Q of quartet subtrees of T, then T can also be recovered from the split-closure of Q. Furthermore, we show that the converse of this result does not hold, and resolve a closely related question posed in [1]

Analysis of the superdefomed rotational bands

All available experimental data for the $\Delta I=2$ transition energies in superdeformed bands are analyzed by using a new one-point formula. The existence of deviations from the smooth behavior is confirmed in many bands. However, we stress that one cannot necessarily speak about staggering patterns as they are mostly irregular. Simulations of the experimental data suggest that the irregularities may stem from the presence of irregular kinks in the rotational spectra. This could be a clue but, at the moment, where such kinks come from is an open question.Comment: 6 pages, RevTex, 7 p.s. figures, submitted to P.R.

Extracellular dsRNA induces a type I interferon response mediated via class A scavenger receptors in a novel Chinook salmon derived spleen cell line

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.dci.2018.08.010 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/Despite increased global interest in Chinook salmon aquaculture, little is known of their viral immune defenses. This study describes the establishment and characterization of a continuous cell line derived from Chinook salmon spleen, CHSS, and its use in innate immune studies. Optimal growth was seen at 14–18 °C when grown in Leibovitz's L-15 media with 20% fetal bovine serum. DNA analyses confirmed that CHSS was Chinook salmon and genetically different from the only other available Chinook salmon cell line, CHSE-214. Unlike CHSE-214, CHSS could bind extracellular dsRNA, resulting in the rapid and robust expression of antiviral genes. Receptor/ligand blocking assays confirmed that class A scavenger receptors (SR-A) facilitated dsRNA binding and subsequent gene expression. Although both cell lines expressed three SR-A genes: SCARA3, SCARA4, and SCARA5, only CHSS appeared to have functional cell-surface SR-As for dsRNA. Collectively, CHSS is an excellent cell model to study dsRNA-mediated innate immunity in Chinook salmon.Natural Sciences and Engineering Research Council of CanadaCanada Research Counci

Newsprint coverage of smoking in cars carrying children : a case study of public and scientific opinion driving the policy debate

Acknowledgements Date of Acceptance:17/10/2014 Acknowledgements: This project was funded by Cancer Research UK (MC_U130085862) and the Scottish School of Public Health Research. Cancer Research UK and the Scottish School of Public Health Research was not involved in the collection, analysis, and interpretation of data, writing of the manuscript or the decision to submit the manuscript for publication. Shona Hilton, Karen Wood, Josh Bain and Chris Patterson are funded by the UK Medical Research Council as part of the Understandings and Uses of Public Health Research programme (MC_UU_12017/6) at the MRC/CSO Social and Public Health Sciences Unit, University of Glasgow. We thank Alan Pollock who provided assistance with coding.Peer reviewedPublisher PD

On the classification of OADP varieties

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and classifying them. Main specific results are: (a) the classification of all OADP surfaces (regardless to their smoothness); (b) the classification of a relevant class of normal OADP varieties of any dimension, which includes interesting examples like lagrangian grassmannians. Following [PR], the equivalence of the classification in (b) with the one of quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in a special issue of Science in China Series A: Mathematic