On the challenge of reconstructing level-1 phylogenetic networks from triplets and clusters

Phylogenetic networks have gained prominence over the years due to their ability to represent complex non-treelike evolutionary events such as recombination or hybridization. Popular combinatorial objects used to construct them are triplet systems and cluster systems, the motivation being that any network $N$ induces a triplet system $\mathcal R(N)$ and a softwired cluster system $\mathcal S(N)$. Since in real-world studies it cannot be guaranteed that all triplets/softwired clusters induced by a network are available, it is of particular interest to understand whether subsets of $\mathcal R(N)$ or $\mathcal S(N)$ allow one to uniquely reconstruct the underlying network $N$. Here we show that even within the highly restricted yet biologically interesting space of level-1 phylogenetic networks it is not always possible to uniquely reconstruct a level-1 network $N$\kelk{,} even when all triplets in $\mathcal R(N)$ or all clusters in $\mathcal S(N)$ are available. On the positive side, we introduce a reasonably large subclass of level-1 networks the members of which are uniquely determined by their induced triplet/softwired cluster systems. Along the way, we also establish various enumerative results, both positive and negative, including results which show that certain special subclasses of level-1 networks $N$ can be uniquely reconstructed from proper subsets of $\mathcal R(N)$ and $\mathcal S(N)$. We anticipate these results to be of use in the design of algorithms for phylogenetic network inference

A ‘Tripadvisor’ for disability? Social enterprise and ‘digital disruption’ in Australia

We explore how social enterprises can use platform technologies to plug ‘informational gaps’ in the provision of disability services. Such gaps are made more apparent by policies promoting self-directed care as a means of giving service users more choice and control. We use a case study of a start-up social enterprise seeking to provide a TripAdvisor style service to examine the potential for social innovation to ‘disrupt’ current models of service. The case study suggests that any disruptive effects of such changes are not due to new digital technology per se, nor to novel platform business models, but rather rest in the manner in which the moral orders which justify current patterns of social disablement can be challenged by social innovation

P2 purinergic receptor modulation of cytokine production

Cytokines serve important functions in controlling host immunity. Cells involved in the synthesis of these polypeptide mediators have evolved highly regulated processes to ensure that production is carefully balanced. In inflammatory and immune disorders, however, mis-regulation of the production and/or activity of cytokines is recognized as a major contributor to the disease process, and therapeutics that target individual cytokines are providing very effective treatment options in the clinic. Leukocytes are the principle producers of a number of key cytokines, and these cells also express numerous members of the purinergic P2 receptor family. Studies in several cellular systems have provided evidence that P2 receptor modulation can affect cytokine production, and mechanistic features of this regulation have emerged. This review highlights three separate examples corresponding to (1) P2Y6 receptor mediated impact on interleukin (IL)-8 production, (2) P2Y11 receptor-mediated affects on IL-12/23 output, and (3) P2X7 receptor mediated IL-1β posttranslational processing. These examples demonstrate important roles of purinergic receptors in the modulation of cytokine production. Extension of these cellular observations to in vivo situations may lead to new therapeutic strategies for treating cytokine-mediated diseases

Programmed cell death and its role in inflammation

Cell death plays an important role in the regulation of inflammation and may be the result of inflammation. The maintenance of tissue homeostasis necessitates both the recognition and removal of invading microbial pathogens as well as the clearance of dying cells. In the past few decades, emerging knowledge on cell death and inflammation has enriched our molecular understanding of the signaling pathways that mediate various programs of cell death and multiple types of inflammatory responses. This review provides an overview of the major types of cell death related to inflammation. Modification of cell death pathways is likely to be a logical therapeutic target for inflammatory diseases

Sharp upper and lower bounds on a restricted class of convex characters

Let $\mathcal{T}$ be an unrooted binary tree with $n$ distinctly labelled leaves. Deriving its name from the field of phylogenetics, a convex character on $\mathcal{T}$ is simply a partition of the leaves such that the minimal spanning subtrees induced by the blocks of the partition are mutually disjoint. In earlier work Kelk and Stamoulis (Advances in Applied Mathematics 84 (2017), pp. 34--46) defined $g_k(\mathcal{T})$ as the number of convex characters where each block has at least $k$ leaves. Exact expressions were given for $g_1$ and $g_2$, where the topology of $\mathcal{T}$ turns out to be irrelevant, and it was noted that for $k \geq 3$ topological neutrality no longer holds. In this article, for every $k \geq 3$ we describe tree topologies achieving the maximum and minimum values of $g_k$ and determine corresponding expressions and exponential bounds for $g_k$. Finally, we reflect briefly on possible algorithmic applications of these results.Comment: 12 pages, 5 figure

Sharp upper and lower bounds on a restricted class of convex characters

Let T be an unrooted binary tree with n distinctly labelled leaves. Deriving its name from the field of phylogenetics, a convex character on T is simply a partition of the leaves such that the minimal spanning subtrees induced by the blocks of the partition are mutually disjoint. In earlier work Kelk and Stamoulis (Advances in Applied Mathematics 84 (2017), pp. 34-46) defined g(k)(T) as the number of convex characters where each block has at least k leaves. Exact expressions were given for g(1) and g(2), where the topology of T turns out to be irrelevant, and it was noted that for k >= 3 topological neutrality no longer holds. In this article, for every k >= 3 we describe tree topologies achieving the maximum and minimum values of g(k) and determine corresponding expressions and exponential bounds for g(k). Finally, we reflect briefly on possible algorithmic applications of these results