Partial Homology Relations - Satisfiability in terms of Di-Cographs

Directed cographs (di-cographs) play a crucial role in the reconstruction of evolutionary histories of genes based on homology relations which are binary relations between genes. A variety of methods based on pairwise sequence comparisons can be used to infer such homology relations (e.g.\ orthology, paralogy, xenology). They are \emph{satisfiable} if the relations can be explained by an event-labeled gene tree, i.e., they can simultaneously co-exist in an evolutionary history of the underlying genes. Every gene tree is equivalently interpreted as a so-called cotree that entirely encodes the structure of a di-cograph. Thus, satisfiable homology relations must necessarily form a di-cograph. The inferred homology relations might not cover each pair of genes and thus, provide only partial knowledge on the full set of homology relations. Moreover, for particular pairs of genes, it might be known with a high degree of certainty that they are not orthologs (resp.\ paralogs, xenologs) which yields forbidden pairs of genes. Motivated by this observation, we characterize (partial) satisfiable homology relations with or without forbidden gene pairs, provide a quadratic-time algorithm for their recognition and for the computation of a cotree that explains the given relations

On Symbolic Ultrametrics, Cotree Representations, and Cograph Edge Decompositions and Partitions

Symbolic ultrametrics define edge-colored complete graphs K_n and yield a simple tree representation of K_n. We discuss, under which conditions this idea can be generalized to find a symbolic ultrametric that, in addition, distinguishes between edges and non-edges of arbitrary graphs G=(V,E) and thus, yielding a simple tree representation of G. We prove that such a symbolic ultrametric can only be defined for G if and only if G is a so-called cograph. A cograph is uniquely determined by a so-called cotree. As not all graphs are cographs, we ask, furthermore, what is the minimum number of cotrees needed to represent the topology of G. The latter problem is equivalent to find an optimal cograph edge k-decomposition {E_1,...,E_k} of E so that each subgraph (V,E_i) of G is a cograph. An upper bound for the integer k is derived and it is shown that determining whether a graph has a cograph 2-decomposition, resp., 2-partition is NP-complete

Namibia's Future: Modeling Population and Sustainable Development Challenges in the Era of HIV/AIDS

Namibia is a young country, having achieved its independence only 11 years ago. It is a land of great potential. The extent to which this potential will be realized is dominated by one issue, the effects of HIV/AIDS. Currently, Namibia has one of the highest HIV/AIDS prevalence rates in the world. In 2001, around 18,000 or about 1% of Namibia's population will die of AIDS. This number will almost double in the next 10 years. Even with significant changes in behavior, our model shows that over half a million Namibians will die of AIDS from 2002 to 2021. This is roughly a third of Namibia's current population. This report summarizes our findings on how HIV/AIDS will influence population, development, and environment interactions in Namibia during the next two decades

Botswana's Future: Modeling Population and Sustainable Development Challenges in the Era of HIV/AIDS

One element dominates current discussions of Botswana's future, the problem of HIV/AIDS. Currently, Botswana has one of the highest HIV/AIDS prevalence rates in the world. We estimate that during the period from 1993 through 2001 there were around 130,000 deaths from HIV/AIDS. In 2001 alone, we expect that roughly 32,000 Botswana or about 2% of the country's population will die of that disease. Even with significant changes in behavior, our model shows that around 540,000 Botswana, a number equivalent to about one-third of the country's current population, will die of HIV/AIDS during the two-decade period 2002-2021

Mozambique's Future: Modeling Population and Sustainable Development Challenges

What are the prospects for sustainable development over the next 20 years in Mozambique? Although it looks as if much of the development prospects are determined by such inherently unpredictable events as war, peace, and weather calamities, there are also many changes and patterns which have a long-term stability and which change only slowly over time. For example, socio-demographic changes, such as labor force skills, and population health have a long momentum. These are very important indicators for the economic development potential of a country. Also, although it is impossible to predict a particular year of heavy rains or droughts, there are long time series of weather from which we can calculate the country's vulnerability to single- or multiple-year weather disasters. To focus our efforts in answering this bold question, we concentrate on four issues: (1) Can poverty be erased in the next 20 years? (2) How will school enrollment lead to higher skills in the labor force by 2020? (3) What role will water play in development, in particular, water provision by rain to rural areas, and infrastructure to cities? (4) And, most importantly, what will be the impacts of the HIV/AIDS pandemic in the next decades

Health Literacy and Medication Practices in Senior Housing Residents

Objective: To conduct a descriptive analysis of health literacy, knowledge of prescribed medications, and methods of administering medications in a cohort of senior housing residents.https://scholarworks.uvm.edu/comphp_gallery/1027/thumbnail.jp

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

Beyond representing orthology relations by trees

Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple relations on a set of sequences called orthology relations may be employed. In addition to being interesting from a practical point of view they are also attractive from a theoretical perspective in that e.\,g.\,a characterization is known for when such a relation is representable by a certain type of phylogenetic tree. For an orthology relation inferred from real biological data it is however generally too much to hope for that it satisfies that characterization. Rather than trying to correct the data in some way or another which has its own drawbacks, as an alternative, we propose to represent an orthology relation $\delta$ in terms of a structure more general than a phylogenetic tree called a phylogenetic network. To compute such a network in the form of a level-1 representation for $\delta$, we formalize an orthology relation in terms of the novel concept of a symbolic 3- dissimilarity which is motivated by the biological concept of a ``cluster of orthologous groups'', or COG for short. For such maps which assign symbols rather that real values to elements, we introduce the novel {\sc Network-Popping} algorithm which has several attractive properties. In addition, we characterize an orthology relation $\delta$ on some set $X$ that has a level-1 representation in terms of eight natural properties for $\delta$ as well as in terms of level-1 representations of orthology relations on certain subsets of $X$

Potentiation of thrombus instability: a contributory mechanism to the effectiveness of antithrombotic medications

© The Author(s) 2018The stability of an arterial thrombus, determined by its structure and ability to resist endogenous fibrinolysis, is a major determinant of the extent of infarction that results from coronary or cerebrovascular thrombosis. There is ample evidence from both laboratory and clinical studies to suggest that in addition to inhibiting platelet aggregation, antithrombotic medications have shear-dependent effects, potentiating thrombus fragility and/or enhancing endogenous fibrinolysis. Such shear-dependent effects, potentiating the fragility of the growing thrombus and/or enhancing endogenous thrombolytic activity, likely contribute to the clinical effectiveness of such medications. It is not clear how much these effects relate to the measured inhibition of platelet aggregation in response to specific agonists. These effects are observable only with techniques that subject the growing thrombus to arterial flow and shear conditions. The effects of antithrombotic medications on thrombus stability and ways of assessing this are reviewed herein, and it is proposed that thrombus stability could become a new target for pharmacological intervention.Peer reviewedFinal Published versio