Recognizing and realizing cactus metrics

The problem of realizing finite metric spaces in terms of weighted graphs has many applications. For example, the mathematical and computational properties of metrics that can be realized by trees have been well-studied and such research has laid the foundation of the reconstruction of phylogenetic trees from evolutionary distances. However, as trees may be too restrictive to accurately represent real-world data or phenomena, it is important to understand the relationship between more general graphs and distances. In this paper, we introduce a new type of metric called a cactus metric, that is, a metric that can be realized by a cactus graph. We show that, just as with tree metrics, a cactus metric has a unique optimal realization. In addition, we describe an algorithm that can recognize whether or not a metric is a cactus metric and, if so, compute its optimal realization in $O(n^3)$ time, where $n$ is the number of points in the space

Making a Network Orchard by Adding Leaves

Phylogenetic networks are used to represent the evolutionary history of species. Recently, the new class of orchard networks was introduced, which were later shown to be interpretable as trees with additional horizontal arcs. This makes the network class ideal for capturing evolutionary histories that involve horizontal gene transfers. Here, we study the minimum number of additional leaves needed to make a network orchard. We demonstrate that computing this proximity measure for a given network is NP-hard and describe a tight upper bound. We also give an equivalent measure based on vertex labellings to construct a mixed integer linear programming formulation. Our experimental results, which include both real-world and synthetic data, illustrate the efficiency of our implementation

Transannular patch repair of double-outlet right ventricle, {s,d,l}, and single right coronary artery

AbstractJ Thorac Cardiovasc Surg 1999;117:622-

Reconstructing tree-child networks from reticulate-edge-deleted subnetworks

Network reconstruction lies at the heart of phylogenetic research. Two well-studied classes of phylogenetic networks include tree-child networks and level-k networks. In a tree-child network, every non-leaf node has a child that is a tree node or a leaf. In a level-k network, the maximum number of reticulations contained in a biconnected component is k. Here, we show that level-k tree-child networks are encoded by their reticulate-edge-deleted subnetworks, which are subnetworks obtained by deleting a single reticulation edge, if k≥2 . Following this, we provide a polynomial-time algorithm for uniquely reconstructing such networks from their reticulate-edge-deleted subnetworks. Moreover, we show that this can even be done when considering subnetworks obtained by deleting one reticulation edge from each biconnected component with k reticulations

Monetary Diet Cost is Associated with not only Favorable but also Unfavorable Aspects of Diet in Pregnant Japanese Women: The Osaka Maternal and Child Health Study

While several observational studies in European countries have shown that higher monetary diet cost is associated with healthier diets, information on the relationship of cost to diet quality in other countries is sparse, including Japan. This cross-sectional study examined the association between monetary diet cost and dietary intake in a group of pregnant Japanese women. Subjects were 596 pregnant Japanese housewives. Dietary intake was estimated using a validated, self-administered, comprehensive diet history questionnaire. Monetary diet cost was calculated using retail food prices. Values of monetary diet cost and nutrient and food intake were energy-adjusted using the density method. Monetary diet cost was associated positively with the intake of protein, total fat, saturated fatty acids, dietary fiber, cholesterol, sodium, potassium, calcium, magnesium, iron, vitamins A, D, E, C, and folate, and inversely with that of carbohydrate. For foods, cost was associated positively with the intake of potatoes, pulses and nuts, fish and shellfish, meat, dairy products, vegetables, and fruits, and inversely with that of rice and bread. No association was seen for noodles, confectioneries and sugars, fats and oils, or eggs. Cost was also associated inversely with dietary energy density. In conclusion, monetary diet cost was associated with not only favorable aspects of diet, including a higher intake of dietary fiber, key vitamins and minerals, fruits, and vegetables and lower dietary energy density, but also unfavorable aspects, including a higher intake of fat and sodium and lower intake of carbohydrate and rice, in a group of pregnant Japanese women

Rooting for phylogenetic networks

This paper studies the relationship between undirected (unrooted) and directed (rooted) phylogenetic networks. We describe a polynomial-time algorithm for deciding whether an undirected binary phylogenetic network, given the locations of the root and reticulation vertices, can be oriented as a directed phylogenetic network. Moreover, we give a mathematical characterization of when this is the case and show that this directed phylogenetic network is then always unique. These results are generalized to the nonbinary case. In addition, we describe an algorithm for deciding whether an undirected binary phylogenetic network can be oriented as a directed phylogenetic network of a certain class. The algorithm is fixed-parameter tractable (FPT) when the parameter is the level of the network and is applicable to a wide range of network classes, including tree-child, tree-based, stack-free and orchard networks. It can also be used to decide whether an undirected phylogenetic network is tree-based and whether a partly-directed phylogenetic network can be oriented as a directed phylogenetic network. Finally, we show that, in general, it is NP-hard to decide whether an undirected network can be oriented as a tree-based network