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Pairwise compatibility graphs (PCGs) with non-negative integer edge weights recently have been used to describe rare evolutionary events and scenarios with horizontal gene transfer. Here we consider the case that vertices are separated by exactly two discrete events: Given a tree T with leaf set L and edge-weights λ : E (T) → N 0 , the non-negative integer pairwise compatibility graph nniPCG (T , λ , 2 , 2) has vertex set L and x y is an edge whenever the sum of the non-negative integer weights along the unique path from x to y in T equals 2. A graph G has a representation as nniPCG (T , λ , 2 , 2) if and only if its point-determining quotient is a block graph, where two vertices are in relation if they have the same neighborhood in G. If G is of this type, a labeled tree (T , λ) explaining G can be constructed efficiently. In addition, we consider an oriented version of this class of graphs. [ABSTRACT FROM AUTHOR]

In the research content of this paper, we characterize the unit interval graphs which are paired k -disjoint path coverable. Specifically, we prove that G is paired k -disjoint path coverable if and only if G is (2 k − 1) -connected, where k > 2. Moreover, we show that G is semi-paired k -disjoint path coverable if and only if G is (2 k − 1) -connected where k ≥ 3 and n ≥ 2 k. [ABSTRACT FROM AUTHOR]

Böcker and Dress (Adv Math 138:105-125, 1998) presented a 1-to-1 correspondence between symbolically dated rooted trees and symbolic ultrametrics. We consider the corresponding problem for unrooted trees. More precisely, given a tree T with leaf set X and a proper vertex coloring of its interior vertices, we can map every triple of three different leaves to the color of its median vertex. We characterize all ternary maps that can be obtained in this way in terms of 4- and 5-point conditions, and we show that the corresponding tree and its coloring can be reconstructed from a ternary map that satisfies those conditions. Further, we give an additional condition that characterizes whether the tree is binary, and we describe an algorithm that reconstructs general trees in a bottom-up fashion. [ABSTRACT FROM AUTHOR]

We present a distance metric learning algorithm for regression problems, which incorporates label information to form a biased distance metric in the process of learning. We use Newton's optimization method to solve an optimization problem for the sake of learning this biased distance metric. Experiments show that this method can find the intrinsic variation trend of data in a regression model by a relative small amount of samples without any prior assumption of the structure or distribution of data. In addition, the test sample data can be projected to this metric by a simple linear transformation and it is easy to be combined with manifold learning algorithms to improve the performance. Experiments are conducted on the FG-NET aging database, the UIUC-IFP-Y aging database, and the CHIL head pose database by Gaussian process regression based on the learned metric, which shows that our method is competitive among the start-of-art. [ABSTRACT FROM AUTHOR]

Rare events have played an increasing role in molecular phylogenetics as potentially homoplasy-poor characters. In this contribution we analyze the phylogenetic information content from a combinatorial point of view by considering the binary relation on the set of taxa defined by the existence of a single event separating two taxa. We show that the graph-representation of this relation must be a tree. Moreover, we characterize completely the relationship between the tree of such relations and the underlying phylogenetic tree. With directed operations such as tandem-duplication-random-loss events in mind we demonstrate how non-symmetric information constrains the position of the root in the partially reconstructed phylogeny. [ABSTRACT FROM AUTHOR]

We show that every interval in the homomorphism order of finite undirected graphs is either universal or a gap. Together with density and universality this “fractal” property contributes to the spectacular properties of the homomorphism order. We first show the fractal property by using Sparse Incomparability Lemma and then by a more involved elementary argument. [ABSTRACT FROM AUTHOR]

Abstract: We prove that for every the homomorphism order of the class of line graphs of finite graphs with maximal degree is universal. This means that every finite or countably infinite partially ordered set may be represented by line graphs of graphs with maximal degree ordered by the existence of a homomorphism. [Copyright &y& Elsevier]

Ontology learning has become a major area of research within the current ontology engineering. The acquisition of concepts and taxonomic relations is one of the key issues of ontology learning. There are various taxonomic ways for the same domain and the related concepts. However, current ontology learning tools have not considered how to generate the most suitable taxonomy for the specific application. In this article, we present a new supervised approach for taxonomic relationship learning. Taking the Chinese unstructured text on the Web as the corpus and a certain particular domain application as the guide, this method uses a given branch of the target ontology and integrates multi-strategy which includes shallow syntactic analysis and kinds of statistical measures to extract concepts and to determine the concepts’ hierarchy numbers and is-a relations. The experiments using a working prototype of the system revealed the improved performance of domain ontology taxonomic relations learning. [ABSTRACT FROM AUTHOR]

Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of non-treelike evolutionary events such as hybridization. Typically, such networks have been analyzed based on their 'level', i.e. based on the complexity of their 2-edge-connected components. However, recently the question of how 'treelike' a phylogenetic network is has become the center of attention in various studies. This led to the introduction of tree-based networks , i.e. networks that can be constructed from a phylogenetic tree, called the base tree , by adding additional edges. While the concept of tree-basedness was originally introduced for rooted phylogenetic networks, it has recently also been considered for unrooted networks. In the present study, we compare and contrast findings obtained for unrooted binary tree-based networks to unrooted non-binary networks. In particular, while it is known that up to level 4 all unrooted binary networks are tree-based, we show that in the case of non-binary networks, this result only holds up to level 3. [ABSTRACT FROM AUTHOR]