Robust, Universal Tree Balance Indices

Balance indices that quantify the symmetry of branching events and the compactness of trees are widely used to compare evolutionary processes or tree-generating algorithms. Yet existing indices have important shortcomings, including that they are unsuited to the tree types commonly used to describe the evolution of tumours, microbial populations, and cell lines. The contributions of this article are twofold. First, we define a new class of robust, universal tree balance indices. These indices take a form similar to Colless’ index but account for node sizes, are defined for trees with any degree distribution, and enable more meaningful comparison of trees with different numbers of leaves. Second, we show that for bifurcating and all other full m-ary cladograms (in which every internal node has the same out-degree), one such Colless-like index is equivalent to the normalised reciprocal of Sackin’s index. Hence we both unify and generalise the two most popular existing tree balance indices. Our indices are intrinsically normalised and can be computed in linear time. We conclude that these more widely applicable indices have potential to supersede those in current use.

Second-Order Disjoint Factor Analysis

Hierarchical models are often considered to measure latent concepts defining nested sets of manifest variables. Therefore, by supposing a hierarchical relationship among manifest variables, the general latent concept can be represented by a tree structure where each internal node represents a specific order of abstraction for the latent concept measured. In this paper, we propose a new latent factor model called second-order disjoint factor analysis in order to model an unknown hierarchical structure of the manifest variables with two orders. This is a second-order factor analysis, which—respect to the second-order confirmatory factor analysis—is exploratory, nested and estimated simultaneously by maximum likelihood method. Each subset of manifest variables is modeled to be internally consistent and reliable, that is, manifest variables related to a factor measure “consistently” a unique theoretical construct. This feature implies that manifest variables are positively correlated with the related factor and, therefore, the associated factor loadings are constrained to be nonnegative. A cyclic block coordinate descent algorithm is proposed to maximize the likelihood. We present a simulation study that investigates the ability to get reliable factors. Furthermore, the new model is applied to identify the underlying factors of well-being showing the characteristics of the new methodology. A final discussion completes the paper.

Research and Development of Delay-Sensitive Routing Tensor Model in IoT Core Networks

In the article, we present the research and development of an improved delay-sensitive routing tensor model for the core of the IoT network. The flow-based tensor model is considered within the coordinate system of interpolar paths and internal node pairs. The advantage of the presented model is the application for IoT architectures to ensure the Quality of Service under the parameters of bandwidth, average end-to-end delay, and the probability of packet loss. Hence, the technical task of delay-sensitive routing is formulated as the optimization problem together with constraints and conditions imposed on the corresponding routing variables. The system of optimality criteria is chosen for an investigation. Each selected criterion concerning the specifics of the demanded routing problem solution aims at the optimal use of available network resources and the improvement of QoS indicators, namely, average end-to-end delay. The analysis of the obtained routing solutions under different criteria is performed. Numerical research of the improved delay-sensitive routing tensor model allowed us to discover its features and proved the adequacy of the results for the multipath order of routing.

City size based scaling of the urban internal nodes layout

The size of a city is not only essential for depicting the scale of the urban system, but also crucial to support the prosperity, order, and high-speed developments. However, its relation to the underlying urban structure has not been empirically investigated in detail. To examine the impact of city size on the city structure and quantify structural features, in this study, a statistical analysis was performed based on network science and an interdisciplinary theoretical system. To obtain the statistical law of internal node layout, the urban system was regarded as a complete graph weighted by the Euclidean distance. The relationship between the urban internal nodes layout (points of interest data, Weibo check-in data, and central point of road intersection data) and the city size was established. The results confirmed the existence of statistical laws in the layout of urban spatial elements, and explored the relationship between the changes in urban node network structure and inequality. This study provided a new perspective of urban structure to understand the complexity of the city, and suggested an approach to adjust this structure to narrow down the gap between the urban and rural areas.

Efficient Approaches to the Mixture Distance Problem

The ancestral mixture model, an important model building a hierarchical tree from high dimensional binary sequences, was proposed by Chen and Lindsay in 2006. As a phylogenetic tree (or evolutionary tree), a mixture tree created from ancestral mixture models, involves the inferred evolutionary relationships among various biological species. Moreover, it contains the information of time when the species mutates. The tree comparison metric, an essential issue in bioinformatics, is used to measure the similarity between trees. To our knowledge, however, the approach to the comparison between two mixture trees is still unknown. In this paper, we propose a new metric named the mixture distance metric, to measure the similarity of two mixture trees. It uniquely considers the factor of evolutionary times between trees. If we convert the mixture tree that contains the information of mutation time of each internal node into a weighted tree, the mixture distance metric is very close to the weighted path difference distance metric. Since the converted mixture tree forms a special weighted tree, we were able to design a more efficient algorithm to calculate this new metric. Therefore, we developed two algorithms to compute the mixture distance between two mixture trees. One requires O(n2) and the other requires O(nh1h2) computational time with O(n) preprocessing time, where n denotes the number of leaves in the two mixture trees, and h1 and h2 denote the heights of these two trees.

Efficient implied alignment

Background Given a binary tree $\mathcal {T}$ T of n leaves, each leaf labeled by a string of length at most k, and a binary string alignment function ⊗, an implied alignment can be generated to describe the alignment of a dynamic homology for $\mathcal {T}$ T . This is done by first decorating each node of $\mathcal {T}$ T with an alignment context using ⊗, in a post-order traversal, then, during a subsequent pre-order traversal, inferring on which edges insertion and deletion events occurred using those internal node decorations. Results Previous descriptions of the implied alignment algorithm suggest a technique of “back-propagation” with time complexity $\mathcal {O}\left (k^{2} * n^{2}\right)$ O k 2 ∗ n 2 . Here we describe an implied alignment algorithm with complexity $\mathcal {O}\left (k * n^{2}\right)$ O k ∗ n 2 . For well-behaved data, such as molecular sequences, the runtime approaches the best-case complexity of Ω(k∗n). Conclusions The reduction in the time complexity of the algorithm dramatically improves both its utility in generating multiple sequence alignments and its heuristic utility.

Detecting Shared Genetic Architecture Among Multiple Phenotypes by Hierarchical Clustering of Gene-Level Association Statistics

Emerging large-scale biobanks pairing genotype data with phenotype data present new opportunities to prioritize shared genetic associations across multiple phenotypes for molecular validation. Past research, by our group and others, has shown gene-level tests of association produce biologically interpretable characterization of the genetic architecture of a given phenotype. Here, we present a new method, Ward clustering to identify Internal Node branch length outliers using Gene Scores (WINGS), for identifying shared genetic architecture among multiple phenotypes. The objective of WINGS is to identify groups of phenotypes, or “clusters,” sharing a core set of genes enriched for mutations in cases. We validate WINGS using extensive simulation studies and then combine gene-level association tests with WINGS to identify shared genetic architecture among 81 case-control and seven quantitative phenotypes in 349,468 European-ancestry individuals from the UK Biobank. We identify eight prioritized phenotype clusters and recover multiple published gene-level associations within prioritized clusters.

Prescribed Hamiltonian Connectedness of 2D Torus

Tori are important fundamental interconnection networks for multiprocessor systems. Hamiltonian paths are important in information communication of multiprocessor systems, and Hamiltonian path embedding capability is an important aspect to determine if a network topology is suitable for a real application. In real systems, some links may have better performance. Therefore, when embedding Hamiltonian path into interconnection networks, it is desirable that these Hamiltonian paths would pass through the links with better performance. Given a two two-dimensional torus T (m, n) with m, n ≥ 5 odd, let L be a linear forest with at most two edges in T (m, n) and let u and v be two distinct vertices in T (m, n) such that none of the paths in L has u or v as internal node or both of them as end nodes. In this paper, we construct a hamiltonian path of T (m, n) between u and v passing through L.