Network science inspires novel tree shape statistics

The shape of phylogenetic trees can be used to gain evolutionary insights. A tree’s shape specifies the connectivity of a tree, while its branch lengths reflect either the time or genetic distance between branching events; well-known measures of tree shape include the Colless and Sackin imbalance, which describe the asymmetry of a tree. In other contexts, network science has become an important paradigm for describing structural features of networks and using them to understand complex systems, ranging from protein interactions to social systems. Network science is thus a potential source of many novel ways to characterize tree shape, as trees are also networks. Here, we tailor tools from network science, including diameter, average path length, and betweenness, closeness, and eigenvector centrality, to summarize phylogenetic tree shapes. We thereby propose tree shape summaries that are complementary to both asymmetry and the frequencies of small configurations. These new statistics can be computed in linear time and scale well to describe the shapes of large trees. We apply these statistics, alongside some conventional tree statistics, to phylogenetic trees from three very different viruses (HIV, dengue fever and measles), from the same virus in different epidemiological scenarios (influenza A and HIV) and from simulation models known to produce trees with different shapes. Using mutual information and supervised learning algorithms, we find that the statistics adapted from network science perform as well as or better than conventional statistics. We describe their distributions and prove some basic results about their extreme values in a tree. We conclude that network science-based tree shape summaries are a promising addition to the toolkit of tree shape features. All our shape summaries, as well as functions to select the most discriminating ones for two sets of trees, are freely available as an R package at http://github.com/Leonardini/treeCentrality.

Growth Dynamics and Tree Shape of Common Beech ( Fagus sylvatica L.) in the International Provenance Test

Provenance tests of forest tree species are important experiments in silviculture and tree breeding. Their results provide information about provenances' growth, adaptability, and other features. The research aimed to determine the dynamics of growth and tree shape of common beech plants per provenances in the international provenance test in Bosnia and Herzegovina to choose the best provenances considering wood production and quality. Research was conducted in the provenance test containing eight provenances from Bosnia and Herzegovina, four from Germany, three from Serbia, two each from Croatia, Romania, and Switzerland, and one from Hungary. Provenance test was established in 2007 by planting 2-year-old and 3-year old seedlings. Height and root collar diameter were measured, and tree shape was assessed in 2019. Data were processed in SPSS 26.0. Descriptive statistics, variance analysis, multiple Duncan's test for all traits, and Pearson's coefficient of corelation among morphological traits and tree shape were calculated. Variance for the height and root collar diameter showed statistically significant differences among different ages of plants and among provenances. Provenance from Croatia (Dilj Čaglinski) had the highest, and provenance from Romania (Alba-Iulia) had the lowest average height. The highest average value of root collar diameter had provenance Dilj Čaglinski, and the lowest value had provenance Sihlwald (Switzerland). The highest percentage of category 10 (ideal tree form) had provenance Bad Wildbad (Germany), and categories 1-4 (no silviculture value) had provenance Alba-Iulia (Romania). Pearson's coefficient showed that height, root collar diameter, and tree shape are highly correlated. Considering all the above, when planning forest-breeding works, it is recommended to continue the research and favor provenances with the best growth and tree shape.

MIMO Based Microstrip Patch Antenna with Tree Shape Patch for 5G Applications

5G technology is the latest technology in market for high data rate communication based applications. There are some problems like signal blocking and attenuation occur at very high data rate and become a problem for 5G communication. This problem can be solved by using MIMO based antennas. Microstrip patch antenna is used for high frequency antenna applications. Multiple array MIMO based microstrip patch antenna is very suitable for high data rate 5G applications. CST software is used for designing and simulation of the proposed MIMO antenna. The proposed work is 2x2 array of MIMO microstrip patch antenna with a tree shape patch and full ground, which is providing better bandwidth of 69 MHz at 3.5 GHz 5G frequency. It is also providing return loss of -24.1 dB which is better than previous work which has achieved return loss of -19dB only. Proposed antenna is very suitable for 5G applications including mobile communication, WLAN etc.

Tree Shape Variability in a Mixed Oak Forest Using Terrestrial Laser Technology: Implications for Mating System Analysis

The accuracy of the description regarding tree architecture is crucial for data processing. LiDAR technology is an efficient solution for capturing the characteristics of individual trees. The aim of the present study was to analyze tree shape variability in a mixed oak forest consisting of four European white oak species: Quercus petraea, Q. frainetto, Q. pubescens, and Q. robur. Moreover, we tested for association between tree shape and individual heterozygosity and whether oak trees identified as pollen donors in a previous genetic study have a larger size in terms of crown and trunk characteristics than non-donors. The woody structure of a tree was defined by the quantitative structure model (QSM) providing information about topology (branching structure), geometry, and volume. For extracting the 3D point clouds a high-speed 3D scanner (FARO FocusS 70) was used. The crown variables were strongly correlated to each other, the branch volume being influenced by branch length, maximum branch order, and the number of branches but not influenced by diameter at breast height (DBH), trunk length, trunk volume, or tree height. There was no relationship between the individual heterozygosity based on nuclear microsatellite genetic markers and crown and trunk characteristics, respectively. Branch volume, total area, DBH, trunk volume, and the total volume of tree were significantly larger in pollen donors compared to non-donor Q. petraea trees. Thus, the mean branch volume was more than three times higher. Pollen donors had nearly two and half times larger total area in comparison to non-donor individuals. Our results suggest that a thorough characterization of tree phenotype using terrestrial laser scanning may contribute to a better understanding of mating system patterns in oak forests.

A study of continuous vector representations for theorem proving

Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods. In this paper, we develop an encoding that allows for logical properties to be preserved and is additionally reversible. This means that the tree shape of a formula including all symbols can be reconstructed from the dense vector representation. We do that by training two decoders: one that extracts the top symbol of the tree and one that extracts embedding vectors of subtrees. The syntactic and semantic logical properties that we aim to preserve include both structural formula properties, applicability of natural deduction steps and even more complex operations like unifiability. We propose datasets that can be used to train these syntactic and semantic properties. We evaluate the viability of the developed encoding across the proposed datasets as well as for the practical theorem proving problem of premise selection in the Mizar corpus.

The Shape of Trees – Limits of Current Diversification Models

To investigate how biodiversity arose, the field of macroevolution largely relies on model-based approaches to estimate rates of diversification and what factors influence them. The number of available models is rising steadily, facilitating the modeling of an increasing number of possible diversification dynamics, and multiple hypotheses relating to what fueled or stifled lineage accumulation within groups of organisms. However, growing concerns about unchecked biases and limitations in the employed models suggest the need for rigorous validation of methods used to infer. Here, we address two points: the practical use of model adequacy testing, and what model adequacy can tell us about the overall state of diversification models. Using a large set of empirical phylogenies, and a new approach to test models using aspects of tree shape, we test how a set of staple models performs with regards to adequacy. Patterns of adequacy are described across trees and models and causes for inadequacy – particularly if all models are inadequate – are explored. The findings make clear that overall, only few empirical phylogenies cannot be described by at least one model. However, finding that the best fitting of a set of models might not necessarily be adequate makes clear that adequacy testing should become a step in the standard procedures for diversification studies.

BoskR – Testing Adequacy of Diversification Models Using Tree Shape

The study of diversification largely relies on model-based approaches, estimating rates of speciation and extinction from phylogenetic trees. While a plethora of different models exist – all with different features, strengths and weaknesses – there is increasing concern about the reliability of the inference we gain from them. Apart from simply finding the model with the best fit for the data, we should find ways to assess a model’s suitability to describe the data in an absolute sense. The R package BoskR implements a simple way of judging a model’s adequacy for a given phylogeny using metrics for tree shape, assuming that a model is inadequate for a phylogeny if it produces trees that are consistently dissimilar in shape from the tree that should be analyzed. Tree shape is assessed via metrics derived from the tree’s modified graph Laplacian spectrum, as provided by RPANDA. We exemplify the use of the method using simulated and empirical example phylogenies. BoskR was mostly able to correctly distinguish trees simulated under clearly different models and revealed that not all models are adequate for the empirical example trees. We believe the metrics of tree shape to be an intuitive and relevant means of assessing diversification model adequacy. Furthermore, by implementing the approach in an openly available R package, we enable and encourage researchers to adopt adequacy testing into their workflow.