Peeling phylogenetic ‘oranges’

We investigate the combinatorics of a topological space that is generated by the set of edge-weighted finite trees. This space arises by multiplying the weights of edges on paths in trees and is closely connected to tree reconstruction problems involving finite state Markov processes. We show that this space is a contractible finite CW-complex whose face poset can be described via a partial order on semilabelled forests. We then describe some combinatorial properties of this poset, showing that, for example, it is pure, thin and contractible.     

On centroid branches of trees from certain families

We obtain various results involving the centroid branches of randomly chosen trees from simply generated families.     

An Improved Extra-Gradient Method for Minimizing a Sum of p-norms—A Variational Inequality Approach

This paper presents a variational inequality (VI) approach to the problem of minimizing a sum of p-norms. First the original problem is reformulated as an equivalent linear VI. Then an improved extra-gradient method is presented to solve the linear VI. Applications to the problem of p-norm Steiner Minimum Trees (SMT) shows that the proposed method is effective. Comparison with the general extra-gradient method is also provided to show the improvements of the new method.     

Model selection based on Lorenz and concentration curves,Gini indices and convex order

In order to determine an appropriate amount of premium, statistical goodness-of-fit criteria must be supplemented with actuarial ones when assessing performance of a given candidate pure premium. In this paper, concentration curves and Lorenz curves are shown to provide actuaries with effective tools to evaluate whether a premium is appropriate or to compare two competing alternatives. The idea is to compare the premium income for sub-portfolios gathering low risks (identified as low by means of the premiums under consideration) to the true one, or equivalently, to the actual losses. Numerical illustrations performed on hypothetical data and real ones demonstrate the usefulness of the proposed approach.     

Ultrasonic techniques for nondestructive testing of standing trees

The aim of this study is to assess wood quality of standing trees with ultrasonic velocity methods. The ultrasonic techniques currently used are: scattering based techniques that use travel time and other wave parameters for measuring the elastic constants of wood, and ultrasonic tomographic imaging techniques which seek to provide a high resolution picture of the defect. Scattering based techniques were firstly used as nondestructive techniques with increment cores of 5 mm diameter. On these specimens measurements with bulk waves--longitudinal and shear were used to detect the influence of sylvicultural treatment (pruning) on wood quality and also to detect defects (slope of grain, wavy figures). High resolution imaging techniques were developed for imaging abnormalities induced by biological attacks of fungi or insects in standing trees. In this case, ultrasonic tomography refers to cross-sectional imaging of trees from data collected by illuminating the tree from different directions. Ultrasonic images were reconstructed from the time of flight. The images were reconstructed from 120 measurements in situ and through the bark with direct transmission technique, using 1 MHz transducers. The resolution is 5 cm.     

The structure of matrices with a maximum multiplicity eigenvalue

There is remarkable and distinctive structure among Hermitian matrices, whose graph is a given tree T and that have an eigenvalue of multiplicity that is a maximum for T. Among such structure, we give several new results: (1) no vertex of T may be “neutral”; (2) neutral vertices may occur if the largest multiplicity is less than the maximum; (3) every Parter vertex has at least two downer branches; (4) removal of a Parter vertex changes the status of no other vertex; and (5) every set of Parter vertices forms a Parter set. Statements (3), (4) and (5) are also not generally true when the multiplicity is less than the maximum. Some of our results are used to give further insights into prior results, and both the review of necessary background and the development of new structural lemmas may be of independent interest.     

Acoustic detection and classification of river boats

We present a robust algorithm to detect the arrival of a boat of a certain type when other background noises are present. It is done via the analysis of its acoustic signature against an existing database of recorded and processed acoustic signals. We characterize the signals by the distribution of their energies among blocks of wavelet packet coefficients. To derive the acoustic signature of the boat of interest, we use the Best Discriminant Basis method. The decision is made by combining the answers from the Linear Discriminant Analysis (LDA) classifier and from the Classification and Regression Trees (CART) that is also accompanied with an additional unit, called Aisles, that reduces false alarms rate. The proposed algorithm is a generic solution for process control that is based on a learning phase (training) followed by an automatic real time detection while minimizing the false alarms rate.     

Coarse equivalences of Euclidean buildings

We prove the following rigidity results. Coarse equivalences between metrically complete Euclidean buildings preserve spherical buildings at infinity. If all irreducible factors have dimension at least two, then coarsely equivalent Euclidean buildings are isometric (up to scaling factors); if in addition none of the irreducible factors is a Euclidean cone, then the isometry is unique and has finite distance from the coarse equivalence.