Arithmetic for Rooted Trees

We propose a new arithmetic for non-empty rooted unordered trees simply called trees. After discussing tree representation and enumeration, we define the operations of tree addition, multiplication and stretch, prove their properties, and show that all trees can be generated from a starting tree of one vertex. We then show how a given tree can be obtained as the sum or product of two trees, thus defining prime trees with respect to addition and multiplication. In both cases we show how primality can be decided in time polynomial in the number of vertices and we prove that factorization is unique. We then define negative trees and suggest dealing with tree equations, giving some preliminary results. Finally we comment on how our arithmetic might be useful, and discuss preceding studies that have some relations with our. To the best of our knowledge our approach and results are completely new aside for an earlier version of this work submitte as an arXiv manuscript.Comment: 18 pages, 8 figure

Direct measurement of tree height provides different results on the assessment of LiDAR accuracy

open8noopenSibona, Emanuele; Vitali, Alessandro; Meloni, Fabio; Caffo, Lucia; Dotta, Alberto; Lingua, Emanuele; Motta, Renzo; Garbarino, MatteoSibona, Emanuele; Vitali, Alessandro; Meloni, Fabio; Caffo, Lucia; Dotta, Alberto; Lingua, Emanuele; Motta, Renzo; Garbarino, Matte

(Non)Commutative Hopf algebras of trees and (quasi)symmetric functions

The Connes-Kreimer Hopf algebra of rooted trees, its dual, and the Foissy Hopf algebra of of planar rooted trees are related to each other and to the well-known Hopf algebras of symmetric and quasi-symmetric functions via a pair of commutative diagrams. We show how this point of view can simplify computations in the Connes-Kreimer Hopf algebra and its dual, particularly for combinatorial Dyson-Schwinger equations.Comment: For March 2006 CIRM conference "Renormalization and Galois theories

Quantitative and qualitative characteristics of greenery in suburban residential districts of Metro Manila

This case study was conducted to better understand the present situation of urban greenery in Marikina City, in the suburbs of metropolitan Manila, a typical large Asian city. A vegetation survey was conducted in residential districts of Marikina City, and the quantitative and qualitative characteristics of trees were analyzed. Lot size had some influence on the quantity of greenery in residential lots. In smaller lots, however, quantity did not increase in proportion to lot size. It appears, then, that the land-use controls for individual lots did not function effectively. Quantitative differences of greenery were related to qualitative differences, depending on the year or period of development of the residential area. In the newly developed residential lots, the greenery is comprised mostly of ornamental trees. Under the present circumstances, there is no assurance of sustaining the desired quantity of greenery in smaller residential lots. From these results, we proposed that regulations on lot size/coverage and promotion of tree planting involving local residents are needed to sustain urban greenery in residential districts

Studies of Stability and Robustness for Artificial Neural Networks and Boosted Decision Trees

In this paper, we compare the performance, stability and robustness of Artificial Neural Networks (ANN) and Boosted Decision Trees (BDT) using MiniBooNE Monte Carlo samples. These methods attempt to classify events given a number of identification variables. The BDT algorithm has been discussed by us in previous publications. Testing is done in this paper by smearing and shifting the input variables of testing samples. Based on these studies, BDT has better particle identification performance than ANN. The degradation of the classifications obtained by shifting or smearing variables of testing results is smaller for BDT than for ANN.Comment: 23 pages, 13 figure

The influence of forest regrowth, original canopy cover and tree size on saproxylic beetles associated with old oaks

Abandoned management has caused many sites with free-standing, large oaks (Quercus robur) to become more shaded. This study shows how forest regrowth affects beetle species associated with old oaks in south-eastern Sweden. Beetles were trapped by pitfall traps placed in hollows and window traps placed near hollows in oak trunks in pasture woodlands. We assessed the influence of forest regrowth, tree size and original canopy cover on the species richness of saproxylic beetles (a total of 120 species identified) and the occurrence of 68 saproxylic beetle species in particular. Species richness was greatest in stands with large, free-standing trees. Large girth as well as low canopy cover increased frequency of occurrence for several species. Forest regrowth was found to be detrimental for many beetle species. As most localities with endangered beetles living in old oaks are small and isolated, ongoing management and the restoration of abandoned pasture woodlands should have a high priority in nature conservation