Axiomization of the center function on trees.

We give a new, short proof that four certain axiomatic properties uniquely define the center of a tree.

Axiomization of the center function on trees.

We give a new, short proof that four certain axiomatic properties uniquely define the center of a tree

Search for W′→tbˉW'\rightarrow t\bar{b} in the lepton plus jets final states with the ATLAS detector at the LHC

This document presents a search for a $W'$ boson, decaying to a top quark and a $b$ quark in an effective coupling approach, using a multivariate method based on boosted decision trees. It reports exclusion limits on the $W'\rightarrow tb$ cross-section times branching ratio and effective couplings as a function of the $W'$-boson mass. The search covers $W'$-boson masses between 0.5 and 3.0 TeV, for right-handed or left-handed $W'$-boson, with 20.3 fb$^{-1}$ of proton-proton collision data produced by the LHC in 2012, at a center-of-mass energy of 8 TeV and collected by the ATLAS detector.Comment: TOP2014, 4 pages, 4 figure

Forest regeneration and edge effects : an ecophysiological analysis after gap-cutting

As continuous cover forestry is an ongoing topic in todays forest debate, questions are raised about eventual issues connected to the management. It is known that seedling performance can be poor near the edge of harvested areas, and around retained trees. This is a critical issue in transitioning toward continuous cover forestry. In the current thesis, seedling abundance and biomass was quantified as a function of the distance to overstory trees after gap-cutting. The gaps had been either planted, planted and scarified, or left as untreated controls. In each gap, sample plots (2m radius) were laid out at distances -10 m (outside the gap, under canopy), 3 m, 10 m and 20 m. Incoming radiation and soil moisture was also measured in each gap. Seedling foliar nitrogen and isotopic analyses (13C/12C and 15N/14N ratio) were also performed to investigate potential causes of observed patterns. Results showed a clear reduction of growth (94%) at the edge compared to the center of the gaps. Proximity to edge-trees had negative effect on both seedling density and biomass, irrespective of treatment. Nitrogen concentration and 15N/14N was lower along the gap edge, while 13C/12C showed the opposite. No signs of light and soil moisture as limiting factors for seedlings growth could be observed. The results implied that competition for nutrients, mainly N, from retained edge-trees was restraining seedlings. The results also indicated presence of a Nsource accessible for center-seedlings but not edge-seedlings, which could be decomposing mycorrhizal mycelium

Unreliable point facility location problems on networks

In this paper we study facility location problems on graphs under the most common criteria, such as, median, center and centdian, but we incorporate in the objective function some reliability aspects. Assuming that facilities may become unavailable with a certain probability, the problem consists of locating facilities minimizing the overall or the maximum expected service cost in the long run, or a convex combination of the two. We show that the k-facility problem on general networks is NP-hard. Then, we provide efficient algorithms for these problems for the cases of k = 1, 2, both on general networks and on trees. We also explain how our methodology extends to handle a more general class of unreliable point facility location problems related to the ordered median objective function.Ministerio de Ciencia y TecnologíaJunta de Andalucí

Radial rapid decay does not imply rapid decay

We provide a new, dynamical criterion for the radial rapid decay property. We work out in detail the special case of the group $\Gamma := \mathbf{SL}_2(A)$, where $A := \mathbb{F}_q[X,X^{-1}]$ is the ring of Laurent polynomials with coefficients in $\mathbb{F}_q$, endowed with the length function coming from a natural action of $\Gamma$ on a product of two trees, to show that is has the radial rapid decay (RRD) property and doesn't have the rapid decay (RD) property. The criterion also applies to irreducible lattices in semisimple Lie groups with finite center endowed with a length function defined with the help of a Finsler metric. These examples answer a question asked by Chatterji and moreover show that, unlike the RD property, the RRD property isn't inherited by open subgroups

I-theory on depth vs width: hierarchical function composition

Deep learning networks with convolution, pooling and subsampling are a special case of hierar- chical architectures, which can be represented by trees (such as binary trees). Hierarchical as well as shallow networks can approximate functions of several variables, in particular those that are com- positions of low dimensional functions. We show that the power of a deep network architecture with respect to a shallow network is rather independent of the specific nonlinear operations in the network and depends instead on the the behavior of the VC-dimension. A shallow network can approximate compositional functions with the same error of a deep network but at the cost of a VC-dimension that is exponential instead than quadratic in the dimensionality of the function. To complete the argument we argue that there exist visual computations that are intrinsically compositional. In particular, we prove that recognition invariant to translation cannot be computed by shallow networks in the presence of clutter. Finally, a general framework that includes the compositional case is sketched. The key con- dition that allows tall, thin networks to be nicer that short, fat networks is that the target input-output function must be sparse in a certain technical sense.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF - 1231216

Tree Felling with a Drill Cone

Motor-manual timber felling is one of the most dangerous operations in the forest and cannot be completely replaced by fully mechanized timber harvesting by a harvester when dealing with large and deciduous trees. Shifting the center of gravity of tree ready to be felled beyond its tipping line using conventional felling wedges is dangerous because the forest worker is directly behind the stem and under the tree crown until just before the tree falls. The worker can be hit by the trunk itself, but also by falling parts of the crown. In a preliminary study for the development of a new type of felling head, felling with a drill cone that can open the felling cut with the help of an applied torque was investigated. A drill cone does not require any special cutting technique, no counter forces to the tree, works without impulses, it is self-retaining and can be unscrewed again. In order to determine the torque required for felling the tree as a function of the tree parameters, the mathematical equation framework was established and practical experiments were used to determine the friction parameters and verify the calculations. The torque of the drill cone is used to bend the intact fibers of the hinge, shift the center of gravity of the tree in the direction of fall, and to overcome the friction of the drill cone on the felling cut. The effects of forward or backward leaning trees on the required torque can also be quantified. It has been shown that the efficiency of a drill cone is low, but this is compensated for by the high internal torque to lift ratio. The maximum measured input torque for felling trees with a felling diameter up to 55 centimeter was 100 Nm