Intrinsic Inference on the Mean Geodesic of Planar Shapes and Tree Discrimination by Leaf Growth

For planar landmark based shapes, taking into account the non-Euclidean geometry of the shape space, a statistical test for a common mean first geodesic principal component (GPC) is devised. It rests on one of two asymptotic scenarios, both of which are identical in a Euclidean geometry. For both scenarios, strong consistency and central limit theorems are established, along with an algorithm for the computation of a Ziezold mean geodesic. In application, this allows to verify the geodesic hypothesis for leaf growth of Canadian black poplars and to discriminate genetically different trees by observations of leaf shape growth over brief time intervals. With a test based on Procrustes tangent space coordinates, not involving the shape space's curvature, neither can be achieved.Comment: 28 pages, 4 figure

Timber harvest and frequent prescribed burning interact to affect the demography of Eucalypt species

Ecosystem management can negatively affect the demography of plant communities through the introduction of novel disturbance regimes. Prescribed burning and timber harvesting are two common and widely applied management strategies across forest ecosystems. Despite this, little is known about the long-term effects that these interacting disturbances have on forest demography. This study examined the effect of timber harvesting and frequent prescribed burning on the mortality, growth and regeneration of trees in a temperate eucalypt forest of south-eastern Australia. The study took place at a long-term experimental site, where experimental coupes were subjected to a one-off selective harvesting treatment (harvested, not harvested), followed by regimes of experimental burning (no fire, ~4 year burn intervals or ~2 year burn intervals) over a 22 year period. Tree communities were surveyed at permanent monitoring sites prior to the application of experimental treatments (1985 – 1989), and resurveyed post treatment (2016) to assess mortality, growth rates and ingrowth of trees \u3e10 cm diameter at breast height. Harvesting directly removed ~40% of trees and indirectly increased the mortality of retained trees through damage (e.g. crown and bole breakage) caused during the harvesting operation. The likelihood of harvesting damage was greater for small trees and increased with harvesting intensity (i.e. the amount of timber removed). Frequent burning increased the likelihood of tree mortality on harvested sites, with large, old trees being particularly vulnerable. Growth rate and ingrowth of trees was elevated at harvested sites, increasing almost linearly with harvesting intensity, which suggests that competitive release had occurred. Fire frequency had no effect on growth rates or ingrowth of trees. This study highlights that frequent prescribed burning and selective timber harvesting can have additive effects on the loss of large trees, reducing the availability of these keystone habitat structures in intensively managed forest ecosystems. Although the elevated rates of growth and ingrowth may hasten the replacement of lost large trees, recovery will require long time frames

Rare event simulation for dynamic fault trees

Fault trees (FT) are a popular industrial method for reliability engineering, for which Monte Carlo simulation is an important technique to estimate common dependability metrics, such as the system reliability and availability. A severe drawback of Monte Carlo simulation is that the number of simulations required to obtain accurate estimations grows extremely large in the presence of rare events, i.e., events whose probability of occurrence is very low, which typically holds for failures in highly reliable systems. This paper presents a novel method for rare event simulation of dynamic fault trees with complex repairs that requires only a modest number of simulations, while retaining statistically justified confidence intervals. Our method exploits the importance sampling technique for rare event simulation, together with a compositional state space generation method for dynamic fault trees. We demonstrate our approach using two parameterized sets of case studies, showing that our method can handle fault trees that could not be evaluated with either existing analytical techniques, nor with standard simulation techniques

Average-case analysis of perfect sorting by reversals (Journal Version)

Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any common interval. B\'erard et al. (2007) make use of strong interval trees to describe an algorithm for sorting signed permutations by reversals. Combinatorial properties of this family of trees are essential to the algorithm analysis. Here, we use the expected value of certain tree parameters to prove that the average run-time of the algorithm is at worst, polynomial, and additionally, for sufficiently long permutations, the sorting algorithm runs in polynomial time with probability one. Furthermore, our analysis of the subclass of commuting scenarios yields precise results on the average length of a reversal, and the average number of reversals.Comment: A preliminary version of this work appeared in the proceedings of Combinatorial Pattern Matching (CPM) 2009. See arXiv:0901.2847; Discrete Mathematics, Algorithms and Applications, vol. 3(3), 201

Longest Common Pattern between two Permutations

In this paper, we give a polynomial (O(n^8)) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general permutations whose complexity depends on the length of the longest simple permutation involved in one of our permutations

Robust Inference of Trees

This paper is concerned with the reliable inference of optimal tree-approximations to the dependency structure of an unknown distribution generating data. The traditional approach to the problem measures the dependency strength between random variables by the index called mutual information. In this paper reliability is achieved by Walley's imprecise Dirichlet model, which generalizes Bayesian learning with Dirichlet priors. Adopting the imprecise Dirichlet model results in posterior interval expectation for mutual information, and in a set of plausible trees consistent with the data. Reliable inference about the actual tree is achieved by focusing on the substructure common to all the plausible trees. We develop an exact algorithm that infers the substructure in time O(m^4), m being the number of random variables. The new algorithm is applied to a set of data sampled from a known distribution. The method is shown to reliably infer edges of the actual tree even when the data are very scarce, unlike the traditional approach. Finally, we provide lower and upper credibility limits for mutual information under the imprecise Dirichlet model. These enable the previous developments to be extended to a full inferential method for trees.Comment: 26 pages, 7 figure