Burning a Graph is Hard

Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We prove that the corresponding graph decision problem is \textbf{NP}-complete when restricted to acyclic graphs with maximum degree three, spider graphs and path-forests. We provide polynomial time algorithms for finding the burning number of spider graphs and path-forests if the number of arms and components, respectively, are fixed.Comment: 20 Pages, 4 figures, presented at GRASTA-MAC 2015 (October 19-23rd, 2015, Montr\'eal, Canada

Woody plant communities of isolated Afromontane cloud forests in Taita Hills, Kenya

In the Taita Hills in southern Kenya, remnants of the original Afromontane forest vegetation are restricted to isolated mountain peaks. To assess the level of degradation and the need for forest restoration, we examined how forest plant communities and their indicator species vary between and within remnant patches of cloud forest. We used ordinal abundance data to compare plant communities in eight forest fragments. We also analyzed data on the diversity and abundance of trees in 57 0.1 ha plots to compare tree communities within and between the largest two of these fragments, Ngangao (120 ha) and Mbololo (220 ha). The extant vegetation of the Taita Hills at landscape scale consists of secondary moist montane to intermediate montane forest. There was a high species dissimilarity between fragments (69%). Variation in species composition coincided with an abiotic gradient related to elevation. At plot level, secondary successional species and species of forest edges were most abundant and most frequent. Inferred clusters of plots almost entirely coincided with the two forest fragments. Indicator species associated with forest margins and gaps were more frequent in the smaller of the two forest fragments, while indicators for the larger fragment were more typical for less disturbed moist forest. Abiotic site variability but also different levels of disturbance determine site-specific variants of the montane forest. Conservation efforts should not only focus on maintaining forest quantity (size), but also on forest quality (species composition). Late-successional rainforest species are underrepresented in the woody plant communities of the Taita Hills and assisting restoration of viable populations of cloud forest climax tree species is urgently needed

Real-Time RGB-D Camera Pose Estimation in Novel Scenes using a Relocalisation Cascade

Camera pose estimation is an important problem in computer vision. Common techniques either match the current image against keyframes with known poses, directly regress the pose, or establish correspondences between keypoints in the image and points in the scene to estimate the pose. In recent years, regression forests have become a popular alternative to establish such correspondences. They achieve accurate results, but have traditionally needed to be trained offline on the target scene, preventing relocalisation in new environments. Recently, we showed how to circumvent this limitation by adapting a pre-trained forest to a new scene on the fly. The adapted forests achieved relocalisation performance that was on par with that of offline forests, and our approach was able to estimate the camera pose in close to real time. In this paper, we present an extension of this work that achieves significantly better relocalisation performance whilst running fully in real time. To achieve this, we make several changes to the original approach: (i) instead of accepting the camera pose hypothesis without question, we make it possible to score the final few hypotheses using a geometric approach and select the most promising; (ii) we chain several instantiations of our relocaliser together in a cascade, allowing us to try faster but less accurate relocalisation first, only falling back to slower, more accurate relocalisation as necessary; and (iii) we tune the parameters of our cascade to achieve effective overall performance. These changes allow us to significantly improve upon the performance our original state-of-the-art method was able to achieve on the well-known 7-Scenes and Stanford 4 Scenes benchmarks. As additional contributions, we present a way of visualising the internal behaviour of our forests and show how to entirely circumvent the need to pre-train a forest on a generic scene.Comment: Tommaso Cavallari, Stuart Golodetz, Nicholas Lord and Julien Valentin assert joint first authorshi

Bounds on the maximum multiplicity of some common geometric graphs

We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, non-weighted common geometric graphs drawn on n points in the plane in general position (with no three points collinear): perfect matchings, spanning trees, spanning cycles (tours), and triangulations. (i) We present a new lower bound construction for the maximum number of triangulations a set of n points in general position can have. In particular, we show that a generalized double chain formed by two almost convex chains admits {\Omega}(8.65^n) different triangulations. This improves the bound {\Omega}(8.48^n) achieved by the double zig-zag chain configuration studied by Aichholzer et al. (ii) We present a new lower bound of {\Omega}(12.00^n) for the number of non-crossing spanning trees of the double chain composed of two convex chains. The previous bound, {\Omega}(10.42^n), stood unchanged for more than 10 years. (iii) Using a recent upper bound of 30^n for the number of triangulations, due to Sharir and Sheffer, we show that n points in the plane in general position admit at most O(68.62^n) non-crossing spanning cycles. (iv) We derive lower bounds for the number of maximum and minimum weighted geometric graphs (matchings, spanning trees, and tours). We show that the number of shortest non-crossing tours can be exponential in n. Likewise, we show that both the number of longest non-crossing tours and the number of longest non-crossing perfect matchings can be exponential in n. Moreover, we show that there are sets of n points in convex position with an exponential number of longest non-crossing spanning trees. For points in convex position we obtain tight bounds for the number of longest and shortest tours. We give a combinatorial characterization of the longest tours, which leads to an O(nlog n) time algorithm for computing them

Estimating site occupancy for four threatened mammals in southeastern Laos

textThe tropical forests of Indochina harbor a suite of globally threatened tropical mammal species. These species are difficult to detect, and subsequently understudied. Noninvasive camera trapping was used to survey terrestrial mammals from a protected area in southeastern Lao PDR (Xe Sap National Protected Area). The presence-absence of four mammals (mainland serow Capricornis milneedwardsii, muntjac Muntiacus spp., macaque Macaca spp., and wild pig Sus scrofa) was modeled in an occupancy framework thereby accounting for detection probabilities. Our goals were to establish baseline occupancy data to assist with biological monitoring and to better understand the factors influencing the distribution of the target species. Naïve occupancy, or the proportion of sites at which the target species was detected, was 0.58 for muntjac, 0.55 for macaque, 0.38 for wild pig, and 0.30 for serow. True occupancy estimates (Ψ ± SE) from top-ranked models was 0.79 ± 0.21 for macaque, 0.74 ± 0.13 for muntjac, 0.51 ± 0.13 for wild pig, and 0.48 ± 0.18 for serow. The results underscore the importance of accounting for imperfect detection rates when studying rare or elusive species. I included two site covariates (forest type and distance to nearest village) in the occupancy models. Estimating occupancy as a function of site covariates improved model performance and provided insight into landscape-level factors that affect species occurrence. In the top-ranked models, serow occupancy was higher in hill evergreen forest (HEGF) than semi-evergreen forest (SEGF). Muntjac occupancy was higher in areas further from villages. Macaque occupancy was higher in areas closer to villages. Wild pig occupancy was higher in areas further from villages and in HEGF. I recommend using an occupancy framework to analyze occurrence data for difficult-to-study tropical mammal species. The results highlight the importance of Xe Sap NPA for large mammal conservation in the region.Ecology, Evolution and Behavio