On Perturbation Resilience of Non-uniform k-Center

The Non-Uniform k-center (NUkC) problem has recently been formulated by Chakrabarty et al. [ICALP, 2016; ACM Trans Algorithms 16(4):46:1–46:19, 2020] as a generalization of the classical k-center clustering problem. In NUkC, given a set of n points P in a metric space and non-negative numbers $$r_1, r_2, \ldots , r_k$$ r 1 , r 2 , … , r k , the goal is to find the minimum dilation $$\alpha $$ α and to choose k balls centered at the points of P with radius $$\alpha \cdot r_i$$ α · r i for $$1\le i\le k$$ 1 ≤ i ≤ k , such that all points of P are contained in the union of the chosen balls. They showed that the problem is $$\mathsf {NP}$$ NP -hard to approximate within any factor even in tree metrics. On the other hand, they designed a “bi-criteria” constant approximation algorithm that uses a constant times k balls. Surprisingly, no true approximation is known even in the special case when the $$r_i$$ r i ’s belong to a fixed set of size 3. In this paper, we study the NUkC problem under perturbation resilience, which was introduced by Bilu and Linial (Comb Probab Comput 21(5):643–660, 2012). We show that the problem under 2-perturbation resilience is polynomial time solvable when the $$r_i$$ r i ’s belong to a constant-sized set. However, we show that perturbation resilience does not help in the general case. In particular, our findings imply that even with perturbation resilience one cannot hope to find any “good” approximation for the problem.

Improved TCP Prediction Congestion in Mobile Ad Hoc Network Based on Cross-Layer and Fuzzy Logic

Mobile ad hoc network (MANET) is among the networks which do not require any infrastructure to put nodes in communication. Due to its own nature, it is used by several applications. Even though it's a network that is extremely challenging and mostly when TCP is applied. In this paper, we have proposed a new improvement in the TCP algorithm that employed fuzzy logic to predict packet loss and avoid congestion. Specifically, we have used tree metrics such as stability, energy, and signal strength to use in fuzzy logic systems. To accomplish our approach, we have established some modifications based on a cross-layer. The results of the relevant simulation performed by NS3 demonstrated that our approach globally improves the performance of TCP in MANET. Precisely reduce the packet overhead and energy consumption also enhance throughput.

The Bourque distances for mutation trees of cancers

Background Mutation trees are rooted trees in which nodes are of arbitrary degree and labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson–Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients often contain different sets of mutation labels. Results We generalize the Robinson–Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. We show the basic version of the Bourque distance for mutation trees can be computed in linear time. We also make a connection between the Robinson–Foulds distance and the nearest neighbor interchange distance.

Parthenogenesis is self-destructive for scaled reptiles

Parthenogenesis is rare in nature. With 39 described true parthenogens, scaled reptiles (Squamata) are the only vertebrates that evolved this reproductive strategy. Parthenogenesis is ecologically advantageous in the short term, but the young age and rarity of parthenogenetic species indicate it is less advantageous in the long term. This suggests parthenogenesis is self-destructive: it arises often but is lost due to increased extinction rates, high rates of reversal or both. However, this role of parthenogenesis as a self-destructive trait remains unknown. We used a phylogeny of Squamata (5388 species), tree metrics, null simulations and macroevolutionary scenarios of trait diversification to address the factors that best explain the rarity of parthenogenetic species. We show that parthenogenesis can be considered as self-destructive, with high extinction rates mainly responsible for its rarity in nature. Since these parthenogenetic species occur, this trait should be ecologically relevant in the short term.

Modelling the Diameter Distribution of Savanna Trees with Drone-Based LiDAR

The diameter distribution of savanna tree populations is a valuable indicator of savanna health because changes in the number and size of trees can signal a shift from savanna to grassland or forest. Savanna diameter distributions have traditionally been monitored with forestry techniques, where stem diameter at breast height (DBH) is measured in the field within defined sub-hectare plots. However, because the spatial scale of these plots is often misaligned with the scale of variability in tree populations, there is a need for techniques that can scale-up diameter distribution surveys. Dense point clouds collected from uncrewed aerial vehicle laser scanners (UAV-LS), also known as drone-based LiDAR (Light Detection and Ranging), can be segmented into individual tree crowns then related to stem diameter with the application of allometric scaling equations. Here, we sought to test the potential of UAV-LS tree segmentation and allometric scaling to model the diameter distributions of savanna trees. We collected both UAV-LS and field-survey data from five one-hectare savanna woodland plots in northern Australia, which were divided into two calibration and three validation plots. Within the two calibration plots, allometric scaling equations were developed by linking field-surveyed DBH to the tree metrics of manually delineated tree crowns, where the best performing model had a bias of 1.8% and the relatively high RMSE of 39.2%. A segmentation algorithm was then applied to segment individual tree crowns from UAV-LS derived point clouds, and individual tree level segmentation accuracy was assessed against the manually delineated crowns. 47% of crowns were accurately segmented within the calibration plots and 68% within the validation plots. Using the site-specific allometry, DBH was modelled from crown metrics within all five plots, and these modelled results were compared to field-surveyed diameter distributions. In all plots, there were significant differences between field-surveyed and UAV-LS modelled diameter distributions, which became similar at two of the plots when smaller trees (<10 cm DBH) were excluded. Although the modelled diameter distributions followed the overall trend of field surveys, the non-significant result demonstrates a need for the adoption of remotely detectable proxies of tree size which could replace DBH, as well as more accurate tree detection and segmentation methods for savanna ecosystems.

Virtual laser scanning (VLS) in forestry – Investigating appropriate 3D forest representations for LiDAR simulations with HELIOS++

&lt;p&gt;Virtual laser scanning (VLS) is a valuable method to complement expensive laser scanning data acquisition in the field. VLS refers to the simulation of LiDAR to create 3D point clouds from models of scenes, platforms and sensors mimicking real world acquisitions. In forestry, this can be used to generate training and testing data with complete ground truth for algorithms performing essential tasks such as tree detection or tree species classification. Furthermore, VLS allows for the in-depth investigation of the influence of different acquisition parameters on the point clouds and thus also the behaviour of algorithms, which is important when relating point cloud metrics to forest inventory variables. Finally, VLS can be used for acquisition planning and optimisation, as different configurations can be tested regarding their ability to create data of the required quality with minimal effort. For these purposes, we developed the open source Heidelberg LiDAR Operations Simulator HELIOS++ (written in C++) which is available on GitHub (https://github.com/3dgeo-heidelberg/helios), as a precompiled command line tool, and as Python package (pyhelios). HELIOS++ provides a high-fidelity framework for full 3D laser scanning simulations with multiple platforms and a flexible system to represent the scene. HELIOS++ models the beam divergence and supports the recording of the full waveform.&lt;/p&gt;&lt;p&gt;One important premise for the usefulness of VLS data is the use of an adequate 3D scene in the simulation. In this context, we conducted a study investigating point clouds simulated based on opaque voxel-based forest models computed from terrestrial laser scanning data using different voxel sizes. Coupling the LiDAR simulation with a database containing point clouds of single trees from terrestrial, UAV-borne and airborne acquisitions, allowed us to compare metrics derived from real and simulated data. Furthermore, by including the tree neighbourhood in the scene, we were able to consider occlusion effects between the trees.&lt;/p&gt;&lt;p&gt;We found that the voxel size is an important parameter, where values of e.g. 0.25 m lead to unrealistic occlusion effects of the mid- and understory, as only few gaps remain in the forest models through which the laser beam can pass. This results in fewer multiple returns, the vertical point distribution is shifted upwards, and tree metrics such as crown projection area and crown base height are estimated poorly. Smaller voxel sizes are therefore preferable, though the appropriate voxel size depends on the resolution of the input point cloud. With very small voxels, the voxel model may become too transparent. To achieve realistic simulations without the need for a high number of voxels we suggest variable downscaling of voxel cubes based on appropriate local metrics such as the plant area density. This approach decreases the computational requirements for the simulation, as fewer primitives are present in the scene. In our study, the use of such scaled voxels derived for a grid size of 0.25 m achieves equally and partly more reliable estimates of point cloud and tree metrics than regular voxels at fixed side lengths of 0.05 and 0.02 m.&lt;/p&gt;

The Bourque Distances for Mutation Trees of Cancers

Background: Mutation trees are rooted trees in which nodes are of arbitrary degree are labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson-Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients often contain different sets of mutation labels. Results: We generalize the Robinson-Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. We show the basic version of the Bourque distance for mutation trees can be computed in linear time. We also make a connection between the Robinson{Foulds distance and the nearest neighbor interchange distance.

Distance metrics for ranked evolutionary trees

Genealogical tree modeling is essential for estimating evolutionary parameters in population genetics and phylogenetics. Recent mathematical results concerning ranked genealogies without leaf labels unlock opportunities in the analysis of evolutionary trees. In particular, comparisons between ranked genealogies facilitate the study of evolutionary processes of different organisms sampled at multiple time periods. We propose metrics on ranked tree shapes and ranked genealogies for lineages isochronously and heterochronously sampled. Our proposed tree metrics make it possible to conduct statistical analyses of ranked tree shapes and timed ranked tree shapes or ranked genealogies. Such analyses allow us to assess differences in tree distributions, quantify estimation uncertainty, and summarize tree distributions. We show the utility of our metrics via simulations and an application in infectious diseases.

The Bourque Distances for Mutation Trees of Cancers

Mutation trees are rooted trees of arbitrary node degree in which each node is labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson–Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients usually contain different sets of mutation labels. Here, we generalize the Robinson–Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. A connection between the Robinson–Foulds distance and the nearest neighbor interchange distance is also presented.