Stable Trees Research Articles

Stable trees as mixings of inhomogeneous continuum random trees

It has been claimed in Aldous et al. (2004) that all Lévy trees are mixings of inhomogeneous continuum random trees. We give a rigorous proof of this claim in the case of a stable branching mechanism, relying on a new procedure for recovering the tree distance from the graphical spanning trees that works simultaneously for stable trees and inhomogeneous continuum random trees.

A recursive distributional equation for the stable tree

A recursive distributional equation for the stable tree

Motion Planning and Control of Autonomous Aggressive Vehicle Maneuvers

Aggressive vehicle maneuvers such as those performed by professional racing drivers achieve high agility motion at the edge of handling limits. These aggressive maneuvers can be used to design human-inspired active safety features for next-generation “accident-free” vehicles. We present a motion planning and control design for autonomous aggressive vehicle maneuvers. The motion planner takes advantages of the sparse stable trees and the enhanced rapidly exploring random tree (RRT*) algorithms. The use of the sparsity property helps to reduce the computational cost of the RRT* method by removing non-useful nodes in each iteration and therefore to rapidly converge to the optimal solution. The proposed motion control design allows the vehicle to operate outside the stability region to accomplish a safe, agile maneuver. A safety region is computed to augment the stability region and the motion control is built on a modified nonlinear model predictive control method. We implement the proposed planner and controller and demonstrate the autonomous aggressive maneuvers on a 1/7-scale racing vehicle platform. Comparison with human expert driver and other existing methods is also presented to demonstrate the performance and robustness. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Motion planning and control of human driver-inspired aggressive vehicle maneuvers is a challenging task because of high-agility, unstable fast vehicle motions. This paper is motivated by addressing this challenge in autonomous driving technologies. Instead of restricting vehicle motions within a stability region that is taken by existing methods, we augment the conservative stability region to a safety region with guaranteed performance. To improve the computational efficiency of sampling-based motion planners, we take advantage of sparsity and also integration of a nonlinear predictive control method to compute feasible vehicle motion in searching space. The stability of the vehicle motion controller and sub-optimality of the motion planner are analyzed and guaranteed. Using a scaled vehicle testbed, we validate and compare the proposed motion planning and control design with other existing methods and human expert driver. The experimental results demonstrate the superior performance than the other methods and comparable with human expert driving skills.

A binary embedding of the stable line-breaking construction

We embed Duquesne and Le Gall’s stable tree into a binary compact continuum random tree (CRT) in a way that solves an open problem posed by Goldschmidt and Haas. This CRT can be obtained by applying a recursive construction method of compact CRTs as presented in earlier work to a specific distribution of a random string of beads, i.e. a random interval equipped with a random discrete measure. We also express this CRT as a tree built by replacing all branch points of a stable tree by i.i.d. copies of a Ford CRT, each rescaled by a factor intrinsic to the stable CRT.

Morphology and phylogenetic significance of the pelvic articular region in elasmobranchs (Chondrichthyes).

The morphology of paired fins is commonly overlooked in morphological studies, particularly the pelvic girdle and fins. Consequently, previous phylogenetic studies incorporating morphological data used few skeletal characters from this complex. In this paper, the phylogenetic significance of pelvic articular characters for elasmobranchs is discussed in light of the morphological variation observed in 130 species, the most comprehensive study exploring the morphology of the pelvic girdle done so far. The 10 morphological characters proposed herein for the pelvic articulation were incorporated into a molecular matrix of NADH2 sequences and submitted to an analysis of maximum parsimony employing extended implied weighting. The most stable tree was selected based on the distortion coefficients, SPR distances (subtree pruning and regrafting) and fit values. Some of the striking synapomorphies recovered within elasmobranchs include the presence of an articular surface for the first enlarged pelvic radial supporting Elasmobranchii and the pelvic articular region for the basipterygium extending from the posterolatral margin of the pelvic girdle over its lateral surface in Echinorhinus + Hexanchiformes. Additionally, the proposed characters and their distributions are discussed considering the relationships recovered and also compared with previous morphological and molecular phylogenetic hypotheses.

Decorated stable trees

Decorated stable trees

Stable graphs: distributions and line-breaking construction

For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured metric spaces (the limiting connected components), each of which is tree-like, in the sense that it consists of an $\mathbb R$-tree with finitely many vertex-identifications (which create cycles). Indeed, given their masses and numbers of vertex-identifications, these components are independent and may be constructed from a spanning $\mathbb R$-tree, which is a biased version of the $\alpha$-stable tree, with a certain number of leaves glued along their paths to the root. In this paper we investigate the geometric properties of such a component with given mass and number of vertex-identifications. We (1) obtain the distribution of its kernel and more generally of its discrete finite-dimensional marginals; we will observe that these distributions are related to the distributions of some configuration models (2) determine the distribution of the $\alpha$-stable graph as a collection of $\alpha$-stable trees glued onto its kernel and (3) present a line-breaking construction, in the same spirit as Aldous' line-breaking construction of the Brownian continuum random tree.

Changes in tree structure, composition and soil in different disturbance categories in Miombo and agroecosystems in Malawi, central Africa

This study aimed to characterise the floristic, structural composition of vegetation and soil status in the three land use types of protected area (PA), harvested woodland (HW) and traditional agriculture land (TA) in Salima District, Malawi. The HW and TA were further divided into categories based on the number of years the land was subjected to use as a disturbance i.e. into 1–5 years, 6–10 years, and 11+ years. Floristic data were collected on tree species, diameter at breast height (1.3 m from the ground) and regeneration categories of seedlings, saplings and poles. Soil samples were collected from the sampled plots where floristic data were collected. The study found 73 tree species from 58 genera and 31 families. High tree species diversity was recorded in HW used for over 11 years (p < 0.05). Tree species dominance depended on land use. Although the HW and TA showed an inverse J-shaped structure indicating stable tree populations, the HW had fewer big trees. The PA showed signs of ageing tree population shown by the bell-shaped structure. The study area was dominated by Sandy loam soils with very high porosity of above 40%. The more the years of disturbance, the higher the fertility loss within the TA in terms of organic matter and organic carbon but the reverse was true for nitrogen. The decrease in soil fertility loss was however, higher in TA as compared to HW and PA. To address the unstable structural status of some species in the land uses, deliberative silvicultural interventions should be introduced in the land uses. There is need to integrate fertility-improvement tree species and manure use in the agricultural land to improve soil fertility.

Feasibility of buffer zone agroforestry farming practices in the conservation of mangrove ecosystems: A case study assessment from some local communities in Central African coastal zone, South Western Cameroon

Mangroves (stretch of intertidal tropical and subtropical forests between inland coastal forests and the sea) are being exploited at a rate that is unprecedented, there is loss of biodiversity because of conflicting and unsuitable uses. This study was aimed at promoting the protection of mangrove and associated coastal forests within Tiko and Limbe III municipalities in south western Cameroon, Central Africa via the contribution of buffer zone agroforestry. Representative traditionally dominant agricultural land use sites were surveyed for the identification and analysis of farming practices using participatory rapid appraisal (PRA). Data collected (qualitative and quantitative) were subjected to descriptive and inferential statistics. Out of twelve (12) agroforestry practices currently carried out by farmers under three widely dominant classic agroforestry systems (agri-silvicultural – plantation and non-plantation, silvo-pastoral and agri-silvo-pastoral systems), 5 of them under plantation and non-plantation systems (palms on crops lands, cocoa-based, rubber on crop lands, scattered trees on farmland and home gardens) were considered climate smart agroforestry practices. The maximum diameter, density, height and crown diameter of trees were dominant in the cocoa-based except for the mango-based which had the maximum tree height. The tree size class for poles (≥10cm to &lt;30cm) was dominant in the 5 practices. For a more inclusive green economy and climate smart agriculture, some improvements on tree density, shade management and choice of multi-purpose trees species (Cedrela sepium, Moringa oleifera, Leucaena leucocephala and fruit trees) for vital functions such as firewood, soil improvement, medicine, food and construction are advocated to enhance sustainable exploitation of adjacent coastal forests thus protecting mangrove. Moreover, on account of resultant stable tree species, structural and use diversity of adjacent coastal forests, further make buffer agroforestry to hold promise for the conservation of fragile and vulnerable mangroves. There is therefore also need to expand the present study in other mangrove areas especially the mangroves of Cameroon Estuary which is the major deforestation hotspot in Cameroon.

Multifactor relationships between the forest structure and water conservation function ofPicea crassifoliaKom. plantations in Qinghai Province, China

AbstractForest structure and ecosystem function/service relationships have attracted considerable attention; however, knowledge of how forest structure systematically affects water conservation function is still lacking. Such research is urgently needed in Qinghai Province, China's Water Tower, to guide forest structure optimization for plantations with weak water conservation functions. Since healthy, stable tree growth is crucial for forests to fulfill their water conservation functions, this study examined the impacts of forest structure on tree growth. We investigated 115 plots in Qinghai Province and analyzed tree size, size heterogeneity, species diversity, competition and spatial distribution effects on the individual tree growth and water conservation function ofPicea crassifoliaKom. using mixed‐effect and structural equation models, respectively. Forest structure was important in modulating tree growth and the water conservation function. Tree size had the greatest impact on growth performance and directly enhanced the water conservation function. High‐size heterogeneity increased the tree growth rate and directly and indirectly improved the water conservation function via competition. Both individual growth and water conservation function were negatively related to competition between trees. Species diversity promotedP. crassifoliagrowth under a given degree of neighbourhood competition and indirectly affected the water conservation function by increasing size heterogeneity and reducing competition. An uneven spatial distribution did not influence tree growth but positively affected the water conservation function. Therefore, we emphasize that for plantations to fulfill their water conservation functions, pure forests with homogeneous structures should be transformed into mixed forests with heterogeneous structures.

Особенности роста вяза приземистого на бурых почвах Астраханской полупустыни

The article presents the current state assessment and suggests the methods for additional moisture supply of soils under stable tree plantations of Siberian elm (Ulmus pumila L.) on brown soils of semi-desert. The research area belongs to the arid zone. This is a treeless zone of dry steppe and semi-desert, where about 1,000 ha of plantations with a predominance of elm of different species have been planted since 1949–1953: shade clumps, pasture protection strips, massifs, separated forest stands. The soils are brown desert-steppe alkaline sandy loam and light clay-loam in combination with solonetz (10 %). Siberian elm stands form plantations of different ages and for different purposes. The research is based on biomonitoring materials and field experiments using standard forest inventory techniques. Test sites of a rectangular shape with an area of 0.4 ha were laid out in order to study the Siberian elm stands. We described in detail the location of the test sites, the soil composition thereon, and gave a comprehensive assessment of the growth and durability of the plantations. It is shown that the stand state is determined by 2 sets of factors: zonal-edaphic and pastoraleconomic. Viable stands of Siberian elm at the age of 57–64 have been preserved on sandy loam and dark-colored soils located in micro- and inter-hill depressions. The dynamics of soil moisture under plantations is largely independent of the tree location method. Satisfactory indicators of growth and durability of plantations depend on the level of availability of soil moisture and the degree of its salinity. The moisture supply of soils under elm plantations can be increased by using melt water runoff in hollows and micro-depressions and increasing the growing space of a tree to 25 m2. Formed elm plantations respond positively to the presence of resting animals. The “alliance” relationship between the stand and livestock does not arise immediately, but rather from a certain age of the stand and the moment it forms a certain structure of the tree layer, which should be provided by forest cultivation and silvicultural measures in conjunction with the regulation of pasture load. There is a positive effect of resting animals at the appropriate load on the growth, state and durability of the Siberian elm stands.

Quality and suitability of fecal biochar in structurally stable urban tree substrates

This study examines the effects of pyrolyzed materials (biochar) from horse manure, plant residues and human feces on the growth of 1-year old birch seedlings cultivated in a novel, structurally stable tree substrate. For this purpose, the composition of the produced biochar, the leachate from the substrates and the health and growth rate of the birch seedlings were observed over a period of 322 days. The results show that each of these biochars complies with the European Biochar Certificate (EBC) guidelines. No toxic heavy metals were detected. Furthermore, the presence of the biochar in the substrates enhanced the survival rate of the birch trees.

Zooming in at the root of the stable tree

We study the shape of the normalized stable Lévy tree T near its root. We show that, when zooming in at the root at the proper speed with a scaling depending on the index of stability, we get the unnormalized Kesten tree. In particular the limit is described by a tree-valued Poisson point process which does not depend on the initial normalization. We apply this to study the asymptotic behavior of additive functionals of the form Zα,β= ∫Tμ(dx)∫0H(x)σ r,xαh r,xβdr as max(α,β)→∞, where μ is the mass measure on T, H(x) is the height of x and σr,x (resp. hr,x) is the mass (resp. height) of the subtree of T above level r containing x. Such functionals arise as scaling limits of additive functionals of the size and height on conditioned Bienaymé-Galton-Watson trees.

Live Crown Ratio as an Indicator for Tree Vigor and Stability of Turkey Oak (Quercus cerris L.): A Case Study

Stability of forests represents a significant objective for climate change mitigation. As stand stability is influenced by the stability of individual trees, promoting stable trees is vital for a sustainable forest management. However, inside stands, trees experience intense competition. As a result, the crown recedes and diameter growth is affected, the trees becoming slender and more susceptible to biotic and abiotic disturbances. Finding effective indicators for tree vigor and stability is therefore important. This study aimed to assess the performance of the live crown ratio as an indicator in deciding the timing of tending operations for obtaining and maintaining vigorous Turkey oak trees. Live crown ratio (LCR) and height to diameter ratio (HDR) were determined for 80 sampled Turkey oak trees. A threshold of 100 for HDR was chosen to classify trees as slender or not slender. Next, conditional inference tree and logistic regression were used to determine the LCR threshold value where trees become slender. As the sample included small trees, using breast height to measure diameter may have affected the results. Therefore, small and large trees were also analyzed separately. For the entire dataset, the methods reached quite different results (LCR threshold of 0.371 for conditional inference tree and of 0.434 for the logistic regression), and relatively high values compared to the literature. For tall trees (height &gt; 12.5 m), the methods reached similar results: 0.386 for the conditional inference tree and 0.382 for the logistic regression. For small trees (height &lt; 12.5 m), the conditional inference tree method could not calculate any LCR threshold estimate, while the one from the logistic regression was unrealistically large (0.628). This confirms that using DBH for small trees to compute slenderness brings systematic errors. The live crown ratio was a good indicator of growth vigor for Turkey oak trees. Therefore, for stable trees (HDR &lt; 100), a LCR of 0.36–0.39 must be maintained and could be used to decide the timing for thinning in Turkey oak stands.

A geometric representation of fragmentation processes on stable trees

We provide a new geometric representation of a family of fragmentation processes by nested laminations which are compact subsets of the unit disk made of noncrossing chords. We specifically consider a fragmentation, obtained by cutting a random stable tree at random points, which split the tree into smaller subtrees. When coding each of these cutpoints by a chord in the unit disk, we separate the disk into smaller connected components, corresponding to the smaller subtrees of the initial tree. This geometric point of view allows us in particular to highlight a new relation between the Aldous–Pitman fragmentation of the Brownian continuum random tree and minimal factorizations of the n-cycle, that is, factorizations of the permutation (12⋯n) into a product of (n−1) transpositions, proving this way a conjecture of Féray and Kortchemski. We discuss various properties of these new lamination-valued processes, and we notably show that they can be coded by explicit Lévy processes.

Comparative Mitogenomics and Phylogenetic Analyses of Pentatomoidea (Hemiptera: Heteroptera).

Pentatomoidea is the largest superfamily of Pentatomomorpha; however, the phylogenetic relationships among pentatomoid families have been debated for a long time. In the present study, we gathered the mitogenomes of 55 species from eight common families (Acanthosomatidae, Cydnidae, Dinidoridae, Scutelleridae, Tessaratomidae, Plataspidae, Urostylididae and Pentatomidae), including 20 newly sequenced mitogenomes, and conducted comparative mitogenomic studies with an emphasis on the structures of non-coding regions. Heterogeneity in the base composition, and contrasting evolutionary rates were encountered among the mitogenomes in Pentatomoidea, especially in Urostylididae, which may lead to unstable phylogenetic topologies. When the family Urostylididae is excluded in taxa sampling or the third codon positions of protein coding genes are removed, phylogenetic analyses under site-homogenous models could provide more stable tree topologies. However, the relationships between families remained the same in all PhyloBayes analyses under the site-heterogeneous mixture model CAT + GTR with different datasets and were recovered as (Cydnidae + (((Tessaratomidae + Dinidoridae) + (Plataspidae + Scutelleridae)) + ((Acanthosomatidae + Urostylididae) + Pentatomidae)))). Our study showed that data optimizing strategies after heterogeneity assessments based on denser sampling and the use of site-heterogeneous mixture models are essential for further analysis of the phylogenetic relationships of Pentatomoidea.

Potentially stable and 5-by-5 spectrally arbitrary tree sign pattern matrices with all edges negative

Characterization of potentially stable sign pattern matrices has been a long-standing open problem. In this paper, we give some sufficient conditions for tree sign pattern matrices with all edges negative to allow a properly signed nest. We also characterize potentially stable star and path sign pattern matrices with all edges negative. We give a conjecture on characterizing potentially stable tree sign pattern matrices with all edges negative in terms of allowing a properly signed nest which is verified to be true for sign pattern matrices up to order 6. Finally, we characterize all 5-by-5 spectrally arbitrary tree sign pattern matrices with all edges negative.

Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces

We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble hbox {CLE}_{kappa '} for kappa ' in (4, 8) that is drawn on an independent gamma -LQG surface for gamma ^2=16/kappa '. The results are similar in flavor to the ones from our companion paper dealing with hbox {CLE}_{kappa } for kappa in (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the hbox {CLE}_{kappa '} in terms of stable growth-fragmentation trees or their variants, which also appear in the asymptotic study of peeling processes on decorated planar maps. This has consequences for questions that do a priori not involve LQG surfaces: In our paper entitled “CLE Percolations” described the law of interfaces obtained when coloring the loops of a hbox {CLE}_{kappa '} independently into two colors with respective probabilities p and 1-p. This description was complete up to one missing parameter rho . The results of the present paper about CLE on LQG allow us to determine its value in terms of p and kappa '. It shows in particular that hbox {CLE}_{kappa '} and hbox {CLE}_{16/kappa '} are related via a continuum analog of the Edwards-Sokal coupling between hbox {FK}_q percolation and the q-state Potts model (which makes sense even for non-integer q between 1 and 4) if and only if q=4cos ^2(4pi / kappa '). This provides further evidence for the long-standing belief that hbox {CLE}_{kappa '} and hbox {CLE}_{16/kappa '} represent the scaling limits of hbox {FK}_q percolation and the q-Potts model when q and kappa ' are related in this way. Another consequence of the formula for rho (p,kappa ') is the value of half-plane arm exponents for such divide-and-color models (a.k.a. fuzzy Potts models) that turn out to take a somewhat different form than the usual critical exponents for two-dimensional models.

Brownian motion on stable looptrees

In this article, we introduce Brownian motion on α-stable looptrees using resistance techniques, where α∈(1,2). We prove an invariance principle characterising it as the scaling limit of random walks on discrete looptrees, and prove precise local and global bounds on its heat kernel. We also conduct a detailed investigation of the volume growth properties of stable looptrees, and show that the random volume and heat kernel fluctuations are locally log-logarithmic, and globally logarithmic around leading terms of rα and t−αα+1 respectively. These volume fluctuations are the same order as for the Brownian continuum random tree, but the upper volume fluctuations (and corresponding lower heat kernel fluctuations) are different to those of stable trees.

Phylogenetic relationships of the shearwater taxa Puffinus/ (sensu/ lato) and Calonectris/ (Aves: Procellariiformes: Procellariidae) based on osteological characters.

Shearwaters are among the most diverse groups of Procellariiformes, and the systematics of genera Calonectris, Ardenna and Puffinus (sensu stricto) is particularly complex. Here we present the first morphology-based phylogenetic hypothesis for the group, using 104 osteological characters (23 continuous and 81 discrete) scored for 20 extant species of shearwaters, representing 62.5% of species currently recognized. Both equal and implied weighting were used for phylogenetic analyses, and the final hypothesis presented herein is the strict consensus of the most stable trees produced by the latter. Calonectris was recovered as monophyletic (Relative Bremer Support = 75), while all other members of shearwaters were included in a single, monophyletic grouping: Puffinus (sensu lato) (RBS = 76). The monophyly of Ardenna, as suggested by all molecular-based hypotheses, was not recovered, whereas a monophyletic Puffinus (sensu stricto) is present within the larger clade. The final hypothesis, wherein shearwaters fall into the sister taxa Calonectris and Puffinus (sensu lato), is consistent with earlier classifications based on osteological evidence.