Tree Expansion Research Articles

Neural Tree Expansion for Multi-Robot Planning in Non-Cooperative Environments

We present a self-improving, Neural Tree Expansion (NTE) method for multi-robot online planning in non-cooperative environments, where each robot attempts to maximize its cumulative reward while interacting with other self-interested robots. Our algorithm adapts the centralized, perfect information, discrete-action space method from AlphaZero to a decentralized, partial information, continuous action space setting for multi-robot applications. Our method has three interacting components: (i) a centralized, perfect-information “expert” Monte Carlo Tree Search (MCTS) with large computation resources that provides expert demonstrations, (ii) a decentralized, partial-information “learner” MCTS with small computation resources that runs in real-time and provides self-play examples, and (iii) policy & value neural networks that are trained with the expert demonstrations and bias both the expert and the learner tree growth. Our numerical experiments demonstrate Neural Tree Expansion's computational advantage by finding better solutions than a MCTS with 20 times more resources. The resulting policies are dynamically sophisticated, demonstrate coordination between robots, and play the Reach-Target-Avoid differential game significantly better than the state-of-the-art control-theoretic baseline for multi-robot, double-integrator systems. Our hardware experiments on an aerial swarm demonstrate the computational advantage of Neural Tree Expansion, enabling online planning at 20 Hz with effective policies in complex scenarios.

Variations in soil aggregation, microbial community structure and soil organic matter cycling associated to long-term afforestation and woody encroachment in a Mediterranean alpine ecotone

Afforestation and subsequent expansion of trees on former grasslands may significantly impact the structure and activity of the soil microbial community, altering soil aggregation and affect its potential to store and cycle organic matter (OM). We investigated OM dynamics in aggregate-size topsoil samples collected along a Mediterranean alpine ecotone consisting of three vegetation types (grassland/shrubland, mixed shrubland-pine, and pine forest) in central Spain. Analytical determinations of soil organic carbon (SOC), total nitrogen (TN), particulate OM (POM), mineral-associated OM (MaOM), and the stable isotopic composition of carbon were conducted in each of the four aggregate-size fractions considered. Additionally, the structure of the microbial community (assessed as PLFA abundance), and the β-glucosidase and β-glucosaminidase activities were determined in bulk soil samples. More than half of the soil mass was contained within small macroaggregates regardless of vegetation type. SOC and TN values increased with decreasing aggregate-size classes across all vegetation types. The stability of microaggregates was negatively affected by the expansion of woody vegetation, which resulted in tree-dominated stands showing comparatively lower SOC and TN values in the smaller aggregate-size classes. On the other hand, these vegetation dynamics promoted soil macro-aggregation. While SOC contents did not show significant differences between land covers, vegetation shifts induced changes in the soil microbial community. Soil δ13C values, the abundance of gram-positive bacteria and β-glucosidase activity were significantly higher in grasslands/shrublands than in forests, while significantly higher fungi/bacteria ratio was observed in forests. Small macroaggregates appear to play a key role in the stabilisation of relatively unprocessed OM across all vegetation types, as suggested by their significantly higher concentrations of POM. However, this fraction represents the most labile pool of OM, and as such, it is the most exposed to mineralisation. We conclude that the afforestation and potential vegetation shifts experienced in Mediterranean alpine grasslands lead to distinct changes in soil microbial communities, aggregation and soil OM dynamics, which given the strong temperature sensitivity to decomposition commonly reported in cold environments, suggests that soil OM in these high-elevation ecosystems may become highly vulnerable to environmental change.

The response of the invasive princess tree (Paulownia tomentosa) to wildland fire and other disturbances in an Appalachian hardwood forest

This study examined the response of princess tree (Paulownia tomentosa) to different disturbances and its potential to spread throughout its current range in the U.S. The study was established in Shawnee State Forest in southern Ohio, USA, which has historically experienced disturbances from mining, logging, ice storms and wildfire. Plots were established for vegetation sampling where fire had occurred with and without princess tree present, and where no fire had occurred with and without princess tree present. To determine the influence of disturbance types on the density of princess tree, redundancy analysis (RDA) was used. High stem density of princess tree seedlings occurred in areas that experienced high fire intensities and herbicide treatment. Seedlings on southwest slopes increased in abundance as the time from the last logging activity increases. Princess tree saplings were present in greater densities in areas that experienced medium fire intensities and the highest ice storm damage. Sapling density is greatest as ground cover and vegetation height increases and slope decreases. Princess trees reach maximum stem density on northeast slopes in areas not impacted by the 2009 fire. All disturbances considered, including wildfire, have created conditions conducive to princess tree growth and expansion into forest areas.

Seasonal Spectral Separation of Western Snowberry and Wolfwillow in Grasslands with Field Spectroradiometer and Simulated Multispectral Bands

Woody plant encroachment (WPE), the expansion of native and non-native trees and shrubs into grasslands, has led to degradation worldwide. In the Canadian prairies, western snowberry and wolfwillow shrubs are common encroachers, whose cover is currently unknown. As the use of remote sensing in grassland monitoring increases, opportunities to detect and map these woody species are enhanced. Therefore, the purpose of this study is to identify the optimal season for detection of the two shrubs, to determine the sensitive wavelengths and bands that allow for their separation, and to investigate differences in separability potential between a hyperspectral and broadband multispectral approach. We do this by using spring, summer, and fall field-based spectra of both shrubs for the calculation of spectral separability metrics and for the simulation of broadband spectra. Our results show that the summer offers higher discrimination between the two species, especially when using the red and blue spectral regions and to a lesser extent the green region. The fall season fails to provide significant spectral separation along the wavelength spectrum. Moreover, there is no significant difference in the results from the hyperspectral or broadband approach. Nevertheless, cross-validation with satellite imagery is needed to confirm the current results.

Enhancing Mixed Traffic Flow Safety via Connected and Autonomous Vehicle Trajectory Planning with a Reinforcement Learning Approach

The longitudinal trajectory planning of connected and autonomous vehicle (CAV) has been widely studied in the literature to reduce travel time or fuel consumptions. The safety impact of CAV trajectory planning to the mixed traffic flow with both CAV and human-driven vehicle (HDV), however, is not well understood yet. This study presents a reinforcement learning modeling approach, named Monte Carlo tree search-based autonomous vehicle safety algorithm, or MCTS-AVS, to optimize the safety of mixed traffic flow, on a one-lane roadway with signalized intersection control. Crash potential index (CPI) is defined to quantitively measure the safety performance of the mixed traffic flow. The CAV trajectory planning problem is firstly formulated as an optimization model; then, the solution procedure based on reinforcement learning is proposed. The tree-expansion determination module and rollout termination module are developed to identify and reduce the unnecessary tree expansion, so as to train the model more efficiently towards the desired direction. The case study results showed that the proposed algorithm was able to reduce the CPI by 76.56%, when compared with a benchmark model without any intelligence, and 12.08%, when compared with another benchmark model that the team developed earlier. These results demonstrated the satisfactory performance of the proposed algorithm in enhancing the safety of the mixed traffic flow.

Discovery of network motifs based on induced subgraphs using a dynamic expansion tree

Biological networks are powerful representations of topological features in biological systems. Finding network motifs in biological networks is a computationally hard problem due to their huge size and abrupt increase of search space with the increase of motif size. Motivated by the computational challenges of network motif discovery and considering the importance of this topic, an efficient and scalable network motif discovery algorithm based on induced subgraphs in a dynamic expansion tree is proposed. This algorithm uses a pruning strategy to overcome the space limitation of the static expansion tree. The proposed algorithm can identify large network motifs up to size 15 by significantly reducing the computationally expensive subgraph isomorphism checks. Further, the present work avoids the unnecessary growth of patterns that do not have any statistical significance. The runtime performance of the proposed algorithm outperforms most of the existing algorithms for large network motifs.

Reversing tree expansion in sagebrush steppe yields population‐level benefit for imperiled grouse

AbstractWoody plant expansion into shrub and grasslands is a global and vexing ecological problem. In the Great Basin of North America, the expansion of pinyon–juniper (Pinus spp.–Juniperus spp.) woodlands is threatening the sagebrush (Artemisia spp.) biome. The Greater Sage‐grouse (Centrocercus urophasianus; sage‐grouse), a sagebrush obligate species, is widespread in the Great Basin and considered an indicator for the condition of sagebrush ecosystems. To assess the population response of sage‐grouse to landscape‐scale juniper removal, we analyzed a long‐term telemetry data set and lek counts with a Bayesian integrated population model in a before‐after‐control‐impact design. Population growth rates (λ) in a treatment area (Treatment) with juniper removal and a control area (Control) without juniper removal indicated the two areas generally experienced population increase, decrease, and stability in the same years. However, the difference in λ between study areas indicated a steady increase in the Treatment relative to the Control starting in 2013 (removals initiated in 2012), with differences of 0.13 and 0.11 in 2016 and 2017, respectively. Retrospective sensitivity analysis suggested the dynamics in λ were driven by increases in juvenile, adult, first nest, and yearling survival in the Treatment relative to the Control. These findings demonstrate the effectiveness of targeted conifer removal as a management strategy for conserving sage‐grouse populations in sagebrush steppe affected by conifer expansion. Examples of positive, population‐level responses to habitat management are exceptionally rare for terrestrial vertebrates, and this study provides promising evidence of active management that can be implemented to aid recovery of an imperiled species and biome.

Improved POMDP Tree Search Planning with Prioritized Action Branching

Online solvers for partially observable Markov decision processes have difficulty scaling to problems with large action spaces. This paper proposes a method called PA-POMCPOW to sample a subset of the action space that provides varying mixtures of exploitation and exploration for inclusion in a search tree. The proposed method first evaluates the action space according to a score function that is a linear combination of expected reward and expected information gain. The actions with the highest score are then added to the search tree during tree expansion. Experiments show that PA-POMCPOW is able to outperform existing state-of-the-art solvers on problems with large discrete action spaces.

Hybrid RRT-A*: An Improved Path Planning Method for an Autonomous Mobile Robots

Although the Basic RRT algorithm is considered a traditional search method, it has been widely used in the field of robot path planning (manipulator and mobile robot), especially in the past decade. This algorithm has many features that give it superiority over other methods. On the other hand, the Basic RRT suffers from a bad convergence rate (it takes a long time until finding the goal point), especially in environments with cluttered obstacles, or whose targets are located in narrow passages. Many studies have discussed this problem in recent years. This paper introduces an improved method called (Hybrid RRT-A*) to overcome the shortcomings of the original RRT, specifically slow convergence and cost rate. The heuristic function of A-star algorithm is combined with RRT to decrease tree expansion and guide it towards the goal with less nodes and time. Various experiments have been conducted with different environment scenarios to compare the proposed method with the Basic RRT and A-star under the same conditions, which have shown remarkable performance. The time consumed to find the path of the worst one of these scenarios is about 4.9 seconds, whereas it is 18.3 and 34 for A-star and RRT, respectively.

Identification of the Optimal Season and Spectral Regions for Shrub Cover Estimation in Grasslands.

Woody plant encroachment (WPE), the expansion of native and non-native trees and shrubs into grasslands, is a less studied factor that leads to declines in grassland ecosystem health. With the increasing application of remote sensing in grassland monitoring and measuring, it is still difficult to detect WPE at its early stages when its spectral signals are not strong enough. Even at late stages, woody species have strong vegetation characteristics that are commonly categorized as healthy ecosystems. We focus on how shrub encroachment can be detected through remote sensing by looking at the biophysical and spectral properties of the WPE grassland ecosystem, investigating the appropriate season and wavelengths that identify shrub cover, testing the spectral separability of different shrub cover groups and by revealing the lowest shrub cover that can be detected by remote sensing. Biophysical results indicate spring as the best season to distinguish shrubs in our study area. The earliest shrub encroachment can be identified most likely only when the cover reaches between 10% and 25%. A correlation between wavelength spectra and shrub cover indicated four regions that are statistically significant, which differ by season. Furthermore, spectral separability of shrubs increases with their cover; however, good separation is only possible for pure shrub pixels. From the five separability metrics used, Transformed divergence and Jeffries-Matusita distance have better interpretations. The spectral regions for pure shrub pixel separation are slightly different from those derived by correlation and can be explained by the influences from land cover mixtures along our study transect.

Climate Aridity and the Geographical Shift of Olive Trees in a Mediterranean Northern Region

Climate change leverages landscape transformations and exerts variable pressure on natural environments and rural systems. Earlier studies outlined how Mediterranean Europe has become a global hotspot of climate warming and land use change. The present work assumes the olive tree, a typical Mediterranean crop, as a candidate bioclimatic indicator, delineating the latent impact of climate aridity on traditional cropping systems at the northern range of the biogeographical distribution of the olive tree. Since the olive tree follows a well-defined latitude gradient with a progressive decline in both frequency and density moving toward the north, we considered Italy as an appropriate case to investigate how climate change may (directly or indirectly) influence the spatial distribution of this crop. By adopting an exploratory approach grounded in the quali-quantitative analysis of official statistics, the present study investigates long-term changes over time in the spatial distribution of the olive tree surface area in Northern Italy, a region traditionally considered outside the ecological range of the species because of unsuitable climate conditions. Olive tree cultivated areas increased in Northern Italy, especially in flat districts and upland areas, while they decreased in Central and Southern Italy under optimal climate conditions, mostly because of land abandonment. The most intense expansion of the olive tree surface area in Italy was observed in the northern region between 1992 and 2000 and corresponded with the intensification of winter droughts during the late 1980s and the early 1990s and local warming since the mid-1980s. Assuming the intrinsic role of farmers in the expansion of the olive tree into the suboptimal land of Northern Italy, the empirical results of our study suggest how climate aridity and local warming may underlie the shift toward the north in the geographical range of the olive tree in the Mediterranean Basin. We finally discussed the implications of the olive range shift as a part of a possible landscape scenario for a more arid future.

Autonomous Data Collection With Timed Communication Constraints for Unmanned Underwater Vehicles

This letter studies the problem of data collection where an autonomous underwater vehicle (AUV) is required to inspect several goals while staying within the communication range of an unmanned surface vehicle (USV) moving along a predefined path. A reward is associated with each inspected goal, and, so the overall objective is to increase the sum of the rewards. The proposed planner takes the AUV dynamics and the obstacles into account in order to generate collision-free and dynamically-feasible trajectories that enable the AUV to inspect multiple goals while maintaining communication with the USV. When not all the goals can be inspected, the planner generates trajectories that increase the sum of the rewards. The proposed planner constructs a roadmap equipped with time information in order to facilitate navigation and maintain communication in complex 3D environments. A crucial aspect is an effective coupling of discrete search with sampling-based motion planning. Specifically, a multi-goal discrete search is proposed to effectively compute roadmap paths that increase the sum of the rewards. These paths then guide the sampling-based expansion of a motion tree. Experiments using complex 3D environments and an AUV model defined by nonlinear second-order differential equations indicate the efficiency of the planner to inspect an increasing number of goals.

Community‐level responses to increasing dryness vary with plant growth form across an extensive aridity gradient

AbstractAimPerennial plant communities are crucial for regulating ecological processes and maintaining ecosystem functions. Variation in community structure is driven by both biotic and abiotic factors, reflecting adaptation strategies of plant communities to various environments. Although much is known about the response of individual perennial plants to drier climates, empirical evidence of the community‐level responses to increasing dryness is limited.LocationEastern Australia; 1500 km gradient.TaxonPerennial plants.MethodsWe measured the abundance and size distribution (median, skewness and variance) of perennial plant communities from different growth forms (trees, shrubs and grasses), the spatial arrangement of trees in the overstorey and both biotic (competition) and abiotic (climate, soil properties) factors at 150 sites along an extensive aridity gradient from humid to arid areas. We used regression analyses and linear models to explore variation in community structure with increasing aridity and key driving factors for different perennial plant communities.ResultsVariation in community structure differed with growth form. As aridity increased, trees had wider canopies and were spatially aggregated, shrubs became miniaturised, but highly variable in size, and grasses comprised more larger individuals. Biotic and abiotic factors exerted different effects on different growth forms, with trees and shrubs consistently affected by competition and aridity, respectively, whereas grasses were weakly affected by aridity, summer rainfall and soil texture.Main conclusionsOur study highlights the idiosyncratic adaptation strategies used by trees, shrubs and grasses in response to drying climates at the community level through their effect on the size distribution or spatial aggregation. The structure of different perennial growth forms was influenced by different effects from either biotic (competition) or abiotic (climate, soil) factors. Under forecasted drier climates, canopy expansion and greater aggregation of trees might enhance resource sinks and shelter for diverse biota, potentially shielding plant communities against predicted aridification.

A Tree Expansion Formula of a Homology Intersection Number on the Configuration Space $$\mathcal {M}_{0,n}$$

In \cite{M}, Sebastian Mizera discovered a tree expansion formula of a homology intersection number on the configuration space $\mathcal{M}_{0,n}$. The formula originates in a study of Kawai-Lewellen-Tye relation in string theory. In this paper, we give an elementary proof of the formula. The basic ingredients are the combinatorics of the real moduli space $\overline{\mathcal{M}}_{0,n}(\R)$ and a combinatorial identity related to the face number of the associahedron.

Holocene expansion of the Caledonian pinewoods: Spatial and temporal patterns at regional and landscape scales

Background : To facilitate climatic change adaptation, landscape and conservation managers require understanding of spatio-temporal patterns of expansion of potential dominant species. Studying past expansions of canopy-dominant trees can contribute such understanding. Aims : Test hypotheses about expansions of dominants using as a model the mid-Holocene expansion of forests dominated by Pinus sylvestris in the Scottish Highlands. Methods : Pollen analysis and radiocarbon dating of Holocene sediments of a larger basin and several small hollows were performed in three landscapes along a north–south transect. A larger basin records expansion timing at landscape scale, whilst small hollows evidence within-landscape spatio-temporal patterns. Results : Vegetation existing prior to the expansion of pinewoods influenced landscape-scale spatio-temporal expansion patterns of P. sylvestris. Open vegetation generally was invaded earlier and/or to a greater extent; invasion was often later, or did not occur, where woodland with a substantial temperate broadleaved tree and shrub component (e.g. Corylus avellana, Quercus spp.) was present. Most small hollows, not just those where pinewoods became locally established, recorded vegetation change during the expansion. Some present landscape-scale forest composition patterns were established at that time. Conclusions : Studying past expansions of dominants provides evidence relevant to planning conservation and landscape management to facilitate ecological adaptation as species adjust their distributions and abundances in response to climatic change.

Estimating Biomass and Carbon Storage by Georgia Forest Types and Species Groups Using the FIA Data Diameters, Basal Areas, Site Indices, and Total Heights

We present here an example of research into methodology of an estimation of carbon and biomass pools in forests using the USDA Forest Service, Forest Inventory and Analysis (FIA), data of the 1989 and 1998 surveys for Georgia forests, as relevant for comparison with other extremely highly-cited estimates of similar, but different, methodologies. Based on the derived estimates, we produce an example map of the biomass density and pools at a sub-county level resolution, which is based on spatially explicit simulations of the potential cover-type polygons implied by the FIA data with approximate plot locations. Our results include estimates of the biomass pools in the belowground biomass in roots, aboveground woody biomass in trees, and the biomass of foliage. We estimated the biomass densities and pools at a tree level using diameters and heights and previously published models, then propagated these results to the plot level using tree expansion factors, and then transformed these estimates to plot-dependent polygons using plot expansion factors. The plot-dependent polygons were spatially simulated using a simplified assumption of homogeneity of conditions surrounding each plot to the extent of the area defined by this plot’s expansion factors. The derived map provides a visual representation of the distribution of forest biomass densities and pools in the state of Georgia with distinctive patterns observed in various areas of urban development, federally owned forests, primary commercial forestland, and other land use areas. Coniferous forests with the highest total biomass density are located mostly in three regions: northern Georgia (Appalachian Highlands), the southern part of Piedmont, and the eastern part of Coastal Plain. Deciduous and mixed forests with the highest biomass density are concentrated mostly in the northern part of the state—especially in the Blue Ridge physiographic province, and in the western part of the East Gulf Coastal Plain. Counties with the highest biomass density were located primarily in the northern part of the state, while counties with the lowest density tended to be located in the Coastal Georgia area.

Automatic QoS-aware web services composition based on set-cover problem

By definition, web-services composition works on developing merely optimum coordination among a number of available web-services to provide a new composed web-service intended to satisfy some users requirements for which a single web service is not (good) enough. In this article, the formulation of the automatic web-services composition is proposed as several set-cover problems and an approximation algorithm has been exploited to solve them. In proposed method, the web-service composition has been carried out within two main phases, the top-down expansion of the composition tree, and the production of composed service by bottom-up traversal of composition tree. In the first phase, the production of a composition tree (similar to the production of tree in problemsolving by searching) is proposed by starting from the output or post-conditions of the requested service towards its input or pre-conditions. Each node or state of the tree is a set of inputs and/or outputs or conditions, and services as tree edges illustrate the transition from one node to another. In the second phase, finding the path from the leaves of the produced composition tree to the root is considered equal to reaching the output of requested service, and this path specifies the involved services and the composition plan. The requested service input set determines the available leaves of the composition tree. To achieve each non-leaf node of the tree, a set-cover problem is produced and solved using a greedy approximation algorithm. If the production and solving of the set-cover problems continues hierarchically until it reaches the root node, the composition plan and cost of the required composition service will be specified. The main focus of this research is the joint sequential and parallel composition with the aim of producing near-optimal and QoS-aware composed services.

Resilience of trees and the vulnerability of grasslands to climate change in temperate Australian wetlands

Observations from wetlands across the globe suggest a consistent pattern of woody encroachment into wetland grasslands, altering habitat structure and ecological function. The extent to which hydrological changes have contributed to woody invasion of wetland grasslands is unclear. Our objective was to compare rates of woody encroachment in Australian floodplain wetlands between wet and dry hydrological phases. We test the hypothesis that contraction of non-woody wetland vegetation (grasses and rushes) would be concentrated in dry phases, co-incident with recruitment of the River Red Gum Eucalyptus camaldulensis lower in the floodplain. We conduct the first detailed mapping of habitat change in two of the largest forested wetlands in inland Australia, comparing wet and dry hydrological phases. Detailed photogrammetry, supported by extensive ground survey, allowed the interpretation of high resolution aerial photography to vegetation community level. We found a consistent pattern of decline in non-woody vegetation, particularly amongst grasses utilising the C4 photosynthetic pathway. The C4 grasses Pseudoraphis spinescens and Paspalum distichum showed steep declines in the Barmah Millewa and Macquarie Marshes respectively, being replaced by River Red Gum E. camaldulensis. C3 sedges proved more resilient in both systems. Our results suggest that a pattern of tree expansion into non-woody wetland vegetation, characteristic of wetlands across the globe, is a major habitat structural change in the Australian floodplain wetlands studied. Projected hydrological impacts of climate change are likely to further restrict wetland grass foraging habitat in these semi-arid floodplain wetlands.

Plant functional groups and species contribute to ecological resilience a decade after woodland expansion treatments

AbstractWoody plant expansions are altering ecosystem structure and function, as well as fire regimes, around the globe. Tree‐reduction treatments are widely implemented in expanding woodlands to reduce fuel loads, increase ecological resilience, and improve habitat, but few studies have measured treatment outcomes over long timescales or large geographic areas. The Sagebrush Treatment Evaluation Project (SageSTEP) evaluated the ecological effects of prescribed fire and cut‐and‐leave treatments in sagebrush communities experiencing tree expansion in North American cold desert shrublands. We used 10 yr of data from the SageSTEP network to test how treatments interacted with pre‐treatment tree dominance, soil climate, and time since treatment to affect plant functional groups and dominant species. Non‐sprouting shrub (Artemisia spp.), sprouting shrub, perennial graminoid, and annual grass responses depended on tree dominance and soil climate, and responses were related to the dominant species' life‐history traits. Sites with warm and dry soils showed increased perennial graminoid but reduced Artemisia shrub cover across the tree dominance gradient after prescribed burning, while sites with cool and moist soils showed favorable post‐burn responses for both functional types, particularly at low to moderate tree dominance. Cut‐and‐leave treatments sustained or increased native perennial plant functional groups and experienced smaller increases in exotic annual plants in both soil climates across the tree dominance gradient. Both treatments reduced biocrust cover. Selecting appropriate tree‐reduction treatments to achieve desired long‐term outcomes requires consideration of dominant species, site environmental conditions, and the degree of woodland expansion. Careful selection of management treatments will reduce the likelihood of undesirable consequences to the ecosystem.

On the derivation of the wave kinetic equation for NLS

AbstractA fundamental question in wave turbulence theory is to understand how the wave kinetic equation describes the long-time dynamics of its associated nonlinear dispersive equation. Formal derivations in the physics literature, dating back to the work of Peierls in 1928, suggest that such a kinetic description should hold (for well-prepared random data) at a largekinetic time scale$T_{\mathrm {kin}} \gg 1$and in a limiting regime where the sizeLof the domain goes to infinity and the strength$\alpha $of the nonlinearity goes to$0$(weak nonlinearity). For the cubic nonlinear Schrödinger equation,$T_{\mathrm {kin}}=O\left (\alpha ^{-2}\right )$and$\alpha $is related to the conserved mass$\lambda $of the solution via$\alpha =\lambda ^2 L^{-d}$.In this paper, we study the rigorous justification of this monumental statement and show that the answer seems to depend on the particularscaling lawin which the$(\alpha , L)$limit is taken, in a spirit similar to how the Boltzmann–Grad scaling law is imposed in the derivation of Boltzmann’s equation. In particular, there appear to betwofavourable scaling laws: when$\alpha $approaches$0$like$L^{-\varepsilon +}$or like$L^{-1-\frac {\varepsilon }{2}+}$(for arbitrary small$\varepsilon $), we exhibit the wave kinetic equation up to time scales$O(T_{\mathrm {kin}}L^{-\varepsilon })$, by showing that the relevant Feynman-diagram expansions converge absolutely (as a sum over paired trees). For the other scaling laws, we justify the onset of the kinetic description at time scales$T_*\ll T_{\mathrm {kin}}$and identify specific interactions that become very large for times beyond$T_*$. In particular, the relevant tree expansion diverges absolutely there. In light of those interactions, extending the kinetic description beyond$T_*$toward$T_{\mathrm {kin}}$for such scaling laws seems to require new methods and ideas.