Kinematic numerators from the worldsheet: cubic trees from labelled trees

In this note we revisit the problem of explicitly computing tree-level scattering amplitudes in various theories in any dimension from worldsheet formulas. The latter are known to produce cubic-tree expansion of tree amplitudes with kinematic numerators automatically satisfying Jacobi-identities, once any half-integrand on the worldsheet is reduced to logarithmic functions. We review a natural class of worldsheet functions called “Cayley functions”, which are in one-to-one correspondence with labelled trees, and natural expansions of known half-integrands onto them with coefficients that are particularly compact building blocks of kinematic numerators. We present a general formula expressing kinematic numerators of all cubic trees as linear combinations of coefficients of labelled trees, which satisfy Jacobi identities by construction and include the usual combinations in terms of master numerators as a special case. Our results provide an efficient algorithm, which is implemented in a Mathematica package, for computing all tree amplitudes in theories including non-linear sigma model, special Galileon, Yang-Mills-scalar, Einstein-Yang-Mills and Dirac-Born-Infeld.

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.

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.

North-Westward Expansion of the Invasive Range of Emerald Ash Borer, Agrilus planipennis Fairmaire (Coleoptera: Buprestidae) towards the EU: From Moscow to Saint Petersburg

Agrilus planipennis is a devastating invasive pest of ash trees in European Russia, Ukraine, and North America. To monitor the north-western limit of its European invasive range, in June 2018 we established 10 study plots along the federal highway M10 (Russia) that runs between Moscow and Saint Petersburg through Tver’ City (approx. 180 km from Moscow), and lined with ash trees. On each plot, 2–4 Fraxinus pennsylvanica trees with heights ranging 6.1–17.0 m and diameters ranging 7.0–18.0 cm were girdled, i.e., 50 cm of their bark were removed. The study plots were visited and girdled trees were examined in September and November, 2018, and in October, 2019. Observations revealed that the current continuous north-western limit of A. planipennis range in European Russia coincides with the north-western border of Tver’ City and this range limit has not distinctly shifted north-westward during 2015–2019. In spite of the rich food supply (due to abundant F. pennsylvanica and F. excelsior plantings) in Tver’ City and along roads going to and from, the population density of A. planipennis in the area is currently low. Recent (September 2020) sudden detection of a spatially isolated A. planipennis outbreak approx. 520 km far north-westward from Tver’ (in Saint Petersburg) suggested that A. planipennis most likely had arrived at Saint Petersburg not by gradual stepwise (flying tree-to-tree) expansion of its continuous invasive range in Tver’ City, but as a result of its accidental introduction by means of, e.g., “insect-hitchhiked” vehicles, transported plants for planting, and/or other commodities. The proximity of the reported A.planipennis outbreak to the borders of the EU (approx. 130 km to Estonia and Finland) requires urgent measures for its containment and control, and constant monitoring.

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.

On the derivation of the wave kinetic equation for NLS

A 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 large kinetic time scale $T_{\mathrm {kin}} \gg 1$ and in a limiting regime where the size L of 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 particular scaling law in 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 be two favourable 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.

Optimistic Monte Carlo Tree Search with Sampled Information Relaxation Dual Bounds

In the paper, “Optimistic Monte Carlo Tree Search with Sampled Information Relaxation Dual Bounds,” the authors propose an extension to Monte Carlo tree search that uses the idea of “sampling the future” to produce noisy upper bounds on nodes in the decision tree. These upper bounds can help guide the tree expansion process and produce decision trees that are deeper rather than wider, in effect concentrating computation toward more useful parts of the state space. The algorithm’s effectiveness is illustrated in a ride-sharing setting, where a driver/vehicle needs to make dynamic decisions regarding trip acceptance and relocations.