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How can one analyze detailed 3D biological objects, such as neuronal and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and computing geodesic deformations between the shapes of such tree-like 3D objects. A hierarchical organization of subtrees characterizes these objects - each subtree has a main branch with some side branches attached - and one needs to match these structures across objects for meaningful comparisons. We propose a novel representation that extends the Square-Root Velocity Function (SRVF), initially developed for Euclidean curves, to tree-shaped 3D objects. We then define a new metric that quantifies the bending, stretching, and branch sliding needed to deform one tree-shaped object into the other. Compared to the current metrics such as the Quotient Euclidean Distance (QED) and the Tree Edit Distance (TED), the proposed representation and metric capture the full elasticity of the branches (i.e., bending and stretching) as well as the topological variations (i.e., branch death/birth and sliding). It completely avoids the shrinkage that results from the edge collapse and node split operations of the QED and TED metrics. We demonstrate the utility of this framework in comparing, matching, and computing geodesics between biological objects such as neuronal and botanical trees. We also demonstrate its application to various shape analysis tasks such as (i) symmetry analysis and symmetrization of tree-shaped 3D objects, (ii) computing summary statistics (means and modes of variations) of populations of tree-shaped 3D objects, (iii) fitting parametric probability distributions to such populations, and (iv) finally synthesizing novel tree-shaped 3D objects through random sampling from estimated probability distributions. 

We report a general method for direct decarbonylative thioetherification of carboxylic acids using air- and moisture-stable nickel precatalysts. In this approach, ubiquitous carboxylic acids are directly used as aryl electrophiles and common thiols serve as sulfide donors. 

Abstract Aeolian sediment transport occurs as a function of, and with feedback to ecosystem changes and disturbances. Many desert grasslands are undergoing rapid changes in vegetation, including the encroachment of woody plants, which alters fire regimes and in turn can change the spatial and temporal patterns of aeolian sediment transport. We investigated aeolian sediment transport and spatial distribution of sediment in the surface soil for 7 years following a prescribed fire using a multiple rare earth element (REE) tracer‐based approach in a shrub‐encroached desert grassland in the northern Chihuahuan desert. Results indicate that even though the aeolian horizontal sediment mass flux increased approximately three‐fold in the first windy season in the burned areas compared to control areas, there were no significant differences after three windy seasons. The soil surface of bare microsites was the major contributor of aeolian sediments in unburned areas (87%), while the shrub microsites contributed the least (<2%) during the observation period. However, after the prescribed fire, the contribution of aeolian sediments from shrub microsites increased considerably (∼40%), indicating post‐fire microsite‐scale sediment redistribution. The findings of this study, which is the first to use multiple REE tracers for multi‐year analysis of the spatial and temporal dynamics of aeolian sediment transport, illustrate how disturbance by prescribed fire can influence aeolian processes and alters dryland soil geomorphology in which distinct soils develop over time at very fine spatial scales of individual plants. 

This paper addresses the problem of training a robot to carry out temporal tasks of arbitrary complexity via evaluative human feedback that can be inaccurate. A key idea explored in our work is a kind of curriculum learning—training the robot to master simple tasks and then building up to more complex tasks. We show how a training procedure, using knowledge of the formal task representation, can decompose and train any task efficiently in the size of its representation. We further provide a set of experiments that support the claim that non-expert human trainers can decompose tasks in a way that is consistent with our theoretical results, with more than half of participants successfully training all of our experimental missions. We compared our algorithm with existing approaches and our experimental results suggest that our method outperforms alternatives, especially when feedback contains mistakes. 

Woody plant encroachment of grassland ecosystems is a geographically extensive phenomenon that can lead to rapid land degradation and significantly alter global biogeochemical cycles, and this ecosystem change has been particularly well documented in the desert grassland of the southwestern United States. Fires are known to decrease vegetation cover and increase soil erodibility, and the shifts in wildfire regimes are currently occurring in Chihuahuan Desert. It is generally recognized that the invasion of woody vegetation into grasslands and savannas will increase the carbon stored in arid ecosystems. However, carbon storage may be complicated by disturbance such as wildfire, which alters the distribution and amount of C pools in the drylands. The relative distribution of each vegetation type to the soil C pool and its variability after fires are not well-understood in this ecosystem. This research will investigate the variations of SOC and its vegetation source partition at microsite scale in the woody shrub encroached grassland after the occurrence of fire, which will provide further information on wildfire’s influence on soil C pool dynamics in arid and semiarid lands. The post-fire changes of the spatial pattern of SOC and vegetation contributions in the shrub encroached grassland will be analyzed using a geostatistical method outlined in Guan et al. (2018). Overall, understanding the post-fire redistribution and sources of SOC may provide insights on the important role played by fire, aeolian processes and vegetation in the dynamics of desert grassland ecosystems.