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  1. Free, publicly-accessible full text available February 1, 2023
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  3. The rhizosphere has been called “one of the most complex ecosystems on earth” be-cause it is a hotspot for interactions among millions of microbial cells. Many of these are microbes are also participating in a dynamic interplay with host plant tissues, sign-aling pathways, and metabolites. Historically, breeders have employed a plant- centric perspective when trying to harness the potential of microbiome-derived benefits to improve productivity and resilience of economically important plants. This is poten-tially problematic because: (i) the evolution of the microbes themselves is often ig-nored, and (ii) it assumes that the fitness of interacting plants and microbes is strictlymore »aligned. In contrast, a microbe-centric perspective recognizes that putatively benefi-cial microbes are still under selection to increase their own fitness, even if there are costs to the host. This can lead to the evolution of sophisticated, potentially subtle, ways for microbes to manipulate the phenotype of their hosts, as well as other mi-crobes in the rhizosphere. We illustrate this idea with a review of cases where rhizo-sphere microbes have been demonstrated to directly manipulate host root growth, architecture and exudation, host nutrient uptake systems, and host immunity and defense. We also discuss indirect effects, whereby fitness outcomes for the plant are a consequence of ecological interactions between rhizosphere microbes. If these consequences are positive for the plant, they can potentially be misconstrued as traits that have evolved to promote host growth, even if they are a result of selection for unrelated functions. The ubiquity of both direct microbial manipulation of hosts and context-dependent, variable indirect effects leads us to argue that an evolutionary perspective on rhizosphere microbial ecology will become increasingly important as we continue to engineer microbial communities for crop production.« less
    Free, publicly-accessible full text available December 2, 2022
  4. In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a 1-Poincare inequality. We show that at almost every point x outside the Cantor and jump parts of a BV function, the asymptotic limit of the function is a Lipschitz continuous function of least gradient on a tangent space to the metric space based at x. We also show that, at co-dimension 1 Hausdorff measure almost every measure-theoretic boundary point of a set E of finite perimeter, there is an asymptotic limit set (E)∞ corresponding to the asymptoticmore »expansion of E and that every such asymptotic limit (E)∞ is a quasiminimal set of finite perimeter. We also show that the perimeter measure of (E)∞ is Ahlfors co-dimension 1 regular.« less
    Free, publicly-accessible full text available November 1, 2022
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  7. A single experiment is reported that measured the apparent stereoscopic shapes of symmetric and asymmetric objects at different viewing distances. The symmetric stimuli were specifically designed to satisfy the minimal conditions for computing veridical shape from symmetry. That is to say, they depicted complex, bilaterally symmetric, plane-faced polyhedra whose symmetry planes were oriented at an angle of 45° relative to the line of sight. The asymmetric stimuli were distorted versions of the symmetric ones in which the 3D position of each vertex was randomly displaced. Prior theoretical analyses have shown that it is mathematically possible to compute the 3D shapesmore »of symmetric stimuli under these conditions, but those algorithms are useless for asymmetric objects. The results revealed that the apparent shapes of both types of objects were expanded or compressed in depth as a function of viewing distance, in exactly the same way as has been reported in many other studies, and that the presence or absence of symmetry had no detectable effect on performance.« less
    Free, publicly-accessible full text available July 1, 2022
  8. Systematic enumeration and identification of unique 3D spatial topologies of complex engineering systems such as automotive cooling layouts, hybrid-electric power trains, and aero-engines are essential to search their exhaustive design spaces to identify spatial topologies that can satisfy challenging system requirements. However, efficient navigation through discrete 3D spatial topology options is a very challenging problem due to its combinatorial nature and can quickly exceed human cognitive abilities at even moderate complexity levels. Here we present a new, efficient, and generic design framework that utilizes mathematical spatial graph theory to represent, enumerate, and identify distinctive 3D topological classes for an abstractmore »engineering system, given its system architecture (SA) — its components and interconnections. Spatial graph diagrams (SGDs) are generated for a given SA from zero to a specified maximum crossing number. Corresponding Yamada polynomials for all the planar SGDs are then generated. SGDs are categorized into topological classes, each of which shares a unique Yamada polynomial. Finally, for each topological class, one 3D geometric model is generated for an SGD with the fewest interconnect crossings. Several case studies are shown to illustrate the different features of our proposed framework. Design guidelines are also provided for practicing engineers to aid the utilization of this framework for application to different types of real-world problems.« less
    Free, publicly-accessible full text available August 17, 2022
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