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  1. Free, publicly-accessible full text available September 1, 2023
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  3. In this article, we introduce a compact representation for measured BRDFs by leveraging Neural Processes (NPs). Unlike prior methods that express those BRDFs as discrete high-dimensional matrices or tensors, our technique considers measured BRDFs as continuous functions and works in corresponding function spaces . Specifically, provided the evaluations of a set of BRDFs, such as ones in MERL and EPFL datasets, our method learns a low-dimensional latent space as well as a few neural networks to encode and decode these measured BRDFs or new BRDFs into and from this space in a non-linear fashion. Leveraging this latent space and themore »flexibility offered by the NPs formulation, our encoded BRDFs are highly compact and offer a level of accuracy better than prior methods. We demonstrate the practical usefulness of our approach via two important applications, BRDF compression and editing. Additionally, we design two alternative post-trained decoders to, respectively, achieve better compression ratio for individual BRDFs and enable importance sampling of BRDFs.« less
    Free, publicly-accessible full text available April 30, 2023
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  8. Shawe-Taylor, John (Ed.)
    Learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation (MNI) problem, a regularized learning problem or, in general, a semi-discrete inverse problem (SDIP), in either Hilbert spaces or Banach spaces. The goal of this paper is to systematically study solutions of these problems in Banach spaces. We aim at obtaining explicit representer theorems for their solutions, on which convenient solution methods can then be developed. For the MNI problem, the explicit representer theorems enable us to express the infimum inmore »terms of the norm of the linear combination of the interpolation functionals. For the purpose of developing efficient computational algorithms, we establish the fixed-point equation formulation of solutions of these problems. We reveal that unlike in a Hilbert space, in general, solutions of these problems in a Banach space may not be able to be reduced to truly finite dimensional problems (with certain infinite dimensional components hidden). We demonstrate how this obstacle can be removed, reducing the original problem to a truly finite dimensional one, in the special case when the Banach space is ℓ1(N).« less
    Free, publicly-accessible full text available September 1, 2022
  9. Abstract Formation of pollen wall exine is preceded by the development of several transient layers of extracellular materials deposited on the surface of developing pollen grains. One such layer is primexine (PE), a thin, ephemeral structure that is present only for a short period of time and is difficult to visualize and study. Recent genetic studies suggested that PE is a key factor in the formation of exine, making it critical to understand its composition and the dynamics of its formation. In this study, we used high-pressure frozen/freeze-substituted samples of developing Arabidopsis (Arabidopsis thaliana) pollen for a detailed transmission electronmore »microscopy analysis of the PE ultrastructure throughout the tetrad stage of pollen development. We also analyzed anthers from wild-type Arabidopsis and three mutants defective in PE formation by immunofluorescence, carefully tracing several carbohydrate epitopes in PE and nearby anther tissues during the tetrad and the early free-microspore stages. Our analyses revealed likely sites where these carbohydrates are produced and showed that the distribution of these carbohydrates in PE changes significantly during the tetrad stage. We also identified tools for staging tetrads and demonstrate that components of PE undergo changes resembling phase separation. Our results indicate that PE behaves like a much more dynamic structure than has been previously appreciated and clearly show that Arabidopsis PE creates a scaffolding pattern for formation of reticulate exine.« less
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