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General plane-wave and spherical-wave solutions are found for Maxwell’s equations with electric and magnetic fields parallel to each other everywhere in a uniform isotropic sourceless medium. For deriving them, Beltrami’s and Chang–Carovillano–Low’s results about a Beltrami flow (or a force-free field) with a non-constant proportionality factor are applied to Uehara–Kawai–Shimoda’s equations. It is proved that other wave solutions, such as a cylindrical-wave solution, cannot be as general as the plane-wave or spherical-wave solution. [ABSTRACT FROM AUTHOR]

In this article, new anisotropic image filters are introduced and their performances are compared with existing isotropic and anisotropic filters. The developed filters were examined according to their image noise removing performances in terms of standard image quality metrics, as well as the edge preserving properties of the filtered images. Mathematical inferences of anisotropic filters are made based on the minimization of the Polyakov action energy integral. New anisotropic metrics are found by means of Finsler metrics that minimize the corresponding integral. The new metrics perform filtering by updating the image with anisotropic Laplace-Beltrami flow. After filtering, it was observed that the introduced metrics perform well against other anisotropic metrics. It is also observed that the developed New Randers, New Normalized Miron, and New Metric filters preserve edges better than other filters, making it a plausible noise removal tool prior to edge detection in image processing. The source codes of proposed filters are publicly available at https://github.com/HAYDARKILIC. [ABSTRACT FROM AUTHOR]

Abstract: Electron tomography (ET) is the leading imaging technique for visualizing the molecular architecture of complex biological specimens. Currently, real-time ET systems allow scientists to acquire experimental datasets with the electron microscope and obtain a preliminary version of the three-dimensional structure of the specimen. In principle, this rough structure allows assessment of the quality of the sample and can also be used as a guide to collect more datasets. However, in practice, the low signal-to-noise ratio of the ET datasets precludes detailed interpretation and makes their assessment difficult. Therefore, noise reduction methods must be integrated in these real-time ET systems for their fully exploitation. This work proposes and evaluates two different multithreaded implementations of a sophisticated noise reduction method with capabilities of preservation of biologically relevant features. The exploitation of the computing power of modern multicore platforms makes this noise reduction method provide datasets appropriate for assessment in a matter of a few minutes, thereby making it suitable for integration in current real-time electron tomography systems. [Copyright &y& Elsevier]