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The library Dionysus implements the computation of vineyards [155] and circle-valued functions [127].
The package Persistence Landscape Toolbox [150] (see [70] for the accompanying tutorial) implements the computation of persistence landscapes, as well as many statistical tools that one can apply to persistence landscapes, such as mean, ANOVA, hypothesis tests, and many more.
javaPlex supports the computation of some constructions from homological algebra (see [66] for details), and Perseus implements the computation of PH with the VR for points with different 'birth times' (see Section 5.1.3).
Because the library javaPlex implements the computation of a variety of complexes and algorithms, we feel that it is the best software for an initial foray into PH computation.
The library TDA Package [140] (see [69] for the accompanying tutorial) implements the computation of confidence sets for persistence diagrams that was developed in [141], distance functions that are robust to noise and outliers [142], and many more tools for interpreting barcodes.
The second systolic array (referred to as the PSM coprocessor) implements the computation of the Point Spread Matrix (PSM) function concurrently over the azimuth and range axes, that is, where, as previously, symbol specifies the concurrent execution of the corresponding computational operations.
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The second coprocessor (referred to as PSM coprocessor) implements the computations of the PSM given by (25) concurrently over the azimuth and the range directions.
We implement the computation of saliency based on the statistics of local image regions.
John Searle (1992) explicitly argues that whether a physical system implements a computation depends on how an observer interprets the system; therefore, for any sufficiently complex object and for any computation, the object can be described as implementing the computation.
They use systolic arrays architecture in conjunction with the CORDIC algorithm to implement the computation of a matrix inverse [8].
Of the six software packages that we study, four implement the computation of the dual algorithm, and four implement the standard algorithm.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com