A small tool to view real-world ActivityPub objects as JSON! Enter a URL
or username from Mastodon or a similar service below, and we'll send a
request with
the right
Accept
header
to the server to view the underlying object.
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"content": "<p>Bonus: (somebody probably already did it)</p>",
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"content": "<p>Additional references:<br /><a href=\"https://graphblas.org/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">graphblas.org/</span><span class=\"invisible\"></span></a> and GraphBLAS pointers: <a href=\"https://github.com/GraphBLAS/GraphBLAS-Pointers\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">github.com/GraphBLAS/GraphBLAS</span><span class=\"invisible\">-Pointers</span></a><br />Introductory blog post: <a href=\"https://sinews.siam.org/Details-Page/graphblas-and-graphchallenge-advance-network-frontiers\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">sinews.siam.org/Details-Page/g</span><span class=\"invisible\">raphblas-and-graphchallenge-advance-network-frontiers</span></a><br />Presentation on GraphBLAS: <a href=\"https://doi.org/10.5281/zenodo.6400356\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">doi.org/10.5281/zenodo.6400356</span><span class=\"invisible\"></span></a><br />Kepner, Jeremy, and John Gilbert. 2011. Graph Algorithms in the Language of Linear Algebra: Software, Environments, and Tools. SIAM. <a href=\"https://doi.org/10.1137/1.9780898719918\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">doi.org/10.1137/1.978089871991</span><span class=\"invisible\">8</span></a>.<br />(6/n, n=6)</p>",
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"en": "<p>Additional references:<br /><a href=\"https://graphblas.org/\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">graphblas.org/</span><span class=\"invisible\"></span></a> and GraphBLAS pointers: <a href=\"https://github.com/GraphBLAS/GraphBLAS-Pointers\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">github.com/GraphBLAS/GraphBLAS</span><span class=\"invisible\">-Pointers</span></a><br />Introductory blog post: <a href=\"https://sinews.siam.org/Details-Page/graphblas-and-graphchallenge-advance-network-frontiers\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">sinews.siam.org/Details-Page/g</span><span class=\"invisible\">raphblas-and-graphchallenge-advance-network-frontiers</span></a><br />Presentation on GraphBLAS: <a href=\"https://doi.org/10.5281/zenodo.6400356\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">doi.org/10.5281/zenodo.6400356</span><span class=\"invisible\"></span></a><br />Kepner, Jeremy, and John Gilbert. 2011. Graph Algorithms in the Language of Linear Algebra: Software, Environments, and Tools. SIAM. <a href=\"https://doi.org/10.1137/1.9780898719918\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">doi.org/10.1137/1.978089871991</span><span class=\"invisible\">8</span></a>.<br />(6/n, n=6)</p>"
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"content": "<p>You can implement these using only a library to manipulate matrices over arbitrary semirings: (sparse) linear algebra is all you need!<br />GraphBLAS is a standard set of primitives to do exactly this, implemented in the SuiteSparse library. There are also <a href=\"https://mathstodon.xyz/tags/Python\" class=\"mention hashtag\" rel=\"tag\">#<span>Python</span></a> and <a href=\"https://mathstodon.xyz/tags/JuliaLang\" class=\"mention hashtag\" rel=\"tag\">#<span>JuliaLang</span></a> wrappers!<br />(5/n)</p>",
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"en": "<p>You can implement these using only a library to manipulate matrices over arbitrary semirings: (sparse) linear algebra is all you need!<br />GraphBLAS is a standard set of primitives to do exactly this, implemented in the SuiteSparse library. There are also <a href=\"https://mathstodon.xyz/tags/Python\" class=\"mention hashtag\" rel=\"tag\">#<span>Python</span></a> and <a href=\"https://mathstodon.xyz/tags/JuliaLang\" class=\"mention hashtag\" rel=\"tag\">#<span>JuliaLang</span></a> wrappers!<br />(5/n)</p>"
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"content": "<p>Many classical graph algorithms have been reinterpreted in this framework, often leading to lower complexity or better computational performance (due to cache efficiency, etc). It's an active research topic, some are still being improved!<br />(4/n)</p>",
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"en": "<p>Many classical graph algorithms have been reinterpreted in this framework, often leading to lower complexity or better computational performance (due to cache efficiency, etc). It's an active research topic, some are still being improved!<br />(4/n)</p>"
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"conversation": "tag:mathstodon.xyz,2022-11-05:objectId=28369321:objectType=Conversation",
"content": "<p>The general idea is to extend traditional matrix multiplication on ℕ, ℝ, or ℂ to arbitrary semirings: C = AB = A⊕.⊗B.<br />Each semiring can then be used for specific algorithms/use cases:<br />- the standard semiring (+, ×) can be used to compute graph traversals (e.g. number of paths)<br />- the tropical semiring (min, +) can be used to compute shortest paths<br />- (∩, ∪) for set operations, useful for database applications<br />- and many more!<br />(3/n)</p>",
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"en": "<p>The general idea is to extend traditional matrix multiplication on ℕ, ℝ, or ℂ to arbitrary semirings: C = AB = A⊕.⊗B.<br />Each semiring can then be used for specific algorithms/use cases:<br />- the standard semiring (+, ×) can be used to compute graph traversals (e.g. number of paths)<br />- the tropical semiring (min, +) can be used to compute shortest paths<br />- (∩, ∪) for set operations, useful for database applications<br />- and many more!<br />(3/n)</p>"
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"content": "<p>The advantage is that linear algebra operations on (sparse) matrices are much easier to optimize. In standard applications, BLAS libraries have demonstrated that optimized micro-kernels constitute a basis on which efficient implementations can be built.<br />But it would also be much more elegant in theory to describe a minimum spanning tree computation using linear algebra alone!<br />(2/n)</p>",
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"content": "<p>A short thread on <a href=\"https://mathstodon.xyz/tags/graph\" class=\"mention hashtag\" rel=\"tag\">#<span>graph</span></a> algorithms in the language of <a href=\"https://mathstodon.xyz/tags/LinearAlgebra\" class=\"mention hashtag\" rel=\"tag\">#<span>LinearAlgebra</span></a> 🧵<br />It is well-known that the adjacency matrix is a useful tool to compute various properties of the underlying graph: the number of connected components, isomorphism to other graphs, etc.<br />But can we go further? Most graph algorithms are still expressed in terms of iterations over all nodes or edges. Can we leverage linear algebra to express these operations more efficiently?<br />(1/n)</p>",
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"content": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@rwxrwxrwx\" class=\"u-url mention\">@<span>rwxrwxrwx</span></a></span> <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@codingquark\" class=\"u-url mention\">@<span>codingquark</span></a></span> good to know! Love browsing into them at random, so it might be time to invest to level up my electronics 😀</p>",
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"content": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@codingquark\" class=\"u-url mention\">@<span>codingquark</span></a></span> <span class=\"h-card\" translate=\"no\"><a href=\"https://mathstodon.xyz/@rwxrwxrwx\" class=\"u-url mention\">@<span>rwxrwxrwx</span></a></span> Does it cover the same material as the "original" book? I always assumed it was kind of a companion guide, not a self-contained handbook.</p>",
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"content": "<p>An interesting book about applications of max-plus algebras to scheduling problems:</p><p>> Heidergott, Bernd, Geert Jan Olsder, and Jacob van der Woude. 2005. Max plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-plus Algebra and Its Applications. Princeton, NJ, USA: Princeton University Press. <a href=\"https://press.princeton.edu/books/hardcover/9780691117638/max-plus-at-work\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">press.princeton.edu/books/hard</span><span class=\"invisible\">cover/9780691117638/max-plus-at-work</span></a>.</p>",
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