5 research outputs found

    Identifiability of Graphs with Small Color Classes by the Weisfeiler-Leman Algorithm

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    On the Weisfeiler-Leman dimension of some polyhedral graphs

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    Let mm be a positive integer, XX a graph with vertex set Ω\Omega, and WLm(X){\rm WL}_m(X) the coloring of the Cartesian mm-power Ωm\Omega^m, obtained by the mm-dimensional Weisfeiler-Leman algorithm. The WL{\rm WL}-dimension of the graph XX is defined to be the smallest mm for which the coloring WLm(X){\rm WL}_m(X) determines XX up to isomorphism. It is known that the WL{\rm WL}-dimension of any planar graph is 22 or 33, but no planar graph of WL{\rm WL}-dimension 33 is known. We prove that the WL{\rm WL}-dimension of a polyhedral (i.e., 33-connected planar) graph XX is at most 22 if the color classes of the coloring WL2(X){\rm WL}_2(X) are the orbits of the componentwise action of the group Aut(X){\rm Aut}(X) on Ω2\Omega^2

    Learning with relational knowledge in the context of cognition, quantum computing, and causality

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    Pacific Symposium on Biocomputing 2023

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    The Pacific Symposium on Biocomputing (PSB) 2023 is an international, multidisciplinary conference for the presentation and discussion of current research in the theory and application of computational methods in problems of biological significance. Presentations are rigorously peer reviewed and are published in an archival proceedings volume. PSB 2023 will be held on January 3-7, 2023 in Kohala Coast, Hawaii. Tutorials and workshops will be offered prior to the start of the conference.PSB 2023 will bring together top researchers from the US, the Asian Pacific nations, and around the world to exchange research results and address open issues in all aspects of computational biology. It is a forum for the presentation of work in databases, algorithms, interfaces, visualization, modeling, and other computational methods, as applied to biological problems, with emphasis on applications in data-rich areas of molecular biology.The PSB has been designed to be responsive to the need for critical mass in sub-disciplines within biocomputing. For that reason, it is the only meeting whose sessions are defined dynamically each year in response to specific proposals. PSB sessions are organized by leaders of research in biocomputing's 'hot topics.' In this way, the meeting provides an early forum for serious examination of emerging methods and approaches in this rapidly changing field
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