{"arxiv_id":"1308.4264","incoming":{"papers":1,"sentences":1,"groups":[],"unlabelled_sentences":1},"outgoing":{"papers":5,"sentences":15,"groups":[{"kind":"extends","label":"Builds on","papers":1,"sentences":1,"quotes":[{"arxiv_id":"0906.0226","title":"Surprising spectra of PT-symmetric point interactions","url":"/paper/0906.0226","section":"Regular case","sentence":"Considering the same boundary conditions at the central vertex on the compact star graph with two edges one obtains that the operators is similar to a self-adjoint Laplacian for any self-adjoint boundary condition imposed at both endpoints simultaneously, in particular for Dirichlet boundary conditions as considered in [ref] .","intent_p":0.83,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1108.4946","title":"On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators","url":"/paper/1108.4946","section":"Riesz basis on compact graphs","sentence":"An alternative method how to derive other closed formulae for the metric operators $Θ$ was developed in [ref] and further employed in [ref] , where one can additionally find an explicit formula for the self-adjoint operator to which $-Δ(A,B)$ is similar.","intent_p":0.85,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":1,"sentences":3,"quotes":[{"arxiv_id":"0906.0226","title":"Surprising spectra of PT-symmetric point interactions","url":"/paper/0906.0226","section":"Irregular compact case","sentence":"This reproduces some of the result form [ref] .","intent_p":0.93,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1211.4143","title":"Maximal-quasi-accretive Laplacians on finite metric graphs","url":"/paper/1211.4143","section":"m-sectorial boundary conditions","sentence":"Furthermore, if $(A,B)$ does not admit such a parametrisation, then the numerical range of $-Δ(A,B)$ is entire $$, see [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":1,"sentences":1,"quotes":[{"arxiv_id":"math-ph/0603010","title":"The inverse scattering problem for metric graphs and the traveling salesman problem","url":"/paper/math-ph/0603010","section":"The Laplacian on finite metric graphs","sentence":"This intuitive picture is formalised here by recalling from [ref] some notation and basic definitions.","intent_p":0.95,"contests_p":null}]}],"unlabelled_sentences":8},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1308.4264"}}