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Bae, Sang Won,Baffier, Jean-Francois,Chun, Jinhee,Eades, Peter,Eickmeyer, Kord,Grilli, Luca,Hong, Seok-Hee,Korman, Matias,Montecchiani, Fabrizio,Rutter, Ignaz,Tó,th, Csaba D. Elsevier 2018 Theoretical computer science Vol.745 No.-
<P><B>Abstract</B></P> <P>We introduce the family of <I>k-gap-planar graphs</I> for k ≥ 0 , i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most <I>k</I> of its crossings. This definition is motivated by applications in edge casing, as a <I>k</I>-gap-planar graph can be drawn crossing-free after introducing at most <I>k</I> local gaps per edge. We present results on the maximum density of <I>k</I>-gap-planar graphs, their relationship to other classes of beyond-planar graphs, characterization of <I>k</I>-gap-planar complete graphs, and the computational complexity of recognizing <I>k</I>-gap-planar graphs.</P>
Moresco Giada,Rondinone Ornella,Mauri Alessia,Costanza Jole,Santaniello Carlo,Colapietro Patrizia,Micaglio Emanuele,Marfia Giovanni,Pesenti Chiara,Grilli Federico,Rinaldi Berardo,Prada Elisabetta,Scuv 한국유전학회 2023 Genes & Genomics Vol.45 No.5
Background Whole-Exome Sequencing (WES) is a valuable tool for the molecular diagnosis of patients with a suspected genetic condition. In complex and heterogeneous diseases, the interpretation of WES variants is more challenging given the absence of diagnostic handles and other reported cases with overlapping clinical presentations. Objective To describe candidate variants emerging from trio-WES and possibly associated with the clinical phenotype in clinically heterogeneous conditions. Methods We performed WES in ten patients from eight families, selected because of the lack of a clear clinical diagnosis or suspicion, the presence of multiple clinical signs, and the negative results of traditional genetic tests. Results Although we identified ten candidate variants, reaching the diagnosis of these cases is challenging, given the complexity and the rarity of these syndromes and because affected genes are already associated with known genetic diseases only partially recapitulating patients’ phenotypes. However, the identification of these variants could shed light into the definition of new genotype–phenotype correlations. Here, we describe the clinical and molecular data of these cases with the aim of favoring the match with other similar cases and, hopefully, confirm our diagnostic hypotheses. Conclusion This study emphasizes the major limitations associated with WES data interpretation, but also highlights its clinical utility in unraveling novel genotype–phenotype correlations in complex and heterogeneous undefined clinical conditions with a suspected genetic etiology.