Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

Defining the landscape of circular RNAs in neuroblastoma unveils a global suppressive function of MYCN

Circular RNAs (circRNAs) are a regulatory RNA class. While cancer-driving functions have been identified for single circRNAs, how they modulate gene expression in cancer is not well understood. We investigate circRNA expression in the pediatric malignancy, neuroblastoma, through deep whole-transcriptome sequencing in 104 primary neuroblastomas covering all risk groups. We demonstrate that MYCN amplification, which defines a subset of high-risk cases, causes globally suppressed circRNA biogenesis directly dependent on the DHX9 RNA helicase. We detect similar mechanisms in shaping circRNA expression in the pediatric cancer medulloblastoma implying a general MYCN effect. Comparisons to other cancers identify 25 circRNAs that are specifically upregulated in neuroblastoma, including circARID1A. Transcribed from the ARID1A tumor suppressor gene, circARID1A promotes cell growth and survival, mediated by direct interaction with the KHSRP RNA-binding protein. Our study highlights the importance of MYCN regulating circRNAs in cancer and identifies molecular mechanisms, which explain their contribution to neuroblastoma pathogenesis

Integratie van constructie en akoestiek bij het ontwerp van houten zwembadoverkappingen

Bij het constructieve ontwerp van zwembaden moet de akoestische beleving van de ruimte een belangrijk aandachtspunt zijn. In dit afstudeerproject is onderzocht in welke mate de dakconstructie zowel een constructieve als akoestische rol kan vervullen. Hierbij is de invloed van de dakconstructie op de "nagalmtijd" als belangrijkste akoestische parameter zowel met handberekeningen als een raytracing programma onderzocht. Het overkappingsprincipe dat op akoestisch en constructief gebied de meeste potentie heeft, is constructief verder uitgewerkt

Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph parameter thickness. By restricting the edges to be straight, we obtain the geometric thickness. By additionally restricting the vertices to be in convex position, we obtain the book thickness. This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth k, the maximum thickness and the maximum geometric thickness both equal ⌈k/2⌉. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth k, the maximum book thickness equals k if k ≤ 2 and equals k + 1 if k ≥ 3. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215–221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity