A Sublinear Bound on the Page Number of Upward Planar Graphs

The page number of a directed acyclic graph G is the minimum k for which there is a topological ordering of G and a k-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ordering. We address the long-standing open problem asking for the largest page number among all upward planar graphs. We improve the best known lower bound to 5 and present the first asymptotic improvement over the trivial O(n) upper bound, where n denotes the number of vertices in G. Specifically, we first prove that the page number of every upward planar graph is bounded in terms of its width, as well as its height. We then combine both approaches to show that every n-vertex upward planar graph has page number $O(n^{2/3} \log(n)^{2/3})$

Directed Acyclic Outerplanar Graphs Have Constant Stack Number

The stack number of a directed acyclic graph $G$ is the minimum $k$ for which there is a topological ordering of $G$ and a $k$-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ordering. We prove that the stack number of directed acyclic outerplanar graphs is bounded by a constant, which gives a positive answer to a conjecture by Heath, Pemmaraju and Trenk [SIAM J. Computing, 1999]. As an immediate consequence, this shows that all upward outerplanar graphs have constant stack number, answering a question by Bhore et al. [GD 2021] and thereby making significant progress towards the problem for general upward planar graphs originating from Nowakowski and Parker [Order, 1989]. As our main tool we develop the novel technique of directed $H$-partitions, which might be of independent interest. We complement the bounded stack number for directed acyclic outerplanar graphs by constructing a family of directed acyclic 2-trees that have unbounded stack number, thereby refuting a conjecture by N\"ollenburg and Pupyrev [arXiv:2107.13658, 2021]

The product structure of squaregraphs

A squaregraph is a plane graph in which each internal face is a 4-cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a subgraph of the semistrong product of an outerplanar graph and a path. We generalise this result for infinite squaregraphs, and show that this is best possible in the sense that “outerplanar graph” cannot be replaced by “forest”

Mycoplasma non-coding RNA: identification of small RNAs and targets

Background: Bacterial non-coding RNAs act by base-pairing as regulatory elements in crucial biological processes. We performed the identification of trans-encoded small RNAs (sRNA) from the genomes of Mycoplama hyopneumoniae, Mycoplasma flocculare and Mycoplasma hyorhinis, which are Mycoplasma species that have been identified in the porcine respiratory system. Results: A total of 47, 15 and 11 putative sRNAs were predicted in M. hyopneumoniae, M. flocculare and M. hyorhinis, respectively. A comparative genomic analysis revealed the presence of species or lineage specific sRNA candidates. Furthermore, the expression profile of some M. hyopneumoniae sRNAs was determined by a reverse transcription amplification approach, in three different culture conditions. All tested sRNAs were transcribed in at least one condition. A detailed investigation revealed a differential expression profile for two M. hyopneumoniae sRNAs in response to oxidative and heat shock stress conditions, suggesting that their expression is influenced by environmental signals. Moreover, we analyzed sRNA-mRNA hybrids and accessed putative target genes for the novel sRNA candidates. The majority of the sRNAs showed interaction with multiple target genes, some of which could be linked to pathogenesis and cell homeostasis activity. Conclusion: This study contributes to our knowledge of Mycoplasma sRNAs and their response to environmental changes. Furthermore, the mRNA target prediction provides a perspective for the characterization and comprehension of the function of the sRNA regulatory mechanisms

Complete response to gemtuzumab ozogamicin in a patient with refractory mast cell leukemia

Mast cell (MC) leukemia (MCL) is a subtype of systemic mastocytosis (SM) defined by the World Health Organization as ⩾ 20% of MCs in the bone marrow (BM) aspirate, with (leukemic variant) or without (aleukemic variant) ⩾ 10% of MCs in peripheral blood (PB). The European/American Consensus Group on Mastocytosis has recently proposed a new subclassification of MCL that distinguishes acute vs chronic MCL based on the presence vs absence of organ damage, respectively.Peer Reviewe

The GEF Trio controls endothelial cell size and arterial remodeling downstream of Vegf signaling in both zebrafish and cell models

Arterial networks enlarge in response to increase in tissue metabolism to facilitate flow and nutrient delivery. Typically, the transition of a growing artery with a small diameter into a large caliber artery with a sizeable diameter occurs upon the blood flow driven change in number and shape of endothelial cells lining the arterial lumen. Here, using zebrafish embryos and endothelial cell models, we describe an alternative, flow independent model, involving enlargement of arterial endothelial cells, which results in the formation of large diameter arteries. Endothelial enlargement requires the GEF1 domain of the guanine nucleotide exchange factor Trio and activation of Rho-GTPases Rac1 and RhoG in the cell periphery, inducing F-actin cytoskeleton remodeling, myosin based tension at junction regions and focal adhesions. Activation of Trio in developing arteries in vivo involves precise titration of the Vegf signaling strength in the arterial wall, which is controlled by the soluble Vegf receptor Flt1. Arterial flow regulates artery diameter but other mechanisms may also affect this. Here, the authors show that the guanine nucleotide exchange factor Trio and GTPases Rac1 and RhoG, triggers F-actin remodeling in arterial endothelial cells, independent of flow, to enhance lumen diameter in zebrafish and cell models.Peer reviewe