On Arrangements of Orthogonal Circles

In this paper, we study arrangements of orthogonal circles, that is, arrangements of circles where every pair of circles must either be disjoint or intersect at a right angle. Using geometric arguments, we show that such arrangements have only a linear number of faces. This implies that orthogonal circle intersection graphs have only a linear number of edges. When we restrict ourselves to orthogonal unit circles, the resulting class of intersection graphs is a subclass of penny graphs (that is, contact graphs of unit circles). We show that, similarly to penny graphs, it is NP-hard to recognize orthogonal unit circle intersection graphs.Comment: Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019

RNA-Seq Mapping and Detection of Gene Fusions with a Suffix Array Algorithm

High-throughput RNA sequencing enables quantification of transcripts (both known and novel), exon/exon junctions and fusions of exons from different genes. Discovery of gene fusions–particularly those expressed with low abundance– is a challenge with short- and medium-length sequencing reads. To address this challenge, we implemented an RNA-Seq mapping pipeline within the LifeScope software. We introduced new features including filter and junction mapping, annotation-aided pairing rescue and accurate mapping quality values. We combined this pipeline with a Suffix Array Spliced Read (SASR) aligner to detect chimeric transcripts. Performing paired-end RNA-Seq of the breast cancer cell line MCF-7 using the SOLiD system, we called 40 gene fusions among over 120,000 splicing junctions. We validated 36 of these 40 fusions with TaqMan assays, of which 25 were expressed in MCF-7 but not the Human Brain Reference. An intra-chromosomal gene fusion involving the estrogen receptor alpha gene ESR1, and another involving the RPS6KB1 (Ribosomal protein S6 kinase beta-1) were recurrently expressed in a number of breast tumor cell lines and a clinical tumor sample

Towards mesoporous Keggin-type polyoxometalates –systematic study on organic template removal

Here, we present systematic studies on the removal of the polymer template from inverse hexagonally ordered poly(butadiene-block-2-dimethylaminoethyl methacrylate)–phosphomolybdic acid (H3PMo12O40) nanocomposites. Highly ordered mesophases are obtained via an evaporation-induced self-assembly process. Different techniques are used to remove the organic template: direct calcination in air, a two-step heat treatment ((1) argon atmosphere and (2) oxidative atmosphere), and a combination of heat and plasma treatment. Our studies show that direct calcination in air and two-step heat treatment lead to a collapse of mesostructure before complete carbon removal is accomplished. In contrast, plasma etching of heat treated ultra-microtomed samples results in hexagonally ordered porous nanofilm

Direct synthesis of inverse hexagonally ordered diblock copolymer/polyoxometalate nanocomposite films

Nanostructured inverse hexagonal polyoxometalate composite films were cast directly from solution using poly(butadiene-block-2-(dimethylamino)ethyl methacrylate) (PB-b-PDMAEMA) diblock copolymers as structure directing agents for phosphomolybdic acid (H(3)[PMo(12)O(40)], H(3)PMo). H(3)PMo units are selectively incorporated into the PDMAEMA domains due to electrostatic interactions between protonated PDMAEMA and PMo(3-) anions. Long solvophilic PB chains stabilized the PDMAEMA/H(3)PMo aggregates in solution and reliably prevented macrophase separation. The choice of solvent is crucial. It appears that all three components, both blocks of the diblock copolymer as well as H(3)PMo, have to be soluble in the same solvent which turned out to be tetrahydrofuran, THF. Evaporation induced self-assembly resulted in highly ordered inverse hexagonal nanocomposite films as observed from transmission electron microscopy and small-angle X-ray scattering. This one-pot synthesis may represent a generally applicable strategy for integrating polyoxometalates into functional architectures and devices

Access to Ordered Porous Molybdenum Oxycarbide/Carbon Nanocomposites

Hexagonally ordered mesoporous molybdenum oxycarbide/carbon (MoC/C) nanocomposites were directly accessed by heat treatment of mesostructured poly(butadiene-block-2-vinylpyridine) (PB-b-P2VP) and molybdophosphoric acid. PB-b-P2VP serves as structure-directing agent and as carbon source. The high specific surface area obtained for the nanocomposites renders the materials interesting for potential applications, such as in the catalytic decomposition of NH3