Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra

We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good 3-orbifolds with planar singular locus and underlying manifold the 3-sphere. The volume bounds follow from techniques related to the proof of Thurston's Orbifold Theorem, Schl\"afli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.Comment: 36 pages, 19 figure

Six topics on inscribable polytopes

Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along the way we collect a list of (new and old) open questions.Comment: 11 page

Density of mechanisms within the flexibility window of zeolites

By treating idealized zeolite frameworks as periodic mechanical trusses, we show that the number of flexible folding mechanisms in zeolite frameworks is strongly peaked at the minimum density end of their flexibility window. 25 of the 197 known zeolite frameworks exhibit an extensive flexibility, where the number of unique mechanisms increases linearly with the volume when long wavelength mechanisms are included. Extensively flexible frameworks therefore have a maximum in configurational entropy, as large crystals, at their lowest density. Most real zeolites do not exhibit extensive flexibility, suggesting that surface and edge mechanisms are important, likely during the nucleation and growth stage. The prevalence of flexibility in real zeolites suggests that, in addition to low framework energy, it is an important criterion when searching large databases of hypothetical zeolites for potentially useful realizable structures.Comment: 11 pages, 3 figure

A discrete Laplace-Beltrami operator for simplicial surfaces

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called ``cotan formula'') except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic functions, discrete mean curvature, and discrete minimal surfaces. The definition of the discrete Laplace-Beltrami operator depends on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. While the existence is known, we prove the uniqueness. Using Rippa's Theorem we show that, as claimed, Musin's harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces.Comment: 18 pages, 6 vector graphics figures. v2: Section 2 on Delaunay triangulations of piecewise flat surfaces revised and expanded. References added. Some minor changes, typos corrected. v3: fixed inaccuracies in discussion of flip algorithm, corrected attributions, added references, some minor revision to improve expositio

Epigenetic Engineering of Ribosomal RNA Genes Enhances Protein Production

Selection of mammalian high-producer cell lines remains a major challenge for the biopharmaceutical manufacturing industry. Ribosomal RNA (rRNA) genes encode the major component of the ribosome but many rRNA gene copies are not transcribed [1]–[5] due to epigenetic silencing by the nucleolar remodelling complex (NoRC) [6], which may limit the cell's full production capacity. Here we show that the knockdown of TIP5, a subunit of NoRC, decreases the number of silent rRNA genes, upregulates rRNA transcription, enhances ribosome synthesis and increases production of recombinant proteins. However, general enhancement of rRNA transcription rate did not stimulate protein synthesis. Our data demonstrates that the number of transcriptionally competent rRNA genes limits efficient ribosome synthesis. Epigenetic engineering of ribosomal RNA genes offers new possibilities for improving biopharmaceutical manufacturing and provides novel insights into the complex regulatory network which governs the translation machinery in normal cellular processes as well as in pathological conditions like cancer

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

CR1 — a dispersed repeated element associated with the Cab-1 locus in tomato

Cab-1 is a complex genetic locus in tomato consisting of four clustered genes encoding chlorophyll a/b-binding polypeptide. Southern blot analysis of total tomato DNA with genomic clones corresponding to the Cab-1 locus has revealed the presence of a repetitive element in the 3 kb spacer regions between two of these genes. This repetitive element, named CR1, has been characterized via sequencing, genetic mapping and hybridization to related solanaceous species. Results indicate that there are as many as 30 copies of this element in the tomato genome and that most, if not all, are found at independent loci. Sites corresponding to 12 of the repeats have been located on different regions of chromosomes 2, 4, 5, 7, 10 and 11. A 1.6 kb Pst I- Eco RI fragment from the Cab-1 locus containing the element was sequenced and found to be 75% AT-rich. No open reading frames larger than 150 bp were detected. Several imperfect inverted repeats flanked by direct repeats could be found at the ends of the element. This arrangement is reminiscent of known transposons. Southern hybridization analysis indicates that multiple copies of CR1 exist in all species of the genus Lycopersicon as well as in Solanum lycopersicoides and S. tuberosum (potato), but not in eggplant, pepper, petunia, Datura or tobacco. Melt-off experiments indicate that members of the CR1 family in the tomato genome are more closely related to one another than to homologous members in the genomes of S. lycopersicoides or S. tuberosum , suggesting some type of concerted evolution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43418/1/11103_2004_Article_BF00014948.pd