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

Minimal surfaces and particles in 3-manifolds

We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit ``nice'' foliations and explicit metrics, and whether the space of these metrics has a simple description in terms of Teichm\"uller theory. In the hyperbolic settings both questions have positive answers for a certain subset of the quasi-Fuchsian manifolds: those containing a closed surface with principal curvatures at most 1. We show that this subset is parameterized by an open domain of the cotangent bundle of Teichm\"uller space. These results are extended to ``quasi-Fuchsian'' manifolds with conical singularities along infinite lines, known in the physics literature as ``massive, spin-less particles''. Things work better for globally hyperbolic anti-de Sitter manifolds: the parameterization by the cotangent of Teichm\"uller space works for all manifolds. There is another description of this moduli space as the product two copies of Teichm\"uller space due to Mess. Using the maximal surface description, we propose a new parameterization by two copies of Teichm\"uller space, alternative to that of Mess, and extend all the results to manifolds with conical singularities along time-like lines. Similar results are obtained for de Sitter or Minkowski manifolds. Finally, for all four settings, we show that the symplectic form on the moduli space of 3-manifolds that comes from parameterization by the cotangent bundle of Teichm\"uller space is the same as the 3-dimensional gravity one.Comment: 53 pages, no figure. v2: typos corrected and refs adde

Safety and Effectiveness of Pharmacologic Conversion of Atrial Fibrillation and Flutter: Results of Multicenter Trial. Part II: Assessment of Safety

Aim. We aimed to assess safety and effectiveness of class III antiarrhythmic drug Refralon for conversion of atrial fibrillation (AFib) and flutter (AFl) in post-registration trial and to compare data of primary center (National medical research center in cardiology) with data of other hospitals.Material and Methods. We performed retrospective cohort study in 727 patients (451 enrolled in primary center and 276 enrolled in other hospitals) admitted between June 24, 2014 and June 24, 2019. Refralon was administered for conversion of AFib and AFl in intense care units in escalating doses (10-30 micrograms/kg) intravenously.Results. Conversion of AFib and AFl into sinus rhythm was achieved in 53,6% after administration of 10 mcg/kg dose, in 73% after administration of 20 mcg/kg dose and in 91,6% after administration of Refralon in dose up to 30 mcg/kg. No mortality and no major adverse cardiac events registered in our study. Asystole >3.0 sec observed in 5% (35 of 727) of patients): in 5% (24 of 451) of patients enrolled in primary center and in 4% (11 of 276) of patients enrolled in other hospitals; 95% confidence interval (CI) [-0.09; 0.113]. Asystole> 5.0 s observed in 1.7% of patients who further required non-urgent implantation of a permanent pacemaker due to manifestations of sinus node dysfunction. Cardiac conduction disturbances (exclusively sinus bradycardia) were registered in 7% (53 of 727) patients: in 8% (37 of 451) of patients enrolled in primary center and in 6% (17 of 276) of patients enrolled in other hospitals; 95% CI: [-0.1; 0.15]. Only 0.14% of patients had symptomatic sinus bradycardia that resolved after atropine injection. Ventricular arrhythmias (exclusively Torsade de pointes tachycardia in excessive QT interval prolongation) were registered in 1.7% (12 of 727) patients: in 2% (9 of 451) of patients in primary center and in 1% (3 of 276) of patients of other hospitals; 95% CI: [-0.06; 0.08]. QTc interval prolongation to values >500 ms documented in 19% (138 of 727) of patients: in 21% (95 of 451) of patients in primary center and in 16% (43 of 276) of patients in other hospitals; 95% CI: [-0.13; 0.24].Conclusion: In post-registration multicenter trial Refralon demonstrated good safety profile in conversion of AFib and AFl. Potential risk of TdP tachycardia mandates precautions with the use of the drug. In other hospitals Refralon did not demonstrate lower safety than in primary medical center

Residual Finiteness Growths of Virtually Special Groups

Let $G$ be a virtually special group. Then the residual finiteness growth of $G$ is at most linear. This result cannot be found by embedding $G$ into a special linear group. Indeed, the special linear group $\text{SL}_k(\mathbb{Z})$, for $k > 2$, has residual finiteness growth $n^{k-1}$.Comment: Updated version contains minor changes incorporating referee comments/suggestions and a simplified proof of Lemma 4.

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

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)