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

Vibration absorbers for chatter suppression: A new analytical tuning methodology

Vibration absorbers have been widely used to suppress undesirable vibrations in machining operations, with a particular emphasis on avoiding chatter. However, it is well known that for vibration absorbers to function effectively their stiffness and damping must be accurately tuned based upon the natural frequency of the vibrating structure. For general vibration problems, suitable tuning strategies were developed by Den Hartog and Brock over 50 years ago. However, the special nature of the chatter stability problem means that this classical tuning methodology is no longer optimal. Consequently, vibration absorbers for chatter mitigation have generally been tuned using ad hoc methods, or numerical or graphical approaches. The present article introduces a new analytical solution to this problem, and demonstrates its performance using time domain milling simulations. A 40-50% improvement in the critical limiting depth of cut is observed, compared to the classically tuned vibration absorber. © 2006 Elsevier Ltd. All rights reserved

Eigenvectors of the discrete Laplacian on regular graphs - a statistical approach

In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical observations, suggesting that the eigenvectors follow a Gaussian distribution. Following this assumption, we reconstruct some properties of the nodal structure which were observed in numerical simulations, but were not explained so far. We also show that some statistical properties of the nodal pattern cannot be described in terms of a percolation model, as opposed to the suggested correspondence for eigenvectors of 2 dimensional manifolds.Comment: 28 pages, 11 figure

Enhancement of wave damping within metamaterials having embedded negative stiffness inclusions

The wave dissipation properties of layered periodic structures are modelled by FE as well as analytical approaches. A linear oscillator incorporating a negative stiffness element and having exceptional energy dissipation properties is exhibited and incorporated within the modelled structures. The structural dynamic stability of both the oscillator and the modelled waveguides is discussed and ensured. The numerical results provide evidence of a drastic increase of several orders of magnitude for the damping ratio of the flexural waves propagating within the structures

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

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

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)