Inflations of ideal triangulations

Starting with an ideal triangulation of the interior of a compact 3-manifold M with boundary, no component of which is a 2-sphere, we provide a construction, called an inflation of the ideal triangulation, to obtain a strongly related triangulations of M itself. Besides a step-by-step algorithm for such a construction, we provide examples of an inflation of the two-tetrahedra ideal triangulation of the complement of the figure-eight knot in the 3-sphere, giving a minimal triangulation, having ten tetrahedra, of the figure-eight knot exterior. As another example, we provide an inflation of the one-tetrahedron Gieseking manifold giving a minimal triangulation, having seven tetrahedra, of a nonorientable compact 3-manifold with Klein bottle boundary. Several applications of inflations are discussed.Comment: 48 pages, 45 figure

Tight contact structures and taut foliations

We show the equivalence of several notions in the theory of taut foliations and the theory of tight contact structures. We prove equivalence, in certain cases, of existence of tight contact structures and taut foliations.Comment: Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper7.abs.htm

Streamwise turbulence modulation in non-uniform open-channel clay suspension flows

Cohesive sediment particles are ubiquitous in environmental flows. The cohesive properties of clay promote the formation of clay flocs and gels and relatively small suspended clay concentrations can enhance or suppress turbulence in a flow. Furthermore, flows are naturally non-uniform, varying in space and time, yet the dynamics of non-uniform open-channel clay suspension flows is poorly understood. For the first time, the adaptation time and length scales of non-uniform clay suspension flows were quantified using novel experiments with spatially varying but temporally uniform flow. Different levels of turbulence enhancement and attenuation were identified as the flow decelerates or accelerates. Results highlight that decelerating clay suspension flows crucially have a longer adaptation time than accelerating clay suspension flows. This is explained by the longer timescale required for the formation of bonds between cohesive particles in turbulence attenuated flows after deceleration than the rapid breakdown of bonds in turbulent flows after acceleration of clay suspension flows. This hysteresis is more pronounced for higher concentration decelerating flows that pass through a larger variety of clay flow types of turbulence enhancement and attenuation. These different adaptation time scales and associated clay flow type transitions are likely to affect clay flow dynamics in a variety of fluvial and submarine settings

Dynamics and Deposition of Sediment-Bearing Multi- Pulsed Flows and Geological Implication

Copyright © 2019, SEPM (Society for Sedimentary Geology) Previous studies on dilute, multi-pulsed, subaqueous saline flows have demonstrated that pulses will inevitably advect forwards to merge with the flow front. On the assumption that pulse merging occurs in natural-scale turbidity currents, it was suggested that multi-pulsed turbidites that display vertical cycles of coarsening and fining would transition laterally to single-pulsed, normally graded turbidites beyond the point of pulse merging. In this study, experiments of dilute, single- and multi-pulsed sediment-bearing flows (turbidity currents) are conducted to test the linkages between downstream flow evolution and associated deposit structure. Experimental data confirm that pulse merging occurs in laboratory-scale turbidity currents. However, only a weak correspondence was seen between longitudinal variations in the internal flow dynamics and the vertical structure of deposits; multi-pulsed deposits were documented, but transitioned to single-pulsed deposits before the pulse merging point. This early transition is attributed to rapid sedimentation-related depletion of the coarser-grained suspended fraction in the laboratory setting, whose absence may have prevented the distal development of multi-pulsed deposits; this factor complicates estimation of the transition point in natural-scale turbidite systems

Dynamics and deposition of sediment-bearing multi-pulsed flows and geological implication

Previous studies on dilute, multi-pulsed, subaqueous saline flows have demonstrated that pulses will inevitably advect forwards to merge with the flow front. On the assumption that pulse merging occurs in natural-scale turbidity currents, it was suggested that multi-pulsed turbidites that display vertical cycles of coarsening and fining would transition laterally to single-pulsed, normally graded turbidites beyond the point of pulse merging. In this study, experiments of dilute, single- and multi-pulsed sediment-bearing flows (turbidity currents) are conducted to test the linkages between downstream flow evolution and associated deposit structure. Experimental data confirm that pulse merging occurs in laboratory-scale turbidity currents. However, only a weak correspondence was seen between longitudinal variations in the internal flow dynamics and the vertical structure of deposits; multi-pulsed deposits were documented, but transitioned to single-pulsed deposits before the pulse merging point. This early transition is attributed to rapid sedimentation-related depletion of the coarser-grained suspended fraction in the laboratory setting, whose absence may have prevented the distal development of multi-pulsed deposits; this factor complicates estimation of the transition point in natural-scale turbidite systems

Mathematicians’ Central Role in Educating the STEM Workforce

In the recent report Engage to Excel,1 President Obama’s Council of Advisors on Science and Technology (PCAST) identifies mathematics as a bottleneck in undergraduate Science, Technology, Engineering, and Mathematics (STEM) education. Among PCAST’s recommendations are ones calling for the development and teaching of college-level mathematics courses “by faculty from mathematics-intensive disciplines other than mathematics” and for “a new pathway for producing K–12 mathematics teachers…in programs in mathematics-intensive fields other than mathematics.”2 While we are in sharp disagreement with these specific recommendations, we do share PCAST’s concern for the state of STEM education. We encourage the mathematics community to focus constructively on the broad view the report sketches. We appeal to the community to amplify its communications with other STEM disciplines, to publicize its teaching innovations, and to redouble its efforts to meet the challenges discussed by PCAST

Efficient Parallel Statistical Model Checking of Biochemical Networks

We consider the problem of verifying stochastic models of biochemical networks against behavioral properties expressed in temporal logic terms. Exact probabilistic verification approaches such as, for example, CSL/PCTL model checking, are undermined by a huge computational demand which rule them out for most real case studies. Less demanding approaches, such as statistical model checking, estimate the likelihood that a property is satisfied by sampling executions out of the stochastic model. We propose a methodology for efficiently estimating the likelihood that a LTL property P holds of a stochastic model of a biochemical network. As with other statistical verification techniques, the methodology we propose uses a stochastic simulation algorithm for generating execution samples, however there are three key aspects that improve the efficiency: first, the sample generation is driven by on-the-fly verification of P which results in optimal overall simulation time. Second, the confidence interval estimation for the probability of P to hold is based on an efficient variant of the Wilson method which ensures a faster convergence. Third, the whole methodology is designed according to a parallel fashion and a prototype software tool has been implemented that performs the sampling/verification process in parallel over an HPC architecture

Eclipses During the 2010 Eruption of the Recurrent Nova U Scorpii

The eruption of the recurrent nova U Scorpii on 28 January 2010 is now the all-time best observed nova event. We report 36,776 magnitudes throughout its 67 day eruption, for an average of one measure every 2.6 minutes. This unique and unprecedented coverage is the first time that a nova has any substantial amount of fast photometry. With this, two new phenomena have been discovered: the fast flares in the early light curve seen from days 9-15 (which have no proposed explanation) and the optical dips seen out of eclipse from days 41-61 (likely caused by raised rims of the accretion disk occulting the bright inner regions of the disk as seen over specific orbital phases). The expanding shell and wind cleared enough from days 12-15 so that the inner binary system became visible, resulting in the sudden onset of eclipses and the turn-on of the supersoft X-ray source. On day 15, a strong asymmetry in the out-of-eclipse light points to the existence of the accretion stream. The normal optical flickering restarts on day 24.5. For days 15-26, eclipse mapping shows that the optical source is spherically symmetric with a radius of 4.1 R_sun. For days 26-41, the optical light is coming from a rim-bright disk of radius 3.4 R_sun. For days 41-67, the optical source is a center-bright disk of radius 2.2 R_sun. Throughout the eruption, the colors remain essentially constant. We present 12 eclipse times during eruption plus five just after the eruption.Comment: ApJ in press. 60 pages, 17 figure

Uganda's experience in Ebola virus disease outbreak preparedness, 2018-2019.

BACKGROUND: Since the declaration of the 10th Ebola Virus Disease (EVD) outbreak in DRC on 1st Aug 2018, several neighboring countries have been developing and implementing preparedness efforts to prevent EVD cross-border transmission to enable timely detection, investigation, and response in the event of a confirmed EVD outbreak in the country. We describe Uganda's experience in EVD preparedness. RESULTS: On 4 August 2018, the Uganda Ministry of Health (MoH) activated the Public Health Emergency Operations Centre (PHEOC) and the National Task Force (NTF) for public health emergencies to plan, guide, and coordinate EVD preparedness in the country. The NTF selected an Incident Management Team (IMT), constituting a National Rapid Response Team (NRRT) that supported activation of the District Task Forces (DTFs) and District Rapid Response Teams (DRRTs) that jointly assessed levels of preparedness in 30 designated high-risk districts representing category 1 (20 districts) and category 2 (10 districts). The MoH, with technical guidance from the World Health Organisation (WHO), led EVD preparedness activities and worked together with other ministries and partner organisations to enhance community-based surveillance systems, develop and disseminate risk communication messages, engage communities, reinforce EVD screening and infection prevention measures at Points of Entry (PoEs) and in high-risk health facilities, construct and equip EVD isolation and treatment units, and establish coordination and procurement mechanisms. CONCLUSION: As of 31 May 2019, there was no confirmed case of EVD as Uganda has continued to make significant and verifiable progress in EVD preparedness. There is a need to sustain these efforts, not only in EVD preparedness but also across the entire spectrum of a multi-hazard framework. These efforts strengthen country capacity and compel the country to avail resources for preparedness and management of incidents at the source while effectively cutting costs of using a "fire-fighting" approach during public health emergencies