Hierarchies and semistability of relatively hyperbolic groups

A finitely presented group is semistable if all proper rays in the Cayley 2-complex are properly homotopic. A long standing open question asks whether all finitely presented groups are semistable. In this article, we prove semistability of groups that are hyperbolic relative to polycyclic subgroups. Key tools in the proof are a result of Mihalik-Swenson on semistability of `atomic' relatively hyperbolic groups, a combination theorem of Mihalik-Tschantz, and a hierarchical accessibility theorem of Louder-Touikan. We analyze an example that illustrates why an understanding of hierarchies is necessary for the proof of semistability in this context.Comment: 10 pages, 2 figure

Calculating and Using Second Order Accurate Solutions of Discrete Time Dynamic Equilibrium Models

We describe an algorithm for calculating second order approximations to the solutions to nonlinear stochastic rational expectations models. The paper also explains methods for using such an approximate solution to generate forecasts, simulated time paths for the model, and evaluations of expected welfare differences across different versions of a model. The paper gives conditions for local validity of the approximation that allow for disturbance distributions with unbounded support and allow for non-stationarity of the solution process.

Electromagnetic Compatibility Considerations for International Space Station Payload Developers

The International Space Station (ISS) is a laboratory for scientific research, innovative technology development, and global education. The ISS provides a number of facilities and platforms for payload developers and investigators to conduct biological, microgravity, and Earth and space observation science, as well as for performing technology development. Due to the unique nature of the ISS vehicle and its electrical power and data systems, achieving electromagnetic compatibility (EMC) with the vehicle requires special considerations by the payload developer. The ISS electromagnetic interference (EMI) requirements and test methods are based on MIL-STD-461, Electromagnetic Emissions and Susceptibility Requirements for the Control of Electromagnetic Interference, Revision C, and MIL-STD-462, Electromagnetic Interference Characteristics, Measurement of, respectively. The low source impedance of the test setup requires special considerations when designing or selecting EMI power filters and switched mode power supplies. Many filters, suited for later revisions of MIL-STD-461, will result in non-compliant designs. ISS electrical power system power quality requirements, imposed to protect the stability of the system, can also affect EMI filter design. The selection and use of commercial-off-the-shelf (COTS) equipment for ISS applications requires special considerations to meet both EMC and crew safety requirements. Furthermore, the ISS environment can provide unique immunity challenges; if the payload developer ignores these challenges, the result is a possible loss of science or impact to technology demonstration. The ISS provides a unique opportunity for the science and technology development community. However, in order to be successful, the payload developer must incorporate special EMC considerations, many of which will be presented

Efficacy and safety of sodium zirconium cyclosilicate in patients with baseline serum potassium level ≥ 5.5 mmol/L: pooled analysis from two phase 3 trials.

BackgroundReliable, timely-onset, oral treatments with an acceptable safety profile for patients with hyperkalemia are needed. We examined the efficacy and safety of sodium zirconium cyclosilicate (SZC; formerly ZS-9) treatment for ≤ 48 h in patients with baseline serum potassium level ≥ 5.5 mmol/L.MethodsData were pooled from two phase 3 studies (ZS-003 and HARMONIZE) among patients receiving SZC 10 g three times daily. Outcomes included mean and absolute change from baseline, median time to potassium level ≤ 5.5 and ≤ 5.0 mmol/L, and proportion achieving potassium level ≤ 5.5 and ≤ 5.0 mmol/L at 4, 24, and 48 h. Outcomes were stratified by baseline potassium. Safety outcomes were evaluated.ResultsAt baseline, 125 of 170 patients (73.5%) had potassium level 5.5-< 6.0, 39 (22.9%) had potassium level 6.0-6.5, and 6 (3.5%) had potassium level > 6.5 mmol/L. Regardless of baseline potassium, mean potassium decreased at 1 h post-initial dose. By 4 and 48 h, 37.5% and 85.0% of patients achieved potassium level ≤ 5.0 mmol/L, respectively. Median (95% confidence interval) times to potassium level ≤ 5.5 and ≤ 5.0 mmol/L were 2.0 (1.1-2.0) and 21.6 (4.1-22.4) h, respectively. Fifteen patients (8.8%) experienced adverse events; none were serious.ConclusionsSZC 10 g three times daily achieved serum potassium reduction and normokalemia, with a favorable safety profile.Trial registrationClinicalTrials.gov identifiers: ZS-003: NCT01737697 and HARMONIZE: NCT02088073