Invariant Measures for Hybrid Stochastic Systems

In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as time-homogeneous Markov processes. In particular, we prove the existence of invariant measures for each embedded system and relate the invariant measures for the various systems through the flow. We calculate these invariant measures explicitly in several illustrative examples.Comment: 18 pages, 7 figure

A weekly Arctic sea-ice thickness data record from merged CryoSat-2 and SMOS satellite data

Sea-ice thickness on a global scale is derived from different satellite sensors using independent retrieval methods. Due to the sensor and orbit characteristics, such satellite retrievals differ in spatial and temporal resolution as well as in the sensitivity to certain sea-ice types and thickness ranges. Satellite altimeters, such as CryoSat-2 (CS2), sense the height of the ice surface above the sea level, which can be converted into sea-ice thickness. Relative uncertainties associated with this method are large over thin ice regimes. Another retrieval method is based on the evaluation of surface brightness temperature (TB) in L-band microwave frequencies (1.4 GHz) with a thickness-dependent emission model, as measured by the Soil Moisture and Ocean Salinity (SMOS) satellite. While the radiometer-based method looses sensitivity for thick sea ice (> 1 m), relative uncertainties over thin ice are significantly smaller than for the altimetry-based retrievals. In addition, the SMOS product provides global sea-ice coverage on a daily basis unlike the altimeter data. This study presents the first merged product of complementary weekly Arctic sea-ice thickness data records from the CS2 altimeter and SMOS radiometer. We use two merging approaches: a weighted mean (WM) and an optimal interpolation (OI) scheme. While the weighted mean leaves gaps between CS2 orbits, OI is used to produce weekly Arctic-wide sea-ice thickness fields. The benefit of the data merging is shown by a comparison with airborne electromagnetic (AEM) induction sounding measurements. When compared to airborne thickness data in the Barents Sea, the merged product has a root mean square deviation (RMSD) of about 0.7 m less than the CS2 product and therefore demonstrates the capability to enhance the CS2 product in thin ice regimes. However, in mixed first-year (FYI) and multiyear (MYI) ice regimes as in the Beaufort Sea, the CS2 retrieval shows the lowest bias

The 2017 Update of the German Clinical Guideline on Epidemiology, Diagnostics, Therapy, Prevention, and Management of Uncomplicated Urinary Tract Infections in Adult Patients. Part II: Therapy and Prevention

Background: We aimed to update the 2010 evidence- and consensus-based national clinical guideline on the diagnosis and management of uncomplicated urinary tract infections (UTIs) in adult patients. Results are published in 2 parts. Part 1 covers methods, the definition of patient groups, and diagnostics. This second publication focuses on treatment of acute episodes of cystitis and pyelonephritis as well as on prophylaxis of recurrent UTIs. Materials and Methods: An interdisciplinary group consisting of 17 representatives of 12 medical societies and a patient representative was formed. Systematic literature searches were conducted in MEDLINE, EMBASE, and the Cochrane Library to identify literature published in 2010–2015. Results: For the treatment of acute uncomplicated cystitis (AUC), fosfomycin-trometamol, nitrofurantoin, nitroxoline, pivmecillinam, and trimethoprim (depending on the local rate of resistance) are all equally recommended. Cotrimoxazole, fluoroquinolones, and cephalosporins are not recommended as antibiotics of first choice, for concern of an unfavorable impact on the microbiome. Mild to moderate uncomplicated pyelonephritis should be treated with oral cefpodoxime, ceftibuten, ciprofloxacin, or levofloxacin. For AUC with mild to moderate symptoms, instead of antibiotics symptomatic treatment alone may be considered depending on patient preference after discussing adverse events and outcomes. Primarily non-antibiotic options are recommended for prophylaxis of recurrent urinary tract infection. Conclusion: In accordance with the global antibiotic stewardship initiative and considering new insights in scientific research, we updated our German clinical UTI guideline to promote a responsible antibiotic use and to give clear hands-on recommendations for the diagnosis and management of UTIs in adults in Germany for healthcare providers and patients

The 2017 Update of the German Clinical Guideline on Epidemiology, Diagnostics, Therapy, Prevention, and Management of Uncomplicated Urinary Tract Infections in Adult Patients: Part 1

Objectives: We aimed to update the 2010 evidence- and consensus-based national clinical guideline on the diagnosis and management of uncomplicated urinary tract infections (UTIs) in adult patients. Materials and Methods: An interdisciplinary group consisting of 17 representatives of 12 medical societies and a patient representative was formed. Systematic literature searches were conducted in MEDLINE, ­EMBASE, and the Cochrane Library to identify literature published in 2010–2015. Results: We provide 75 recommendations and 68 statements in the updated evidence- and consensus-based national clinical guideline. The diagnostics part covers practical recommendations on cystitis and pyelonephritis for each defined patient group. Clinical examinations, as well as laboratory testing and microbiological pathogen assessment, are addressed. Conclusion: In accordance with the global antibiotic stewardship initiative and considering new insights in scientific research, we updated our German clinical UTI guideline to promote a responsible antibiotic use and to give clear hands-on recommendations for the diagnosis and management of UTIs in adults in Germany for healthcare providers and patients

Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate

The authors present inferences of diapycnal diffusivity from a compilation of over 5200 microstructure profiles. As microstructure observations are sparse, these are supplemented with indirect measurements of mixing obtained from (i) Thorpe-scale overturns from moored profilers, a finescale parameterization applied to (ii) shipboard observations of upper-ocean shear, (iii) strain as measured by profiling floats, and (iv) shear and strain from full-depth lowered acoustic Doppler current profilers (LADCP) and CTD profiles. Vertical profiles of the turbulent dissipation rate are bottom enhanced over rough topography and abrupt, isolated ridges. The geography of depth-integrated dissipation rate shows spatial variability related to internal wave generation, suggesting one direct energy pathway to turbulence. The global-averaged diapycnal diffusivity below 1000-m depth is O(10?4) m2 s?1 and above 1000-m depth is O(10?5) m2 s?1. The compiled microstructure observations sample a wide range of internal wave power inputs and topographic roughness, providing a dataset with which to estimate a representative global-averaged dissipation rate and diffusivity. However, there is strong regional variability in the ratio between local internal wave generation and local dissipation. In some regions, the depth-integrated dissipation rate is comparable to the estimated power input into the local internal wave field. In a few cases, more internal wave power is dissipated than locally generated, suggesting remote internal wave sources. However, at most locations the total power lost through turbulent dissipation is less than the input into the local internal wave field. This suggests dissipation elsewhere, such as continental margins

Climate Process Team on internal wave–driven ocean mixing

Author Posting. © American Meteorological Society, 2017. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 98 (2017): 2429-2454, doi:10.1175/BAMS-D-16-0030.1.Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatiotemporal patterns of mixing are largely driven by the geography of generation, propagation, and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (NOAA)-supported Climate Process Team has been engaged in developing, implementing, and testing dynamics-based parameterizations for internal wave–driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here, we review recent progress, describe the tools developed, and discuss future directions.We are grateful to U.S. CLIVAR for their leadership in instigating and facilitating the Climate Process Team program. We are indebted to NSF and NOAA for sponsoring the CPT series.2018-06-0

Climate Process Team on Internal-Wave Driven Ocean Mixing

Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean, and consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Climate models have been shown to be very sensitive not only to the overall level but to the detailed distribution of mixing; sub-grid-scale parameterizations based on accurate physical processes will allow model forecasts to evolve with a changing climate. Spatio-temporal patterns of mixing are largely driven by the geography of generation, propagation and destruction of internal waves, which are thought to supply much of the power for turbulent mixing. Over the last five years and under the auspices of US CLIVAR, a NSF and NOAA supported Climate Process Team has been engaged in developing, implementing and testing dynamics-base parameterizations for internal-wave driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here we review recent progress, describe the tools developed, and discuss future directions

Climate Process Team On Internal Wave-Driven Ocean Mixing

The study summarizes recent advances in our understanding of internal wave–driven turbulent mixing in the ocean interior and introduces new parameterizations for global climate ocean models and their climate impacts