The Frobenius number in the set of numerical semigroups with fixed multiplicity and genus

Electronic version of an article published as International Journal of Number Theory, 2017, Vol. 13, No. 04 : pp. 1003-1011 https://doi.org/10.1142/S1793042117500531 © copyright World Scientific Publishing Company http://www.worldscientific.com/We compute all possible numbers that are the Frobenius number of a numerical semigroup when multiplicity and genus are fixed. Moreover, we construct explicitly numerical semigroups in each case.Both authors are supported by the project MTM2014-55367-P, which is funded by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER, and by the Junta de Andalucía Grant Number FQM-343. The second author is also partially supported by Junta de Andalucía/Feder Grant Number FQM-5849

The Airborne Cloud-Aerosol Transport System

The Airborne Cloud-Aerosol Transport System (ACATS) is a multi-channel Doppler lidar system recently developed at NASA Goddard Space Flight Center (GSFC). A unique aspect of the multi-channel Doppler lidar concept such as ACATS is that it is also, by its very nature, a high spectral resolution lidar (HSRL). Both the particulate and molecular scattered signal can be directly and unambiguously measured, allowing for direct retrievals of particulate extinction. ACATS is therefore capable of simultaneously resolving the backscatterextinction properties and motion of a particle from a high altitude aircraft. ACATS has flown on the NASA ER-2 during test flights over California in June 2012 and science flights during the Wallops Airborne Vegetation Experiment (WAVE) in September 2012. This paper provides an overview of the ACATS method and instrument design, describes the ACATS retrieval algorithms for cloud and aerosol properties, and demonstrates the data products that will be derived from the ACATS data using initial results from the WAVE project. The HSRL retrieval algorithms developed for ACATS have direct application to future spaceborne missions such as the Cloud-Aerosol Transport System (CATS) to be installed on the International Space Station (ISS). Furthermore, the direct extinction and particle wind velocity retrieved from the ACATS data can be used for science applications such 27 as dust or smoke transport and convective outflow in anvil cirrus clouds

Validation of the cardiovascular risk model NORRISK 2 in South Asians and people with diabetes

To evaluate the predictive ability of the previously published NORRISK 2 cardiovascular risk model in Norwegian-born and immigrants born in South Asia living in Norway, and to add information about diabetes and ethnicity in an updated model for South Asians and diabetics (NORRISK 2-SADia). Design. We included participants (30–74 years) born in Norway (n = 13,885) or South Asia (n = 1942) from health surveys conducted in Oslo 2000–2003. Cardiovascular disease (CVD) risk factor information including self-reported diabetes was linked with information on subsequent acute myocardial infarction (AMI) and acute cerebral stroke in hospital and mortality registry data throughout 2014 from the nationwide CVDNOR project. We developed an updated model using Cox regression with diabetes and South Asian ethnicity as additional predictors. We assessed model performance by Harrell’s C and calibration plots. Results. The NORRISK 2 model underestimated the risk in South Asians in all quintiles of predicted risk. The mean predicted 13-year risk by the NORRISK 2 model was 3.9% (95% CI 3.7–4.2) versus observed 7.3% (95% CI 5.9–9.1) in South Asian men and 1.1% (95% CI 1.0–1.2) versus 2.7% (95% CI 1.7–4.2) observed risk in South Asian women. The mean predictions from the NORRISK 2-SADia model were 7.2% (95% CI 6.7–7.6) in South Asian men and 2.7% (95% CI 2.4–3.0) in South Asian women. Conclusions. The NORRISK 2-SADia model improved predictions of CVD substantially in South Asians, whose risks were underestimated by the NORRISK 2 model. The NORRISK 2-SADia model may facilitate more intense preventive measures in this high-risk population.publishedVersio

Validation of the cardiovascular risk model NORRISK 2 in South Asians and people with diabetes

Objectives To evaluate the predictive ability of the previously published NORRISK 2 cardiovascular risk model in Norwegian-born and immigrants born in South Asia living in Norway, and to add information about diabetes and ethnicity in an updated model for South Asians and diabetics (NORRISK 2-SADia). Design. We included participants (30–74 years) born in Norway (n = 13,885) or South Asia (n = 1942) from health surveys conducted in Oslo 2000–2003. Cardiovascular disease (CVD) risk factor information including self-reported diabetes was linked with information on subsequent acute myocardial infarction (AMI) and acute cerebral stroke in hospital and mortality registry data throughout 2014 from the nationwide CVDNOR project. We developed an updated model using Cox regression with diabetes and South Asian ethnicity as additional predictors. We assessed model performance by Harrell’s C and calibration plots. Results. The NORRISK 2 model underestimated the risk in South Asians in all quintiles of predicted risk. The mean predicted 13-year risk by the NORRISK 2 model was 3.9% (95% CI 3.7–4.2) versus observed 7.3% (95% CI 5.9–9.1) in South Asian men and 1.1% (95% CI 1.0–1.2) versus 2.7% (95% CI 1.7–4.2) observed risk in South Asian women. The mean predictions from the NORRISK 2-SADia model were 7.2% (95% CI 6.7–7.6) in South Asian men and 2.7% (95% CI 2.4–3.0) in South Asian women. Conclusions. The NORRISK 2-SADia model improved predictions of CVD substantially in South Asians, whose risks were underestimated by the NORRISK 2 model. The NORRISK 2-SADia model may facilitate more intense preventive measures in this high-risk population.publishedVersio

CATS Near Real Time Data Products: Applications for Assimilation Into the NASA GEOS-5 AGCM

From February 2015 through October 2017, the NASA Cloud-Aerosol Transport System (CATS) backscatter lidar operated on the International Space Station (ISS) as a technology demonstration for future Earth Science Missions, providing vertical measurements of cloud and aerosols properties. Owing to its location on the ISS, a cornerstone technology demonstration of CATS was the capability to acquire, process, and disseminate near-real time (NRT) data within 6 hours of observation time. CATS NRT data has several applications, including providing notification of hazardous events for air traffic control and air quality advisories, field campaign flight planning, as well as for constraining cloud and aerosol distributions in via data assimilation in aerosol transport models. Recent developments in aerosol data assimilation techniques have permitted the assimilation of aerosol optical thickness (AOT), a 2-dimensional column integrated quantity that is reflective of the simulated aerosol loading in aerosol transport models. While this capability has greatly improved simulated AOT forecasts, the vertical position, a key control on aerosol transport, is often not impacted when 2-D AOT is assimilated. Here, we present preliminary efforts to assimilate CATS aerosol observations into the NASA Goddard Earth Observing System version 5 (GEOS-5) atmospheric general circulation model and assimilation system using a 1-D Variational (1-D VAR) ensemble approach, demonstrating the utility of CATS for future Earth Science Missions

CATS Version 2 Aerosol Feature Detection and Applications for Data Assimilation

The Cloud Aerosol Transport System (CATS) lidar has been operating onboard the International Space Station (ISS) since February 2015 and provides vertical observations of clouds and aerosols using total attenuated backscatter and depolarization measurements. From February March 2015, CATS operated in Mode 1, providing backscatter and depolarization measurements at 532 and 1064 nm. CATS began operation in Mode 2 in March 2015, providing backscatter and depolarization measurements at 1064 nm and has continued to operate to the present in this mode. CATS level 2 products are derived from these measurements, including feature detection, cloud aerosol discrimination, cloud and aerosol typing, and optical properties of cloud and aerosol layers. Here, we present changes to our level 2 algorithms, which were aimed at reducing several biases in our version 1 level 2 data products. These changes will be incorporated into our upcoming version 2 level 2 data release in summer 2017. Additionally, owing to the near real time (NRT) data downlinking capabilities of the ISS, CATS provides expedited NRT data products within 6 hours of observation time. This capability provides a unique opportunity for supporting field campaigns and for developing data assimilation techniques to improve simulated cloud and aerosol vertical distributions in models. We additionally present preliminary work toward assimilating CATS observations into the NASA Goddard Earth Observing System version 5 (GEOS-5) global atmospheric model and data assimilation system

Prevalence and incidence rates of atrial fibrillation in Norway 2004-2014

Objective: To study time trends in incidence of atrial fibrillation (AF) in the entire Norwegian population from 2004 to 2014, by age and sex, and to estimate the prevalence of AF at the end of the study period. Methods: A national cohort of patients with AF (≥18 years) was identified from inpatient admissions with AF and deaths with AF as underlying cause (1994–2014), and AF outpatient visits (2008–2014) in the Cardiovascular Disease in Norway (CVDNOR) project. AF admissions or out-of-hospital death from AF, with no AF admission the previous 10 years defined incident AF. Age-standardised incidence rates (IR) and incidence rate ratios (IRR) were calculated. All AF cases identified through inpatient admissions and outpatient visits and alive as of 31 December 2014 defined AF prevalence. Results: We identified 175 979 incident AF cases (30% primary diagnosis, 69% secondary diagnosis, 0.6% out-of-hospital deaths). AF IRs (95% confidence intervals) per 100 000 person years were stable from 2004 (433 (426–440)) to 2014 (440 (433–447)). IRs were stable or declining across strata of sex and age with the exception of an average yearly increase of 2.4% in 18–44 year-olds: IRR 1.024 (1.014–1.034). In 2014, the prevalence of AF in the adult population was 3.4%. Conclusions: We found overall stable IRs of AF for the adult Norwegian population from 2004 to 2014. The prevalence of AF was 3.4% at the end of 2014, which is higher than reported in previous studies. Signs of an increasing incidence of early-onset AF (<45 years) are worrying and need further investigation.publishedVersio

Cloud-Aerosol Transport System (CATS) 1064 nm calibration and validation

The Cloud-Aerosol Transport System (CATS) lidar on board the International Space Station (ISS) operated from 10 February 2015 to 30 October 2017 providing range-resolved vertical backscatter profiles of Earth's atmosphere at 1064 and 532 nm. The CATS instrument design and ISS orbit lead to a higher 1064 nm signal-to-noise ratio than previous space-based lidars, allowing for direct atmospheric calibration of the 1064 nm signals. Nighttime CATS version 3-00 data were calibrated by scaling the measured data to a model of the expected atmospheric backscatter between 22 and 26 km a.m.s.l. (above mean sea level). The CATS atmospheric model is constructed using molecular backscatter profiles derived from Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) reanalysis data and aerosol scattering ratios measured by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP). The nighttime normalization altitude region was chosen to simultaneously minimize aerosol loading and variability within the CATS data frame, which extends from 28 to −2 km a.m.s.l. Daytime CATS version 3-00 data were calibrated through comparisons with nighttime measurements of the layer-integrated attenuated total backscatter (iATB) from strongly scattering, rapidly attenuating opaque cirrus clouds. The CATS nighttime 1064 nm attenuated total backscatter (ATB) uncertainties for clouds and aerosols are primarily related to the uncertainties in the CATS nighttime calibration technique, which are estimated to be ∼9  %. Median CATS V3-00 1064 nm ATB relative uncertainty at night within cloud and aerosol layers is 7 %, slightly lower than these calibration uncertainty estimates. CATS median daytime 1064 nm ATB relative uncertainty is 21 % in cloud and aerosol layers, similar to the estimated 16 %–18 % uncertainty in the CATS daytime cirrus cloud calibration transfer technique. Coincident daytime comparisons between CATS and the Cloud Physics Lidar (CPL) during the CATS-CALIPSO Airborne Validation Experiment (CCAVE) project show good agreement in mean ATB profiles for clear-air regions. Eight nighttime comparisons between CATS and the PollyXT ground-based lidars also show good agreement in clear-air regions between 3 and 12 km, with CATS having a mean ATB of 19.7 % lower than PollyXT. Agreement between the two instruments (∼7 %) is even better within an aerosol layer. Six-month comparisons of nighttime ATB values between CATS and CALIOP also show that iATB comparisons of opaque cirrus clouds agree to within 19 %. Overall, CATS has demonstrated that direct calibration of the 1064 nm channel is possible from a space-based lidar using the atmospheric normalization technique

Association of prenatal exposure to benzodiazepines and child internalizing problems: A sibling-controlled cohort study

Background: During pregnancy, many women experience sleep problems and anxiety that require treatment. The long-term safety for the child of maternal benzodiazepine (BZD) and z-hypnotic use during pregnancy remains controversial. Method We conducted a cohort and a sibling control study using data from the Norwegian Mother and Child Cohort Study. Data on use of BZD and z-hypnotics, internalizing and externalizing outcomes, and covariates were collected from mothers at gestational weeks 17 and 30 and when children were 0.5, 1.5, and 3 years of age. The total sample consisted of 71,996 children (19,297 siblings) at 1.5 years and 55,081 children (13,779 siblings) at 3 years. Short-term use was defined as use in one pregnancy period only. Long-term use was defined as use in two or more pregnancy periods. Linear full cohort random-effect and sibling-matched fixed-effect regression models were used to compare internalizing and externalizing behavior in children prenatally exposed compared to those unexposed in the full cohort of pregnancies accounting for family clusters, as well as within sibling clusters comparing pregnancies with discordant exposures. Propensity score (PS) adjustment included variables on indication for use (sleep problems, symptoms of anxiety and depression) and other potential confounding factors. Results: Long-term prenatal exposure to BZD or z-hypnotics was associated with increased internalizing behavior in crude cohort analyses and at age 1.5 years after PS adjustment in sibling-matched fixed-effect models [β 0.60, 95% confidence interval 0.17–0.95]. Analyses on specific drug groups showed that prenatal exposure to BZD-anxiolytics was associated with increased internalizing problems at both 1.5 years [β 0.25, 0.01–0.49] and 3 years [β 0.26, 0.002–0.52] while exposure to z-hypnotics was not associated with any adverse outcomes after adjustment. Conclusion: The findings suggest a moderate association between BZD-anxiolytic exposure and child internalizing problems that is not likely due to stable familial confounding factors