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ObjectivesTo determine whether data captured in electronic medical records (eMR) is sufficient to serve as a clinical data source to make a reliable determination of ST elevation myocardial infarction (STEMI) and non-ST elevation myocardial infarction (NSTEMI) and to use these eMR derived diagnoses to validate ICD-10 codes for STEMI and NSTEMI.DesignRetrospective validation by blind chart review of a purposive sample of patients with a troponin test result, ECG record, and medical note available in the eMR.SettingTwo local health districts containing two tertiary hospitals and six referral hospitals in New South Wales, Australia.ParticipantsN = 897 adult patients who had a hs-troponin test result indicating suspected AMI.Primary outcome measuresInter-rater reliability of clinical diagnosis (κ) for ST-elevated myocardial infarction (STEMI) and Non-ST elevated myocardial infarction (NSTEMI); and sensitivity, specificity, and positive predictive value (PPV) of ICD-10 codes for STEMI and NSTEMI.ResultsThe diagnostic agreement between clinical experts was high for STEMI (κ = 0.786) but lower for NSTEMI (κ = 0.548). ICD-10 STEMI codes had moderate sensitivity (Se = 88±6.7), very high specificity (Sp = 99±0.7) and high positive predictive value (PPV = 91±6). NSTEMI ICD-10 codes were lower in each case (Se = 69±6.4, Sp = 96.0±1.5, PPV = 84±6).ConclusionsThe eMR held sufficient clinical data to reliably diagnose STEMI, producing high inter-rater agreement among our expert reviewers as well as allowing reasonably precise estimates of the accuracy of administrative ICD-10 codes. However the clinical detail held in the eMR was less sufficient to diagnose NSTEMI, indicated by a lower inter-rater agreement. Efforts should be directed towards operationalising the clinical definition of NSTEMI and improving clinical record keeping to enable an accurate description of the clinical phenotype in the eMR, and thus improve reliability of the diagnosis of NSTEMI using these data sources.Article SummaryStrengths and limitations of this studyExpert chart review provided a robust evaluation of the reliability and sufficiency of data directly extracted from the EMR for the diagnosis of AMIComputational interrogation and extraction of the eMR (via SPEED-EXTRACT) allowed us to use a wide selection for inclusion in the sample on the basis of clinical data independent of ICD-10 code, enabling the capture of missed cases (i.e., uncoded AMI) and so determine estimates for the false negative rate and sensitivityResults were necessarily based on the subset of patients with sufficient clinical data in the eMR. Inferences from this subset to the wider patient pool will be biased when the availability of records varies with diagnosisAt least two sources of uncertainty in the gold reference standard we used are indistinguishable: uncertainty due to poor clinical detail in the eMR, and uncertainty due to a weak operational definition of the diagnosis (e.g., NSTEMI).

Laparoscopic cholecystectomy (LC) in complicated acute calculus cholecystitis (ACC) poses multiple challenges. This prospective, observational study assessed the utility and safety of a set protocol and intraoperative steps in LC for complex ACC. All cases of ACC from 2008 to 2018 were graded as per Tokyo guidelines; moderate and severe ACC were termed as ‘complex ACC (CACC).’ Patients were subjected to upfront LC or percutaneous drainage (PCD) followed by LC. Seven intraoperative safety steps were used to achieve critical view of safety (CVS). Use of safety steps, duration of surgery, and length of hospital stay were compared between moderate and severe ACC; complications were classified using Clavien–Dindo classification. We analyzed 145 patients with moderate (74.5%) and severe (25.5%) ACC. There were significantly more male (p = 0.0059) and older (p = 0.0006) patients with severe ACC. Upfront LC was performed in 81.4%; PCD required in 6.9%. Timing of LC from symptom onset was

The new generation of deep photometric surveys requires unprecedentedly precise shape and photometry measurements of billions of galaxies to achieve their main science goals. At such depths, one major limiting factor is the blending of galaxies due to line-of-sight projection, with an expected fraction of blended galaxies of up to 50%. Current deblending approaches are in most cases either too slow or not accurate enough to reach the level of requirements. This work explores the use of deep neural networks to estimate the photometry of blended pairs of galaxies in monochrome space images, similar to the ones that will be delivered by the Euclid space telescope. Using a clean sample of isolated galaxies from the CANDELS survey, we artificially blend them and train two different network models to recover the photometry of the two galaxies. We show that our approach can recover the original photometry of the galaxies before being blended with $\sim$7% accuracy without any human intervention and without any assumption on the galaxy shape. This represents an improvement of at least a factor of 4 compared to the classical SExtractor approach. We also show that forcing the network to simultaneously estimate a binary segmentation map results in a slightly improved photometry. All data products and codes will be made public to ease the comparison with other approaches on a common data set., Comment: 16 pages, 12 figures, submitted to MNRAS, comments welcome

Background The high burden of malaria and limited funding means there is a necessity to maximize the allocative efficiency of malaria control programmes. Quantitative tools are urgently needed to guide budget allocation decisions. Methods A geospatial epidemic model was coupled with costing data and an optimization algorithm to estimate the optimal allocation of budgeted and projected funds across all malaria intervention approaches. Interventions included long-lasting insecticide-treated nets (LLINs), indoor residual spraying (IRS), intermittent presumptive treatment during pregnancy (IPTp), seasonal mass chemoprevention in children (SMC), larval source management (LSM), mass drug administration (MDA), and behavioural change communication (BCC). The model was applied to six geopolitical regions of Nigeria in isolation and also the nation as a whole to minimize incidence and malaria-attributable mortality. Results Allocative efficiency gains could avert approximately 84,000 deaths or 15.7 million cases of malaria in Nigeria over 5 years. With an additional US$300 million available, approximately 134,000 deaths or 37.3 million cases of malaria could be prevented over 5 years. Priority funding should go to LLINs, IPTp and BCC programmes, and SMC should be expanded in seasonal areas. To minimize mortality, treatment expansion is critical and prioritized over some LLIN funding, while to minimize incidence, LLIN funding remained a priority. For areas with lower rainfall, LSM is prioritized over IRS but MDA is not recommended unless all other programmes are established. Conclusions Substantial reductions in malaria morbidity and mortality can be made by optimal targeting of investments to the right malaria interventions in the right areas. Electronic supplementary material The online version of this article (doi:10.1186/s12936-017-2019-1) contains supplementary material, which is available to authorized users.

Importance The large contribution of psychiatric disorders to premature death and persistent disability among young people means that earlier identification and enhanced long-term care for those who are most at risk of developing life-threatening or chronic disorders is critical. Clinical staging as an adjunct to diagnosis to address emerging psychiatric disorders has been proposed for young people presenting for care; however, the longer-term utility of this system has not been established. Objectives To determine the rates of transition from earlier to later stages of anxiety, mood, psychotic, or comorbid disorders and to identify the demographic and clinical characteristics that are associated with the time course of these transitions. Design, Setting, and Participants A longitudinal, observational study of 2254 persons aged 12 to 25 years who obtained mental health care at 2 early intervention mental health services in Sydney, Australia, and were recruited to a research register between June 18, 2008, and July 24, 2018 (the Brain and Mind Centre Optymise Cohort). Main Outcomes and Measures The primary outcome of this study was transition from earlier to later clinical stages. A multistate Markov model was used to examine demographic (ie, age, sex, engagement in education, employment, or both) and clinical (ie, social and occupational function, clinical presentation, personal history of mental illness, physical health comorbidities, treatment use, self-harm, suicidal thoughts and behaviors) factors associated with these transitions. Results Of the 2254 individuals included in the study, mean (SD) age at baseline was 18.18 (3.33) years and 1330 (59.0%) were female. Data on race/ethnicity were not available. Median (interquartile range) follow-up was 14 (5-33) months. Of 685 participants at stage 1a (nonspecific symptoms), 253 (36.9%) transitioned to stage 1b (attenuated syndromes). Transition was associated with lower social functioning (hazard ratio [HR], 0.77; 95% CI, 0.66-0.90), engagement with education, employment, or both (HR, 0.47; 95% CI, 0.25-0.91), manic-like experiences (HR, 2.12; 95% CI, 1.19-3.78), psychotic-like experiences (HR, 2.13; 95% CI, 1.38-3.28), self-harm (HR, 1.42; 95% CI, 1.01-1.99), and older age (HR, 1.27; 95% CI, 1.11-1.45). Of 1370 stage 1b participants, 176 (12.8%) transitioned to stage 2 (full-threshold) disorders. Transition was associated with psychotic-like experiences (HR, 2.31; 95% CI, 1.65-3.23), circadian disturbance (HR, 1.66; 95% CI, 1.17-2.35), psychiatric medication (HR, 1.43; 95% CI, 1.03-1.99), childhood psychiatric disorder (HR, 1.62; 95% CI, 1.03-2.54), and older age (HR, 1.24; 95% CI, 1.05-1.45). Conclusions and Relevance Differential rates of progression from earlier to later stages of anxiety, mood, psychotic, or comorbid disorders were observed in young persons who presented for care at various stages. Understanding the rate and factors associated with transition assists planning of stage-specific clinical interventions and secondary prevention trials.

Background Child stunting due to chronic malnutrition is a major problem in low- and middle-income countries due, in part, to inadequate nutrition-related practices and insufficient access to services. Limited budgets for nutritional interventions mean that available resources must be targeted in the most cost-effective manner to have the greatest impact. Quantitative tools can help guide budget allocation decisions. Methods The Optima approach is an established framework to conduct resource allocation optimization analyses. We applied this approach to develop a new tool, ‘Optima Nutrition’, for conducting allocative efficiency analyses that address childhood stunting. At the core of the Optima approach is an epidemiological model for assessing the burden of disease; we use an adapted version of the Lives Saved Tool (LiST). Six nutritional interventions have been included in the first release of the tool: antenatal micronutrient supplementation, balanced energy-protein supplementation, exclusive breastfeeding promotion, promotion of improved infant and young child feeding (IYCF) practices, public provision of complementary foods, and vitamin A supplementation. To demonstrate the use of this tool, we applied it to evaluate the optimal allocation of resources in 7 districts in Bangladesh, using both publicly available data (such as through DHS) and data from a complementary costing study. Results Optima Nutrition can be used to estimate how to target resources to improve nutrition outcomes. Specifically, for the Bangladesh example, despite only limited nutrition-related funding available (an estimated $0.75 per person in need per year), even without any extra resources, better targeting of investments in nutrition programming could increase the cumulative number of children living without stunting by 1.3 million (an extra 5%) by 2030 compared to the current resource allocation. To minimize stunting, priority interventions should include promotion of improved IYCF practices as well as vitamin A supplementation. Once these programs are adequately funded, the public provision of complementary foods should be funded as the next priority. Programmatic efforts should give greatest emphasis to the regions of Dhaka and Chittagong, which have the greatest number of stunted children. Conclusions A resource optimization tool can provide important guidance for targeting nutrition investments to achieve greater impact.

Comparisons between observed and predicted strong lensing properties of galaxy clusters have been routinely used to claim either tension or consistency with $\Lambda$CDM cosmology. However, standard approaches to such cosmological tests are unable to quantify the preference for one cosmology over another. We advocate approximating the relevant Bayes factor using a marginal likelihood that is based on the following summary statistic: the posterior probability distribution function for the parameters of the scaling relation between Einstein radii and cluster mass, $\alpha$ and $\beta$. We demonstrate, for the first time, a method of estimating the marginal likelihood using the X-ray selected $z>0.5$ MACS clusters as a case in point and employing both N-body and hydrodynamic simulations of clusters. We investigate the uncertainty in this estimate and consequential ability to compare competing cosmologies, that arises from incomplete descriptions of baryonic processes, discrepancies in cluster selection criteria, redshift distribution, and dynamical state. The relation between triaxial cluster masses at various overdensities provide a promising alternative to the strong lensing test., Comment: 15 pages, 6 figures, 1 table, accepted to MNRAS

The disciplines of astronomy and statistics are coming together to answer some of the biggest questions in modern science. By Joseph M. Hilbe Impacts from space rocks have set off mass extinctions at least twice in Earth's history. Should we be worried that another strike is imminent? Joseph M. Hilbe and Jamie Riggs assess the risks An overview of meteorite strikes observed through the ages, designed by Carlo Zapponi If you want to know why the universe is the way it is, you have to understand its initial state. Benjamin Wandelt takes us back billions of years to show how statistics is helping cosmologists understand the origins of everything – including life itself Astronomy data sets are astronomically big – that is why statistical approaches are needed to analyse, organise and unravel the mysteries of the universe. By Rafael de Souza and Emille Ishida There's more to the universe than meets the eye – over 80% is made up of stuff we cannot see. Jessi Cisewski explores the nature of dark matter, and how statistics is helping locate it 30 billion? 225 billion? 400 billion? Vladimir Surdin finds no exact answer, but plenty of estimates There isn't a set of scales big enough to measure the most massive objects in the universe. Madhura Killedar considers alternative methods, and the associated statistical challenges Our universe is fine-tuned for life to such a degree that it would seem improbable were it the only universe in existence – which means there is a good chance that we live in a multiverse. Roberto Trotta explains the idea, and the discoveries that gave rise to it It began with a bang, but current models suggest the universe will go out with a whimper. Chris Impey explores the long, dark fate that awaits

Additional file 1. Detailed description of epidemiological model (including equations, program implementations and calibration), model parameters, estimates of current spending and additional charts.

The nature of the dark sector of the Universe remains one of the outstanding problems in modern cosmology, with the search for new observational probes guiding the development of the next generation of observational facilities. Clues come from tension between the predictions from {\Lambda}CDM and observations of gravitationally lensed galaxies. Previous studies showed that galaxy clusters in the {\Lambda}CDM are not strong enough to reproduce the observed number of lensed arcs. This work aims to constrain the warm dark matter cosmologies by means of the lensing efficiency of galaxy clusters drawn from these alternative models. The lensing characteristics of two samples of simulated clusters in the warm dark matter ({\Lambda}WDM) and cold dark matter ({\Lambda}CDM) cosmologies have been studied. The results show that even though the CDM clusters are more centrally concentrated and contain more substructures, the WDM clusters have slightly higher lensing efficiency than their CDM counterparts. The key difference is that WDM clusters have more extended and more massive subhaloes than CDM analogues. These massive substructures significantly stretch the critical lines and caustics and hence they boost the lensing efficiency of the host halo. Despite the increase in the lensing efficiency due to the contribution of massive substructures in the WDM clusters, this is not enough to resolve the arc statistics problem., Comment: 10 pages, 12 figures, submitted to MNRAS

[Abridged] In this paper, we carry out a detailed analysis of the performance of two different methods to identify the diffuse stellar light in cosmological hydrodynamical simulations of galaxy clusters. One method is based on a dynamical analysis of the stellar component. The second method is closer to techniques commonly employed in observational studies. Both the dynamical method and the method based on the surface brightness limit criterion are applied to the same set of hydrodynamical simulations for a large sample about 80 galaxy clusters. We find significant differences between the ICL and DSC fractions computed with the two corresponding methods, which amounts to about a factor of two for the AGN simulations, and a factor of four for the CSF set. We also find that the inclusion of AGN feedback boosts the DSC and ICL fractions by a factor of 1.5-2, respectively, while leaving the BCG+ICL and BCG+DSC mass fraction almost unchanged. The sum of the BCG and DSC mass stellar mass fraction is found to decrease from ~80 per cent in galaxy groups to ~60 per cent in rich clusters, thus in excess of what found from observational analysis. We identify the average surface brightness limits that yields the ICL fraction from the SBL method close to the DSC fraction from the dynamical method. These surface brightness limits turn out to be brighter in the CSF than in the AGN simulations. This is consistent with the finding that AGN feedback makes BCGs to be less massive and with shallower density profiles than in the CSF simulations. The BCG stellar component, as identified by both methods, are slightly older and more metal-rich than the stars in the diffuse component., 18 Pages, 15 figures. Matches to MNRAS published version

The observed abundance of giant arcs produced by galaxy cluster lenses and the measured Einstein radii have presented a source of tension for LCDM. Previous cosmological tests for high-redshift clusters (z>0.5) have suffered from small number statistics in the simulated sample and the implementation of baryonic physics is likely to affect the outcome. We analyse zoomed-in simulations of a fairly large sample of cluster-sized objects, with Mvir > 3x10^14 Msun/h, identified at z=0.25 and z=0.5, for a concordance LCDM cosmology. We start with dark matter only simulations, and then add gas hydrodynamics, with different treatments of baryonic processes: non-radiative cooling, radiative cooling with star formation and galactic winds powered by supernova explosions, and finally including the effect of AGN feedback. We find that the addition of gas in non-radiative simulations does not change the strong lensing predictions significantly, but gas cooling and star formation together significantly increase the number of expected giant arcs and the Einstein radii, particularly for lower redshift clusters and lower source redshifts. Further inclusion of AGN feedback reduces the predicted strong lensing efficiencies such that the lensing probability distributions becomes closer to those obtained for simulations including only dark matter. Our results indicate that the inclusion of baryonic physics in simulations will not solve the arc-statistics problem at low redshifts, when the physical processes included provide a realistic description of cooling in the central regions of galaxy clusters. [Abridged]

High redshift sources suffer from magnification or demagnification due to weak gravitational lensing by large scale structure. One consequence of this is that the distance-redshift relation, in wide use for cosmological tests, suffers lensing-induced scatter which can be quantified by the magnification probability distribution. Predicting this distribution generally requires a method for ray-tracing through cosmological N-body simulations. However, standard methods tend to apply the multiple thin-lens approximation. In an effort to quantify the accuracy of these methods, we develop an innovative code that performs ray-tracing without the use of this approximation. The efficiency and accuracy of this computationally challenging approach can be improved by careful choices of numerical parameters; therefore, the results are analysed for the behaviour of the ray-tracing code in the vicinity of Schwarzschild and Navarro-Frenk-White lenses. Preliminary comparisons are drawn with the multiple lens-plane ray-bundle method in the context of cosmological mass distributions for a source redshift of $z_{s}=0.5$.

Comparisons between observed and predicted strong lensing properties of galaxy clusters have been used to claim either tension or consistency with ΛCDM cosmology. However, standard approaches to such tests are unable to quantify the preference for one cosmology over another. We advocate a Bayesian approach whereby the parameters defining the scaling relation between Einstein radii and cluster mass are treated as the observables. We demonstrate a method of estimating the likelihood for observing these parameters under the ΛCDM framework, using the X-ray selected z > 0.5 MACS clusters as a case in point and employing both N-body and hydrodynamic simulations of clusters. We account for cluster lens triaxiality within the modelling of the likelihood function. Cluster selection criteria is found to play as important a role as the uncertainty related to the description of star formation and feedback.

The evolution of the expansion rate of the Universe results in a drift in the redshift of distant sources over time. A measurement of this drift would provide us with a direct probe of expansion history. The Lyman alpha forest has been recognized as the best candidate for this experiment, but the signal would be weak and it will take next generation large telescopes coupled with ultra-stable high resolution spectrographs to reach the cm/s resolution required. One source of noise that has not yet been assessed is the transverse motion of Lyman alpha absorbers, which varies the gravitational potential in the line of sight and subsequently shifts the positions of background absorption lines. We examine the relationship between the pure cosmic signal and the observed redshift drift in the presence of moving Lyman alpha clouds, particularly the collapsed structures associated with Lyman limit systems (LLSs) and damped Lyman alpha systems (DLAs). Surprisingly, the peculiar velocities and peculiar accelerations both enter the expression, although the acceleration term stands alone as an absolute error, whilst the velocity term appears as a fractional noise component. An estimate of the magnitude of the noise reassures us that the motion of the Lyman alpha absorbers will not pose a threat to the detection of the signal.

Structural properties of clusters of galaxies have been routinely used to claim either tension or consistency with the fiducial cosmological hypothesis, known as ΛCDM. However, standard approaches are unable to quantify the preference for one hypothesis over another. We advocate using a ‘weighted’ variant of approximate Bayesian computation (ABC), whereby the parameters of the strong lensing-mass scaling relation, α and β, are treated as the summary statistics. We demonstrate then, for the first time, the procedure for estimating the likelihood for observing α and β under the ΛCDM framework. We employ computer simulations for producing mock samples, and account for variation between samples for modelling the likelihood function. We also consider the effects on the likelihood, and consequential ability to compare competing hypotheses, if only simplistic computer simulations are available.

Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific inquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper -- the first in a series aimed at illustrating the power of these methods in astronomical applications -- we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes from cosmological hydro-simulations including detailed chemistry, gas physics, and stellar feedback. We predict that for a dark mini-halo with metallicity $\approx 1.3 \times 10^{-4} Z_{\bigodot}$, an increase of $1.2 \times 10^{-2}$ in the gas molecular fraction, increases the probability of star formation occurrence by a factor of 75%. Finally, we highlight the use of receiver operating characteristic curves as a diagnostic for binary classifiers, and ultimately we use these to demonstrate the competitive predictive performance of GLMs against the popular technique of artificial neural networks., Comment: 20 pages, 10 figures, 3 tables, accepted for publication in Astronomy and Computing

We present an analysis of the properties of the ICM in an extended set of cosmological hydrodynamical simulations of galaxy clusters and groups performed with the TreePM+SPH GADGET-3 code. Besides a set of non-radiative simulations, we carried out two sets of simulations including radiative cooling, star formation, metal enrichment and feedback from supernovae, one of which also accounts for the effect of feedback from AGN resulting from gas accretion onto super-massive black holes. These simulations are analysed with the aim of studying the relative role played by SN and AGN feedback on the general properties of the diffuse hot baryons in galaxy clusters and groups: scaling relations, temperature, entropy and pressure radial profiles, and ICM chemical enrichment. We find that simulations including AGN feedback produce scaling relations that are in good agreement with X-ray observations at all mass scales. However, our simulations are not able to account for the observed diversity between CC and NCC clusters: unlike for observations, we find that temperature and entropy profiles of relaxed and unrelaxed clusters are quite similar and resemble more the observed behaviour of NCC clusters. As for the pattern of metal enrichment, we find that an enhanced level of iron abundance is produced by AGN feedback with respect to the case of purely SN feedback. As a result, while simulations including AGN produce values of iron abundance in groups in agreement with observations, they over-enrich the ICM in massive clusters. The efficiency of AGN feedback in displacing enriched gas from halos into the inter-galactic medium at high redshift also creates a widespread enrichment in the outskirts of clusters and produces profiles of iron abundance whose slope is in better agreement with observations., 23 pages, 14 figures, 1 table, accepted for publication in MNRAS

(Abridged) We explore new observationally-constrained sub-resolution models of galactic outflows and investigate their impact on the circumgalactic medium (CGM) over redshifts z = 2 - 4. We perform cosmological hydrodynamic simulations, including star formation, chemical enrichment, and four cases of SNe-driven outflows: no wind (NW), an energy-driven constant velocity wind (CW), a radially varying wind (RVWa) where the outflow velocity has a positive correlation with galactocentric distance (r), and a RVW with additional dependence on halo mass (RVWb). Overall, we find that the outflows expel metal-enriched gas away from galaxies, significantly quench star formation, and enrich the CGM. At z = 2, the radial profiles of gas properties around galaxy centers are most sensitive to the choice of the wind model for halo masses (10^9 - 10^11) M_sun. We infer that the RVWb model is similar to the NW case, except that it substantially enriches the CGM: the carbon metallicity (Z_C) is 10 times higher in RVWb than in NW at r > R_200; and the warm gas of 10^4 - 10^5 K and delta < 100 is enriched to 50 times higher than in NW. We also find that the impact of models CW and RVWa are similar, with the following differences. RVWa causes a greater suppression of star formation rate at z < 5, and has a higher fraction of low-density (delta < 10), warm-hot (10^4 - 10^6 K) gas than in CW. Outflows in CW produce a higher and earlier enrichment of some IGM phases than RVWa. By visual inspection, we note that the RVWa model shows more pronounced bipolar outflows and galactic disks. We present fitting formulae for [Z_C-delta] and [Z_C-r], also for the abundance of CIV as a function of r. We predict observational diagnostics to distinguish between different outflow scenarios: Z_C of the CGM gas at r = (30 - 300) kpc/h comoving, and CIV fraction of the inner gas at r < (4 - 5) kpc/h comoving., Version accepted for publication in MNRAS. Manuscript file with higher resolution Fig. 2 can be found here: http://adlibitum.oats.inaf.it/barai/AllPages/Images-Movies/RadialVarWind.pdf