Assessments of climate forecast skill depend on choices made by the assessor. In this perspective, we use forecasts of the El Niño-Southern-Oscillation to outline the impact of bias-correction on skill. Many assessments of skill from hindcasts (past forecasts) are probably overestimates of attainable forecast skill because the hindcasts are informed by observations over the period assessed that would not be available to real forecasts. Differences between hindcast and forecast skill result from changes in model biases from the period used to form forecast anomalies to the period over which the forecast is made. The relative skill rankings of models can change between hindcast and forecast systems because different models have different changes in bias across periods. Many different methods have been developed to forecast climate phenomena like the El Nino-Southern Oscillation (ENSO) which makes a fair comparison of their capabilities crucial. In this perspective, the authors discuss how choices in the evaluation method can lead to an overestimated perceived skill of ENSO forecasts. Seasonal climate forecasts aim to predict those processes of climate variability that evolve and carry memory on the seasonal time scale, and which transmit their expression into weather systems and other features of interest2. These processes are often related to so called modes of variability, of which the El Niño Southern Oscillation (ENSO)5 in the tropical Pacific is one of the most important ones for seasonal to interannual climate forecasts. This is mainly because it evolves on seasonal and longer timescales, and it provides discernable influences on weather systems across large swathes of the Pacific and Indian Ocean basins and into the Antarctic region6, so called teleconnections7.Climate forecasts attempt to track the evolution of the more slowly evolving parts of the climate system. They can extend over any time scale longer than weather forecastsHere, we discuss the influence a number of methodological decisions can have on the assessment of predictive skill of ENSO forecasts. While we focus on evaluating ENSO forecast skill here, the issues arising in the interaction of forecast processing and skill apply more generally to all climate forecasts.8, with more routine forecasts emerging in the 1990’s to include those made through coupled general circulation models (CGCMs)9. The forecasts from CGCMs sit alongside those from simpler physical models or empirical statistical models that use past climate data to form relationships to predict future outcomes. There is a general expectation in the community that forecast skill from the CGCMs has, or at least will eventually, outstrip that from statistical models11  than statistical models14. Despite this, it is still unclear whether and when CGCMs are better than statistical models and whether either model type has meaningful skill in forecasting the onset of ENSO.Forecasts of ENSO have been issued since the late 1980s10 concludes that ENSO skill in CGCMs now exceeds that in the statistical models used to forecast ENSO. On the other hand, DelSole and Tippett15 finds that a set of CGCMs16 are no more skillful than a simple regression model in forecasting ENSO. On the question of forecasting onset, L’Heureux et al.17 propose the 2015/16 El Niño as an example of successful ENSO prediction, while Glantz18 reviews past El Niño forecasts and concludes that there is little skill in forecasting onset.These questions have been answered differently by different studies. For example, Barnston et al.13. The small number of events limits the power of any statistical tests of skill19. The assessment of ENSO forecast skill will depend on the period  chosen to test and the number and type of ENSO events in the period10. The predictability of ENSO may vary from period to period in the sense that the predictability of chaotic systems varies due to flow dependency20. The predictability will also appear to vary for different periods simply because they will contain different very small samples of ENSO behaviour21. Another factor that can influence the forecast skill assessment is the inclusion of artificial skill in the evaluation procedure.There are a range of reasons why there is no real definitive view on ENSO forecast skill in dynamical models. A major difficulty with all skill assessments of ENSO is that there are only a handful of major ENSO events of each type  in the period since the 1980s and 1990s when ENSO hindcasting and forecasting commenced21. Hindcast skill can be an overestimate of real forecast skill if the hindcasts contain artificial skill22, or an underestimate if there is variability in skill sampled from different periods. The term ‘artificial skill’ here is understood to refer to skill in hindcasts that would not be attainable in a real forecast system due to some aspect of the idealised nature of the hindcasts; e.g., using data that would not be available in a comparable forecast situation.The apparent forecast skill of ENSO varies depending on whether skill is assessed in hindcasts (forecasts over periods in the past) or forecasts (predictions over yet-to-be observed future periods). Most ENSO skill assessments have been based on hindcasts. Hindcast datasets can contain many more forecasts than actual forecast archives, and so offer a chance for more robust statistics in the assessment of skill. On the other hand, hindcasts present more idealised conditions for forecasts than for actual forecasts because they allow for more complete ingestion of data for initial conditions, tuning and calibration of the model over events that will be included in model tests, and opportunities to provide more systematic post-processing of the forecasts. These differences imply that hindcast skill can be a poor estimate of true forecast skillThe production of artificial skill is important as it can mislead the users of climate forecasts about the true skill and utility of the forecasts for their operations. All climate models have some bias relative to the real world see Box . The posOur discussion of bias-correction methods see Box  divides Box 1 Model biasa for a sequence of model starts. The model climatology at 0*-months lead is therefore close to the observed climatology, as is evident in Fig. Box 1 panel b, which shows the near-identical model and observed climatologal distributions for each calendar month of the year. At longer lead times the model forecast will revert towards the model’s preferred climatology. This is evident at lead 11 in Fig. Box 1 panel c, by which time the model no longer tracks observations so closely. The climatology of the model at lead 11 now shows clear differences from the observed in Fig. Box 1 panel d. The model means for each month have shifted from the observed means, and the shape of the model distribution is different from the observed. The model’s mean bias is typically removed from forecast fields by subtracting the difference between model mean and observed mean climatologies  for each month for each model lead time. This correction does not address any differences between the shapes of the model and observed distributions.Since climate models are not perfect representations of the real world, the climatology of any forecast model (the mean climate formed from a set of the forecasts made) will never reproduce the observed climatology exactly. The time averaged difference between the model and observed climatology is called model bias. For climate forecasts, the model is initialised to start the forecast close to the observations as shown in Fig. Box 1 panel a and c show Niño3.4 temperature for observations and the aer04 model ensemble mean at lead 0* (the start of the forecast) and after 11 months, for a sequence of forecasts issued a month apart. The observations values are simply the time series of Niño3.4 temperature and are identical at lead 0* and lead 11. The model values at lead 11 are the values predicted by forecasts initialised 11 months prior to the time shown. The panels b and d show the distribution of lead 0*   and lead 11 values for the model and observations for each calendar month. These are again identical for observations, but change for the model. The dots on these plots show the mean of the distributions.Fig. Box 1: Model bias schematic. Panels Box 2 Bias correction methods43. We have divided the hindcast archive period into two such periods (1982–1998 & 1999–2015) as shown in schematic form in Fig. Box 2. In practice, model groups make a range of different choices of reference climatology. We summarise the main approaches as follows.When evaluating climate forecasts, the target forecast variable is often converted to anomalies (about some specified mean climatology) for comparison to observations. This process may remove mean model bias over the chosen climatological period. The choices made in forming this climatology can have an impact on the assessment of skill. For assessment of hindcast data, it is good practice to define a period of time to be used as a reference climatology for the bias-correction (a training period), and a separate period to be used for testing the hindcasts (testing period)biased develops a climatology in the training period from observations 46. For the biased method, observed values of Niño3.4 are averaged as a function of calendar month and used as a climatology to subtract from all matched calendar months in the forecast data. No variation in the climatology is made for lead time here, since there is no lead-time dependence in the observed climatology. By not subtracting the model’s own climatology, any offset or bias in where the model climatology sits relative to observations is retained in the anomalies.unfair uses a baseline climatology for the forecasts from the set of all forecasts  in the test period (pink box). Though this method is widely used for deriving forecast anomalies56, it is a form of ‘cheating’ in skill evaluation45, as it uses observed data in the test period for which the model will be evaluated to adjust the forecast anomalies in that period. The reference climatology in the test period is made up of forecasts initialised in this period, which require observations to initialise. These observations would not be available to actual forecasts.unfair-cv is a variant of the unfair method that applies a form of ‘cross-validation’, whereby a period of time centred around the current forecast time is removed, and then the current anomaly is computed with respect to the climatology of the remaining data57 (red boxes). This method is important in the literature as it is often posed as a form of best practice45. This method is still in the unfair category as it uses information from the future period after the forecast is made.fair derives the model climatology from the appropriate training period (green box). A ‘fair’ forecast can not use any observations of the climate system that apply to the period after the forecast commences, since such observations are never available for real-time forecasting. Some hindcasts have been assessed with the fair method58, and of course all assessments of real-time forecasts59 are fair. Variants of fair include fair-sliding, which uses a sliding window behind the forecast as a reference period (blue box), and fair-all with a growing window that includes all forecasts initiated prior to the current forecast (orange box).Fig. Box 2: Schematic bias correction plot. The schematic shows a time series of the observed variable at the top and hindcast/forecast time series at different lead times (to 11 months) on the bottom. The time series are divided in half to give a training period (blue shade) and a testing period (tan shade). The training period is typically reserved for computing the model climatology of the forecasts, and the testing period is used to test the bias-corrected forecasts. The coloured lines depict the periods used in forming the reference climatologies for the different bias correction methods described above. Solid lines indicated fixed periods. Dashed lines indicate periods that move as the forecast start date moves.15 and  are generated over the period from 1982 matching the CGCM forecasts. Most forecasts are run a year from initiation. The resolution of the forecasts is monthly, allowing for lead times out to a year. The forecasts are made for the value of Niño3.4, which is a typical index of ENSO. The CGCM forecasts are represented by the ensemble mean of 10-member ensembles for each CGCM. An example of the resulting forecasts is shown in Fig. We compare the skill of the set of dynamical model hindcasts/forecasts of Niño3.4 with the skill of the simple regression models. We use a test period of 1999–2016 to assess the model skill. We further divide our skill assessment into cases where the bias-correction of the forecasts uses a training period of 1982–1998 (fair methods), and where it uses forecasts (and observations) from the testing period after the commencement of the forecast (unfair methods). These methods are described in detail in Box RWSS) in Fig. RWSS line is indicative of any changes in the proportion by which one forecast is beating another. A positive or negative slope indicates a change in the proportion of wins of one or other of the forecast systems relative to the prior win proportion. For the first few years in each of the plots in Fig. 15.The results for the random walk comparison at lead time 3 months  are shown in Fig. 15. For the unfair method there is no difference between the CGCMs and the regression forecasts  in Fig. fair-sliding and fair-all than fair. This is understandable in that the fair reference climatology is fixed in the training period and is further separated in time from each new forecast start in the testing period as the forecasts march through the testing period in the random walk score. The reference climatologies for fair-sliding and fair-all move along behind each new forecast in the testing period and so do not suffer the disadvantage of using a reference climatology increasingly removed from the testing period.The results for the fair methods  are generally a bit worse than the linear regression model unless the bias-correction method for the models is the unfair one. The results for the comparison with a linear regression model here are broadly similar if using a logistic regression model instead  is shown for each of the bias correction methods. The changes in ranking between unfair and fair methods are striking. For example, florA and aer04 are among the most skillful models for unfair and among the least skillful for fair. The relative rankings change much less among the different variants of the fair method.One important feature of the results in panels f–j in Fig. unfair than fair. In this section we perform a direct comparison between unfair and fair methods for the same forecast model bias corrected in the two different ways. A direct comparison using fair and unfair methods for all dynamical models is shown in Fig. fair and unfair, and another set  where the unfair method is more skillful than fair. By lead 6 (panel b) almost all the models (excepting only cm4i) are now in the zone where unfair is more skillful than fair. For the second group of models above the advantage is striking where the unfair method wins 80% of forecast comparisons to fair’s 20%.Thus far we have seen that the dynamical models perform better relative to simple regression models when using RWSSn,  where unfair dominates fair by about lead 3, and another group  where this occurs by about lead 4 or 5. The exceptions to the progressive dominance of unfair with lead time are cola, where a change in initial condition error between training and testing periods dominates the performance at low lead times  about a degree too warm, whereas the unfair method anomalies are much closer to observations. The distributions of the forecast anomalies at lead 0*  are well centred for fair and unfair forecasts, but by lead 6  the fair forecast anomalies are generally offset. The consequences of the fair anomaly offset for the skill of the fair ENSO forecasts are quite drastic because the anomaly shift of about 1 ∘C is twice the magnitude of the Niño3.4 anomaly (0.5 ∘C) used to define an ENSO event.To visualise the advantage that the unfair method can be made fairer by carrying out a form of cross-validation when deriving the reference climatology in the testing period45. In the cross-validated form of the unfair method, unfair-cv, whenever an anomaly is calculated, a window of forecasts centred about the anomaly is removed from the set of forecasts used to compute the baseline forecast climatology. As the data comprising the forecast climatology contains significant autocorrelation, it is argued that a span of typically about 3 years needs to be excluded in the anomaly window45. We have tested this with odd-length windows from 1 to 7 years width. The results are not very sensitive to the width selected and so we chose a 7-year window to maximise the effect of cross validating. The unfair-cv method is just as skillful as the unfair method in outperforming the fair method . Leaving some data out of that climatology does not de-centre the anomalies anywhere near as much as using the training period (solid lines). To show how little difference the cross-validation makes to the unfair method, the unfair and unfair-cv anomalies are plotted together, and practically lie on top of one another in both the time series  and pdfs in Fig. Box 3 panels b and c. The near equivalence of the unfair and unfair-cv anomalies explains why the skill determinations are nearly identical for these two methods. Since the cross-validated climatology, unfair-cv, makes almost the same transgressions (of test data) as the unfair method and retains most of the benefits of those transgressions, we do not regard it as a valid way to make the unfair method fairer.Some have argued that the a the black line shows observed Niño3.4 anomalies in the testing period. The red lines are for the florB ensemble mean Niño3.4 anomalies at lead time 6 for anomalies calculated by the methods fair, unfair, and unfair-cv. The unfair-cv anomalies are calculated removing a 7-year cross-validation window. The probability density distribution of the anomalies is shown for each dynamical model over all months at lead time 0* (panel b) and lead 6 months (panel c) in the testing period. The anomalies have been calculated according to the anomaly methods, fair (solid lines), unfair (dashed), and unfair-cv (dotted).Fig. Box 3: Observed and model forecast Niño3.4 anomalies. In panel unfair method benefits so much by using a reference climatology from the test period, one needs to assess the climatologies formed in the training and test period and how they shape the forecast anomalies in the test period. The model forecast climatologies are typically broken down by calendar month and lead time as shown in Fig. F〉m,τ is shown in row e. Any difference between these reference climatologies leads to different outcomes for the fair and unfair methods. We show why this is so and examine the contributions to this difference.To understand why the fair and unfair methods by subtracting the reference climatologies in the training (row a) and testing (row c) periods respectively from the forecast values. For the unfair method, since the reference climatology covers the period tested, the climate state and model biases are estimated exactly and removed such that the mean of the forecast anomalies (as functions of month and lead) are zero. This means that the unfair forecast anomalies are all well centred . However, for the fair method, any shift in climate state or change in model bias from the training to testing period is retained in the forecast anomalies, which are offset by the amounts shown in row e of Fig. ∘C for some months and leads and detract from skill of the fair forecasts.The model forecast anomalies are generated for the the nonstationarity or shift in climate between the periods (a change in the observed climatology)the change in model bias from training period to testing periodThere are two major contributors to the differences in reference climatology between the training and testing period:There will also be differences in mean climatology due to the limited sample sizes of the climatological distributions here, which are hard to quantify.O〉m,τ, is represented by the difference between the observed climatologies in the training and testing period in the first column of row e. There is actually a slight cooling in Niño3.4 from the training to test period. This cooling is consistent with the change in phase of the Pacific Decadal Oscillation24 from a predominatly warm phase (El Niño dominated) in the training period to a predominantly cold phase (La Niña dominated) in the testing period25. The change in model climate from the training to testing period, Δ〈F〉m,τ, is shown in the remaining columns of row e. At short lead times, the cooling climate shift in observations is communicated to the forecast climatologies because each of the forecasts making up the forecast climatologies are initialised about the set of observations in these periods. At longer lead times, the model forecast climatologies are increasingly too warm , tending to overheat El Niño’s and underplaying the colder La Niña events.The climate shift contribution, Δ〈21, and since there is a shift in climate state between the periods, there is a change in the profile of model bias between the periods. The model bias is the difference between the forecast climatology and observed climatology and is shown for the training and test periods in rows b and d of Fig. Bm,τ, is shown in row f. The warming of the biases is evident with the preponderance of positive values in this row. The models fall into roughly two groups. A high ΔBm,τ group  has relatively large change in bias across the periods, and a low ΔBm,τ group  has smaller change in bias. The gmao model is somewhat intermediate between the two groups. The high ΔBm,τ models warm substantially in the testing period relative to the training period, whereas the observations cool, which results in a larger change in bias. For all models here, the magnitude of ΔBm,τ increases with lead time, τ, as expected.The bias in the models depends on the climate statefair method have a mean offset relative to those for the unfair method given by the change in model climatology from training to testing period, Δ〈F〉m,τ, in row e of Fig. Bm,τ, is still small and the change in model climatology, Δ〈F〉m,τ, is dominated by the climate shift in observations, Δ〈O〉m,τ. This is evident in the cooling (blue shades) in model climatology in months 1–5 (Jan–May) at short leads in row e. At longer leads (>3 months), the change in climatology is increasingly positive for all models, and it is clear that most of the contribution to Δ〈F〉m,τ then comes from the model warm bias shift, ΔBm,τ. This point can be illustrated by considering these changes for a single calendar month (March) in row g. The climate shift in observations, Δ〈O〉τMarch, (blue bars) is the same at all lead times of course, whereas the change in model bias, ΔBτMarch,, tends to increase with lead time (red bars). The sum of these is the change in model climatology, Δ〈F〉τMarch,, which is nearly equal to Δ〈O〉τMarch, for leads < 3, and then is increasingly positive with lead as the model change in bias tends to dominate the sum.The forecast anomalies for the Bm,τ = 0) would still exhibit sensitivity to the choice of fair or unfair methods whenever there is any change in the observed climate. Conversely, a model for which there is no change in climatology from training to testing period  would be insensitive to choice of fair or unfair, but it would also mean that the model hasn’t accurately captured any observed change in climate  between the two periods. The models here that have lowest sensitivity to fair or unfair  partly do so because their warming biases in months 1–5 are nearly opposite to the observed cooling in these months, and partly cancel to produce lower changes in forecast climatology. This cancellation is particularly apparent in the month of March for cm4i, which has near zero change in climatology from lead 3 onwards  neutral state . For this full set of forecasts we find that the dynamical models are generally no better than simple regression models. One might expect that the dynamical models come into their own when ENSO itself changes state, such as during the onset and decay of El Niño and La Niña events. We now restrict our evaluation of the ENSO forecasts to just those forecasts relating to onset.fair method here, since this is more indicative of actual forecast skill. We use the onset case study to further highlight variability in apparent skill that results from different hindcast periods. This is explored by considering the standard case where the reference period is 1982–1998 and the testing period is 1999–2016, and a switched case where the reference period is 1999–2016 and the testing period is 1982–1998. In the switched case, the change in bias with lead time of the model climatologies is in the opposite sense to the standard case. The models tend to cool with increasing lead time in the switched case, and the change in observed climatology is now a warming. That is, rows e and f in Fig. For onset we discuss hindcasts using the The skill scores for El Niño onset at 6 months lead relative to the linear regression model are shown in Fig. We now turn to forecasts of La Niña onset. Since La Niña onset represents a cooling of sea surface temperatures with lead time, we might expect the opposite behaviour here to the El Niño onset case. That is, we’d expect the dynamical models to be about the same (or a bit worse) than the linear regression model for La Niña onset at all leads for the original training and testing periods, because the models’ increasing warm bias with lead works against onset of a cold event. Moreover, we’d expect the dynamical models to be better than the regression model at most leads for the switched periods, where the model cold bias with lead assists their forecasts of cold event onset. That is precisely what we do see in Fig. We now have the conundrum that if we choose our original training and testing periods, the dynamical models are better/worse for El Niño/La Niña onset than regression models, and if we switch the periods the reverse is true. This result highlights the interaction between model biases, the underlying ENSO time series, and the nature of the event tested. Where the sign of an event onset (warming/cooling) lines up with lead-dependent change in climatological bias in the dynamical models, it is possible to substantially enhance (when in the same direction) or degrade (when in the opposite direction) apparent skill for onset. To guard against this, we would ideally have many periods over which to test onset, though that is not possible with our limited observational record. As such, it is important to be aware how the model biases change from training to testing periods, and how they interact with the event tested. Otherwise, conclusions about the relative skill for onset of El Niño and La Niña may substantially reflect the periods chosen.fair forecasts, because they retain lead-time-dependent change in bias across periods. For the unfair method, these biases are removed and the sensitivity of results to choice of period is attenuated (see Supplementary Note The sensitivity of skill results to the choice of period applies to unfair method). When the reference period does not overlap the testing period (the fair method), then there will inevitably be some difference between the climatology of forecasts made in the testing and reference periods. This difference in forecast climatology changes the skill of fair forecasts relative to unfair forecasts. The difference in forecast climatology results from any climate shift in observations from the reference to the testing period, and from changes in model bias (the difference between the model and observed climatology) between the reference and testing period. At short lead times (1 or 2 months), the change in model bias is typically small, and the shift in observations is the dominant contributor to the change in forecast climatology here. At lead times beyond 3 months, the change in model climatological bias is the dominant contributor to the change in model forecast climatology between the reference and testing periods, and is thus also the main contributor to degradation of skill of fair forecasts relative to unfair forecasts.The manner in which bias correction methods can affect hindcast skill can be understood from the set of hindcasts assessed here. Hindcast skill will typically be inflated if the reference period used to form ENSO anomalies overlaps with the testing period in which hindcast skill is assessed (the unfair bias correction methods progressively inflate skill (relative to fair methods) as lead time increases. This is true for even the best performing models here . The best performing models have low initial condition error and low change in bias between the reference and testing periods, but their change in bias also grows with lead time such that unfair forecasts progressively beat fair forecasts.The magnitude of the change in bias (between the reference and testing periods) increases with lead time for all of the models here. That means that unfair method here) may reflect some amount of artificial skill not realisable in real forecasts where the future is unknown. unfair method forecasts remove both the contributions of climate drift26 and change in model bias from the forecast anomalies. They provide an indication of what skill could be if the model biases were eliminated in the forecast models. For any fair forecast, the changes in model bias from the period in which the reference climatology is formed to the period in which the forecast is evaluated, constitute the dominant enduring contribution to skill degradation for the dynamical model forecasts tested here.As such, assessments of ENSO seasonal hindcast skill can be sensitive to the method used to define the reference climatology and associated forecast anomalies. Any method that uses the forecast testing period as a basis for the reference climatology  method. The relative rankings of models change depending on the nature of the biases in the different forecast systems. For example, some of the models tested here  have relatively low bias changes across different reference periods, and thus their skill scores are not too sensitive to the way the model biases are processed. The other models tested have larger bias changes across different climate periods and perform much better when their forecasts are processed with the unfair method than with the fair method. This means that the relative model rankings change depending on how they are bias corrected.We have emphasised the importance of processing and comparing hindcasts in the same way. However, even if all hindcasts are compared using the same unfair-based methods in hindcast assessments is widespread and perhaps understandable. Resources to develop long hindcast databases are often lacking, and the user faced with limited hindcast data needs to use all hindcast runs to get a more stable estimate of model biases28. However, the use of unfair-based methods in hindcast assessment is sometimes rationalised on the basis that if all models are processed similarly, then that maintains a level-playing field to assess models relative to one another30. Unfortunately, that is not the case, as we showed that the relative rankings of models can change in going from an unfair to fair-based method.The prevalence of unfair-based methods in hindcast assessment continues to be recommended for use in climate forecast guidance and standards documents28. The pitfalls around this may be transparent in the climate forecast community. However, those who use hindcast databases to assess forecast utility for applications are often not aware that their assessments could be based on artificial skill (if the hindcasts have been processed using unfair-based methods). For example, much of the assessed value of seasonal climate forecasts for Australian agriculture is based on hindcasts processed using unfair methods31, which therefore contain artificial skill. This can be misleading for farmers who must make tactical decisions using real forecasts, not hindcasts, and thus are likely to have lower forecast skill than expected.The use of When the assessment of model skill is fair, the skill of the NMME and C3S dynamical forecast models for ENSO is generally not demonstrably better than simple regression models. We tested whether dynamical models would perform better if forecast comparisons were restricted to just the more dynamically challenging onset aspects of El Niño and La Niña events. We drew no clear conclusions in this regard because the results for onset are critically sensitive to the direction of the change in forecast climatological bias in the models from calibration to testing periods. If this change in bias is toward warming, then warm event (El Niño) onset skill is high, and conversely if toward cooling, then cold event (La Niña) onset skill is high. However, since the change in climatological bias in the models is a function of the periods assessed , then so too is the perception of relative skill for El Niño and La Niña onset.fair and unfair methods here, we can deduce that the skill of actual forecasts of ENSO will be limited by the growth with lead time of climate-state-dependent biases in the dynamical models. A partial solution to this problem is to use more sophisticated bias-reduction schemes that take into account the state of ENSO33, the underlying trends in the observed and model hindcast climatologies34, and the extension to multivariate processes35. That will reduce, but not eliminate, the effects of climate-state-dependent biases. The long-term goal remains to diagnose the reasons for climatological biases and to reduce their magnitudes and effects on forecast skill.From the comparison of hindcast skill of ∘S–5∘N; 170∘W–120∘W). The sst data used are from OISST v236. All analysis was repeated with HadISST37, which does alter some of the details of the results, but not the more general conclusions drawn. We define El Niño/La Niña events when the 3-month running mean of Niño3.4 anomalies is above or below ± 0. 5 ∘C, respectively. The general results presented here are unchanged if Niño3 or Niño4 are used instead of Niño3.4.The observations used in the analysis cover sea surface temperature (sst) in the Niño3.4 region (516 and the Copernicus Climate Change Service (C3S)38. The advantage of the NMME archive is that it contains a rich set of runs from many CGCMs over a relatively long period from 1982 to the present. Another advantage is that the NMME archive has been the source of a number of prior ENSO skill assessments41. We selected models from these two archives that satisfied the criteria of: raw (uncorrected) hindcast data available, lead-time forecasts out to at least 6 months, at least 10 ensemble members per forecast, and hindcasts/forecasts span the period 1982–2015. The subset of models satisfying these criteria are CMC1-CanCM3 (cm3), CanCM4i (cm4i), COLA-RSMAS-CCSM4 (cola), GEM-NEMO (nemo), GFDL-CM2.1-aer04 (aer04), GFDL-CM2.5-FLOR-A (florA), GFDL-CM2.5-FLOR-B (florB), NASA-GMAO-062012 (gmao), and CDS-C3S-ECMWF-SEAS5 (seas5). The only qualifying model from C3S is seas5. All other models are from NMME. All models contain leads to 12 months, except GMAO to 9 months, and seas5 to 6 months. The cola model has a documented discontinuity in initial conditions (see Supplementary Note The models used here are from the North American Multimodel Ensemble (NMME)16. The model forecasts have exchangable members , except for COLA-RSMAS-CCSM4, which employs a lagged atmosphere15. We use the first 10 ensemble members from each model. As the forecasts may start after the first day of the first calendar month, the first calendar month in principle contains some assimilated observations and some period of pure forecast. This month thus represents in part the initial state and in part some forecast, but is not strictly either. As such, we denote the lead time for the calendar month in which the forecast commences as lead 0*, where the * indicates that the lead is in fact not well defined here. The forecasts for the second calendar month span leads of roughly half a month to one and a half months, and thus have an average lead time of 1 month. We designate these as lead 1 (month), and so on for subsequent lead times.Though we refer to the NMME outputs as ‘forecasts’, the archive contains a mix of hindcasts and forecasts. The hindcasts all commence in 1982 and switch over to forecasts in 2011 for the CanCM models and GFDL-aer04, and in 2014 for the remaining models. Some of the hindcasts commence on the first of each month, whereas forecasts may commence after the first of each month15 in using ordinary linear regression on observations of Niño3.4. The regression provides a fit between Niño3.4 values in the calendar month, m, where the forecast is initiated, τ being forecast, 23 based on the categories La Niña, neutral, El Niño from Niño3.4 values.We use two simple regression models as skill baselines. The first follows DelSole and Tippett15. This test provides an intuitive way to visualise the difference between two forecasts, f1, and a reference forecast fr, with an assessment of confidence that does not depend on particular distributional assumptions about the forecast errors. A sequence of instances, i, of n matched forecasts, RWi incrementing/decrementing by one whenever the squared error of the model being tested, 42. Serial correlation among the forecasts is an issue for many skill scores, including this one15. Binary scoring will reward a model that is closer to observations more often, even if it does sometimes have large forecast errors. The binary count traces a random walk, which can be compared with an envelope encompassing the range of counts that would be observed 95% of the time by chance under independent Bernoulli trials for p = 1/2. The envelope expressing this range is approximated by 15. We develop and apply here a standardised version of the random walk as a random walk skill score: RWSSi = (1/i)RWi, i =  forecast comparisons. The chance envelope for this score is also (1/i) times the RW envelope. For any comparison, i, the RWSS sits between 1  and −1 (reflecting a forecast that loses to the reference every time).The method used to compare forecasts here is the random walk sign test introduced by DelSole and TippettRWSSi for the last forecast comparison (i = n). This value, RWSSn, represents our final estimate of the relative skill of the two models tested at each lead time. The score for RWSSn ranges from 1  through 0 (model ties with reference) to −1 . The plots of RWSSn also include the 95% chance envelope, where the bounds of the envelope are those that pertain to the last forecast comparison for RWSS.To compare results for the random walk sign test as a function of lead time, at each lead time (for lead months 1–11) we take the value of The random walk score described above uses a distance test (squared error) to reward the model lying closest in distance to the observations at each forecast comparison. In principle, any test can be used for each forecast comparison in the random walk framework. The random walk score can easily be adapted to categorical forecasts, and we do that here for use with the categorically based logistic regression forecasts. In the categorical forecast tests, all forecasts are translated in terms of ENSO category . If one model forecasts the correct category but the other model doesn’t, then the correct model scores one for that test. If the models forecast the same category (right or wrong), no score increment is made for that forecast comparison. No increment to the score is made if both models forecast the wrong category. In particular, no credit is given if one model lands closer to the observed category than the other model if neither are in the correct category. Thus, with the categorical random walk scores, there will be many ‘draws’ where no increment is made, unlike the case for the distance-based random walk score, where draws are unusual. In other respects though, the categorical random walk scores are identical to those described above for the conventional distance-based random walk skill scores.r, for the forecast as a function of both calendar month, m, and lead time, τ, denoted 〈r〉m,τ where 〈 ⋅ 〉 indicates temporal averaging. The reference climatology is then subtracted from the forecasts, F, (as a function of m and τ) to produce an anomaly forecast, f. All results in the paper were repeated with the training and testing periods reversed . For the analysis of ENSO onset the ordering matters and both sets of results (standard and switched) are presented. For all other forecast assessments here the results are qualitatively similar either way, and so only results for the standard periods are presented.We use several different methods to generate anomalies for the model forecasts. The methods are represented schematically in Fig. Box 2. The schematic shows a time series of the observed variable at the top, with the time series divided in half to give a training period and a test period. The training period is typically reserved for generation of a climatology to serve as a baseline reference for the forecasts, and the test period is used to test the anomalised forecasts. For each anomaly calculation method, the calculation is performed by developing a reference climatology, biased’ method as it retains model bias in forming the anomalies. The reference climatology is built from observations in the training period, Otrain,  on model forecasts in the test period , unfair-cv method the reference climatology in the test period is calculated in a cross-validated sense, where a segment of the set of forecasts is removed from Ftest in the period surrounding the time at which each ffcst,test is calculated. Here, we remove the year in which the anomaly is calculated and an additonal set of years either side of that year. We test variants of this with 1, 3, 5, and 7 years total removed in a centred window on the year in which the anomaly is calculated. This cross-validated unfair method is denoted as unfair-cv and is represented by the dashed red lines in Fig. Box 2. The results for unfair-cv are not very sensitive to the window length used here, so we show results for the 7-year window to maximise any potential affect of cross-validation.In the fair. The fair reference climatology, fair anomaly forecasts are For this method the reference forecast climatology is based appropriately in the training period. We refer to this method as fair tested here (fair-sliding), we maintain the same number of years in the reference climatology as fair, but the reference climatology is allowed to slide along behind each forecast , and thus does extend into the testing period for some forecasts (but still uses only observations available at the time the forecast is started). The reference climatology for fair-sliding always contains 17 years up to the year of the current forecast, y, such that the fair-sliding anomaly forecasts are In one variant of fair-all), the reference climatology includes all years in the training and testing period that precede the forecast, and thus the number of years in the reference climatology grows as the forecasts step through the testing period . The first year of the training period is 1982, so the reference climatology for fair-all extends from then to the year of the current forecast, y. The fair-all anomaly forecasts are given by fair variants relative to one another is given in Supplementary Note fair variants are shown in Supplementary Note In another fair variant, (unfair forecasts the observed anomalies are fair forecasts the observed anomalies are When the forecasts are verified against observations, the observed anomalies use the same periods for the reference climatology as the forecasts. For example, for the Forecasting onset of ENSO events involves issuing a forecast of the event before the event has begun. We represent onset forecasts schematically for El Niño in Fig. Supplementary Information FileEditorial policy checklist file


The Ilizarov method has become a widely recognised surgical technique. A bibliometric analysis of the 50 most-cited publications relating to the Ilizarov method was carried out. Cumulative number of citations was 4,918. Mean number of citations was 98. h-index was 50. Impact factor of these journals ranged from 0.5-5.082. Our study suggests that a highly cited and influential paper likely originated from an American journal with a high impact factor and was published in the 1990s/2000s. Our compilation of the 50 most influential papers on the Ilizarov method will prove invaluable to those in training and those involved in further advancing the technique. Famously, his method of distraction osteogenesis for bone lengthening was discovered by accident when callus was seen in a subject who distracted his frame instead of the usual compression.Our understanding of this technique has grown with its continued use and multiple publications. We stand to learn much from those that have gone before us with this technique and their experiences in the published literature are a crucial part of advancements in the field. An in-depth look and subsequent ranking of these publications allows us to ascertain which papers have had the most influence in terms of our clinical decision-making.Citations are a form of recognition between authors of the impact that a colleague's work has had on their own research. Looking at how frequently an article is cited, we can evaluate the impact that article has had on the progression of the field in question. Citations are used in the metric for determining an article's impact factor (IF). We are drawn to journals with a higher impact factor and so citations can be said to indirectly influence the journals we read. IF is equal to the total number of citations for all publications in a journal over the past year divided by the total number of publications published in that journal in the previous two years.Other authors have sought to find the most influential papers across a broad range of surgical specialties including orthopaedics,Our aim with this study was to discover the 50 most-cited papers pertaining to the Ilizarov method by carrying out a bibliometric analysis of previous publications using the Web of Science database see .2To examine the top 50 articles regarding the Ilizarov method, the Web of Science Collection search engine was employed in August 2021. A single search term, “Ilizarov method” was used and articles from 1945 to 2021 were examined. There were no limitations applied to our search filter. 1,480 papers were recovered on the initial search. These papers were then ordered from most citations to least number of citations. Two independent authors reviewed the results and complete agreement between authors was required for an article to be included. If an abstract did not yield sufficient information to decide on article inclusion, a full-text review was carried out. Papers deemed not relevant to the Ilizarov method were excluded. The first 75 papers were examined thoroughly. This led to the exclusion of 25 papers based on irrelevance to the topic in question . A decis3The cumulative total of citations for the most-cited 50 publications was 4,918. Each paper was cited 98 times on average. The h-index of this list of articles was 50. The top 50 articles can be found in Clinical Orthopaedics & Related Research (n = 13) produced the highest number of papers on the list – followed by Journal of Bone & Joint Surgery – British Volume (n = 6), Journal of Bone & Joint Surgery – American Volume (n = 4), Journal of Orthopaedic Trauma (n = 4) and Osteoarthritis & Cartilage (n = 4). The definitive list of journals can be found in The 1990s saw the greatest number of papers (n = 27). The 20 year period between 1990 and 2010 made up 94% of the top 50 papers . These 510 unique countries contributed to the top 50. USA provided the most articles with 24 (48%), followed by Italy with 5 (10%) and Netherlands with 5 (10%). A full list of countries of origin can be found in 4In our study,we searched the Web of Science database to find the 50 most-cited papers on the Ilizarov method. In this way, we hoped to establish the papers which had influenced the field. A citation analysis such as this one, is important to the wider orthopaedic community as it chronicles the papers, authors, journals and eras that have shaped the discipline as we know it. Our study provides insight into the practice-changing developments that have taken place over the past 76 years.In our study, citation number was used to estimate the influence of a certain paper and warrant its inclusion in the top 75. This method of citation analysis has been debated by some,The most-cited paper was “The principles of the Ilizarov method”The second most-cited paper was Paley's “Ilizarov bone transport treatment for tibial defects”,10 unique countries contributed to the top 50, with the USA contributing the majority . That th,There are several inherent limitations to a bibliometric analysis such as ours. This has been detailed and acknowledged by previous authors carrying out a similar study type.Obliteration by incorporation is one of these. This refers to the highly-influential or “classic” articles becoming incorporated into clinical practice and widely-acknowledged and so, the need to cite them no longer remains.Incomplete citing may also occur within papers if an author is attempting to persuade their audience instead of acknowledging a previous piece of work.Aspects of a bibliometric analysis make it difficult to control for bias, as was the case in our study. Self-citation, language bias, journal bias and in-house bias (among others) were not controlled for in this study.5Our study highlights the 50 most-cited papers pertaining to the Ilizarov method. In this way, we have established those papers which have influenced the development and implementation of the technique. We have seen the journals, countries and authors that have made the greatest contribution. We are aware that a citation analysis does not directly measure scientific quality but it does indicate those papers which have significantly contributed to the area of interest. This compilation of influential papers will prove invaluable to orthopaedic trainees along with those involved in advancing the Ilizarov method as a surgical technique.“This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.”“The authors have no conflicts of interest to disclose.”


This work presents experiments about the transmission of electrons with an energy of around 15 keV with beam currents up to 20 µA through macroscopic glass capillaries. A systematic study was conducted to experimentally investigate the transmission of electrons through borosilicate glass capillaries with curve angles of 90°, 180°, 270° and 360° for the first time. The focus of the work was to identify the conditions under which the injected electron current is transmitted through the capillary. It was also shown that the transmission process in the macroscopic capillaries can be optically observed by cathodoluminescence—the interaction of electrons with the capillary surface causes locally a blue glow. Different distinctive “glow states” were observed and are found to correlate with different states of electron transmission. Since then, tests with different ion species, particle energies, capillaries ranging in size from nanocapillaries to macrocapillaries and different geometries , materials like ceramics, polymers and glass and energies in the range from several hundred eV to MeV have been done. For this, we refer to an extensive review paper by Stolterfoht et al.2 and some newer papers4. The transport of ions through the capillaries has been mostly attributed to charge patches at the inner capillary surfaces created from part of incoming ions. These patches repulse other incoming ions and prevent them from colliding with the walls. Several simulations8 have aided in understanding this effect which has become known as “ion guiding”.While the standard method to steer the trajectory of charged particles is by means of electrostatic and magnetic optics, insulating capillaries also show the ability to deflect and focus injected charged particle beams. This phenomenon was first observed nearly two decades ago by Stolterfoht et al. when highly charged Similar research has been carried out with electrons that passed through dielectric capillaries ranging from foils with arrays of holes with nanometer sized diameters to single capillaries with lengths of several centimeters and diameters ranging from micrometers to several millimeters.2O3 nanocapillaries with slow electrons with energies of 200 to 350 eV11. At the Western Michigan University, several experiments with the transmission of slow electrons (≤ 1000 eV) were conducted with PET nanocapillaries and subsequently extended to polycarbonate nanocapillaries and glass macrocapillaries with straight and tapered geometries17. Additional simulations were performed by the Vienna University of Technology to investigate the underlying mechanisms19.First investigations of this kind were performed in 2007: At the University of Belgrade Milosavljević et al. irradiated Al20. These tests began in 2010 with experiments on the transmission of electrons through several macro-sized tubes, polycapillary columns and cones with electron energies between 2 to 10 keV and currents of up to several µA21. Subsequent tests included more tests on tubes, tapered capillaries and PET nanocapillaries25.Several experiments were carried out at the Moscow State University and at the Belgorod State University. Interestingly, during many experiments the electron energy was higher on the order of 10 keV26 conducted experiments with a 15° curved SiO2 tube  and observed the transmission of electrons in the energy range of 1100 to 1500 eV. Measurements with a position sensitive Faraday cup showed a symmetric angular distribution of the transmitted electrons, which was interpreted by Wang that a certain fraction of the electrons is transmitted without collisions through the capillary. However, no direct measurements of the energy of the transmitted particles were conducted. Petukhov et al.27 characterized the transmission properties of macroscopic glass and polyurethane tubes  with curve angles of 0°, 45°, 90° and 180° in the energy range of 10 to 20 keV with currents of 5 to 50 µA. The transmission coefficients and the energy spectra were measured with a cylindrical electrostatic analyzer and the X-ray spectra produced by electrons exiting the tube were also investigated. The current transmission factor did not so much depend on the initial energy of the electrons but dropped from approximately 80% at 0° to below 50% at 90° bending angle°. However, the electrons lost kinetic energy during the transmission process: For higher bending angles the maxima of the transmission spectrum energies dropped to lower energies, the spectrum broadened with a significant increase of low energy electrons.The investigations were also extended to curved macrocapillaries. Wang et al.28. This means that the transport of electrons through dielectric capillaries significantly differs from the ion guiding mechanism. Nevertheless, the term “capillary guiding” is understood to describe the transmission of particles along the capillary axis, whether they are deflected electrostatically by charge patches or by scattering on atoms of the bulk material. Only secondary electrons are specifically excluded from this definition2. Thus the transmission of electrons through capillaries will be referred to as “electron guiding”.The electron transport process is still not fully understood but believed to be based on a combination of small angle elastic and inelastic scattering of the electrons with atoms in the bulk material of the capillary walls as well as similar to ion guiding formation of charge patches in deeper layers of the capillary surface. This is based on the observation of elastic as well as inelastic transmitted electrons and a measured time delay between the injection of electrons and the transmission at the outlet of capillariesIn this work we describe the transmission of electrons through curved macrocapillaries with bending angles up to 360° and currents of around 20 µA. By doing so, we significantly expanded the range in which the successful transmission of electrons has been described in the open literature. Furthermore, as we will discuss in this work, large transparent capillaries enable a new approach for the investigation of the guiding effect for electrons because the transmission process is accompanied by the local emission of light in the visual range from cathodoluminescence, indicating regions in the capillary where electrons hit the wall. This work is mainly focused on observing these two aspects without investigating the energy spectrum of the transmitted particles. Therefore, we cannot make definite statements about the underlying transmission mechanism. Energy measurements are planned for future tests.This paper is structured as follows: The next two sections describe the experimental setup and the capillary samples. Then, the experimental results are presented and discussed in a separate section. We conclude with a summary and outlook.For the electron guiding experiments the glass capillaries were tested one after another in a cylindrical vacuum chamber (Ø0.9 m × L1 m) equipped with a Pfeiffer HiPace 2300 turbomolecular pump capable of providing a base pressure of 1E-6 mbar. A viewport in the chamber allowed the visual observation of the experiment.The experimental setup consists of the capillary itself, which is mounted to a holder. An electron source is positioned in front of the capillary inlet. A target electrode is placed in a certain distance from the exit of the capillary to collect the transmitted electron current. An overview of the setup is shown in.A custom made hot filament electron source consisting of a v-shaped tungsten filament enclosed by a Wehnelt cylinder and a grounded acceleration electrode was used for the experiments. The filament is capable of emitting several hundreds of microamperes. The acceleration voltage is up to 16 kV.The capillaries were mounted to an insulating holder at the inlet region. An aperture system is placed in front of the inlet. It consists of two electrodes which are electrically insulated from each other by a 3 mm thick insulating spacer. The first electrode consists of a graphite sheet and has as an aperture diameter of 4 mm . It faces towards the electron source and collects any currents emitted by the electron source which do not enter the capillary. This way the maximum electron beam divergence becomes 5 degrees in a distance of 50 mm to the electron source. The second electrode is directly attached to the capillary inlet with an aperture diameter of 6 mm and collects the current that enters the capillary but is not transmitted. It therefore acts as “back-flow” collector. An offset voltage was created between the Wehnelt cylinder and the filament by inserting a pre-resistor in the range of 100 kOhm to 1 MOhm. This provided further control over the beam shape and the current density. The emission current from the electron source The transmitted current mentclass2pt{minimThe currents were measured with a LabJack T7 pro based data acquisition system with a resolution of 0.1 µA and 5 Hz.Preparatory to installing the capillaries into the setup, efforts were made to remove any residual charges on the inner and outer surface of the capillaries that may have built up during handling and storage by cleaning the surface with isopropanol.For the experiments the focus lied on the transmission of electrons through macroscopic capillaries with different curve angles. To limit the amount of parameters, capillaries with different bending angles were manufactured that all shared the same inner diameter of approximately 6 mm, a wall thickness of 2 mm, a curve radius of 140 mm and a straight inlet region with a length of 150 mm. The inner diameter of the capillaries together with the straight inlet region ensured a large aspect ratio  for all capillaries. Samples with the following curve angles were custom manufactured: 90°, 180°, 270°, 360° and their geometric properties are summarized in Table Four different capillaries were tested in sequence from the smallest curving angle (90°) to the largest (360°). Due to time constraints every capillary was tested only once.The first test was carried out with the cleaned 90° capillary in which an electron beam with an energy of 14.8 keV was injected. To create a more narrow beam, an off-set voltage of entclass1pt{minimaThe total testing duration was 4 h to investigate long term behaviour of the guiding performance. It can be seen, that the transmitted current was very low at the beginning when about 2 µA reached the target, which is assumed to be the result of small angle scattering processes and secondary electron emission inside the capillary. At the 20 min mark, the target current fell close to zero for a few seconds, then abruptly rose to about 94% of the maximum injected current of 15 µA and afterwards the electron transmission was stable for the next 160 min, as the data in Fig. When testing the 180° capillary, we faced some issues concerning the beam injection as unfortunately the capillary inlet and the electron beam were not properly aligned. Hence an adjustment was made where the electron beam was broadened by reducing the offset voltage on the Wehnelt cylinder to For the test including the 270° capillary the electron beam was narrowed again by applying an off-set voltage of On–off tests were carried out similar to those for the 180° capillary with similar results which supports the model of charge patch assisted guiding.In Fig. 29. Throughout the tests, we were able to observe different glow states which appear to correlate with the electron transport. The 90° capillary and the 360° capillary were chosen for a detailed investigation of this phenomenon. Although the bright patches at the inlet and curved parts of the capillaries could be observed with the naked eye, the photos were taken with high exposure times, which made the glow pattern in the capillaries better visible. An f-number of F/3.5, a shutter speed of 30 s and an ISO value of 100 were used. As far as we know, there are no studies concerning an optical observation of the electron guiding effect yet. In Fig. A blueish glow of the capillaries could be observed in the course of all tests. This is most likely attributed to the cathodoluminescence of glass where impacting electrons lead to the creation of electron–hole pairs in the material which subsequently recombine and emit photons in the visible spectrumFigure The 360° capillary was mounted in a way that every section could be observed, as depicted in Fig. The successful transmission of electrons through all capillary configurations.The observed time delay before the start of the transmissionBlocking of capillary after long-time transmissionStable transmission in on–off testsVisual observability of guiding process due to cathodoluminescence.In the discussion of the experimental observations we want to focus on the five following aspects:Electron transmission through all four capillary configurations was achieved in all tests with a particle energy of approximately 15 keV. This value was determined from preliminary tests. Other parameters varied: For example the currents that were injected into the capillaries varied from 3.3 µA to 20 µA and the transmission efficiency was found to be between 73% to nearly 100%. Due to a lack of a device to measure the particle energy of the transmitted electrons, it is not possible to clearly define if the particles were transported through the dielectric tubes primarily be elastic scattering, inelastic scattering or the guiding from assembled negative charge patches. Future tests will have to show if there is a minimum kinetic energy for the transmission process.17. The scenario of electron transmission after a quiet period has been observed in several studies28, where electrons were guided through PET nanocapillaries. However, the current densities were much smaller compared with our experiments. Furthermore, Petukhov et al.27 mentioned no time delay for the transmission of currents through capillaries with 90° and 180°. The filament electron gun in our experiment is a source of uncertainty. A variable focus was achieved by means of the negative voltage offset created by a pre-resistor of the Wehnelt cylinder. The aperture electrode in front of the capillary inlet provides an additional collimation. But it is unclear, if the local beam current density and beam alignment were similar in all experiments and stable with time. The focus of the electron source could only be significantly changed by changing the pre-resistor, which prevented a dynamic adaption of the focus without switching the source on and off in between.The irradiation of the capillaries showed a significant time delay before efficient guiding was achieved. One exception was the 270° capillary which was irradiated with two different beam configurations before the current was transmitted. Therefore, no exact charge up phase could be determined for this sample. In studies performed with nano- and microsized capillaries, the time delay before high transmission was a clear indicator for the build-up of negative charges on the inner capillary surface assisting the electron guiding process. This might also be the case in our experiment. The build-up of a charge distribution could lead to the deflection of further incoming particles towards the capillary exit. A long-term test with the 90° capillary showed a stable electron transport over the course of 2.5 h. An interruption of the electron transport lead to a sudden breakdown of the transmitted current from over 90% to only 15% (see Fig. The current transmitted through the 180° sample showed a more stable behaviour and the quiet period was shorter than for the 90° capillary. It has to be noted, that in this test a much lower current and also a lower current density was injected into the capillary due to misalignment in the setup. These factors appear to have a strong influence on the guiding performance, as the following 270° test showed. Here a focused beam could not be transmitted, whereas an injection with lower current density lead to guiding. This shows that the potential charge distribution inside macroscopic capillaries also depends on a number of beam parameters e.g. the current density, the angle of injection and the beam divergence which affect the charge distribution on the inner capillary walls.17. During the equilibrium the transmission efficiency was at around 74%, which is much lower compared to the previous samples. This might be attributed to the greater capillary length and higher aspect ratio as well as the larger bending angle but has to be examined in further studies.While a quiet period followed by an instant transmission phase was observed in the 90° and 180° samples, the data of the 360° helix capillary test show an intermediate phase in which the transmission was accompanied by strong noise. This is most likely the phase in which the transmission varies as a result of the dynamic evolution of additional negative charge patches, possibly accompanied with sudden discharges as reported by DassanayakeAn overview of parameters used in the presented tests are given in Table 5. A study on the time dependence of electron transmission through a single glass capillary performed in 2010 reported a decay constant of 8 min17. However this experiment was conducted with incident energies of up to 800 eV and in geometrically a smaller sample than in our experiment. Thus we assume that the relaxation time in our case is much larger due to larger geometries and higher incident energies, which in turn lead to larger drift distances and stronger penetration of the particles into the bulk material. That said this subject definitely has to be looked more into in future investigations.Preliminary on–off tests to investigate the durability of the capillary state were carried out. An example of the corresponding data is displayed in Fig. 30. In 2013 an experiment was performed by Dassanayake in which the irradiation of a single glass capillary was repeated after a discharge time of 6 days with differing results14. Therefore multiple tests on the same sample with reduced parameters are planned for future experiments to investigate the repeatability and look for further potentially influencing aspects such as possible damage of the capillary material caused by irradiation or the dependence of the guiding performance on temperature and ambient pressure.As already mentioned, due to time constraints every sample was only tested once. A study on electron transmission of 10 keV electrons through a tapered glass capillary was conducted by Vokhmyanina et al. in 2018 where transmission was achieved, but the repeatability of the results were not stableDuring transmission, the glowing spots are regions where electrons penetrate inside the bulk whereas the particles are deflected above the surface in the dark areas.Electrons are also scattered in the dark regions but the incident particles do not transfer enough energy to enable light emission.Non-glowing parts of the capillary might indicate regions where the incident electrons are too slow to enable light emission.The cathodoluminescence effect and its correlation with the transmission stage is in our opinion a very interesting and valuable observation in the research of electron guiding through glass capillaries. The intensity of the glow might give information about the energy of the incident particles. . Also, since the electrons need to hit the wall with sufficient energy, the glow patterns give new information about the transport mechanisms inside the capillary. The following possible explanations might be considered:The correlation between the glow states and the guiding phases should definitely be investigated more in further research.Transmission of electrons through macroscopic glass capillaries with curve angles of 90°, 180°, 270° and 360° were tested with a high energy electron beam. Overall stable electron transport of around 74% was achieved in the 360° capillary whereas a transmission efficiency of more than 90% with total currents up to 20 µA was observed in the remaining samples. We also observed a clear time dependence of the transmission similar to the temporal behaviour reported in previous studies with lower energies and smaller capillaries. Due to the overall differences in capillary size and the parameters of the incident particles, it is difficult to apply the results of the studies performed with smaller capillaries one by one. Nevertheless, the observed time delay is a strong indicator that a charge deposition inside the capillary is required to create a field distribution which leads to the deflection of further incoming particles towards the capillary exit. The variation of the beam properties also revealed its influence on the guiding efficiency as the transmission of beams with lower current density was more successful.A blueish glow of the samples was visible in all tests, which is attributed to the cathodoluminescence of borosilicate glass and is most likely a strong indicator for the interactions of the electrons with the material. The glow was visible in different regions of the capillary samples and the formation transformed depending on the guiding stage. The 360° helix clearly showed different spots, which appear to correlate with the charge distribution and the guiding state of the capillary.Additional work is required to further examine the electron transport process through bent capillaries. To understand the guiding mechanism, investigation of the energy distribution of the transmitted beam is crucial and will be implemented in future tests. Also additional studies are necessary to investigate the influence of different parameters on the guiding performance, such as primary energy, current density, beam shape, capillary size and many more.The cathodoluminescence of the capillary samples is an evident indicator for the current guiding stage. It is expected to be a part of future studies concerning the electron guiding through macroscopic glass capillaries to reveal more information about the underlying mechanism of the guiding process.


Gerda) collaboration searched for neutrinoless double-Gerda dataset, tailored to preserve the excellent resolution of the individual germanium detectors when combining data over several years.The GERmanium Detector Array ( Gerda) collaboration searched for the Q-value of Neutrinoless double-mentclass2pt{minimWe used three types of enriched germanium detectors: 30 broad energy germanium (BEGe) detectors, 7 coaxial detectors, and 5 newer inverted coaxial (IC) detectors. The BEGe detectors are smaller (average 0.7 kg) but offer superior energy resolution and pulse shape discrimination (PSD) properties compared to the coaxial detectors  but withThe array of germanium detectors was immersed in a cryostat filled with 64 metail in .Igex [Gerda experiment were added and the liquid argon volume around the detector array was instrumented with photosensors as a veto against radioactivity [The first phase of the experiment was operated with 18 kg of coaxial detectors  format , 17 and software , as is tsoftware . An imprsoftware , which rspectrum .A set of heuristic event selection criteria is applied to ensure that events recorded during calibration are of a physical origin, and to reduce pile-up events. The underestimation of energy for these events cause low-energy tails in the spectra of low 0.1% .Nuclei of the mentclass2pt{minimT is applied assuming a linear energy scale without offset:The TSpectrum class of ROOT is used to find peak positions in the uncalibrated spectrum, such that all peaks with amplitudes exceeding 1/20 of the amplitude of the most prominent peak are found. This threshold was chosen to avoid the detection of spurious peaks. The peak with the highest energy is identified as the full energy peak (FEP) of the r effect .To determine the position g(E) is used to model the peak, and a linear function n, Minimally, a Gaussian For high statistics peaks , the SEP, and the DEP, a step function is used to model the flat backgrounds occurring only above or below the peak from multiple Compton scatters:For the high statistics peaks as defined above, a low-energy tail is additionally used to model the effects of incomplete charge collection and the residual presence of pile-up events:mentclass2pt{minimPeaks are excluded after the fit if any of the following heuristic rules are fulfilled: (i) the estimated FWHM is above 11 keV or below 1.5  keV; (ii) the peak maximum is lower than 2.5 times the linear component of the background or lower than 10 counts; (iii) the fitting error on the FWHM is larger than the FWHM itself. These rules are purely heuristic and designed to remove peaks that cannot be fitted well, mainly due to low statistics.Typically around 5–8 peaks per detector survive all selection criteria. The FEP is always identified, since the peak identification algorithm requires it. In T into a physical energy in keV. We plot the peak positions in terms of the uncalibrated energy estimator T of identified peaks against their physical energies From the obtained peak positions, we determine the calibration curve which is a function to convert the uncalibrated energy estimator e values , and theTypically, a calibration curve is used to calibrate the physics data following a calibration run. However, if a calibration is taken after changes in the experimental setup, or instabilities in the detector array, the calibration curves may be applied retrospectively to additionally calibrate the period between the changes or instabilities and the calibration run. The unstable period itself would not be used for physics analysis.After the 2018 upgrade, several detectors  exhibited larger residuals in their calibration curves compared to other detectors, up to 2.5 keV at 1.5 MeV. Whether these effects are directly related to a change in cable routing is unknown. These effects could be largely accounted for by the incorporation of a quadratic correction to the calibration curves,The parameters entclass1pt{minimaTo consistently combine data over an extended period of time while preserving the excellent energy resolution of the HPGe detectors, it is vital to monitor the stability of the energy scale between calibrations and exclude periods with significant shifts and fluctuations which would contribute to the width of the peaks. As previously mentioned, test pulses are regularly injected into the readout electronics to monitor the stability of the data acquisition system. Their signal magnitude corresponds to an energy of about 3 MeV. Periods with significant jumps or drifts (>1 keV) in the amplitude of the test pulses are excluded from data analysis and a calibration is performed once the detector stabilizes. The corresponding loss of exposure is at the few-percent level. The origin of these shifts is largely unknown, but may be caused by temperature changes in the electronics.Additionally, we monitor the stability of the FEP position in the calibration spectrum. If the position of this line changes by more than 1 keV between successive calibrations without an identifiable reason , the data of the respective detector are discarded from the analysis for that period of time. The corresponding exposure loss is at the few-percent level. Smaller or temporary drifts may still affect the obtainable energy resolution and are discussed as a systematic uncertainty in Sect. Gerda analysis [Due to hardware changes, the detectors may experience changes in their energy resolution and energy scale over longer periods of time. To more accurately reflect the properties of a detector at a certain time, for the final analysis  we dividGerda reported in [Gerda data were analyzed, we calculated a resolution for each partition, a much more fine-grained approach. At the expense of increased complexity, the partition approach improves the physics result by capturing the variations among the detectors as well as the variation over time.Depending on the specific physics analysis, we calculated the energy resolution either by partition, described in the previous section, or by detector type. For the orted in , where torted in , where aGerda  and any other experiment with a modular detector setup, here, we discuss both approaches. While the detector type approach was replaced in favor of partitioning for the final Since both methods are applicable for To obtain the The peak identification and fit procedure described in Sect. The SEP is broadened due to the known Doppler effect and is thus excluded . We alsoE is then fitted with the function [a and b are fit parameters. The former accounts for the contributions from electronic noise, while the latter accounts for statistical fluctuations in the number of charge carriers. The resolution at The dependence of the function 8\documenThe resultant FWHM resolutions at The appropriate method for calculating effective resolutions by detector type depends on the specific application.For background modeling, energy dependent resolutions are required, i.e. resolution curves. To calculate these for a DTD, the procedure is similar to that for the partitions, though weighting is now required to combine the resolutions from different detector partitions. When data from multiple partitions are combined by adding their energy spectra, Gaussian peaks in the individual spectra combine to become a Gaussian mixture, namely the sum of multiple Gaussian distributions with different centroids and resolutions. The resolution of individual partitions in a DTD is stable within a factor of 1.7 for BEGe and IC detectors. For coaxial detectors there is a slightly higher fluctuation, but still within a factor of three. The variation in position of the centroid is much smaller than the energy resolution, typically around 0.2 keV. Therefore the shape of a peak in the combined energy spectra remains approximately Gaussian and can be characterized by an effective resolution, computed from the resolution of individual partitions.The variance of a Gaussian mixture is given by:aussians .For a DTD comprised of individual partitions, these parameters stand for the individual partitions’ resolution Since the biases in the energy scale are small, we can neglect the differences in the peak positions. Eq. For instance, the simplified model of the FEP is a Gaussian with a mean of 2614.5 keV and a width fixed to the effective resolution see Eq.  of the DTo calculate the effective resolution curves for each DTD, first the Once the effective resolutions for each energy and DTD have been determined by weighting partition resolutions with Eq. The obtained effective resolutions and functions of the three detector types are shown in Fig. GerdaGerda Phase II data, very few events  are observed close to As mentioned before, in earlier  such as , partitientclass1pt{minimaThe statistical uncertainty on the energy resolution decreases with rising statistics over time, and is on the order of only a few eV. As such, the uncertainty on the energy resolution is dominated by systematic effects. We consider various sources of systematic uncertainty, given here in decreasing order of their contribution: (i) resolution shifts over time; (ii) energy scale shifts over time; (iii) choice of the resolution fitting function. Due to the nature of these uncertainties, their magnitude will not decrease over time, but could change if the detector setup or analysis methods change.In the following sections, we explain how individual contributions to the systematic uncertainty were determined Sects. –5.3, anda and b of Eq. We consider a systematic uncertainty estimated from the fluctuations in the resolution obtained for each calibration over time. For each partition, we calculate the standard deviation of the resolution at FEP, Once the energy scale has been determined via a calibration as described in Sect. This additional contribution was estimated using the position of test pulser events  decays . The meaGiven their proximity in energy, the extracted resolution for each of the two lines is expected to coincide within 0.05 keV. Indeed, no significant difference between the resolutions of the two peaks was found.We compared the resolution obtained in the potassium lines with the one predicted from the resolution curves extracted from the combined energy spectra (see Sect. Gerda experiment. The event energies are reconstructed using the ZAC filter to minimize the effects of low-frequency noise. To preserve the excellent energy resolution of the germanium detectors when combining data over a long period of time, they are calibrated weekly using A reliable and stable energy scale is crucial to the search for For each calibration, the stability of the energy scale and resolution is monitored via the 2.6 MeV FEP from To more accurately reflect the properties of a detector at a certain time, we have introduced the partitioning of the detectors’ data into stable sub-periods. The stability is based on the long-term changes of the energy resolution at the FEP and the residual at the SEP.For each partition, a combined calibration analysis is performed to calculate the energy resolution used for the Alternatively, effective resolution curves per detector type are calculated by modeling the signal by a single Gaussian with a width according to the standard deviation of a Gaussian mixture of the individual detector partition contributions. Over Phase II we obtained exposure-weighted average resolutions at Dedicated studies were performed to determine the resolution systematic uncertainties for the The energy bias for the events near Gerda described in [Gerda program in reaching the world’s most stringent Legend in developing the next generation of The energy scale, partitioning, resolutions, and energy biases discussed in this paper are essential to the final search for ribed in . The suceriments .


Let  Let Robin boundary conditions are used in heat conductance theory to interpolate between a perfectly insulating boundary, described by Neumann boundary conditions ues (see ). Our goues   :1.1\docThe first result concerns the mean value of the gaps:Let Since the differences n’s, Let x and every other point of x so that it is star-shaped with respect to x.Recall that a domain Let Note that for quantum star graphs, this lower bound fails .We give a quantitative upper bound:Assume that While quite poor, it is the best individual bound that we have in general. Below, we will indicate how to improve it in special cases.unbounded?Are there planar domains where the differences We believe that this happens in several cases, e.g. the disk, but at present can only show this for the hemisphere , which iTo a piecewise smooth planar domain one associates a billiard dynamics. When this dynamics is ergodic, as for the stadium billiard see Fig. , we can Let all the gaps converge to the mean.If the billiard dynamics is uniformly hyperbolic, we expect that more is true, that A key ingredient in the proofs of the above results is that they can be connected to ps Lemma \documentMost of the above results easily extend to higher dimensions: The upper bound Theorem , the meaIn Sect. For the special case of rectangles, we show that the RN gaps are bounded:n,Let P(s) of the sequence is then defined asWe use Theorem It is well known that the level spacing distribution for the Neumann (or Dirichlet) eigenvalues on the square is a delta-function at the origin, due to large arithmetic multiplicities in the spectrum. Once we put a Robin boundary condition, we can show  that theThe level spacing distribution for the desymmetrized Robin spectrum on the square is a delta-function at the origin.As we will explain, upper bounds for the gaps For the unit disk, for any fixed We present some numerical experiments on the fluctuation of the RN gaps. In all cases, we took the Robin constant to be In Fig. The disk admits separation of variables, and as is well known the Dirichlet eigenvalues on the unit disk are the squares of the positive zeros of the Bessel functions mentclass2pt{minimFor the remaining cases we used the finite elements package FreeFem , 20. In It is also of interest to understand rational polygons, that is simple plane polygons all of whose vertex angles are rational multiples of t}π Fig. , when weThe case of dynamics with a mixed phase space, such as the mushroom billiard investigated by Bunimovich   in  using a Let According to  are The frequencies for the interval [0, l result , we dedum, n) lying in a set The interval In this section, we show that the level spacing distribution of the Robin eigenvalues for the desymmetrized square is a delta function at the origin, as is the case with Neumann or Dirichlet boundary conditions.P(s) of the sequence is then defined asRecall the definition of the level spacing distribution: We are given a sequence of levels Recall that the Robin spectrum has systematic double multiplicities (σ) . Hencey. Of these, there are at most I such that C, y are fixed, we conclude thatP(s) is a delta function at the origin. Denote by  Theorem : \documef Landau  states tNote that the claim is not that all gaps In this section we prove Theorem Let We first note that  gives10.Below we implement this strategy for the disk to obtain Theorem The eigenvalues of the Laplacian on the disk are squares of zeros of Bessel functions and understanding Weyl’s law leads to requiring knowledge of the semiclassical asymptotics of these Bessel zeros; the nature of these asymptotics leads to an exotic lattice point problem, as was exploited by Kuznetsov and Fedosov  and ColiDefine the domainLetFix The argument extends   \documeThe ssing in .k we will use the following estimate:For large values of There exists a constant By Lemma By Lemma


Bipolar disorder is a chronic and recurring psychiatric illness. Emphasis on enhancing key protective factors like social support systems and promoting this to minimize risk factors like non‐compliance is one of the key strategies tied to enhance overall psychological, intellectual, and emotional health for symptoms remission and relapse prevention even during adverse situations like the COVID‐19 crisis. We intend here to point out implication of the dynamics of the protective and risk factors for bipolar mood through a 23‐year patient from eastern Nepal, which is largely harmonious in its multi‐ethnic, multilingual and multicultural social composition. This attribute of social cohesiveness and compassion is evident in this case report. When disturbed and ill, neighbors from native semi‐urban Nepalese society did support even in the times of crisis of COVID‐19 pandemic. The support of other people including neighbors is a key factor for the short‐term and long‐term management of bipolar mood. It is important in the management of bipolar case to enhance protective factors like social support systems and to minimize risk factors like non‐compliance for symptoms remission and relapse prevention even during the COVID‐19 Pandemic. The overall lifetime prevalence of bipolar spectrum disorders, based on a large cross‐sectional survey, was 2.4%, with an account of 0.6% prevalence for bipolar type I and 0.4% for bipolar type II.The Second wave of COVID‐19 was recorded in Nepal by April/May 2021, after the exponential rise of cases.2A 23‐year‐old unmarried Hindu male from Bishwakarma (ironsmith), a Dalit (oppressed) ethnicity,The history of substance use was present in a problematic pattern in his father and three elder brothers. The mother passed away when the patient was 5 years of age. Father committed suicide by hanging after 6 months of the death of their mother under the influence of alcohol. The third elder brother with a history of multiple substance use  was kept in prison for possession of an illegal amount of cannabis and involvement in a fight and robbery. He died during his stay in prison.At the age of 13 years, the patient took his first puff of tobacco smoke under influence of his peer and the pattern of use was 2–3 sticks per day. Two days later of tobacco smoking, he started using marijuana out of curiosity and the current pattern was 1–2 sticks every 3–4 days. Three years later, he started using tablets of Nitrazepam 5 mg 2 tablets on and off that, as per the patient, gave him more energy while working as a conductor. Later, he used Spasmoproxyvon, Nitrazepam, and Opidol in combination, with 10 tablets per day, from his peer circle. If not available, he also used cough syrup (opioids), shared among friends. He would occasionally use locally distilled alcohol, the amount being 50 ml/day. The last use of all substances was 7 days before the presentation to our hospital.After damaging a battery connecting to the wrong charging point and asking the workplace supervisor for money with an excessive desire to get married soon, he was fired from his job. He entered one of the neighbor's houses without permission and requested a young girl to get married to him. The patient started talking in a loud tone, the content of being a billionaire, having excessive money and power, and changing the topic frequently. He started playing television in a loud volume and cleaning the television and furniture at night time. He started overdemanding for food items asking for tea without finishing the current meal which was served to the patient. Despite a decreased number of hours of sleep, he appeared fresh and energetic in the morning roaming in his place. He was brought forcefully by his family members to an emergency. Initially, he was admitted with a diagnosis of substance‐induced psychotic disorder with harmful use of nicotine, cannabis, benzodiazepine, opioids, and alcohol. The Clinical Opiate Withdrawal Scale (COWS) score was 3. Blood investigation parameters were within normal limits. Young Mania Rating Scale (YMRS) was 36/60 at the time of admission. However, during the ward course of 43 days, he had a persistent mood elevation with the delusion of grandiosity and lack of insight. The diagnosis was revised to mania with psychotic symptoms. He gradually recovered after Olanzapine was optimized up to 30 mg. Lithium 900 mg was added as an augmenting agent for the predominant euphoric picture. Injectable Haloperidol 10 mg and Promethazine 50 mg were kept initially for behavioral control. At the time of discharge, the YMRS was 2/60. He was non‐compliant 2 months after the discharge and was in the same pattern of substance use until the current illness started.After the death of his parents, the eldest brother who was the primary caretaker continued using alcohol in the problematic pattern. The patient was brought up in a community belonging to different ethnic castes who were concerned about the patient's illness. Three years later, the patient was brought to this hospital by his neighbors who belong to different ethnicity castes 3Early parental loss is one of the specific life events linked with risk for mood/bipolar disorder, which was present in our case.The Eastern part of Nepal, like other parts, is largely harmonious in its multi‐ethnic, multilingual, and multicultural social composition despite traces of the caste system.It would be pertinent to review the following Table  to under4This case report entails highlighting some of the illustrated protective and risk factors of bipolar mood through a 23‐year‐old man from eastern Nepal who became ill the second time during the second wave of COVID‐19. Even during adverse situations like this, harmonious relationships displayed by the neighbors in the community can play a role in the management of this recurring and chronic illness; such favorable social support is associated with a potentially good outcome even in bipolar illness. Considering the social context during admission and targeting the approaches to enhance the neighborhood and social support is one of the key strategies tied to improve patient outcomes.The authors state that there is no conflict of interest.DRS involved in conception, design, collection of data, and drafted and edited the manuscript. SRU collected the data, drafted the manuscript. DRS and SRU published the final approval of the version.Ethics approval was not required.Written informed consent was obtained from the patient to publish this report in accordance with the journal's patient consent policy.