dataesr/scientific-paragraphs-categorization huggingface dataset:
For the purposes of this study, an eighth step-refining the data-was added, because experimental data is frequently not normally distributed, which in turn prevents the drawing of empirical models. As detailed in Figure  1 , this adapted workflow will serve as an outline for this study. Although the planning of a DoE is closely linked to the system under study, the methodology described in this paper is adaptable to other designs. This paper illustrates the setup of an OCD designed to understand the effect of formulation on the capacity of Li-ion batteries at high currents. The mathematics on which the DoE are based will not be discussed here, as there are already numerous resources on this topic  [5] [6] [7]. As these calculations are complex, software assistance in the planning and analysis of the design is highly recommended.
Here, Design Expert (Stat-Ease Inc. ) was used as a data analytics tool, in conjunction with Matlab (Mathworks) to store and manipulate experimental data. Standard DoE studies are typically articulated around seven or fewer steps  [3, [5] [6] [7]. For the purposes of this study, an eighth step-refining the data-was added, because experimental data is frequently not normally distributed, which in turn prevents the drawing of empirical models. As detailed in Figure  1 , this adapted workflow will serve as an outline for this study.
Refining the Data Experimental data often lacks key properties, such as a normal distribution, to create meaningful empirical equations. This normality is an essential assumption required to use further statistical tests and use a regression to reach empirical models with appropriate confidence. This section addresses how to circumvent this issue and refine the data to improve precision and robustness. Model quality was judged on several parameters, including their regression coefficient R 2 and normality, as well as the residuals for each experiment. The first step is to seek outliers, as even one can significantly degrade the model's precision. A strong outlier can alter predicted values to the point that it can fail to be identified as such. Externally studentized residuals, or studentized deleted residuals, are an appropriate solution to this issue because the model with which the predicted value is calculated is made without this experiment's value  [5] [6] [7].
Hence, if the transformation normalizes the distribution, it should be used even if a physical interpretation of the transformation is not yet possible. The best transformation to apply can be inferred from the Box-Cox representation in Figure  5b. The curve's minimum, marked by the red vertical line, represents the value of λmin for which Y λ has the most normal distribution, and the 95% confidence interval is comprised between the two blue vertical lines. For λmin = 1, no transformation is necessary. In the case of λmin = 0, the transformation yielding the best normality would be log(Y). Aside from these two, all other values suggest a power transformation. In Figure  5b , the Box-Cox method indicates that the dataset would be more normal with a power transformation of λ = 0. 46. The additive term k is generally used if some values are not strictly positive.
The curve's minimum, marked by the red vertical line, represents the value of λ min for which Y λ has the most normal distribution, and the 95% confidence interval is comprised between the two blue vertical lines. For λ min = 1, no transformation is necessary. In the case of λ min = 0, the transformation yielding the best normality would be log(Y). Aside from these two, all other values suggest a power transformation. In Figure  5b , the Box-Cox method indicates that the dataset would be more normal with a power transformation of λ = 0. 46. The additive term k is generally used if some values are not strictly positive. Figure  5c  presents the same dataset after the transformation. The data is no longer skewed (both tails are of equal length), but normality is still not achieved since one residual sits very far from its predicted value.
Therefore, this experimental run is a possible outlier and should be repeated for validation. If reformulating a new electrode did not provide normality to the data and if the standard deviation of the replicated measurements is within acceptable bounds, it would be worth investigating why and how the model diverges so much at this candidate point. In our case, binder content had a more than anticipated impact on high-current capacities, and its content should be minimized. This very strong impact could be further investigated in a new DoE by studying the squared effect of binder content on electrochemical performance. In Figure  5d , the transformed data with the outlier removed from the dataset shows residuals that essentially define a straight line: the response has a normal distribution and no outlier may be identified.
Materials and Methods The active material Li 4 Ti 5 O 12 EXM5075 was obtained from Johnson-Matthey. Timcal provided the C65 carbon black and the carbon nanofibers were the Pyrograph ® -III grade, with a diameter of 100 nm and a length of 50-200 µm. The polymers polyvinylidene fluoride and Lotader 5500 were ordered, respectively, from Sigma-Aldrich and Arkema, and dissolved in N-methyl pyrrolidone (Sigma-Aldrich, purity 99. 5%) and toluene (Sigma-Aldrich, purity 99. 5%), respectively. All electrodes were made by tape casting  [18] , and assembled in coin cells, as described in our previous work  [14]. Design Expert V11 (Stat-Ease) was used to plan the DoE and to refine and extrapolate the data into empirical equations. Matlab 2017b (Mathworks) was used to aggregate and organize the experimental data, as well as plotting the empirical models.
Conclusions A DoE approach is an extremely powerful and useful statistical tool to quantify a parameter's likelihood to influence a process with a minimum number of experiments. However, careful planning and implementation are required to increase precision and predictability, particularly in the first iteration. Although the mathematics governing this statistical approach can be complex, thorough knowledge is not required as they have been incorporated in multiple solutions. However, this software should not be used as a "black box," since false positive results such as non-significant models are easily obtained. The DoE method's viability for electrode formulation was proven to be compatible with Li-ion battery electrode formulation to optimize the capacity at high currents. This response had high descriptive statistics, even though electrodes are microscopically very heterogeneous; this can impact the standard deviation of measurements taken at different spots on a single electrode  [30].
As all data collected was used to build the empirical model, the response's equation was as strong as the quality of the results. In fact, it can be challenging to perform all experiments with the same protocol. At times, the same run was conducted multiple times to ensure certain factors remained within the desired consistency level. The subsequent empirical model was more accurate once the appropriate transformation and model reduction processes were applied. Finally, an optimal combined design is a very versatile tool to identify limiting factors and optimal settings for any mixture, be it a polymer blend, electrolyte formulation or material synthesis. It may also be used in conjunction with multi-scale simulations to obtain smaller, statistically comparable datasets  [21, [31] [32] [33].
, the blue line represents the predicted values and should serve as a guideline for the residuals' distribution. The Box-Cox method represented in Figure 5b is well-adapted to determining which transformation might bring the most normality to the dataset. It plots the residual sum of squares as a function of λ, the transformation coefficient. Batteries 2019, 5, x FOR PEER REVIEW 8 of 15 might bring the most normality to the dataset. It plots the residual sum of squares as a function of λ, the transformation coefficient.
Introduction Macromolecular crystallography (MX) has been the primary method for the determination of biological structures over the last 70 years. As such, much effort has been devoted to the development of methods to improve the ability to grow crystals, optimize their quality and collect the best possible data from them once they have been placed in an X-ray beam. The end results from these often long and tortuous experiments, structure factors and atomic coordinates, are deposited in one of the earliest examples of a searchable scientific open database: the Protein Data Bank (PDB;  Berman et al. , 2000). Many studies have used this resource to draw conclusions on the properties of crystals, often with interesting conclusions  (Abad-Zapatero, 2012; Berman et al. , 2013 Berman et al. , , 2015;; Robert et al.
, 2017). However, while the database is incredibly useful as a general repository of atomic structures for biologists, it has two fundamental limitations when attempting to draw conclusions on the properties of the crystals themselves. Firstly, the deposited data represent probably the best data that were obtained for a sample and were, as such, the result of extensive screening, thereby hiding the potentially thousands of crystals that stand behind the final structure. Secondly, experimental details, such as the size, shape and quality variation of the crystals, the data-collection strategy etc. , are often lost, even if recorded in the primary citation. These data are therefore difficult to collate. Detailed studies have been made on individual systems, studying the morphology of the crystals and the packing of the protein, but a general survey across different proteins has never been made, presumably owing to the difficulty in gathering such information.
The crystal cohort MASSIF-1 started taking user samples in September 2014 and has been gathering data on all aspects of these crystals since then. To date, the beamline has processed 56 459 samples from 1306 declared projects from laboratories across Europe and the world  (Bowler et al. , 2016). We believe that this number and distribution of samples represents a reasonable snapshot of crystals for modern structural biology projects. This cohort can therefore form the basis of an analysis that we hope will be generally applicable. The fate of these samples is shown in Table  1. Of the samples received, only 60% were successfully centred; these 33 905 crystals form the basis of the study presented here. The remaining 40% either diffracted too weakly, were salt crystals or the sample mount was empty, preventing further analysis.
Databases and analysis All of the information gathered and used in the automatic location, characterization and data collection from crystals processed on MASSIF-1 is stored in two databases: one is related to the sample location, positioning and characterization processes  (Brockhauser et al. , 2012; Svensson et al. , 2015 ; BES-DB, Support Square; https://supportsquare. io/products/), while the second, ISPyB (Delageniere et al. , 2011), records the results of characterization and data processing. The information for samples contained in each database can be correlated using a data-collection ID that is unique to each sample. This allowed us to reconcile the data for samples between databases. A simple Python GUI was developed to access data from both databases and store relevant parameters for each sample in JSON format.
Analysis of these data was performed using SciPy and matplotlib  (Hunter, 2007; Oliphant, 2007). Crystal dimensions are measured from the X-ray centring routine. The dimensions x, y and z are the measured crystal width parallel to the spindle axis, the height orthogonal to the spindle axis and the depth orthogonal to the spindle axis 90 away in !, respectively. The full widths at half maximum (FWHMs) of diffraction signal over images are used to determine crystal dimensions. Oversampling means that the minimum distance that can be measured using the 50 mm diameter beam is 25 mm; dimensions smaller than this are determined using smaller beam apertures. As the automesh algorithm  (Svensson et al. , 2015)  will place the sample mount at either the smallest or widest orientation of the mount in !, depending on whether single or multiple data collections are requested  (Svensson et al.
Results and discussion 3. 1. The size and shape of protein crystals Accurately determining the dimensions, and therefore the volume, of a protein crystal is primarily important in determining the dose that the crystal can absorb before significant radiation damage  (Bourenkov & Popov, 2010; Bowler et al. , 2016; Svensson et al. , 2015; Zeldin et al. , 2013)  and in determining the diameter of the beam that should be used to maximize the signal-to-noise ratio  (Evans et al. , 2011; Svensson et al. , 2018). However, the gathering of volumetric data has many other potential uses, not least in being able to correlate crystal size with quality for individual projects. The data collected for all samples processed on MASSIF-1 provide an opportunity, for the first time, to define the broad distribution of protein crystal dimensions.
Relationship between crystal volume, molecular weight of the protein and resolution The scattering power of a crystal depends on the number of unit cells that can be illuminated in the beam, meaning that the volume of both the crystal and of the unit cell, as well as the properties of the molecule, are critical to a successful experiment  (Holton, 2009). Practically, this means that the larger the molecule being studied, the larger its B factor and the higher the required resolution, the larger the crystal will have to be. How does this relate to the actual measured values of crystals that yielded data sets on MASSIF-1? Firstly, the number of unit cells can be plotted against the crystal volume (Fig. 5 ). While not surprising, it is informative to see how the number ranges across projects that make it through to indexing: 10 12 unit cells is the most common (mode) and the smallest number that led to a processed data set was 2.
A more informative plot shows the molecular weight of the molecule crystallized plotted against the volume of the crystal coloured by the final resolution obtained from the data set (Fig. 7 ). The most striking observation is that, on average, the larger the molecule, the smaller the crystal. This is rather unfortunate given the dependence on volume for a given resolution. It is also interesting as a distribution of the molecules studied: there is a clear drop off after $200 kDa, showing the current range of samples studied on MASSIF-1. This cutoff is significant when considering the role of synchrotron beamlines in the future of structural biology. With technological advances in cryo-electron microscopy (cryo-EM) allowing structure determination at medium resolutions for very large complexes  (Subramaniam et al.
Conclusion The fully automatic collection of data at MASSIF-1 has allowed the study and comparison of the physical and molecular properties of a wide range of crystals and their constituent macromolecules for the first time. The results provide an overview of how size and shape is distributed over these crystals to a high level of precision, superseding assumptions based on individual systems. Coupling these data to the internal properties of these crystals from the processing of derived data sets, we can start to challenge assumptions and theoretical treatments. Have our assumptions been correct? Regarding crystal shapes and sizes, many have been wrong. These data demonstrate that an 'average' crystal on MASSIF-1 is more likely to be a plate or needle with a minimum dimension in the 30-50 mm range.
New, highly intense, beamlines with submicrometre beams are being constructed across the world that will be excellent for microcrystals and timeresolved experiments  (Cohen et al. , 2014; Sanchez-Weatherby et al. , 2019). For more standard experiments, the data presented here demonstrate that microfocus beamlines will still be needed and, crucially, beamlines with larger focal spots should not be neglected. Further insights could also be gained by linking the data collected here to crystallization databases from highly automated facilities  (Ng et al. , 2016; Shaw Stewart & Mueller-Dieckmann, 2014) , providing a further link between crystallogenesis and the final result. This link could inform the crystallization laboratory on the highest quality data as well as volumetric data and how these relate to the conditions that produced them.
The lack of independence challenges the notion of a 'model democracy' , in which each model is weighted equally  17. The growing number and complexity of models, the expanding suite of outputs they produce, the multitude of downstream applications and the growing availability of observational datasets drive a need for more routine and systematic evaluation, utilizing a comprehensive set of existing model performance metrics and diagnostics. Newly developed CMIP evaluation tools  18, 19  will ultimately enhance our ability to identify model errors, to investigate their causes and to quantify and potentially reduce projection uncertainties. In this Perspective, we summarize key advances since AR5 and key scientific opportunities for improving climate model analyses that will be assessed in the AR6.
These differences motivated a range of targeted analyses exploring model performance, internal variability, external forcing and observational uncertainty  25. Although the magnitude of the slowdown differs slightly depending on which global observational dataset is analysed, this focused effort revealed that the observed slowdown was due to a combination of factors, chiefly involving internally generated decadal-timescale variability in the tropical Pacific  26, 27  and the missing effects of a series of moderate volcanic eruptions  28. Averaging the time series across a collection of coupled model simulations strongly reduces the effects of internally generated variability, more clearly revealing the underlying externally forced response. There is, therefore, a mismatch between the precise observed sequence of variability and the smooth evolution of temperature in the multimodel mean.
Just as efforts to improve models continue, there is a parallel effort to improve observationally based datasets. Even for a very basic climate quantity such as temperature, this involves refined corrections for biases and incomplete global coverage in the raw surface observations  33  and corrections for biases in satellite retrievals  34. Observations are also critically important in model tuning  35, 36  , which should be clearly documented and taken into account in model evaluation studies. One difficulty in comparing models against observations is posed by inconsistency in the sampling or definition of the quantities compared (for example, model data may be daily averages whereas satellite samples may be for a certain time of day). This inconsistency can be addressed by incorporating simulators of specific instruments into climate models  37.
ESMValTool also has the capability to reproduce figures from several chapters of AR5 and incorporates targeted analysis packages, such as the National Center for Atmospheric Research (NCAR) Climate Variability Diagnostics Package  39. CMEC comprises the PCMDI Metrics Package (PMP  19  ), the International Land Modeling Benchmarking Project package (ILAMB  40  ) and the parallel toolkit for extreme climate analysis (TECA  41  ). CMEC emphasizes a diverse suite of physical and biogeochemical summary statistics gauging the consistency between models and observations across a range of space and timescales. Both ESMValTool and CMEC have undergone rapid development over the past few years, and are now mature, well-tested tools that provide end-to-end provenance tracking to ensure reproducibility.
In addition to testing whether projections of a specific variable and metric can be improved through weighting, thorough out-of-sample testing can help guard against other potential issues with weighting. For example, there is no single metric that reliably captures all aspects of model performance for all purposes, even if interest is restricted to a very specific scientific question  74. Out-of-sample testing can tell us whether optimizing in one metric or variable transfers any benefits to other metrics or variables  71. It can also indicate whether internal variability has played a role in any in-sample success of weighting, help to avoid the issue of the same datasets being used to calibrate and weight models, and reveal whether weighting has artificially reduced ensemble spread. A further problem is the risk of systematic errors in observational products producing inappropriately weighted ensembles.
Annual mean temperature and precipitation, monsoon timing and intensity, and modes of variability that can alter the probability of extreme events have been evaluated in the CMIP5 ensemble  7. The Expert Team on Climate Change Detection and Indices compiled a set of indices to quantify extreme events  80. Observational estimates of these indices have been used to evaluate CMIP5 models  81  , and are now incorporated into the ESMValTool for evaluation of CMIP6 models. The overall model performance was mixed in capturing the observed behaviour of these extreme event metrics. However, such comparisons remain difficult to interpret because of substantial uncertainties and data gaps in many of the observational datasets, and due to limited availability of CMIP5 model output at sub-monthly and daily frequencies.
Applications in different impact sectors have also been advanced by hybrid climate forcing datasets combining models and observations  86  , and by sector-specific information such as the geographic distribution of nitrogen fertilizer or irrigation applications and land-use patterns for agricultural modelling  87. Interactions between the climate modelling and applications communities are facilitated by the Vulnerability, Impacts, Adaptation, and Climate Services (VIACS) Advisory Board  88  , a CMIP6-Endorsed MIP  5. This Board is an effort to draw a broader array of climate experts, practitioners and information brokers into the CMIP process, and to leverage the community engagements organized under the Global Programme of Research on Climate Change Vulnerability, Impacts and Adaptation (PROVIA) and as part of efforts such as the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP  89  ).
The VIACS Advisory Board has solicited sustained community engagement: (1) on priority experiments; (2) on output variables to inform CMIP6 data requests; and (3) to highlight evaluations that would help to establish model credibility with the VIACS community. Given that it is common practice to adjust model biases with monthly mean information from present-day fields, the evaluation of the seasonal evolution and distributions of monthly climate at regional scales is among the highest priorities for VIACS users  90. ESMs often have less variance than observations at hourly, daily and interannual timescales, which can lead to spurious effects when bias adjustment relies on standardized anomalies. Tropical rainfall biases are particularly problematic.
In addition, it has been demonstrated that CMIP models are not independent. Most inferences in the literature about model interdependence are derived from error correlation  13, 79. This cannot identify the specific model components that are interdependent. Identification of these common components is a difficult task due to the large number of models involved in CMIP and lack of detailed information regarding individual model versions. Further work is required to understand how interdependence can best be assessed. These efforts can proceed in tandem with research to better understand the effects of model construction and genealogy. Comprehensive databases of shared code, parameterizations, model development and tuning practices could help disentangle how models are related, and for what purposes they can be considered independent estimates of change.