dataesr/scientific-paragraphs-categorization huggingface dataset:
To overcome this problem, we introduce a new phase to compute a matrix representation for the linearly-combined control laws. The matrix representation is computed by solving a regression problem of the first kind, similar to a function fitting problem, for all the linearly-combined control laws. First, each control law K i is evaluated on randomly sampled inputs s rand. The resulting output K i (s rand ) is used to solve a secondary optimization problem: K * M = arg min K M (K M (s rand ) -K i (s rand )) 2 (3. 1) where • denotes the Euclidean norm. This optimization problem is a function fitting problem that we solve with linear genetic programming. The LGP parameters are the same used for the gMLC so the computed individuals are compatible with the ones in the database. The best fitting control law K * M has then a matrix representation and is used as a substitute for the original linear combination of control laws.
The substitutes are then employed for the evolution phase even though they may not be perfect substitutes of the original control laws. Indeed, following the stopping criterion and population size of the secondary LGP optimization, the control law substitutes may not be able to reproduce all the characteristics of the linearly-combined control laws. An accurate but costly representation may not be needed as the control laws will be recombined afterwards. Moreover, the introduction of some error may be beneficial to improve the exploration phase and enrich our database. Once the matrix representations are computed, a new cycle may begin with a new evolution phase. In this phase, if any individual has a better performance than the N sub individuals in the simplex, then the least performing individuals among the N sub individuals are replaced.
Thus, each evolution phase replaces elements in the simplex, allowing exploration beyond the initial subspace. Then, the optimization continues with the exploitation phase on the updated N sub individuals. Figure  4  illustrates the initialization, exploration and exploitation of gMLC. The exploration is based on LGP. Also the exploitation requires LGP. In the downhill simplex method, the individuals are linear combinations of the subplex basis and are finally approximated as matrices. This process is repeated until the stopping criterion is reached. The Gradient-enriched Machine Learning Control (gMLC) is summarized by pseudo code in algorithm 2. The source code is freely available at https://github. com/gycm134/ gMLC. Finally, figure  5  summarizes the exploration and exploitation phases for EGM and gMLC.
Explorative Gradient Method Result: b * , the best individual Initialize the N p + 1 individuals of the dataset B I ; Test all the individuals; Build the simplex S by taking the N p + 1 best individuals; while Stopping criterion is not reached do Exploration phase-Latin hypercube sampling Select b LHS by solving: b LHS := arg max b∈B min bi∈B I bb i Test b LHS ; Augment dataset: B I := B I ∪ b LHS ; Update simplex: replace the worst individual of S by b LHS ; end Exploitation phase-Downhill simplex Sort and relabel S such as: J S of S excluding b Np+1 ; Reflection: compute and test b r.
1 then Expansion: compute and test b e := c + 2 (c -b Np+1 ) ; Update simplex: b Np+1 := min {b r , b e }; else if J S Np+1 J S r then Contraction: compute and test b c := 1/2 (c + b Np+1 ); if J S c < J S Np+1 then Update simplex: b Np+1 := b c ; else Shrink: compute and test b s,i := 1/2 (b 1 + b i ), i = 2,. , N p + 1; Update simplex: b i := b s,i , i = 2,. , N p + 1; end end Augment dataset: add all the new individuals to B I ; end end a k-dimensional subspace and a downhill simplex algorithm optimizes the control law in this subspace.
Algorithm 1 : 1 Explorative Gradient Method Result: b * , the best individual Initialize the N p + 1 individuals of the dataset B I ; Test all the individuals; Build the simplex S by taking the N p + 1 best individuals; while Stopping criterion is not reached do Exploration phase-Latin hypercube sampling Select b LHS by solving: b LHS := arg max b∈B min bi∈B I bb i Test b LHS ; Augment dataset: B I := B I ∪ b LHS ; Update simplex: replace the worst individual of S by b LHS ; end Exploitation phase-Downhill simplex Sort and relabel S such as: J S of S excluding b Np+1 ; Reflection: compute and test b r.
Pathway enrichment analysis Differentially expressed (DE) proteins and proteins within different modules were further nominated for pathway analysis using WebGestalt software (http://www. webgestalt. org/). Briefly, DE proteins or proteins within a module were assembled into a "protein list" and all 4001 proteins measured by the SOMAscan assay were used as "background. " This enrichment analysis was performed on the Kyoto Encyclopediat of Genes and Genomes database.
Funding information Innovative Medicines Initiative Joint Undertaking , Grant/Award Number: n • 115372; European Union's  Seventh Framework Programme , Grant/Award Number: FP7/2007-2013;  European Commission  within the  5th framework program , Grant/Award Numbers:  QLRT-2001-2455 , # 37670 ; Stichting voor  Alzheimer Onderzoek , Grant/Award Numbers: # 11020 , # 13007 , # 15005 ;  Department of Health of the Basque Government , Grant/Award Number:  17. 0. 1. 08. 12. 0000. 2. 454. 01. 41142. 001. H;  University of Antwerp Research Fund; Vetenskapsrådet , Grant/Award Number: # 2018-02532 ;  H2020   European Research Council , Grant/Award Number: # 681712 ;  Swedish State Support for Clinical Research , Grant/Award Number: # ALFGBG-720931 ;  UK Dementia Research Institute.
Global measurements of absorbing aerosol optical depth (AAOD) are scarce and mostly provided by the ground network AERONET (AErosol RObotic NETwork). In recent years, several satellite products of AAOD have been developed. This study's primary aim is to establish the usefulness of these datasets for AEROCOM (Aerosol Comparisons between Observations and Models) model evaluation with a focus on the years 2006, 2008 and 2010. The satellite products are super-observations consisting of 1 • × 1 • × 30 min aggregated retrievals. This study consists of two papers, the current one that deals with the assessment of satellite observations and a second paper  (Schutgens et al. , 2021)  that deals with the evaluation of models using those satellite data. In particular, the current paper details an evaluation with AERONET observations from the sparse AERONET network as well as a global intercomparison of satellite datasets, with a focus on how minimum AOD (aerosol optical depth) thresholds and temporal averaging may improve agreement between satellite observations.
All satellite datasets are shown to have reasonable skill for AAOD (three out of four datasets show correlations with AERONET in excess of 0. 6) but less skill for SSA (singlescattering albedo; only one out of four datasets shows correlations with AERONET in excess of 0. 6). In comparison, satellite AOD shows correlations from 0. 72 to 0. 88 against the same AERONET dataset. However, we show that performance vs. AERONET and inter-satellite agreements for SSA improve significantly at higher AOD. Temporal averaging also improves agreements between satellite datasets. Nevertheless multi-annual averages still show systematic differences, even at high AOD. In particular, we show that two POLDER (Polarization and Directionality of the Earth's Reflectances) products appear to have a systematic SSA differ-Published by Copernicus Publications on behalf of the European Geosciences Union.
6896 N. Schutgens et al. : AEROCOM and AEROSAT AAOD and SSA study -Part 1 ence over land of ∼ 0. 04, independent of AOD. Identifying the cause of this bias offers the possibility of substantially improving current datasets. We also provide evidence that suggests that evaluation with AERONET observations leads to an underestimate of true biases in satellite SSA. In the second part of this study we show that, notwithstanding these biases in satellite AAOD and SSA, the datasets allow meaningful evaluation of AEROCOM models.
As it now stands, we have almost no observations of absorbing aerosol over the oceans, in particular in continental outflow regions. However, in recent years a number of satellite AAOD products have been developed, often based on POLDER (Polarization and Directionality of the Earth's Reflectances) measurements. For example,  Lacagnina et al. (2015)  used POLDER data to evaluate SSA (single-scattering albedo) from AEROCOM (Aerosol Comparisons between Observations and Models) models over oceans,  Peers et al. (2016)  evaluated over ocean above-cloud SSA in AEROCOM models for the African fire season,  Lacagnina et al. (2017)  estimated the global direct radiative effect of aerosol, and  Hasekamp et al. (2019b)  estimated aerosol-cloud interactions. Chen et al. (2018 Chen et al. ( , 2019) )  assimilated POLDER AOD and AAOD observations to estimate aerosol emissions, while  Tsikerdekis et al.
(2021)  showed the benefit of jointly assimilating POLDER AOD (aerosol optical depth), AE (Ångström exponent) and SSA (single-scattering albedo) observations. Kacenelenbogen et al. (2019)  used combinations of A-Train sensors to infer AAOD over clouds and estimate short-wave direct aerosol effects. The challenge in retrieving AAOD from satellites is made clear by the challenge in retrieving AAOD from AERONET measurements. AERONET AAOD observations are known to be more uncertain than AOD observations. Dubovik et al. (2000)  estimated that AERONET SSA uncertainties for AOD ≤ 0. 2 at 440 nm would be at least 0. 05, using numerical sensitivity tests. A recent in-depth estimate of the uncertainty in Inversion V3 data  (Sinyuk et al. , 2020)  for four different sites suggested SSA uncertainties at AOD (at 440 nm) equal 0.
A traditional evaluation of satellite datasets with AERONET data is unlikely to establish this, partly because the model aspect is ignored and partly because AERONET covers some very interesting aerosol source regions (e. g. oceans, most deserts and boreal fire scapes) only sparsely. In the first part of this study (the current paper) we complement the traditional evaluation with a satellite intercomparison (in itself not unusual) to broaden our understanding of satellite performance over diverse regions. In the second part (a follow-up paper,  Schutgens et al. , 2021) , we present a novel analysis that combines satellite evaluation and intercomparison with model evaluation and allows for the assessment of model biases in the context of satellite biases. We will use satellite data aggregated over 1 • ×1 • ×30 min as this allows spatio-temporal collocation amongst datasets (satellite, AERONET, AEROCOM) which should strongly reduce representation errors in our analyses  (Schutgens et al.
, 2016a, b). All analyses, even of multi-year averages, will start from spatio-temporally collocated datasets. This paper is the result of discussions in the AERO-COM (Aerosol Comparisons between Observations and Models, https://aerocom. met. no, last access: 4 May 2021) and AEROSAT (International Satellite Aerosol Science Network, https://aero-sat. org, last access: 4 May 2021) communities. Both are grassroots communities, the first organized around aerosol modellers and the second around retrieval groups. They meet every year to discuss common issues in the field of aerosol studies. The observational datasets used in this study are described in Sect. 2. The collocation and analysis methodology are described in Sect. 3. A first look at the satellite datasets is presented in Sect. 4. Evaluation of satellite AOD, AAOD and SSA with AERONET is performed in Sect 5, and a more detailed intercomparison of satellite data is shown in Sect.
Remote sensing data Original satellite L2 data (estimates of geophysical variables on the spatio-temporal sampling pattern of the radiances; see also  Mittaz and Merchant, 2019)  were aggregated unto a regular spatio-temporal grid with spatio-temporal grid boxes of 1 • ×1 • ×30 min. The resulting super-observations (1 • ×1 • × 30 min aggregates) are more representative of global model grid boxes (∼ 1-3 • in size) while allowing accurate temporal collocation with other datasets. At the same time, the use of super-observations significantly reduces data amount without much loss of information (at the scale of global model grid boxes). A list of products used in this paper is given in Table 1. A colour legend to the different products can be found in Fig. 1. More explanation of the aggregation procedure can be found in Appendix A.
Super-observations of AOD and AAOD at the same location and time were derived from the same set of L2 data and therefore measure the exact same scene (note an exception for the GRASP dataset described below). The main data are AOD and AAOD at 550 nm, the wavelength at which models typically provide (A)AOD. If (A)AOD was not retrieved at this wavelength, it was logarithhttps://doi. org/10. 5194/acp-21-6895-2021 Atmos. Chem. Phys. , 21, 6895-6917, 2021   Kacenelenbogen et al. (2019, Appendix A). In brief, FL-MOC uses the L2 retrieved aerosol properties as input to a simple lookup table retrieval of aerosol types and concentrations, under the assumption that aerosol properties are consistent with the L2 aerosol observations within the stated uncertainties of each sensor's retrieval. This technique also assumes that the surface reflectance and clouds are properly treated in the underlying retrievals.
Over land, FL-MOC uses OMAERUV (see Sect. 2. 1. 2) AAOD, and over ocean it uses OMAERO AAOD. OMAERO is an advanced multi-wavelength UV-VIS algorithm that uses 17 wavelengths in the 331-500 nm range in order to calculate the aerosol optical depth and to discriminate between various types of aerosols. It is an extension of the near-UV TOMS (Total Ozone Mapping Spectrometer) method (see the OMAERUV product) to a wider wavelength range. The OMAERO algorithm is applied over all surface types; however, its primary objective is to derive aerosol properties over the oceans due to the limited availability of spectral surface reflectivity databases over land.
POLDER-GRASP For a description of the POLDER instrument, see the previous subsection. GRASP (Generalized Retrieval of Aerosol and Surface Properties) is a unified retrieval algorithm for atmosphere properties from diverse remote sensing observations  (Dubovik et al. , 2011 (Dubovik et al. , , 2014)) , based on earlier work by  Dubovik and King (2000) , and  Dubovik et al. (2002)  and  Dubovik et al. (2006)  for AERONET inversions. In the current paper, retrievals from the so-called "models" dataset are used. Aerosol is assumed to be an external mixture of five different aerosol components which are retrieved together with spectral parameters of surface BRDF and BPDF (bidirectional polarization distribution function). The aerosol is assumed to be a mixture of spherical and nonspherical particles.
Each fraction is characterized by particle size distributions similarly to AERONET retrievals. The nonspherical component is modelled as a mixture of randomly oriented spheroids with fixed shape distribution  (Dubovik et al. , 2006). The details of the "models" approach are discussed by  Lopatin et al. (2021)  and  Chen et al. (2020). The actual inversion uses multi-pixel retrieval  (Dubovik et al. , 2011)  where horizontal pixel-to-pixel variations of aerosol and day-to-day variations of surface reflectance are enforced to be smooth. The full archive of POLDER/PARASOL observations was retrieved using GRASP and can be found at https://www. grasp-open. com (last access: 4 May 2021). In addition to the "models" dataset, two other datasets are available ("optimized" and "high-precision") that use slightly different assumptions in the retrieval.
The detailed discussion and validation of all three 0. 1 • PARASOL/GRASP retrievals are provided by  Chen et al. (2020). The "models" dataset used in this paper is considered the most applicable for a wide range of circumstances. The dataset used in the current paper is aggregated to 1 • spatial resolution (details are listed at https://www. grasp-open. com). The "models" dataset provides AOD and AAOD aggregated from slightly different L2 samplings: an additional minimum AOD threshold is used when aggregating AAOD. To select data of higher quality, AAOD retrievals were used only for cases with sufficient aerosol loading. The same AOD threshold is used for SSA as well. Specifically, minimum AOD (at 440 nm) thresholds of 0. 3 over land and 0. 02 over ocean were applied (the threshold over ocean is probably too low to assure high-quality AAOD, but higher thresholds result in significant data loss).
In the current study we prefer to use aggregated AOD and AAOD data that describe the exact same scene, and this is https://doi. org/10. 5194/acp-21-6895-2021 Atmos. Chem. Phys. , 21, 6895-6917, 2021 the case for the FL-MOC, OMAERUV and POLDER-SRON datasets mentioned earlier. For the GRASP product, we decided to assume that the aggregated SSA represents the same scene as the AOD aggregate and recalculated an AAOD from that AOD and SSA. Consequently, the AAOD product (indicated as GRASP-M) presented in this paper is different from the AAOD found in the official L3 "models" product. In situ measurements  (Delene and Ogren, 2002; Andrews et al. , 2011 Andrews et al. , , 2017;; Schmeisser et al. , 2018)  have suggested a change in SSA at lower AOD, so our SSA assumption may introduce additional biases.
However, GRASP-M AAOD evaluated better against AERONET than "models" AAOD which showed a high bias vs. AERONET due to the aforementioned minimum AOD threshold. For this study the L3 GRASP data were additionally filtered based on the fitting residual field, which was required to be smaller than 0. 05 (over land) or 0. 1 (over ocean). This subset evaluates substantially better for AOD retrievals and somewhat better for AAOD retrievals than the full dataset.
AERONET AERONET  (Holben et al. , 1998 ) DirectSun V3 L2. 0  (Giles et al. , 2019; Smirnov et al. , 2000)  and Inversion V3 L1. 5 and 2. 0 data were downloaded from https://aeronet. gsfc. nasa. gov (last access: 4 May 2021), logarithmically interpolated to values at 550 nm and aggregated by averaging over 30 min. The DirectSun dataset contains only AOD (at multiple wavelengths). These observations are based on direct transmission measurements of solar light and have a low uncertainty of ±0. 01  (Eck et al. , 1999; Schmid et al. , 1999) , at 400 nm and larger. The Inversion dataset contains AAOD and SSA (at multiple wavelengths) based on measurements of scattered solar light from multiple directions. This inversion uses radiative transfer calculations  (Dubovik and King, 2000)  and yields larger errors than the DirectSun measurements.
2 significantly lower SSA values were observed by AERONET. A confounding issue for the evaluation of SSA (or, for that matter, AAOD) datasets is that there is no established gold standard. The Inversion dataset also contains AOD (from DirectSun retrievals) which is actually used in the inversion. Here we only use those AOD values in the Inversion dataset that have corresponding AAOD and SSA values, so that aggregate values always describe the same scene. Inversion L2. 0 is a subset of L1. 5 (which contains almost 30 times more observations), based on further cloud screening and the requirement that AOD at 440 nm ≥ 0. 4. This last criterion results in a minimum AOD at 550 nm of 0. 25 in the Inversion L2. 0 product. Since an individual AERONET site is not necessarily representative of a 1 • × 1 • grid box, satellite evaluation may be negatively affected.
Collocation and analysis methodology To evaluate and intercompare the remote sensing datasets, they will need to be collocated in time and space to reduce representation errors  (Colarco et al. , 2014; Schutgens et al. , 2016a Schutgens et al. , , 2017)). In practice this collocation is another aggregation (performed for each dataset individually) to a spatiotemporal grid with slightly coarser temporal resolution (1 or 3 h; the spatial grid box size remains 1 • × 1 • ). This is followed by a masking operation that retains only aggregated data if they exist in the same grid boxes for all involved datasets. More details can be found in Appendix A. We need to allow some flexibility in the time separation between data (here 3 h) to ensure sufficient numbers of collocated data pairs for further analysis.
7. As the FL-MOC dataset, based on CALIOP measurements, is smaller than the other satellite datasets, we were compelled to collocate FL-MOC with AERONET within 2 • instead of 1 •. Even so, the data count for the FL-MOC evaluation is low. After spatio-temporally collocating two or more datasets, the data may be further averaged in space and/or time for analysis purposes. Spatio-temporally averaged SSA is al- ways derived from averaged AOD and AAOD: SSA = 1 -AAOD/AOD. (1) During the evaluation of products with AERONET, a distinction will be made between either land or ocean grid boxes in the common grid. A high-resolution land mask was used to determine which 1 • × 1 • grid box contained at most 30 % land (designated an ocean box) or water (designated a land box). Most ocean boxes with AERONET observations will be in coastal regions, with some over isolated islands.
Taylor diagrams A suitable graphic for displaying multiple datasets' correspondence with a reference dataset (truth) is provided by the Taylor diagram  (Taylor, 2001). In this polar plot, each data point (r, φ) shows basic statistical metrics for an entire dataset. The distance from the origin (r) represents the internal variability (standard deviation) in the dataset. The angle φ through which the data point is rotated away from the horizontal axis represents the correlation with the reference dataset, which is conceptually located on the horizontal axis at radius 1 (i. e. every distance is normalized to the internal variability of the reference dataset). It can be shown  (Taylor, 2001)  that the distance between the point (r, φ) and this reference data point at (1, 0) is a measure of the root mean square error (RMSE, unbiased).
41 to 0. 69. The explanation for this is not entirely clear, although it turns out that POLDER-GRASP-M evaluates more poorly with AERONET for 2010 than for 2006 and 2008 (POLDER-SRON is currently limited to 2006; see Table  2. 1). Although the poorer evaluation for 2010 can be seen in AOD, AAOD and SSA, it is only statistically significant for SSA. The impact of statistical noise on the AAOD evaluation is explored in Fig. 6. Using a bootstrapping technique, the spread in correlation and standard deviation were explored. For most datasets, the results seem fairly robust, except for FL-MOC, which yielded only 24 data points. A proper intercomparison of products requires collocation (of all the satellite data), which reduces available cases even further. Figure  S2  shows that results are not very different from Fig.
, 2020). Figure  8  shows results when bias (signless) and correlation per site (that yielded at least 32 collocations) are averaged over all sites for each satellite product. The same 52 sites are used for all datasets, although each product is individually collocated with AERONET. For FL-MOC, no site provided at least 32 observations, and this is not included in the analysis. For POLDER-SRON, only 18 sites provided at least 32 collocated observations, and this was similarly excluded. As was also shown in  Schutgens et al. (2020) , OMAERUV shows rather large biases compared to the other AOD products. POLDER-GRASP-M, on the other hand, shows the smallest bias. The filtering of GRASP retrievals described in Sect. 2. 1 plays a significant role in this result (without filtering, POLDER-GRASP-M shows a bias twice as large).