N Méger

H Courteille
email: hermann.courteille@univ-smb.fr

A Benoit

A Atto

D Ienco
email: dino.ienco@inrae.fr

EXPLAINING A DEEP SPATIOTEMPORAL LAND COVER CLASSIFIER WITH ATTENTION AND REDESCRIPTION MINING

Keywords: Explainable AI, Deep Learning, Land Cover Classification, Satellite Image Time Series, Attention, Redescription Mining, Grouped Frequent Sequential Patterns

Deep learning-based land cover classifiers learnt from Satellite Image Time Series (SITS) are known to reach high performances. In order to explain, at least partly, the rationale leading to each one of their decisions, attention-based architectures have been proposed to automatically weight the importance of predefined data components in the classification process. Though generated for each decision separately, the informational content conveyed by such explanations can remain insufficient to end-users because of the complex nature of SITS. Moreover, getting a general perspective about the way a classifier works requires merging all explanations for each class and relating them to its mode of operation, which is not always straightforward. A preliminary and complementary approach for automatically identifying the data features detected by a pixel-wise deep spatiotemporal land cover classifier and explaining its behavior at the class level is therefore proposed in this paper. Classified pixels are first described using interpretable features coming under the form of data mining patterns. A redescription mining technique is then employed to automatically select, for each class, the features matching the different activation level configurations of the layer that is assumed to capture the aforementioned patterns. Experiments based on a Sentinel-2 time series and a deep spatiotemporal neural network implementing a channel-separated processing as well as a channel-based attention mechanism show the interest of such a combined approach.

INTRODUCTION

Land Cover Classification (LCC) is a task that has been benefiting from the last advances in deep learning for several years [START_REF] Vali | Deep Learning for Land Use and Land Cover Classification Based on Hyperspectral and Multispectral Earth Observation Data: A Review[END_REF]. Many works such as [START_REF] Pelletier | Temporal Convolutional Neural Network for the Classification of Satellite Image Time Series[END_REF], [START_REF] Rußwurm | Self-attention for raw optical Satellite Time Series Classification[END_REF] or [START_REF] Censi | Attentive Spatial Temporal Graph CNN for Land Cover Mapping From Multi Temporal Remote Sensing Data[END_REF] shows that high-performance deep land cover classifiers can be learnt from Satellite Image Time Series (SITS). Moreover, the black-box nature of these Deep Neural Networks (DNNs) has been being addressed using different methods designed to gain insights into the rationale leading to their decisions [START_REF] Campos-Taberner | Understanding deep learning in land use classification based on Sentinel-2 time series[END_REF]. Among them, Saliency Masks (SMs) have been proven to be effective at explaining each one of the outcomes. These masks can be produced by recent explanation methods such as Grad-CAM [START_REF] Selvaraju | Grad-cam: Visual explanations from deep networks via gradient-based localization[END_REF] and SHAP [START_REF] Lundberg | A unified approach to interpreting model predictions[END_REF]. Other explanation methods can be established by integrating specific operators to both enhance model relevance and provide insights on the predictions, for example using attention-based architectures. Works such as [START_REF] Garnot | Satellite Image Time Series Classification with Pixel-Set Encoders and Temporal Self-Attention[END_REF], [START_REF] Rußwurm | Self-attention for raw optical Satellite Time Series Classification[END_REF], [START_REF] Ienco | Weakly Supervised Learning for Land Cover Mapping of Satellite Image Time Series via Attention-Based CNN[END_REF], [START_REF] Censi | Attentive Spatial Temporal Graph CNN for Land Cover Mapping From Multi Temporal Remote Sensing Data[END_REF] or [START_REF] Courteille | Channel-based attention for land cover classification using sentinel-2 time series[END_REF] follow this direction. These architectures weight the importance of predefined data components in the classification process. To our knowledge, no proposal taking into account all SITS dimensions has emerged so far. In addition, no explanation regarding the results supplied by attention mechanisms themselves is provided. Finally, as decisions are explained independently from each other, getting a general perspective about the way a classifier works requires merging all explanations for each class and relating them to its mode of operation, which is complex.

A preliminary and complementary approach for identifying automatically the dataset features detected by a pixel-wise deep spatiotemporal land cover classifier and explaining its functioning at the class level is therefore proposed in this paper. Each classified pixel is first described using interpretable features coming under the form of data mining patterns. These features, built using all SITS dimensions, are detailed in Section 2. Each pixel is then also characterized by the activation levels of the layer that is assumed to summarize a large part of the processing performed by the network and capture high level concepts similar to the aforementioned intepretable features. Finally, pixel descriptions are analyzed for each class separately using redescription mining [START_REF] Galbrun | Redescription Mining[END_REF] to automatically extract correspondence rules between the interpretable features and the different activation level configurations. The redescription mining technique adopted in this paper is presented in Section 3. The proposed approach is assessed using a Sentinel-2 time series and a spatiotemporal deep neural network implementing a channel-separated processing as well as a channel-based attention mechanism. This experimental setting is described in Section 4. Obtained results are made available in Section 5. They show that, while preserving good performances, the attention-based explanations of the decisions are meaningful and can be enriched with class level explanations relying on intepretable features identified by redescription mining. Section 6 concludes this paper by summarizing the main contribution, discussing its limits and pointing to possible future work directions.

GROUPED FREQUENT SEQUENTIAL PATTERNS

The first step of the proposed approach consists in characterizing each pixel for which a ground truth is available with interpretable features. It is assumed that some of these features are captured by deep SITS land cover classifiers and could help understand how the latter distinguish classes. With the object of exploiting all SITS dimensions, spatiotemporal features extracted from each available channel are focused on. They are obtained by mining the so-called Grouped Frequent Sequentiel patterns originally proposed in [START_REF] Julea | Unsupervised Spatiotemporal Mining of Satellite Image Time Series Using Grouped Frequent Sequential Patterns[END_REF]. These patterns are spatiotemporal data mining patterns designed to describe and summarize SITS at the pixel level in an unsupervised way [START_REF] Julea | Unsupervised Spatiotemporal Mining of Satellite Image Time Series Using Grouped Frequent Sequential Patterns[END_REF]. We propose to characterize each pixel with such patterns by extracting them from each channel separately. Let us consider a given channel. Its pixel values are first quantized with standard techniques such as equal frequency bucketing or clustering [START_REF] Julea | Unsupervised Spatiotemporal Mining of Satellite Image Time Series Using Grouped Frequent Sequential Patterns[END_REF]. Quantized pixel values are then associated with symbols denoting the quantization intervals they belong to. As a result, each pixel is described by a symbolic series containing as many symbols as the number of images involved in the SITS. The set of symbolic series describing pixels is then mined to extract all possible sequential patterns such as 2 ) 3 ) 2. This pattern, if observed for a symbolic series, indicates that, some time in the series, the value of the pixel it describes is denoted by quantization interval '2', then, some times later, by interval '3', and finally, some times later by interval '2' once again. No timing constraint is imposed, and there might be other symbols occurring in-between the occurrences of the pattern symbols. Moreover, if this pattern is observed for several other symbolic series, i.e., it affects other pixels, no synchronisation constraint between pattern occurrences is considered. In other words, such a pattern is allowed to occur anywhere in space and in time.

In order to reject spurious patterns and safely prune the search space, two spatial constraints must be fulfilled. A pattern is retained if: 1) it affects a sufficient number of pixels, i.e., it covers a minimum surface and 2) affected pixels are sufficiently connected to each other on average, i.e., they form homogeneous regions in space, whatever their shapes. The first constraint is simply set using a minimum surface threshold termed minimum frequency threshold and denoted σ. The second constraint is evaluated by considering the 3 × 3 neighbourhood of each affected pixel, counting the number of immediate neighbours that are also affected by the same pattern, averaging all of these counts and checking whether this mean exceeds or not a minimum grouping threshold denoted κ. If unclassified pixels are located in the neighborhood of affected pixels, it is assumed that they are not affected by any pattern. Applying these spatial constraints allow to target sequential patterns whose occurrences are frequent and grouped, hence the name of Grouped Frequent Sequential Patterns or GFS-patterns. In addition, only maximal GFS-patterns are selected to focus on the most specific ones. A pattern is maximal if it is not contained in any other pattern of the output collection. The reader is referred to [START_REF] Julea | Unsupervised Spatiotemporal Mining of Satellite Image Time Series Using Grouped Frequent Sequential Patterns[END_REF] for a more formal definition of GFS-patterns and details regarding the corresponding extraction algorithm. Finally, maximal GFS-patterns are ranked using a dedicated and efficient randomization approach designed to guide end-users towards the most promising GFS-patterns, i.e., the patterns that are the less or the more likely to occur in randomized versions of the symbolic datasets. More details about this ranking method can be found in [START_REF] Méger | Ranking evolution maps for Satellite Image Time Series exploration: application to crustal deformation and environmental monitoring[END_REF]. Back to this paper, it is proposed to describe each pixel for which a ground truth is available by indicating, for each channel, which are the most promising maximal GFS-patterns occurring in its symbolic series, if any. In the following, the most promising maximal GFS-patterns are simply referred to as patterns when clear from the context.

REDESCRIPTION MINING

Redescription mining is 'a data analysis task that aims at finding distinct common characterizations of the same objects' [START_REF] Galbrun | Redescription Mining[END_REF]. For instance, if geographical areas are described on one side by the presence of mammal species, and, on the the other side by their temperatures, it is possible to find the following redescription: 'The areas inhabited by either the Eurasian lynx or the Canada lynx are approximately the same areas as those where the maximum March temperature ranges from -24.4 • C to 3.4 • C.' [START_REF] Galbrun | Redescription Mining[END_REF]. More precisely, let us suppose that each studied object is described by as many tables as they are distinct characterisations. Within such tables, each object, i.e. a row, is described by attributes, i.e. columns, whose type can be numerical, categorical or Boolean. Each table can be separately used to produce descriptions of the objects, i.e. expressions built using the attributes of the table. Each expression allows to assign a Boolean value to each object by checking whether it characterizes it, even partially, or not. Back to the first redescription example, it can be alternately expressed with descriptions p = Eurasian lynx ∧ Canadian lynx and q = [-24.5 ≤ M arch maximum temperature ≤ 3.4] originating from the table denoting the presence of mammal species and the table reporting the temperatures respectively. The set of objects for which a description is true is termed support. A redescription is a pair of descriptions such as (p, q), also denoted p ∼ q, each description being produced from a different table. In order to rank redescriptions according to their accuracy, the Jaccard index of each description p ∼ q is computed as |supp(p)∩supp(q)| |supp(p)∪supp(q)| . It allows to evaluate to which extent the objects for which a description is valid can be also characterized by the other description, i.e., to which extent descriptions p and q are similar. The set of objects characterized by both p and q is the support of redescription p ∼ q. Finally, redescription mining is about finding all redescriptions by taking into account potential additional constraints such as limiting the support of redescriptions, limiting the length of descriptions or selecting redescriptions that are statistically significant. The reader is referred to [START_REF] Galbrun | Redescription Mining[END_REF] for a more formal and general overview of redescription mining.

In this paper, objects are pixels described by 1) the different activation levels of the neurons of the layer that is assumed to capture GFS-patterns, and 2) GFS-patterns themselves. Let ai denote the activation level of neuron i. Since we aim to automatically match the different activation level configurations with the presence of patterns, redescriptions such as [0.2 ≤ a1 ≤ 0.3] ∧ [0.7 ≤ a17 ≤ 0.9] ∼ 2 ) 3 ) 2 are expected. The ReReMi algorithm proposed in (Galbrun and Miettinen, 2012a) is therefore considered. It can indeed handle Boolean data and automatically determine the optimal numerical intervals that should be considered when establishing a description from numerical attributes. In addition, a wide range of descriptions are explored. Disjonctions and conjonctions can be employed, and variables can be negated. Some restrictions are nevertheless considered to make extractions tractable: the descriptions are evaluated from left to right, irrelevant of the operator precedence, and every variable can be used only once. Basically, ReReMi can extract redescriptions whose Jaccard index is above a user-defined threshold and whose descriptions are statistically dependent. This dependence is checked using a p-value expressing the probability that the supports of descriptions overlap as much as observed. Such a test tends to favor redescriptions with low support and can be counter-balanced by rejecting those whose support is below a user-defined threshold. Even if such additional constraints are fulfilled, the search space remains exponential and an heuristic pruning is performed: the algorithm starts from the best redescriptions whose descriptions contain only one variable and greedily expand their descriptions as long as they form the best redescriptions. More details about the algorithm can be found in (Galbrun and Miettinen, 2012a).

EXPERIMENTAL SETTING

The experimental setting comprises a SITS for which a ground truth and accurate classifiers are available in the literature as well as a dedicated deep spatiotemporal land cover classifier whose design is inspired by state-of-the-art classifiers.

The Sentinel-2 Time Series

A Sentinel-2 SITS covering the Réunion island, for which the ground truth is available in [START_REF] Dupuy | Mapping land cover on Reunion Island in 2017 using satellite imagery and geospatial ground data[END_REF] and land cover classifiers have been proposed in [START_REF] Ienco | Weakly Supervised Learning for Land Cover Mapping of Satellite Image Time Series via Attention-Based CNN[END_REF] and [START_REF] Courteille | Channel-based attention for land cover classification using sentinel-2 time series[END_REF], is used. It consists of 21 images with size 6667 pixels × 5916 pixels. They were acquired between January and December 2017 and cover a 67 km x 59 km scene with a 10 m spatial resolution. Clouds are filtered using a multi-linear interpolation [START_REF] Ienco | Weakly Supervised Learning for Land Cover Mapping of Satellite Image Time Series via Attention-Based CNN[END_REF]. The following spectral bands are available: B2 (blue), B3 (green), B4 (red) and B8 (near-infrared). The Normalized Difference Vegetation Index (NDVI) and the Normalized Difference Water Index (NDWI) [START_REF] Mcfeeters | The use of the Normalized Difference Water Index (NDWI) in the delineation of open water features[END_REF] are also supplied. These standard indexes are defined by N DV I = f (B8, B4) and N DW I = f (B3, B8) with f (x, y) = x-y x+y , an homogeneous function from

R * + × R * + to [-1; 1].
Regarding the ground truth, 2% (880,828 pixels) of the pixels are annotated according to 11 unbalanced land cover classes listed in Table 3 along with their class ratios.

The Deep Spatiotemporal Land Cover Classifier

The Deep Spatiotemporal Land Cover Classifier (DSLCC) used in this paper is designed to be as interpretable as possible. Neural networks based on recurrent cell models such as Long Short Term Memory (LSTM) ones [START_REF] Ienco | Land Cover Classification via Multitemporal Spatial Data by Deep Recurrent Neural Networks[END_REF] are thus discarded in favor of Convolutionnal Neural Networks (CNN) such as [START_REF] Pelletier | Temporal Convolutional Neural Network for the Classification of Satellite Image Time Series[END_REF] or [START_REF] Ienco | Weakly Supervised Learning for Land Cover Mapping of Satellite Image Time Series via Attention-Based CNN[END_REF]. Moreover, the CNN field of view (fov), i.e., the extent of the input neighborhood influence, can be controlled by design. This allows us to specify the temporal fov, which is crucial when dealing SITS as they generally contain few acquisitions. Following the work of [START_REF] Courteille | Channel-based attention for land cover classification using sentinel-2 time series[END_REF], all the convolutions are performed for each channel separately, and a auxiliary attention branch weighting the importance of each channel in the decision of the classifier is added. Such an attention operator is chosen because it delivers meaningful explanations that can be easily merged for each class using box plots [START_REF] Courteille | Channel-based attention for land cover classification using sentinel-2 time series[END_REF]. Its architecture is detailled in Table 1. Inspired by the work of [START_REF] Pelletier | Temporal Convolutional Neural Network for the Classification of Satellite Image Time Series[END_REF], temporal convolutions (layers 3

⃝ and 4 ⃝) are applied at the pixel level. They are carried out after having computed spatiotemporal ones whose spatial footprint is 3 × 3 to match the spatial extent used to extract GFSpatterns (layers 2 ⃝). As a result, a description based on 96 neurons is obtained for each channel independently (layers 4 ⃝). These neurons are assumed to summarize a large part of the processing performed by the network and capture high level concepts similar to GFS-patterns. Their number is set so as to limit the number of activation level configurations and ease interpretability. Finally, channel-wise features are gathered and then summarized with dimension reduction layers ( 5⃝, 7 ⃝ and 8 ⃝). For each channel, an auxiliary attention branch (layer 6 ⃝) is added to weight the importance of each channel in the decision of the classifier. To fit the Réunion SITS with T = 21 timestamps, the size of convolutional kernels is adjusted to set a temporal field of view such that k1 = k2 = k3 = 7. Finally, the number of convolutional filters progressively decreases with N1 = 256, N2 = 64, and N3 = 32.

EXPERIMENTS

Layer

Operation

Specifications

Tensor output shape 1 ⃝ split 6 input channels (T, 3, 3, 1)(×6)

2 ⃝ (x 6) conv3d kernel=(k 1 , 3, 3), no padding, n f ilters = N 1 (T 1 , 1, 1, N 1 ) 3 ⃝ (x 6) conv1d kernel=(k 2 ), no padding , n f ilters = N 2 (T 2 , N 2 ) 4 ⃝ (x 6) conv1d kernel=(k 3 ), no padding, n f eat = N 3 (T 3 , N 3 )

Pattern extraction

All pixels for which a ground truth is available are characterized using patterns (see Section 2). The whole extraction process, from pixel value quantization to pattern ranking is run using the free prototype DFTS-P2miner [START_REF] Nguyen | A pattern-based mining system for exploring Displacement Field Time Series[END_REF]. Original pixel values are quantized with three intervals using equal frequency bucketing. As a result, for each channel, pixel values are denoted by symbols '1', '2', and '3', that respectively report 'low values', 'medium values' and 'high values'. Such a preprocessing is commonly adopted to mine patterns [START_REF] Julea | Unsupervised Spatiotemporal Mining of Satellite Image Time Series Using Grouped Frequent Sequential Patterns[END_REF]. The minimum surface of a pattern is set so as to be able to find patterns for each class. The class that is less represented, namely 'greenhouse crops', only contains 1, 931 pixels. Assuming that about half of these pixels share the same kind of evolution, the minimum surface was set to 881 pixels, which is a very weak constraint since it represents 0.1% of annotated pixels. The average connectivity constraint imposed on the pixels affected by a pattern is set to 5, which is a standard setting when processing optical SITS [START_REF] Julea | Unsupervised Spatiotemporal Mining of Satellite Image Time Series Using Grouped Frequent Sequential Patterns[END_REF]. The 20 patterns that are the more likely to occur in randomized versions of the data are retained along with the 20 patterns that are the less likely to do so, which is once again a standard setting [START_REF] Méger | Ranking evolution maps for Satellite Image Time Series exploration: application to crustal deformation and environmental monitoring[END_REF]. For a given channel, each pixel is thus described by indicating the absence or presence of 40 patterns.

Training of the DSLCC

The model optimisation is performed using TensorFlow2. Inputs are normalised channel-wise between 0 and 1 using a min-max feature scaling to facilitate the convergence of the training process. A stratified sampling preserving class ratios is employed to split annotated pixels into a training dataset (60%), a validation and test dataset (20% each). Pixels belonging to a same object all belong to the same dataset. The network is learnt by considering the standard unweighted categorical cross-entropy CE and defining the loss as

L global = CE(Y, Y main) +0.5×CE(Y, Yaux)
where Ymain and Yaux are the model main and auxiliary outputs. Gradients are back-propagated using an Adam optimizer and an L 2 -regularization with a weight decay of 1.10 -6 to avoid overfitting on all layers.

The performances of the DSLCC is assessed against a classical random forest (500 trees, 200 splits) and two deep land cover classifiers, namely TempCNN [START_REF] Pelletier | Temporal Convolutional Neural Network for the Classification of Satellite Image Time Series[END_REF] and Sdeep-B-Multi-ii [START_REF] Courteille | Channel-based attention for land cover classification using sentinel-2 time series[END_REF]. Both work at the pixel level, ignore the spatial dimension, exploit all bands and indexes, and rely on temporal convolutions. In addition, Sdeep-B-Multi-ii is equipped with an attention operator weighting the importance of each channel in the final classification decision. The random forest, TempCNN, Sdeep-B-Multi-ii and the DSLCC respectively reach 90.4%, 91.3%, 92.2% and 84.4% of accuracy. Though less accurate, the performance of DSCLC is still decent. It is detailled in Table 2.

Explaining the DSLCC decisions

In order to produce explanations as general as possible, all annotated pixels are supplied to the DSLCC to infer their classes. As expected, the overall accuracy is still high with a score of 87%. The precision and the recall obtained for each one the classes are listed in Table 3. 3. Precision and recall by class for the DSLCC for all annotated pixels (880,828 pixels).

Class

Attention:

As shown in Figure 1 for some classes of interest and all annotated pixels, the attention weights differ from one class to another, which illustrates the interest of the attention operator. It can be noted that all bands are exploited to take decisions. These weights are extremely similar to the ones obtained at the scale of the validation and test sets. One exception is class 'Water'. This can be explained by the presence of different evolution sub-classes. Finally, let us remark that merging attention weights is simple when considering channels or the temporal dimension. Contrarily, doing so for the spatial dimension or a set of dimensions is far from being straightforward.

Redescription mining:

Channel attention-based explanations given by Figure 1 are enriched with redescriptions extracted from annotated pixel descriptions, i.e., patterns and the activation levels of layer 4 ⃝ observed at inference time. This is performed for each predicted class of interest and each channel using the free prototype SIREN (Galbrun and Miettinen, 2012b). In order to extract expressive but yet simple redescriptions, disjunctions and negated variables are not considered, the maximum number of variables is set to 4 for the neuron activation level ones and 1 for pattern ones. The minimum Jaccard index is set to the SIREN default value, i.e., 0.01, to extract as much redescriptions as possible. The minimum number of pixels supporting a redescription is arbitrarily set to the SIREN default value, i.e. 5%. The maximum p-value is set to the standard value 0.05. All other SIREN parameters resort to default values. Finally, once redescriptions are extracted, redondant ones are filtered out by removing those supported by pixels supporting other redescriptions whose Jaccard index is better.

The following table gives, for each predicted class of interest and each band, the number of extracted redescriptions (r), the fraction of pixels supporting all of them (S all ), the minimum and maximum cardinality of their supports (Smin, Smax) as well as their minimum and maximum Jaccard indices (Jmin and Jmax). Though redescriptions are statistically significant since their p-values are lower or equal to 0.05, the match between the activation level configurations and the patterns is not complete. According to Jmin and Jmax, redescription accuracy indeed varies between 0.08 and 0.66. Moreover, since S all reaches 0.7 as a maximum, redescriptions extracted from different bands should be therefore considered jointly to explain as much decisions as possible, which is no suprise since the classifier itself adopts this strategy to infer classes (see Section 5.3.1).

The cover of decisions by redescriptions Cr, i.e. the percentage of decisions that can be explained with one or more redescriptions is given for each class in Table 5. This cover is provided along with the minimum, maximum and mode numbers of redescriptions per decision, Rm, RM , R d , and the minimum, maximum and mode numbers of bands from which these decisions originate, Bm, BM , B d . As it can be observed, a majority of decisions are covered by redescriptions (between 65% and 91%) using up to 8 redescriptions and all 6 bands. Reported modes also show that decisions are most frequently covered by one ore two redescriptions extracted from one or two bands. Considering several patterns coming from different bands to explain decisions also makes sense when considering input data characteristics. For example, 97% of the pixels labelled as 'Pasture' by the classifier are indeed affected by up to 10 redescription patterns (i.e., the patterns occurring in redescriptions, not redescriptions themselves) while no more than 5 redescriptions patterns can be supplied by a single band for class 'Pasture'. This cover of decisions by redescription patterns, Crp, is given Table 5 for each class along with the minimum, the maximum and mode numbers of redescription patterns covering decisions, Rm, RM , and B d . Finally, since not all decisions can be associated with redescriptions, other extraction parameter settings could be tried, in particular for the support of redescriptions and the number of patterns retained to describe each band.

For class 'Pasture', a very high attention is reported for B8, which is expected as it is a vegetation class. Redescriptions obtained for B8 are given hereafter along with their accuracy, J, and the number of pixels supporting them, S:

• r1: [3.347221 < a10] ∼ 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 ) 3 (J = 0.42, S = 0.40) • r2: [-35.42756 < a33 < -5.023269] ∧ -[7.611569 < a62 < -1.214998] ∧ [0.322748 < a70 < 1.388656] ∼ 3 ) 3 ) 3 ) 3 ) 2 ) 2 ) 2 ) 2 ) 2 (J = 0.19, S = 0.08)
These descriptions illustrates the fact that a pattern can be captured using a single or more neurons. Redescription r1 indicates that 40% of the decisions are associated with a pattern exhibiting a continuous presence of vegetation at a quite high level: symbol '3' occurs in 20 images (the series contains 21 images). Though accounting for 8% of the decisions, redescription r2 is interesting as it shows a loss of biomass with a series of 4 symbols '3' followed by five symbols '2'. Both patterns can be localized within the ground truth areas actually covered by pastures using synthetic colors to denote both their spatial extent and the date at which they ends in the SITS. The temporal color palette used in this paper is given by Figure 2. The white color is also used to point out the pixels of the ground truth belonging to class 'Pasture' that are not affected by patterns. Remaining pixels, i.e. black ones, are simply not covered by pastures according to the ground truth. These SpatioTemporal Localizations Maps (STL-maps) [START_REF] Méger | Ranking evolution maps for Satellite Image Time Series exploration: application to crustal deformation and environmental monitoring[END_REF] have been computed and cropped to focus on a 12 km × 12 km area of interest located inland, in the region of la Plaine des Cafres.

The resulting maps are presented with figures 3 and 4 for the r1 and r2 patterns respectively. No significant temporal behavior is observed for the r1 pattern, which is expected as it covers almost all the images of the SITS, i.e., 20 images out of 21. Contrarily, the r2 pattern shows more dispersed settings since it is shorter and can end at different dates. This dispersion is particularly visible in the northern part of La Plaine des Cafres as shown in Figure 5. As also evidenced by the STL-maps, and since no pixel can be covered both by the r1 pattern and the r2 pattern1 , these patterns are complementary spatially. These maps thus show that using these patterns to predict class 'Pasture' makes sense even if, as underlined by white pixels, they do not characterize all of its pixels. Knowing that the classifier is very accurate for that class, this is far from being surprising since about half of the decisions are explained by r1 and r2 (S=0.48). STL-maps computed with respects to decisions 'Pasture' (and not the actual class 'Pasture') are extremely similar for the same reason. They are presented in figures 6 and 7. The same color palette is used to denote the presence of the pattern as well as its ending dates. The white color is used to show decisions for which the activation level conditions are not fulfilled and the pattern is absent. The brown color is associated with decisions such that the activation levels conditions are satisfied and the pattern is absent. If the pattern is present and the activation level conditions are not meet, then the gray color is assigned to pixels. Regarding NDVI, even if designed to monitor vegetation, the DSLCC hardly exploits it according attention weights (see Figure 1). pattern 1 ) 1 ) 3 ) 2 ) 2 ) 2 ) 2 ) 2 ) 2 and thus expresses a gain and then a loss of biomass. Since behaviors similar to B8 ones could also be expected, this confirms that mobilizing NDVI to detect pastures is indeed not of primary interest for this SITS. Class 'Water' is detected by exploiting all channels at quite high levels according attention weights (see Figure 1). Though being the less exploited according to attention weights, NDWI is generally expected to detect water. This is confirmed by a single but strong redescription:

• r3: [-31.58766 < a92 < -2.46482] ∼ 1 ) 1 ) 2 ) 1 ) 1 ) 1 ) 1 (J = 0.66, S = 0.60)

Redescription r3 allows to describe 60% of the decisions leading to class 'Water', which is the highest support reported for the redescriptions extracted for the classes of interest. Its 22 km × 17 km STL-maps, for areas located along the northwest coast between the towns of Saint-Paul and Saint-Denis, are given by Figure 8 and Figure 9. Though the r3 pattern contains few symbols, there is few temporal dispersion with ending dates located at the end of the year. According to the ground truth, it mainly characterizes maritime waters, i.e., the eight large blocks picked up by the experts in coastal waters. Contrarily, a set of inland water zones, grouped at the lower left corner of the image is not captured by the pattern. They belong to the Réserve naturelle nationale de l'étang de Saint-Paul and can not be detected using redescription patterns extracted from B2, B3 or B4. The latter indeed focus on maritime waters as well. In more details, B2 is associated to redescription patterns expressing gradual increases as well series of changes, all reflectance levels being mobilized. Band B3 supplies redescription patterns expressing the stability of either medium or high reflectance values. Band B4 is exploited through a redescription expressing an abrupt increase from symbol '1' to symbol '3'.

Finally, B8 and NDVI do not seem to be captured by the network in the way patterns do since no redescription is to be reported for these bands. Knowing that the DSLCC identifies maritime waters as well as inland waters such as those of the Réserve naturelle nationale de l'étang de Saint-Paul, one could simply argue that patterns do not characterize such areas. Among the 40 patterns automatically extracted from B8, 7 can be manually identified as being able to detect such areas. This is reasonable since vegetation is present in this pond region. Pattern 3 ) 3 ) 3 ) 2 ) 2 ) 2 ) 2 ) 2 ) 2 is a good example. Its STL-map for the whole 22 km × 17 km is presented with Figure 10. Please note that it is not restricted to actual water areas or areas identified as such by the DSLCC. As evidenced, the inland water of the Réserve naturelle nationale de l'étang de Saint-Paul as well as other vegetated areas are well exhibited while maritime waters are not detected. The pattern extraction parameters as well as the redescription extraction parameters can thus be questioned. For example, more patterns could be considered to characterize each band and/or a lower redescription support could be envisaged. If the latter option is chosen, and if the minimum number of pixels supporting a decision is set to 1% instead of 5%, then 5 redescriptions are extracted. Two of them rely on the inland water patterns identified manually, and pattern 3 ) 3 ) 3 ) 2 ) 2 ) 2 ) 2 ) 2 ) 2 is one of them. It is thus possible to relate inland water decisions with patterns, as long as the support is correctly set. Interestingly, no such patterns are reported for NDVI while its attention weights are higher than those of B8.

According to attention weights, class 'Rocks' mainly mobilizes visible and near-infrared channels. Rocks are indeed less likely to be detected by vegetation nor water indices. They are also not likely to change that much, which is confirmed by available redescription patterns. They indeed indicate that reflectance levels are quite stable. Though symbol '1' can occur in a row, these levels are mainly medium and high ones for B2, B3, and B4 (symbols '2' and '3') while they are lower ones for B8, NDVI, and NDWI. (symbols '1' and '2'). Regarding the redescriptions provided for class 'Urban area', quite stable evolutions based on medium or high reflectance values are extracted for B2, B3, B4. Contrarily, an increase from symbol to '1' to '2' is reported for NDVI and NDWI. NDWI also provides a redescription pattern showing stability at low levels. Band B8 unveils more complex evolutions, i.e., stable ones with series of symbol '2' as well as decreases, either from symbol '2' to symbol '1' or from symbol '3' to symbol '2'. This diversity is exploited by the DSLCC since it mainly relies on B8 according to attention weights (see Figure 1).

CONCLUSION

An original approach for explaining the behavior of a deep spatiotemporal land cover classifier is presented in this paper. It unveils, for each channel and each class, the intepretable spatiotemporal features captured at the pixel level by the last convolutional layer. These features are extracted using dedicated data mining patterns and matched with the different neuronal activation level configurations using redescription mining. In order to demonstrate the feasibility of the proposed approach, a simple architecture applying spatiotemporal and and temporal convolutions for each channel separately is considered for the deep classifier. As shown by experiments on a Sentinel-2 time series, such explanations are meaningful and can enrich channel attention-based explanations. Nevertheless, though indeed captured by the network, it is yet unclear to which extent they do account for the final decisions. Masking methods are for example envisaged to assess this crucial aspect. Moreover, since some expected redescription-based explanations are missing and decisions are not always covered by redescriptions, the selection of the patterns and the redescriptions can also be questioned. In particular, the number of most promising GFS-patterns describing the pixels could be higher and the support of the redescriptions could be lower. A method for setting them automatically would be of interest. More complex redescriptions, e.g., with more activation level variables and disjunctions could also be extracted. In addition, it would be of interest to check whether the presence/absence of patterns could help in understanding classifier errors or not. Finally, other layers such as the final dense one should be studied, and other interpretable features could be considered, in particular the WECS (Wavelet Energies Correlation Screening), a wavelet-based change measure recently proposed by [START_REF] Fonseca | Wavelet spatio-temporal change detection on multi-temporal polsar images[END_REF]. Figure 10. STL-map of pattern 3 ) 3 ) 3 ) 2 ) 2 ) 2 ) 2 ) 2 ) 2, between the towns of Saint-Paul and Saint-Denis.

Figure 1 .

 1 Figure 1. All annotated pixels: box plots of channel weight attention for 4 classes, normalized by class sums. Horizontal lines depict activation thresholds (0.5 for a sigmoid).

Figure 2 .

 2 Figure 2. Temporal color palette: 21 acquisitions, from January 2017 (red) to December 2017 (magenta).

Figure 3 .

 3 Figure 3. STL-map of the r1 pattern, for ground truth areas covered by pastures, in the region of la Plaine des Cafres.

Figure 8 .

 8 Figure 8. STL-map of the r3 pattern for ground truth areas covered by maritime waters, between the towns of Saint-Paul and Saint-Denis.

Figure 9 .

 9 Figure 9. STL-map of the r3 pattern for areas identified as waters by the DSLCC, between the towns of Saint-Paul and Saint-Denis.

Table 1 .

 1 DSLCC architecture. Features are extracted by 3 different convolutional layers computed for each one of the 6 channels (6

	5 ⃝	stack	6 channels from 4	(6, T 3 , N 3 )
	6 ⃝	attention	6 attention weights α i
	7 ⃝ from 5 ⃝ hidden dense + relu	256 neurons
	8 ⃝	final dense	+ softmax	11 neurons
		times layers 2 ⃝, 3 ⃝, 4 ⃝). Attention layer 6 ⃝ is outing 6 channel attention weights.

Table 2 .

 2 Precision and recall by class for the DSLCC on the test set (176,166 pixels).

		Precision Recall % of annotated pixels
	Sugar cane	88	89	10.1
	Pasture	88	84	7.7
	Market gardening 61	65	2.0
	Greenhouse crops 17	35	0.2
	Orchards	62	67	3.8
	Wooded areas	83	86	23.3
	Moor	84	79	17.6
	Rocks	92	92	17.5
	Relief shadows	78	91	6.2
	Water	98	84	9.2
	Urban area	81	80	2.2
	Mean	75.8	77.4	-
	Class	Precision Recall % of annotated pixels
	Sugar cane	96.7	96.6	12.4
	Pasture	92.8	94.0	7.3
	Market gardening 75.1	74.3	2.3
	Greenhouse crops 52.9	52.3	0.2
	Orchards	80.1	83.7	3.9
	Wooded areas	87.3	94.4	23.5
	Moor	92.4	77.9	16.0
	Rocks	97.5	97.7	21.4
	Relief shadows	94.3	98.7	5.1
	Water	99.9	99.4	6.1
	Urban area	84.6	91.0	1.8
	Mean	86.7	87.3	-

Table

Table 4 .

 4 Class / Band r S all S min S max J min J max Support and accuracy of extracted redescriptions.

	Pasture / B2	2 0.28	0.05	0.23	0.18	0.45
	Pasture / B3	3 0.33	0.05	0.18	0.19	0.47
	Pasture / B4	5 0.70	0.06	0.20	0.23	0.40
	Pasture / B8	2 0.48	0.08	0.40	0.19	0.42
	Pasture / NDVI	1 0.05	0.05	0.05	0.15	0.15
	Pasture / NDWI	2 0.41	0.14	0.27	0.27	0.45
	Rocks / B2	2 0.11	0.05	0.06	0.08	0.33
	Rocks / B3	3 0.20	0.05	0.10	0.11	0.41
	Rocks / B4	5 0.33	0.05	0.09	0.15	0.40
	Rocks / B8	3 0.15	0.05	0.05	0.12	0.24
	Rocks / NDVI	1 0.05	0.05	0.05	0.17	0.17
	Rocks / NDWI	4 0.38	0.08	0.12	0.22	0.39
	Water / B2	2 0.31	0.14	0.17	0.48	0.51
	Water / B3	4 0.36	0.05	0.16	0.17	0.44
	Water / B4	1 0.06	0.06	0.06	0.39	0.39
	Water / B8	0	-	-	-	-	-
	Water / NDVI	0	-	-	-	-	-
	Water / NDWI	1 0.60	0.60	0.60	0.66	0.66
	Urban area / B2	1 0.15	0.15	0.15	0.48	0.48
	Urban area / B3	1 0.05	0.05	0.05	0.08	0.08
	Urban area / B4	2 0.10	0.05	0.05	0.13	0.21
	Urban area / B8	4 0.26	0.06	0.08	0.23	0.39
	Urban area / NDVI	2 0.11	0.05	0.06	0.19	0.23
	Urban area / NDWI 2 0.27	0.09	0.18	0.20	0.27

Table 5 .

 5 Let us have a look at the only one and quite weak redescription extracted for this index. It is supported by 5% of the pixels with anClassC r C rp R m R M R d B m B M B d RP m RP M RP d Decision covers.accuracy of 0.15%. It refers to

	Pasture	0.91 0.97	1	8	2	1	6	2	1	10	2
	Rocks	0.72 0.83	1	6	1	1	5	1	1	8	1
	Water	0.73 0.78	1	7	1	1	4	1	1	7	1
	Urban area 0.65 0.80	1	5	1	1	4	1	1	8	2

There is only one symbol left undescribed for pixels affected by the r1 pattern, and this pattern contains no symbol '2' while the r2 pattern contains 5 symbol '2'.

ACKNOWLEDGEMENTS

This work was supported by CNES, focused on the MultiSpectral Instrument and on the Sentinel-2 mission.


David Thivel

Michele Tardieu

Pauline Genin

Alicia Fillon

Benjamin Larras

Pierre Melsens

Julien Bois

Frederic Dutheil

Francois Carre

Gregory Ninot

COVID-19-Related National Re-confinement: Recommendations From the National French Observatory for Physical Activity and Sedentary Behaviors (ONAPS)

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

COVID-19-Related National Re-confinement: Recommendations From the National French Observatory for Physical Activity and Sedentary Behaviors (ONAPS)

David Thivel, Michéle Tardieu, Pauline Genin, Alicia Fillon, Benjamin Larras, Pierre Melsens, Julien Bois, Frédéric Dutheil, Francois Carré, Gregory Ninot, Jean-Francois Toussaint, Daniel Rivière, Yves Boirie, Bruno Pereira, Angelo Tremblay, and Martine Duclos aaa While a declined physical activity level (PAL) and an increase of sedentary behaviors at all ages during the COVID-19-induced first confinement period have been unanimously observed worldwide, the lately instituted new social distancing strategies and lockdowns around the world require the formulation and dissemination of adapted and accessible recommendations to promote physical activity (PA) and limit the progression of sedentary time (SED) in the upcoming weeks. From a public health perspective, it appears imperative to encourage the adoption of healthy movement behaviors despite the new activity restrictions imposed by governments to slow down the alarming progression of the SARS-CoV-2 pandemic.

On top of their well-known impact on physical and metabolic health in both healthy individuals and patients, 1 both PA and sedentary behaviors have been shown to be strongly associated (in an opposite way) with depression, anxiety, stress, and overall wellbeing. [START_REF] Netz | Is the comparison between exercise and pharmacologic treatment of depression in the clinical practice guideline of the American College of Physicians evidence-based?[END_REF][START_REF] Omorou | 10-year cumulative and bidirectional associations of domain-specific physical activity and sedentary behaviour with health-related quality of life in French adults: Results from the SU.VI.MAX studies[END_REF][START_REF] Stubbs | Pain and severe sleep disturbance in the general population: Primary data and meta-analysis from 240,820 people across 45 low-and middle-income countries[END_REF] Decline of PA and increase of SED during the first confinement period have been clearly related to a deterioration of several mental health indicators at all ages. [START_REF] Ugbolue | An assessment of the novel COVISTRESS Questionnaire: COVID-19 impact on physical activity, sedentary action and psychological emotion[END_REF][START_REF] Carriedo | Resilience and physical activity in people under home isolation due to COVID-19: a preliminary evaluation[END_REF][START_REF] Chouchou | The importance of sleep and physical activity on well-being during COVID-19 lockdown: reunion island as a case study[END_REF][START_REF] Werneck | Changes in the clustering of unhealthy movement behaviors during the COVID-19 quarantine and the association with mental health indicators among Brazilian adults[END_REF][START_REF] Alves | Associations between affect, physical activity, and anxiety among US children during COVID-19[END_REF] Moreover, sedentariness plays a major role in COVID-19 mortality worldwide, while inactivity partly determines the proportion of patients requiring intensive care due its subsequent metabolic disorders (obesity, hypertension, diabetes). [START_REF] De Larochelambert | Covid-19 mortality worldwide: a matter of vulnerability among nations facing limited margins of adaptation[END_REF] It appears then necessary to elaborate effective strategies to maintain the PAL of already active individuals but also to encourage inactive people to improve their activity, while, obviously, fighting against the instauration of a sort of "supra-sedentariness" favored by social distancing and increased teleworking. Maintaining and encouraging PA during a confinement period appears indeed essential to preserve our health capital but also to reinforce our immunity, which seems actually of high importance to face the COVID-19 virus.

In order to face this worrying situation induced by the first quarantine period related to the COVID-19 virus, the World Health Organization (WHO) proposed some recommendations aimed at improving individuals' total daily activity level. 11,[START_REF]#HealthyAtHome -Physical Activity[END_REF] Briefly, WHO encouraged adults to increase their household chores, to integrate online PA programs, to exercise while listening to enjoyable music, to climb stairs as much as possible and to perform resistance exercises. For children and adolescents (5 to 17 years old), WHO recommended participation in online physical activities, active plays, indoor challenging games, the realization of activities mobilizing muscle groups, and the development of new motor abilities and skills.

Since the first confinement, some authors proposed adapted PA and SED recommendations for older adults, [START_REF] Jiménez-Pavo ´n | Physical exercise as therapy to fight against the mental and physical consequences of COVID-19 quarantine: Special focus in older people[END_REF][START_REF] Lakicevic | Stay fit, don't quit: geriatric exercise prescription in COVID-19 pandemic[END_REF][START_REF] Hammami | Physical activity and coronavirus disease 2019 (COVID-19): Specific recommendations for home-based physical training[END_REF] for children and adolescents, [START_REF] Lakicevic | Stay fit, don't quit: geriatric exercise prescription in COVID-19 pandemic[END_REF][START_REF] Hammami | Physical activity and coronavirus disease 2019 (COVID-19): Specific recommendations for home-based physical training[END_REF][START_REF] Guan | Promoting healthy movement behaviours among children during the COVID-19 pandemic[END_REF] and for the overall population. [START_REF] Ricci | Recommendations for physical inactivity and sedentary behavior during the coronavirus disease (COVID-19) pandemic[END_REF][START_REF] Chtourou | Staying physically active during the quarantine and self-isolation period for controlling and mitigating the COVID-19 pandemic: A systematic overview of the literature[END_REF][START_REF] Jurak | Physical activity recommendations during the coronavirus disease-2019 virus outbreak[END_REF] Briefly, all these recommendations underlined the need for home-based adapted versions of the usual PA recommendations, proposing adequate durations and intensities and stressing the particular need to adopt some sedentary break strategies.

The French National Observatory for Physical Activity and Sedentary Behaviors (ONAPS), altogether with the French Minister of Sports, conducted one of the largest worldwide surveys evaluating the impact of the first confinement on PA and SED. [START_REF] Genin | Promoting physical activity and reducing sedentary time among tertiary workers: Position stand from the French National Observatory for Physical Activity and Sedentary Behaviors (ONAPS)[END_REF] Importantly, this survey questioned the impacts of the lockdown from childhood to elderly and the conducted analysis also explored whether these changes were associated with the initial levels of PA and SED of individuals (for complete and detailed results, see ONAPS' position stand [START_REF] Genin | Promoting physical activity and reducing sedentary time among tertiary workers: Position stand from the French National Observatory for Physical Activity and Sedentary Behaviors (ONAPS)[END_REF] ). Briefly this survey showed, altogether with an alarming general reduction of PA, a dramatic increase in sitting time per day in nearly 50% of participants (reaching +72% in initially sedentary children and adolescents) and, except in older people, a huge increase in screen time per day (children and adolescents: +62 to 69%, adults: +57%). According to our results, a very large proportion of initially active individuals decreased Tremblay is also with the Département de l'éducation Physique, Faculté des Sciences de l'éducation, Université Laval, Québec City, QC, G1V 0A6, Canada. Thivel (david.thivel@uca.fr) is corresponding author.

their PAL during the confinement while previously inactive ones tended to start exercising, mainly following online training classes that remain to be considered with caution as non-individualized and adapted to everyone (especially inactive people). Interestingly, people who maintained or increased their PAL during the first days of the previous lockdown were more likely to remain active and less sedentary during the whole confinement (which was positively associated with overall mental health and wellbeing). Our results also pointed out the necessity to help children and adolescents to remain active as they showed a dramatic increase of their overall unhealthy movement behaviors (decreased PAL and increased screen time). The main results of this survey have been previously detailed. [START_REF] Genin | Promoting physical activity and reducing sedentary time among tertiary workers: Position stand from the French National Observatory for Physical Activity and Sedentary Behaviors (ONAPS)[END_REF] At the dawn of a new generalized episode of confinement, ONAPS proposes here some new key recommendations and advices, based on the actually available evidences and on the results of its COVID-19 national survey, [START_REF] Genin | Promoting physical activity and reducing sedentary time among tertiary workers: Position stand from the French National Observatory for Physical Activity and Sedentary Behaviors (ONAPS)[END_REF] to prevent the decline in active behaviors and rise in SED that have been observed during the first confinement (from March to May 2020). Importantly, these recommendations and advices (Table 1) are not substitutes to the general PA guidelines, but propose an adapted approach to avoid the already observed negative impacts of a lockdown on our daily active and sedentary behaviors.

While not exhaustive, these advices should be considered as simple strategies proposed to avoid the observed confinementinduced decline of PAL and rise of SED. There is no one-sizefits-all solution, but everyone has to realize the importance of maintaining an active lifestyle despite such particular circumstances. Importantly, according to what was observed during the previous lockdown, initially active people with a low or moderate time devoted to sedentary behaviors are particularly at risk of adopting unhealthy movement behaviors, as well as adolescents, older people, and women.

Although highly restrictive, this new wave of the COVID-19 pandemic and the instituted new confinement (for at least several weeks) should be considered as a potential opportunity to analyze our usual daily activities and sedentary behaviors, and to adopt new habits, on an individual and/or family basis, to improve our PAL, reduce our time spent sedentary, and then enhance our overall mental and physical health. • Favor any daily movement, whatever its intensity and duration, keeping in mind that our overall level of physical activity needs every single and simple movement.

• We encourage the adoption of an active daily lifestyle from the very early days of this new confinement. Similarly, a particular attention should be given to our sedentary behaviors from the first days, to avoid their instauration and adopt healthy movement behaviors and habits.

• As for the first confinement, it remains possible to perform 1 hour of outside physical activity per day. We encourage the adoption of daily walks or runs. Several days a week, we encourage to share these outdoor activities with the other members who compose the family home.

• Initially active individuals must be careful to maintain their level of practice, keeping in mind that our usual daily activities related to active transportation and occupational activities will be drastically decreased and should be compensated for by favoring other kinds of activities such as active plays with kids, walking, and housekeeping.

• In case of telecommuting, it is important to warm up and stretch 5 to 10 minutes before setting up at your desk, emphasizing on the back, shoulders, and pelvis. A warm-up of the main muscle groups is also recommended.

• Initially inactive individuals, or those with a low level of physical activity, should engage in a gradual and a step-by-step approach to progressively reach the recommendations. A brutal engagement in an important volume of physical activity has been shown counterproductive and does not favor a long-term adoption of physical activity behaviors.

• Online physical activity classes can be followed and have to be encouraged keeping in mind that they might not be individualized and that everyone has to auto-adapt their practice based on their own physical and exertion sensations. Exercising does not have to be painful and we have to listen to our own feelings and capacities to progressively improve. A scale of perceived difficulty (0 to 10) can be used instead of proper intensities; a rating between 5 and 7 being appropriate to ensure long-term engagement.

• Parents and legal representatives should encourage physical activity among children and adolescents. Performing active games 1 hour or so per day with our young kids, even combined with 1 hour of outdoor walk or play, is not enough to maintain their daily physical activity level. Regular short blocks of games and activities should be encouraged (which could join up with the active breaks recommended to break our sedentary time).

• In order to break this sedentary time in both youth and parents, we suggest the adoption of active breaks that involve the whole family (or several members), based on small active plays and games. We also encourage the instauration of relatively short periods of relaxing activities such as stretching before and after a whole day of teleworking.

• On top of the recommended active breaks, homemade active desks can be created to turn our usual tables or desk into standing desk, for instance. When possible cycling drives can be purchased. Simple strategies could be adopted such as systematically walking while on the phone.

• Families and peers should regularly, on a daily basis, encourage older people to engage in simple activities such as walking. The government gives the opportunity to visit individuals who necessitate help and support and we believe that the maintenance of our elders' physical activity is a challenge that has to be considered during this new lockdown.

• Importantly, the practice of physical activity should be conditioned to our health status. Fever, persistent fatigue, and other symptoms (related or not to COVID-19), as well as muscle or joint pain, should lead everyone to adapt their activity.

• Patients with chronic disease should not stop physical activity that is an integral part of their treatment. They have to adapt indoor and outdoor physical activity to reach at least 30 minutes of physical activity every day and to break regularly (hourly) sedentary behaviors.

  Thivel, Tardieu, Genin, Fillon, Larras, Melsens, Bois, Carré, Ninot, Toussaint, Rivière, Boirie, Pereira, Tremblay, and Duclos are with the National Observatory for Physical Activity and Sedentary Behaviors (ONAPS), Clermont-Ferrand, France. Dutheil is with Occupational Medicine, University Hospital CHU G. Montpied, Clermont-Ferrand, France; University Clermont 1, UFR Medicine, Clermont-Ferrand, France; and Université Clermont Auvergne, CNRS, LaPSCo, Physiological and Psychosocial Stress. Thivel is also with Clermont Auvergne University, EA 3533, Laboratory of the Metabolic Adaptations to Exercise under Physiological and Pathological Conditions (AME2P), CRNH Auvergne, Clermont-Ferrand, France. Bois is also with the Universite de Pau & des Pays de l'Adour, e2s UPPA, MEPS, Tarbes, France. Boire and Duclos are also with University Clermont 1, UFR Medicine, Clermont-Ferrand, France. Carré is also with Cardiologie et maladies vasculaires, médecine du sport, CHU Pontchaillou, université Rennes 1, Inserm 1099, Rennes, France. Ninot is also with Unité de recherche IDESP, Université de Montpellier, Institut du Cancer de Montpellier, Montpellier, France. Toussaint is also with the Institut de Recherche Biomédicale et d'Épidémiologie du Sport (IRMES), Institut National du Sport, de l'Expertise et de la Performance (INSEP); EA7329 Institut de Recherche BioMédicale et d'Épidémiologie du Sport (IRMES); and the Centre d'Investigation en Médecine du Sport, Paris, France. Boirie is also with the Departement of Human Nutrition, Clermont-Ferrand University Hospital, G. Montpied Hospital, Clermont-Ferrand, France; and INRA, UMR 1019, Clermont-Ferrand, France. Pereira and Duclos are also with Clermont-Ferrand University Hospital, Biostatistics unit (DRCI), Clermont-Ferrand, France. Duclos is also with the Department of Sport Medicine and Functional Explorations, Clermont-Ferrand University Hospital, G. Montpied Hospital, Clermont-Ferrand, France.

Table 1

 1 Recommendations and Advices From the French National Observatory for Physical Activity and Sedentary Behaviors (ONAPS)

	Recommendation or Advice

JPAH Vol. 18, No. 5, 2021

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Thomas Dumas

Matthieu Virot

Denis Menut

Christelle Tamain

Cyril Micheau

Sandrine Dourdain

Olivier Diat

Size and structure of hexanuclear plutonium oxo-hydroxo clusters in aqueous solution from synchrotron analysis

Introduction

Because plutonium is highly radiotoxic, it represents one of the major long-term risk in the nuclear waste management. To predict and control the plutonium behavior in various environmental conditions, thermodynamic models are currently developed to describe plutonium solubility and surface interactions. (Altmaier et al., 2013;Geckeis et al., 2013;Kersting et al., 1999) Nevertheless, new experimental inputs are still necessary in order to improve the reliability of these models. Among them, any additional fundamental knowledge on the complex plutonium chemistry at the molecular scale is highly desirable for long term nuclear disposal safety. In this scope, and within the large variety of plutonium chemical and redox states, hydrolyzed forms of tetravalent plutonium are crucial objects to consider. Due to its high charge density in aqueous solution, the Pu 4+ ion has a high tendency for hydrolysis reactions and can further polymerize through oxolation and/or olation reactions. The intermediate clusters formed through these reactions can further condensate to yield colloidal plutonium nanoparticles which might enhance its mobility. (Dalodiere et al., 2017;Gerber et al., 2020;Micheau et al., 2020;Neck et al., 2007;Walther et al., 2007;Walther & Denecke, 2013) Until now, the addition of complexing molecules was considered to limit the growth of colloids leading to smaller polynuclear species and affecting plutonium solubility in complexing humic acid conditions. (Marsac et al., 2014) Even if analogous tetravalent cations can also form polynuclear clusters with different number of metallic cations M 4+ in the nuclear core (Hennig et al., 2012;Hennig et al., 2017;Knope et al., 2011;Takao et al., 2012), only recent works have characterized small polynuclear plutonium clusters. Knope et al. (Knope & Soderholm, 2013) first revealed the formation of a solid Li6[Pu6(OH)4O4(H2O)6(HGly)12]Cl18•10.5 H2O, which consists of a mixed hydroxo/oxo plutonium(IV) hexanuclear cluster. More recently, Tamain et al. (Tamain et al., 2016;Tamain et al., 2017) used visible and X-ray Absorption Spectroscopy (XAS) techniques to correlate solid state and solution structures of another hexanuclear complex exhibiting the same [Pu6(OH)4O4] 12+ core, stabilized with the polyamino carboxylic acid DOTA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid). Visible absorption and reflectance spectra as well as Extended X-ray Absorption Fine Structure (EXAFS) measurements confirmed the stability of the hexanuclear core from the solid state to the solution. However both spectroscopic approaches only provide plutonium centered information and indicate that the plutonium hexanuclear core is preserved in solution. To describe long range interactions in solution, Small Angle X-ray Scattering (SAXS) was applied in combination with EXAFS in aqueous solution. SAXS offers a complementary image of the plutonium species in solution. This technique was already used for other actinides polynuclear compounds characterization, in solution. For instance, SAXS was used on U oxoclusters by Martin et al. to follow the U(IV) hydrolysis, condensation and growth up to the formation of U-38 clusters (Martin et al., 2018). It was also applied to uranyl peroxo nanospheres (Falaise & Nyman, 2016) (Dembowski et al., 2017;Zhang et al., 2019) and even to the small hexanuclear uranium core clusters by Falaise et al. (Falaise et al., 2017). Recently SAXS measurements became available for plutonium samples at the MARS beamline and were used in combination with XAS to study plutonium colloids. (Micheau et al., 2020) Although the molecular structure of the hexanuclear DOTA plutonium clusters are well identified by single crystal XRD and the ability of the mars beamline to perform SAXS measurements on plutonium colloids were previously demonstrated, this work take the opportunity to probe the more challanging hexanuclear core clusters of plutonium in aqueous solution. The idea of probing small hexanuclear cluster core of plutonium was twofold: (i) assign as a test the ability of this set-up to detect small and diluted object in aqueous solution, and propose a more detailed description of the set-up (ii) provide information on the external shape of hexanuclear plutonium clusters in solution, that were beforehand only defined by the first two coordination shell of plutonium atoms.

Material and Method:

Synthesis of the [Pu6(OH)4O4(H2O)8(HDOTA)4] cluster.

The plutonium DOTA hexanuclear cluster was synthesized as previously reported (Tamain et al., 2016). 47 mg of protonated DOTA was dissolved in 400 µL of water (under heating) and 80 µL of HNO3 1 mol•L -1 was added after complete dissolution of the ligand. The plutonium solution was added to the ligand one ([Pu]/[L] = 1/5). The solution was left overnight to give crystals of plutonium(IV) hexamer.

The SAXS sample was prepared by dissolution of 2.3 mg of crystals in 1 M HNO3. The sample purity and concentration of 0.01 M (concentration of Pu involved in the hexamer) were checked using UV-Vis absorption spectroscopy in the visible range (400-800 nm) (see Figure 1). The spectrum collected in the visible range is identical to the one reported previously and insure the sample purity. The slight baseline deviation observed below 600 nm is related to a variation of HNO3 concentration between the two samples. In this section, we shall give a brief summary of the design and the relevant characteristics of the Multi Analyses on Radioactive Samples (MARS) beamline at the synchrotron SOLEIL (Saint-Aubin, France). (LLorens et al., 2014;Sitaud et al., 2012), as well as presenting more specific developments making the beamline especially suitable for scattering experiments.

From its inception, MARS was designed to accommodate the wide-ranging scientific requirements of the radionuclide and actinide sciences (up to highly radioactive materials) covering areas from biology, environmental science through to advanced materials to directly characterize of the chemistry and microstructure with the use of synchrotron-based techniques. The beamline is licensed to receive samples with radioisotope activities up to 2 Million times their isotope specific European exemption limits and complies with all legal requirements and safety precautions to avoid contaminating aerosol dissemination and guarantee the public dose rate outside the beamline. It has successfully shown its flexibility by accommodating a wide array of diverse sample environments during its years of operation. (Bechade et al., 2012;Menut et al., 2015;Bechade et al., 2013;LLorens et al., 2014;Dumas et al., 2018;Bengio et al., 2020) X-rays are sourced from a 1,71 T bending magnet providing a continuous spectrum of photons with a critical energy of 8,6 keV. A Double-Crystal Monochromator (Oxford Danfysik, Oxford, UK) allows tunable monochromatization in the continuous energy range 3.5 keV to 35 keV and horizontal focusing with a sagittal bender. The original feature of this DCM is its ability to exchange Si(111) and Si(220) crystals sets under vacuum to optimize the photon flux and energy resolution over the energy rangeTwo long mirrors are inserted before and after the DCM for high-energy harmonics rejection and to provide respectively a vertically collimated and focused beam. These mirrors consist of silicon blocks with two different reflective surfaces: a 60 mm width silicon uncoated strip for energy setup below 14 keV and a 50 mm width platinum coated strip (thickness 60 nm) for high energies. The X-ray beam at the second end-station of the MARS beamline (CX3), where were performed the scattering and absorption measurements described in the following, can be focused down to a 300 microns x 150 microns spot

[full width at half-maximum (FWHM), horizontal (H) x vertical (V)] with the possibility to further microfocus the beam down to 15 x 15 microns on the second end-station in the reduced range 3,5 keV to 21 keV by inserting additional rhodium coated mirrors in the Kirkpatrick-Baez geometry). Two kind of 2-dimensionnal detectors (image plate or hybrid pixel) are available for the scattering and/or diffraction analyses which can be moved along the X-ray axis. Thus, depending on the energy used and the exact geometry of the scattering set up, the Q-range achievable may be adapted.

As SAXS is contingent on the accurate subtraction of all background scattering contributions (optical elements, windows, slits, air, …), reducing the effects of parasitic scattering is vital not only to improve signal-to-noise ratios in the data but also to remove sources of scattering that may perturb the extraction of structural parameters. The instrument background at MARS was reduced by a standard three-pairedslits collimator system where the first slits define the beam and adjust the flux, the second slits cut out the parasitic scattering fan coming from the optics and passing through the first pair of slits, and the third and last pair of slits remove the weaker secondary scattering produced by the second pair of slits.

To further reduce this background, third slits are set-up by hybrid scattering slits from Xenocs (Sassenage, France). These scatterless slits are composed of heavy metal blades with Ge-monocrystal lateral edges oriented far from any Bragg peak position with respect to the incident beam. Based on comparison of the energy-dependent attenuation lengths of Ge, it actually offers the best attenuation of energies above 12 keV for synchrotron-based SAXS instrument where they could yield even higher performance enhancements with the incident beam intensity. (Li et al., 2008). Extendable vacuum pipes sealed with Kapton windows are attached to the beamline to minimize the air gap around the sample position to a few centimeters and to keep the background scattering from air to a minimum, aided by motorized (Tx, Tz) sample stages with 1 micron resolution over a 100 mm range of motion. As radiation damage to samples, and even more especially for solution, may resulting in the formation of aggregates can cause significant problems at high-brilliance synchrotron source, the MARS beamline is equipped with a beam attenuator composed of 8 pneumatic holders for aluminum foils of 0.05 mm to 8.0 mm thicknesses allowing a fine tune of the beam attenuation to achieve the optimal balance between lowering useful signal and reducing the effects of radiation damage.

Finally, a crucial step in SAXS data processing is the subtraction of the sample environment scattering from that of the sample, and these two independent patterns must be appropriately normalized to consider possible variation in the beam flux and differences in transmission. This operation can be conveniently accomplished by using an active beamstop. A miniature 3 mm x 2 mm active beamstop Small Angle X-ray Scattering (SAXS).

SAXS experiments were carried out using the 2D image plate detector (MAR345, marXperts GmbH, Germany), with an X-ray energy of 17 keV corresponding to an average wavelength of 0.7294 Å -1 , and a sample to detector distance of 785.70 mm. The calibration of the angular axis was made by the powder diffraction pattern of silver behenate. This configuration allows covering a Q-range between about 0.1 nm -1 and 18.8 nm -1 . Sample transmissions were recorded during 10 s using photodiodes and scattering diagrams were recorded during 5 s per sample. Isotropic 2D scattering data were azimuthally averaged to obtain the scattering intensity I(Q) using Fit2D software. (Hammersley et al., 1996) Sample scattering intensity was then normalized by the acquisition time, transmission and thickness, and multiplied by a normalization constant determined with the help of the scattering intensity of polyethylene (PE) at Q= 0.36 nm -1 that corresponds to 4.9 cm -1 . The absolute intensity scattered by the cluster was finally obtained by subtracting the empty cell, solvent and background contributions. Data were simulated using the SasView 4.2.0 software (http://www.sasview. Org) especially for core-shell, lamella and disk form factors.

Pu L3-edge X-ray Absorption Spectroscopy (XAS)

Experimental spectra were recorded in fluorescence mode using a Ge multi-element detector (ORTEC, Oak Ridge, Tennessee, USA) at the Pu L3-edge. The samples were oriented at 45° with respect to the incident beam. The incident energy was calibrated using a metallic Zr foil (K-edge defined at 17.988 keV). Pu ionization energy was defined at the maximum of the white line and corresponds to 18.068 keV. The spectrum corresponds to the average of 6 pre-processing scans obtained after 60 min of analysis each. EXAFS data were analyzed with Athena and Arthemis software from the IFEFFIT package. (Ravel & Newville, 2005) Data fitting was performed using a Keiser-Bessel window with a cluster size of 1-5 Å for the Fourier Transform (FT) in the 2 Å < k < 14 Å range (Feff version 8.4). Two parameters were fitted: atomic distances (R), and Debye-Waller factor (DWF). Coordination numbers are fixed to the crystal structure value.

Results

The SAXS data processing operations performed on the signal acquired on the plutonium cluster are summarised in the into DOTA polyamino carboxylate PuO2 clusters (corresponding to a volume fraction of 0.018). Note that a substraction artifact related to the Kapton® is still visible at 4 nm -1 . Small intensity variation are also observed at low Q vector. This can be attributed to a subtraction artifact due to the low scattering intensity of such dilute samples, or to a structure factor linked to cluster interaction or aggregation.

Further investigation at higher concentration are planned in order to investigate this diagram region.

Nevertheless, the normalised SAXS diagram of the plutonium clusters (Figure 2.c) in absolute unit can be fitted using simple fitting models. This diagram displays a Q 0 slope at low wave vector and tends to a Q -4 slope at higher wave vectors which behaviour is a typical signature of three dimensional and compact objects with a sharp interface. The scattering intensity is generally described as the product between an initial intensity I0 (when Q tends to 0), a form factor P(Q) relative to the shape of the solute, and a structure factor S(Q) related to the interaction between solutes.(O. Glatter and O. Kratky, Small angle x-ray scattering, Academic Press, London, New York, 1982) Atarthe first approximation, and considering a very dilute solution, S(Q) is considered equal to 1. Two approaches were employed in the 1 -6 nm -1 Q range to determine the size of the plutonium clusters: (i) Guinier analysis, and (ii) a monodisperse sphere form factor fitting (Fig. 2c). In these two models, the initial intensity 𝐼 𝑜 is defined as follows (Eq. ( 1)).

𝐼 𝑜 = 𝜑 𝑐 𝑉 𝑐 Δ𝜌 2 (Eq. 1)

with 𝜑 𝑐 , the volume fraction of the clusters, 𝑉 𝑐 , the volume of one cluster and Δ𝜌 2 , the scattering length density contrast with the solvent. Table 1 summarizes the scattering length density ρc and the contrast Δρ 2 used for the calculations. The Guinier analysis gives a first estimation of the cluster radius of gyration 𝑅 𝑔 . A radius of gyration of ca. 0.48 nm is found. Considering spherical and filled entities, the radius of the cluster can be deduced with the following equation (Eq. ( 2)) where R is the radius of the sphere. This leads to a sphere radius of 0.62 nm (cf. 1.22 nm diamter).

𝑅 𝑔 = 𝑅√(3 5 ⁄ ) (Eq. 2)
The best fits obtained with the monodisperse sphere form factor model is consistent with a sphere radius R of about 0.62 nm which is in full agreement with the results obtained with the Guinier analysis. The fitting parameters are summarised in Table 2.

Table 2: Simulated results of SAXS diagrams obtained with SasView software: I0 is the intensity for Q → 0, Rg the gyration radius, and R the radius of the sphere.

Sample information Model

Guinier Sphere Name I0 (cm -1 )

Rg (nm) R (nm) R (nm)
Pu cluster 0.006±0.003 0.48±0.05 0.62±0.05 0.62±0.06

Finally, both models conclude in the description of the cluster as quite spherical particules measuring 1.2 nm in diameter in nitric solution. The size probed with SAXS approach using a monodisperse sphere form factor may be compared to the one expected from the crystallographic data of the plutonium hexanuclear clusters (Tamain et al., 2016). The [Pu6(OH)4O4(H2O)8(HDOTA)4] complex is made of a [Pu6(OH)4O4] 12+ core decorated with four DOTA polyamino carboxylate ligands which forms an oblate spheroid with a 0.45 nm radius in the axial direction and 0.8 nm radius in the equatorial direction (Figure 4). Indeed the value obtained using a sphere form factor of 0.62 is intermadiate between the two values and appears to be a good geometrical approximation. A more accurate approximation of the overall cluster shape in solution would involve more sphisticated geometry and electron contrast models.

However, in this experiment, the experimental SAXS signal does not allow such a pecise desciption.

With a better normalization that suffer less from the sample holder scattering signal, this limit may be overcome with an optimized set-up in future works. The best fit spectra (red lines on Figure 4 and Table 3) were obtained using the crystal structure already published, (Tamain et al., 2016) and are in excellent agreement with the experimental data. In the fit procedure, distances, Debye-Waller Factors (DWF), the amplitude reduction factor (S0²) and the energy shift (E 0 ) were refined while the coordination numbers were fixed according to the crystal structure. In aggrement with the latter, the first actinide coordination shell is well repoduced by two distinct Pu-O subshell. The first one corresponds to two capping µ3-O 2-oxygens at a distance of 2.18 Å (±0.01 Å).

Conclusion

The characterization of the Pu(IV) hexanuclear cluster using synchrotron SAXS coupled with EXAFS undertakes an analytical challenge to describe actinide coordination mode and structure in dilute solutions. These species are of great interest for obvious environmental reasons and require a thorough characterization and speciation. Spectroscopic techniques as well as crystallographic characterization initially paved the way in this sense. In this experiment, we extend our knowledge on these compounds by combining synchrotron X-ray scattering and absorption techniques. The synthesis of the hexanuclear cluster was controlled by UV-visible-NIR spectroscopy and the EXAFS analyses were fully consistent with previous results. The SAXS identify 1.2 nm diameter spherical particles in good agreement agreeing with the shape of the [Pu6(OH)4O4(H2O)8(HDOTA)4] complex descrided previously by single crystal XRD.

The instrumental setup description fulfils the expectations of users for measuring highly radioactive samples in environmental dilute conditions even for weakly scattering clusters. Nevertheless, the instrument is being further developed. Thus, the MARS beamline is equipped with a Pilatus 3 2M (Dectris, Switzerland) hybrid photon-counting pixel detector having practically no detector readout noise, a high dynamic range and a short readout time. It is mounted on a new (Tx, Ts, Rx) motorized support to form camera lengths anywhere from 0.35 m to 3 m in 0.25m steps. On the SAXS camera nosecone, a second detector affording partial 2-dimensionnal access to Wide Angle X-ray Scattering (WAXS) information will be operated to complement full 2D SAXS in the appropriate configuration.

With careful beamline set up, these detectors allow overlap of the reduced 1D SAXS and WAXS data over the full camera length capability of the beamline. Thus, any reasonable size sample environment can be accommodated whilst minimizing air gaps and attendant background scatter. To capitalize on the energy tunability of the beamline, anomalous SAXS might be exploited to probe changes of the scattering properties of selected atoms to gain information on the distribution of the resonant atoms within the sample.

Figure 1 :

 1 Figure 1: UV-Vis spectrum of the SAXS-XAFS sample compared to the Pu(IV)-DOTA-hexamer identified by single crystal XRD.

Figure 2 :

 2 Figure 2 : MARS Beamline CX3 end-station configuration to perform combined SAXS-XAS analyses.

Figure 3 .

 3 Figure 3.c. after subtracting the solvent contribution while considering the total conversion of Pu(IV)

Figure 3 .

 3 Figure 3. SAXS data of the plutonium clusters solution at different processing steps: a) raw data of the sample (black) and empty cell (light blue) in arbitrary unit (a.u.); b) Normalized data in absolute unit after empty cell subtraction for the cluster sample (black) and the pure solvent (green); and c) cluster signal (black) after solvent contribution substraction and fit models: Sphere form factor (red line) and Guinier plot (dark blue line). The vertical dot line in each graph corresponds to the expected position of the Kapton® scattering peak.

Figure 4 :

 4 Figure 4 : Comparison of the SAXS Gunier and sphere form factor models to the [Pu6(OH)4O4(H2O)8(HDOTA)4] complex structure from single crystal XRD(Tamain et al., 2016). The complex structure, in the solid state, shows the anisotropic DOTA complexation on the octaerdal [Pu6(OH)4O4] 12+ core which results in an oblate spheroid.

Figure 4 .

 4 Figure 4. Fourier Transform of the k 3 weighted EXAFS spectra (black lines) and best fit results (red lines) of the plutonium solutions prepared by dissolution of Pu(IV) hexanuclear cluster crystals. k 3 weighted EXAFS oscillations and fits are presented in the insert and the imaginary part of the Fourier Transform are the black and red dashed lines.

Table 1 :

 1 X-ray scattering length density (ρc) and electron contrast (Δρ 2 ) used for SAXS diagram simulation calculations. Values for plutonium cluster takes into account both organic volume of the DOTA polyamino carboxylate ligands and the [Pu6(OH)4O4] 12+ core.

		ρc (10 10 cm -2 )	Δρ 2 (10 20 cm -4 )
	Pu cluster	13.5	Pu cluster/H2O	16.6
	H2O	9.43

  Considering the hexanuclear cluster geometry, the Pu-Pu signal splits into two shells. The edge sharing shell consist in four Pu-Pu scattering path with a 3.77 Å bond length. A longer bond coresponds to the opposite Pu atoms in the octahedron at 5.31 Å. Overall, all parameters are fully consistent with previous reports on this type of hexanuclear complexes and agrees well with the crystalographic structure.

	The second Pu-O subshell at 2.40 Å contains the other six Pu-O distances (µ3-OH -, water molecules and
	O from carboxylate functions). As this sub-shell contains different type of bonds and distances, the
	Debye Waller Factor (DWF) is large (0.008 Ų) in comparison to the short oxygen shell (0.004 Ų).

Table 3 :

 3 EXAFS refined metrical parameters obtained for the best fit of the soluble Pu-DOTA

	hexanuclear clusters.
	E0=-0.9(20) eV S0 2 =0.75(15)	An-µ3O 2-	An-(µ3OH -, Oc, H2O)	An-C	An-An1	An-An2
	CN*	2*	6*	2*	4*	1*
	σ 2 (Å 2 )	0.004(2)	0.008(2)	0.003(4)	0.006(2)	0.003(3)
	R (Å)	2.18(2)	2.40(2)	3.35(3)	3.77(2)	5.3(3)
	RXRD (Å)	2.20	2.36	3.34	3.76	5.31
	Errors in brackets only reflect the mathematical uncertainty provided by the proposed model.

* : fixed values

Acknowledgements

We gratefully acknowledge Hervé Hermange for his fruitful assistance in the mechanical design and integration of the active beamstop and fitting of the SAXS setup on the CX3 end-station of the MARS beamline. This work was supported by the CEA through the chemistry research program (RCHIM) from the cross-cutting basic research program (RTA).