dataesr/scientific-paragraphs-categorization huggingface dataset:
A. Datasets For target recognition, we utilize two datasets. The first one is MSTAR database  [15]  which include ten different categories of ground targets (armed personnel carrier: BMP-2, BRDM-2, BTR-60, and BTR-70; tank: T-62, T-72; rocket launch: 2S1; air defense unit: ZSU-234; truck: ZIL-131; bulldoze: D7) as shown in Fig. 2. They were collected using an X-band SAR sensor, in a 1-ft resolution spotlight mode with a full aspect coverage (in the range 0° to 360°). The second datasets, SynISAR  [16] , is composed of 7 classes of aircrafts as illustrated in Fig. 3 , which each class contains 181 images. We have reduced the initial size of the images which is 300×300 to 32×32, so that the center of the image obtained is the same as that of the initial image. We note also that for the ISAR database we have mapped the images in 70% (840 images) for the learning base and 30% (427 images) for the test base.
In the output layer, we have 7 classes which correspond to 7 neurons. For the minimization of the error and the optimization of the network, a learning rate of 0. 5 was chosen. After learning and updating the weights and biases, we obtain a recognition rate of 92. 97% for the ISAR database. For classification of SAR images (10 classes), we have configured the network with 102 neurons according to  [17]. Since there are 1024 neurons in the input layer and 10 neurons in the output layer. The overall recognition rate is 62. 24%. With the CNN architecture; we adopted the approach used for the networks of deep neurons, which requires a judicious choice of the number of epochs and the size of the block. These two parameters make it possible to define an optimal number of iterations to arrive at a minimum error rate.
The first architecture of deep neural network is the convolutional neural network, there are different models of this network, depending on the size of the data inputs, the configuration of the layers, the number of filters, the size of kernels and the sub-sampling steps. The architecture of this network is given in Fig. 4. At each convolution layer, a bias is added to the convolved images before passing through an activation function. In this architecture 1 of CNN (Fig. 4 ), we used a sigmoid function which presents the correction layer. The last 8 images obtained are sized 5×5 and concatenated into a vector, which is the input of the neural network. The input layer contains 200 neurons and the output layer contains neurons as the number of classes (7 neurons for ISAR Dataset and 10 neurons for MSTAR Dataset) with a sigmoid function as activation function.
Note that the neural network in this architecture has no hidden layer. Using this CNN, we obtained 96. 48% with ISAR images and 72. 82% with SAR images. The obtained results on SAR and ISAR datasets are given in Table  I. The CNN use relatively little pre-processing, unlike the other classical algorithms such as KNN and MLP. The absence of initial parameterization and human intervention for the extraction of the characteristics is a major asset of the CNN, in addition to these advantages; the recognition rate is better by applying the CNN. To evaluate the performance of CNN architecture, the convolution layers and the hidden layer on the classification step (see Fig. 1 ) are studied. The influence of these layers are presented and discussed in the section below.
The input vector of the perceptron has 1568 neurons with an output layer of 7 neurons. With this configuration, we obtained a recognition rate of 92. 27% with an estimated learning time of 21 seconds for ISAR dataset. We also used this architecture for the MSTAR database; the perceptron in this case contains 1586 neurons in the input layer and 10 neurons for the output layer (10 classes). We found 62. 27% as the recognition rate, with a learning time of 55 seconds. The obtained recognition results on MSTAR dataset show that this fist architecture fails to recognize the 3 classes (recognition rates are 0% for ZSUS234, BTR70 and T72). In the next architecture, we added a hidden layer to the perceptron. • 2 nd architecture In this configuration a hidden layer was added according to rule  [17].
For the ISAR dataset, the input layer is composed of 1568 neurons and the output layer consists of 7 neurons so we inserted a hidden layer of 105 neurons. We obtained a recognition rate of 95. 31% with a learning time of 27 seconds for all ISAR images of learning dataset. For the MSTAR database, the perceptron is configured with a hidden layer of 125 neurons, we obtained a recognition rate of 70. 74%. The learning time for this learning database is 85 seconds. We can see from these two configurations that by adding a hidden layer the recognition rate increases. It should also be noted that the learning time becomes more important by increasing the number of hidden layers. With this configuration, the adding of a hidden layer improves the system performances. We observe that this CNN can recognize two classes (ZSUS234, BTR70) but the third remains always unknown (T72).
• 3 rd architecture Using this architecture, we can assess the impact of convolution and sub-sampling, by adding the second convolution layer. The 8 images of the last sub-sampling step are of size 5×5. After the concatenation of these images, the feature vector is of size 200. For the connected layers, the input layer is 200 neurons, the output layer is 7 neurons (ISAR data base) and the hidden layer according to  [17]  is of 38 neurons. For the MSTAR datasets which have 10 classes, so we configured the hidden layer with 45 neurons. We obtain a recognition rate of 97. 19% with a learning time of 37 seconds for the ISAR images and recognition rate of 75. 98% with 105 Input 32×32   seconds on learning SAR images dataset. We have found that adding a convolution layer the recognition rate as well as the learning time increases.
In this proposed architecture, all classes are recognized with enhancing of the classification rate but make the learning time more long. The table II summarizes the results obtained by the different CNNs on the two databases. We noticed that adding a hidden layer to the PMC or adding a convolution layer results improve the recognition rate. On the other hand it serves to increase the learning time. For the improvement of the recognition architecture by reducing the learning time, we opted for the last configuration which gives us a good classification. We then use a convolutional auto-encoder for the generation of filters.
D. CNN using CAE As previously described, Convolutional Auto-Encoder (CAE) addresses the task of defining filters in a different perspective. Instead of using CNN convolutional random filters, we used the CAE to learn the optimal kernels that minimize the reconstruction error, after we use these filters for the two layers of our CNN. Since we have 2 layers of convolutions, we first start by implementing a 2-layer CAE, each layer gives us the 8 filters intended to be used in the CNN. For the ISAR database, we obtained 96. 72% with a learning time of 40 seconds. Howevern for MSTAR database we obtained a rate accuracy of 82. 15% with 110 seconds. For learning step including CAE times learning. Note that the accuracies are roughly equal to that found without CAE with increased learning time. In order to reduce the learning time without loss system's performances, we introduce an AE in order to obtain the optimal weights that will be used for the hidden layer of the perceptron.
• 4 th architecture Using the weights given by the auto-encoder, we obtain 97. 65% as a classification rate for a learning time of 47 seconds with the ISAR database, and a rate of 83. 27% with a learning time is 117 seconds for the MSTAR database. Note here that the recognition rate is improved while the learning time has increased. In order to reduce learning time, we sought to reduce the number of filters generated by the CAE. The first simulations are carried out with 8 filters in the first convolution layer and 8 filters in the second  (8, 8) , we have reduced the number to (2, 2) to bring out the influence of this step on the classification rate and learning time. With two filters in the two convolutions layers, a recognition rate of 98. 12% with a learning time of 25 seconds, is obtained, which implies an improvement in the results in terms of rate and calculation time.
We found the same improvement for the MSTAR database, a classification rate of 90. 09% is achieved with a learning time of 78 seconds. The obtained results using CAE and AE are presented un Table  3. In this work, we studied and applied different classification methods: K-NN, RN, and CNN, which are evaluated in terms of recognition rates and learning time. We evaluated also the influence of the addition of the layers of convolutions and the hidden layers on the performances of the network. The results presented in the last section shows the effectiveness of deep learning methods for the classification of radar images. By varying the number of filters with the use of various deep learning techniques (CAE and CNN), we achieved a better classification rate with optimal number of filters and one hidden layer.
48(  8 ) cm 3 Kmol À1 )t han in solid state (1. 77(8) cm 3 Kmol À1 ;s ee details in the Supporting Informa tion). Ac susceptibility measurements were also performed to probe the magnetization dynamics of these complexes and in particular the possible single molecule magnet (SMM) prop erties. [20] Frequency and temperature dependent ac signals were revealed under as mall applied dc field (600 Oe; Supporting Information, Figures S9 S12) only for 2. T o probe the effect of the applied dc field on the slow relaxation of magnetization, the characteristic time, t,w as extracted by fitting both variable field and temperature ac susceptibility data with the generalized Debye model. Thebest fit of t(T,H) was obtained considering only Direct and Raman relaxation mechanisms (Supporting Information, Figure  S13 ), which are thus at the origin of the SMM properties of 2.
Acknowledgements This work was supported by the  ANR  ( ANR 16 CE29 0001 01 ,  Active Magnet  project), the  University of Bordeaux , the  RØgion Nouvelle Aquitaine ,the  CNRS ,the  MOLSPIN COST action CA15128  and the  CSC  for the PhD funding of X. M. E. A. S. t hanks EPSRC for support ( EP/N006895/1 ), the  IRIDIS High Performance Computing Facility  and associated services at the  University of Southampton  and the  RSC  for atravel grant. Theauthors thank also  D. Woodruff , J. L. Liu ,  A. Mondal , and  S. Exiga  for their assistance and fruitful discussions as well as the GdR MCM 2:M agnØtisme et Commutation MolØculaires.
Section 4 illustrates the results of our algorithm under three categories of atmospheric conditions (encountered in the three different datasets) and discusses the calibration coefficients used for each dataset in relation to the coefficient values found in the literature. Finally, in Sect. 5, we apply our method to the retrieving of high-resolution humidity profiles between two consecutive radiosonde observations and discuss the possibility of using it as an operational product. For one specific dataset we took advantage of the measurements of a ground-based Raman lidar located close to the WPR to validate the high-frequency (15 min) humidity profiles retrieved by our algorithm. 1 We consider as rainfall the droplets whose size is large enough to be detected by WPRs (typically larger than 100 µm  ; Ralph, 1995).
, 1998; Stankov et al. , 2003)  assume that the partial derivatives in Eqs. (  4 ) and (  5 ) are constant and can be estimated from standard atmosphere profiles. This assumption also imposes the neglect of the contribution by the second term. In this paper we do not make this assumption, especially because one of our datasets is characterized by relatively moist conditions near the surface, which forces us to consider all three terms in Eq. (  6 ). As also demonstrated by  Tsuda et al. (2001) , the differential Eq. (  6 ) can be solved after introducing the Brunt-Väisälä frequency N BV (s -1 ) given by (N BV ) 2 = g θ dθ dz = g d ln θ dz , (7) where θ = 1000 P 2/7 and g are the air potential temperature (K) and the acceleration of gravity (9. 8 m s -2 ), respectively. This leads to M = 5.
is related to the estimation of the second-order moment, i. e. , the broadening of the radar spectra. F. Saïd et al. :  Humidity profiles from wind profiler radar measurements Let us now discuss the coefficient α 2. Assuming the radar to be calibrated, so that K is known and the structure coefficient C 2 n is an absolute value,  Gossard et al. (1998)  took a constant value for α 2 of 0. 44 regardless of the M 2 profile and the considered level in the profile. This value is obtained by comparing refractive index profiles obtained from balloon measurements to those estimated by a 440 MHz UHF radar, after an accurate post-processing of the first-and secondorder moments of the spectral data and an accurate radar calibration (that provided K). In fact, they measured an average value for L w L φ of 4, which, after  Gossard et al.
Luckily the BLLAST measurements, in contrast to the HyMeX observations, were systematically carried out in clear air, which mitigated the uncertainties in the MODEM measurements. WPRs in the framework of BLLAST and HyMeX were deployed by the Centre de Recherches Atmosphériques (Laboratoire d'Aérologie) and the Centre National de Recherches Météorologiques (Météo-France), respectively. Both profilers are five-beam model PCL 1300 manufactured by Degreane. A detailed description of the WPRs, their main working parameters and the processing methods are provided in  Saïd et al. (2016). Both radars were operated almost continuously at both sites over long periods (exceeding 18 months). For the purpose of this work, we will concentrate on the data collected from 19 June to 6 July 2011 during BLLAST, from 13 September to 5 November 2012 during HyMeX SOP1 and from 1 February to 15 March 2013 during HyMeX SOP2.
Two operational modes were considered. The first mode (low mode), associated with a pulse length of 0. 5/1 µs, sampled the lower troposphere from 75/150 m a. g. l. to 5/5. 7 km a. g. l. (for BLLAST/HyMeX, respectively). The second mode (high mode) was specified for higher altitude sampling, from 150 m to 8 km a. g. l. , and a pulse length of 2. 5 µs was considered for both experiments. The vertical resolution was 75/150 m (for BLLAST/HyMeX, respectively) in low mode and 375 m in high mode. The high mode was oversampled and provided data every 150 m. The inter-pulse period (IPP) was 40/45 µs (for BLLAST/HyMeX, respectively) in low F. Saïd et al. :  Humidity profiles from wind profiler radar measurements mode and 80 µs in high mode for both experiments. The radar beam was steered into five directions: one vertical and four oblique directions at zenith angle of azimuths spaced 17 and 90 •.
The drop fall speed in still air can be related to the droplets' diameter taking into account the change of density with height  (Atlas et al. , 1973; Foote and Du Toit, 1969). The parameters of the gamma distribution can be obtained using the mean vertical velocity and the radar reflectivity factor  (Chu and Su, 2008). Finally, the rain rate is derived by integrating the droplets' distribution over the diameter interval supposed to extend from zero to infinity. During each of the rainfall events selected for the calibration, the radar constant was modified until the best agreement was found between rain gauge and radar measurements. An average of the results was retained as the final calibration constant. As stated before, the WPRs used in the framework of BLLAST and HyMeX had provided longer datasets than the datasets we refer to for the present work.
Data conditioning for the humidity gradient retrieval During BLLAST, the balloon took around 4 min to cross the ABL, whose top level was typically situated at level 2000 m above sea level (a. s. l. ; 1400 m a. g. l. ). Within the ABL, the wind remained weak (around 4 m s -1 ), which corresponded to the preferred conditions for the experiment (clear air, anticyclonic conditions). A nocturnal low level jet sometimes occurred at night, but it was seldom stronger than 6 m s -1. During the first 4 min, the balloon drifted horizontally by 1 km from the release site, located nearby the radar site (150 m). The balloon reached the typical maximum height of the BLLAST radar soundings (4 km) in 17 min (from the release), which corresponds approximately to three full cycles of the profiler. Therefore, for the humidity gradient comparison we used 15 min of radar data, during which the balloon drifted horizontally between 5 and 15 km from the radar site, according to the wind conditions in the free troposphere.
Similarly, some unexpected large values of q were put to the humidity saturated value provided by the RS. This occurred during HyMeX SOP1 when moist conditions were frequently encountered. This limitation enabled us to minimize the error accumulation in case of divergence of the integration. We will provide illustrations of such situations in the following. Another improvement consisted in testing different values of the Hlim level in case of the presence of relative maxima in radar reflectivity profiles. An example is provided in Fig. 2. The C 2 n profile in Fig. 2a  shows three peaks. The dominant peak at 902 m corresponds to the lower level of a cloud, since q observed with the RS is saturated (the red solid and dashed lines are superimposed in Fig. 2b ). The double integration of the radar data upward and downward to this level leads to the radar profile of q illustrated in Fig.
Comparison between the RS and radar retrieved humidity profiles We gathered in Fig. 4  the results of the comparison between the radar estimation of the humidity profile and the observed RS humidity profiles for the three data sets in low mode. Panels (a), (c), (e) and (g) show the scatter plots of radar vs. radiosonde data, and panels (b), (d), (f) and (h) show the vertical profile of the deviations between radiosonde and radar data, all of them obtained from low mode data. The red line in the scatter plots represents the linear regression line drawn from the data, which can be compared to the slope 1 : 1, i. e. , the black line. HyMeX SOP1 data, the most numerous in terms of number of profiles, were split into two graphs. The vertical resolution of the BLLAST WPR measurements is 3 times higher than the one characterizing HyMeX measurements, which explains the larger sample size in Fig.
4a. Results are also summarized in Table  1 , where the high mode has been added. The best results are clearly those obtained during HyMeX SOP2, since the correlation coefficient is exceeding 0. 93, the mean bias is 0. 04 g kg -1 or smaller and the mean standard deviation is 0. 18 g kg -1 or smaller. These successful retrievals are linked to the peculiar conditions of the HyMeX SOP2 experiment (limited variability of the humidity content). So we cannot rely upon this example to assess the effectiveness of our method. In most other cases, with the exception of the BLLAST data in high mode, the correlation coefficient exceeds 0. 8, the slope of the regression lines is close to unity, the mean bias is equal or smaller than 0. 24 g kg -1 and the standard deviation is not exceeding 1 g kg -1 (Table  1 ).
We identified the reason why the BLLAST dataset gave poorer results in high mode than in low mode. In high mode these are 0. 73, 0. 36 g kg -1 and 1. 19 g kg -1 for the correlation coefficient, mean bias and standard deviation, respectively (Table  1 ). These relatively lower-quality results are due to the presence of thin layers of dry air (-300 m vertical depth) that the radar fails to reproduce in high mode since its vertical resolution (375 m) is not high enough. The other results in Table  1  do not exhibit an outperformance at any of the two modes. Concerning the variability of the error and its standard deviation along the vertical, we cannot draw any general conclusion even if the HyMeX results seem to be better (smaller bias, smaller standard deviation) above 2500 m (Fig. 4d  and f ).
Variability of the calibration coefficients With the aim of comparing our estimates of the calibration coefficient α 2 in Eq. (  16 ) with values found in literature and studying its variability relative to the stability conditions, we first considered the coefficients within each dataset, which enabled us to avoid possible issues about the radar calibration. According to Eqs. (  14 ) and (  16 ) and considering the same WPR, the variability in α 2 should reflect the variability of the ratio of the two outer scales L w L φ. Gossard et al. (1998)  expected this quantity to be dependent on the stability conditions, at least inside the ABL, where the turbulence is homogeneous. Small ratios should occur under stable conditions, which would correspond to large α 2 values, and the opposite behavior under unstable conditions.
To check this hypothesis, we used the radiosonde data to get an estimation of the stability conditions based on the gradient Richardson number: R i = g θ v dθ v dz dV dz 2 , (19) where θ v is the virtual potential temperature. We chose the BLLAST dataset, since summer conditions provide the largest range of stability conditions. Figure  5a  shows the calibration coefficients obtained from the BLLAST dataset in low mode as a function of the stratification with a differentiation of the lower part and upper part of the profiles, located below and above Hlim, respectively. The color scale indicates the hour of the day. During the (dry) convective period of the day, the lowest portion of the profiles is expected to correspond to a mixed ABL, with Richardson numbers potentially negative in the surface layer and close to zero above.
First, the average of the transition levels (Hlim) is 1193 m a. g. l. in high mode versus 928 m a. g. l. in low mode, and the distribution is clearly shifted towards higher Hlim values in high mode, which means that the transition level is certainly higher than the boundary layer top in most cases. Second, we obtained rather large values of the coefficients (6 values larger than 10) for the lower part of the profiles, which we attribute to the poorer vertical resolution in high mode in an area of sharp variations of the humidity. The same analysis was applied to the HyMeX datasets from which no clear result arose, during either SOP1 or SOP2 (not shown). During HyMeX, the development of the boundary layer was most of the time generated by mechanical turbulence (due to the wind intensity or to the roughness change at the sea-land transition).
04 on average) and BLLAST (0. 13 on average). We recall that both radars were calibrated. We assume that we can rely on this calibration since (i) values of C 2 n determined for BLLAST in high mode are similar to those obtained in low mode and (ii) the two calibrations, based on the rain gauge measurements, are independent. During HyMeX SOP1, atmospheric thermodynamic conditions were close to saturation most of the time (as shown for example in Fig. 2c ). Although we discarded the rainy radar profiles when the rainfall affected the whole air column, it is likely that isolated pockets of rainfall may have locally increased the radar C 2 n , which implies a decrease in α 2. We checked the distributions of C 2 n for the three datasets and found that the logarithmic averages of C 2 n (close to the median values) are 1.