dataesr/scientific-paragraphs-categorization huggingface dataset:
In Figs. 3  and 4  we give examples of such motion trajectories. Figure  3  shows a monomer of the SARS-CoV-2 spike glycoprotein (closed state) (PDB code: 6vxx  9  ). We can see that there is a good range of motion from the crystal structure when following the normal mode modes into either positive or negative changes along the mode vector. Figure  4  shows the motion for the dimer structure of the SARS-CoV-2 main protease (PDB code: 6lu7, in complex with inhibitor N3. We have removed the inhibitor in the motion analysis here)  16. Again, one can see considerable motion, although due to the complexity of the structure, it is difficult to distinguish individual movement patterns from such a frozen image. Much better insight can be gained when watching for full range of motion as a movie. Direct access to the movie for the spike ecto domain monomer (6vxx) is provided via Ref.
36  , while the motion of the main protease dimer can be viewed at Ref. 37. We have made a dedicated web download page  38  where movies for the complete set of PDB codes as given in Table  S1  are publicly available. The movies are being offered for various modes m 7 to m 12 as well as E cut values, at least containing results for E cut = -1 kcal/mol , -2 kcal/mol and -3 kcal/mol , respectively. In addition, the site includes the rigidity resolutions discussed above and all intermediate structures needed to make the movies. This allows for the calculation of relative distances and other such structural measures along each motion trajectory as desired. For a detailed analysis of the SARS-CoV-2 main protease with similar methods, we refer the reader to Ref. 39.
SARS-CoV-2 spike ecto domain structures. The trans-membrane spike glycoprotein mediates entry into host cells  8, 9. As such, it is a "main target for neutralizing antibodies upon infection and the focus of therapeutic and vaccine design"  9. It forms homotrimers protruding from the viral surface  3. Up to the end of May 2020, 3 structures of the trans-membrane spike glycoprotein have been deposited in the PDB. These transmission electron cryomicroscopy (cryo-EM) studies have led to structures with PDB codes 6vsb 8 , 6vxx 9 and 6vyb 9 now being available. With RMS resolution of 3. 5 Å, 6vsb has a slightly lower resolution than 6vxx at 2. 8 Å and 6byv at 3. 2 Å. In the following, we shall discuss the resulting rigidity and flexibility properties of these three structures in their full trimer form.
Prefusion SARS-CoV-2 spike glycoprotein with a single receptor-binding domain open. The rigidity pattern of the homotrimer for this structure (PDB: 6vsb, 440. 69 kDa , 22854 atoms, 2905 residues) is dominated by a large rigid cluster encompassing most of the trimer structure except for a region from roughly residue 330 to residue 525 (With nearly 3000 residues in the structure of the trimer, is it impossible to capture the behaviour in a single figure that at the same time would allow the reader to see enough detail. The reader is referred to Ref. 38  for access to the electronic images. ). This corresponds to the S B domain of S1 in each monomer. In the trimer configuration, it is known that one of the S B domains can change from the closed to an open configuration  8. At |E cut | = 0. 016 kcal/mol , the 6vsb structure of the trimer breaks into many different rigid parts, but the original large cluster remains a dominating feature across the rigidity dilution plot.
Other SARS-CoV-2 structures of interest. Similar results have been obtained  38  for the other about 300 Covid-19 structures thus far deposited in the PDB. For example, from those structures deposited from late May to August 2020, the nsp7-nsp8c complex (PDB code: 6m5i)  44  is potentially interesting as this complex is part of the RNA transcription and replication machinery. The motion of the hetero dimer shows an intriguing movement restricted to just one of the total seven α helices. The motion of ORF3a (PDB code: 6xdc)  45  , a putative ion channel, might be important in understanding the inflammatory response resulting from Covid-19 infection, i. e. as deletion has been shown to reduce viral titer. We find considerable flexibility in the homo dimer structure between the α-helix-rich and the β-sheet regions.
These intermediate conformations can also be used as convenient starting points for further MD-based dynamics studies to evaluate thermodynamic properties of the structures. This shows the power of FIRST and FRODA to complement structure determinations and MD simulations to make valid predictions about the dynamics of proteins. Similarly detailed structural analyses and further MD work is also possible for the other structures included in this work. The classification of the protein structures into four types of dynamics provides information about the level of flexibility of a protein which is relevant to drug discovery. For more detailed information rigidity dilution plots and motion movies are available for download at Ref. 38. In addition, the code underlying our study is accessible at Ref.
Rigidity analysis. In each case we start the rigidity, flexibility and mobility modelling with a given protein crystal structure file in PDB. pdb format. Hydrogen atoms absent from the PDB crystal structures are added using the software Reduce  50. Alternate conformations that might be present in the protein structure file are removed if needed and the hydrogen atoms are renumbered in PyMol  51. We find that for some protein structures the addition of hydrogen atoms is not possible without steric clashes. Consequently, identification of a viable structure and its continued analysis is not possible. These proteins are labelled in Table  S1. We observe five structures which exhibit such steric clashes. For the remaining proteins we produce the "rigidity dilution" or rigid cluster decomposition (RCD) plot using First  20.
The plots show the dependence of the protein rigidity on an energy cutoff parameter, E cut < 0. It parametrizes a bonding range cutoff based on a Mayo potential  52, 53  such that larger (negative) values of E cut correspond to more open bonds, i. e. a smaller set of hydrogen bonds to be included in the rigidity analysis. Elastic network modes. We obtain the normal modes of motion using elastic network modelling (ENM)  54  implemented in the ElNemo software  23, 24. This generates a set of elastic eigenmodes and associated eigenfrequencies for each protein. The low-frequency modes are expected to have the largest motion amplitudes and thus be most significant for large conformational changes. The six lowest-frequency modes (modes 1-6) are just trivial combinations of rigid-body translations and rotations of the entire protein.
Acknowledgements This work received funding by the  CY Initiative of Excellence  (grant " Investissements d' Avenir "  ANR-16-IDEX-0008 ) and developed during R. A. R. 's stay at the  CY Advanced Studies , whose support is gratefully acknowledged. We thank  Warwick's Scientific Computing Research Technology Platform  for computing time and support. Special thanks to overleaf. comfor free premium access during the March-June Covid-19 lockdown. UK research data statement: Data accompanying this publication are available for download 38.
Similarly,  Vukovic et al. (2013)  found that math anxiety was related to arithmetic performance for grade 2 students, and to a composite measure of more complex skills (including algebra, word problems, data analysis, and probability), but not to geometry scores. Thus, our research (see also  Ching, 2017; Vukovic et al. , 2013)  is consistent with the finding that arithmetic is most often related to math anxiety among elementary school children. Timed arithmetic is a demanding task for children in early elementary school. In general, these results support the view that relatively complex math skills (i. e. , relative to the participants' age and experience;  Douglas & LeFevre, 2018; Zhang et al. , 2019)  are most strongly correlated with math anxiety. Further research that includes a range of measures of math performance that vary in difficulty is needed with this age group.
Math anxiety increased significantly from grade 2 to grade 3, although the size of the increase was small. Arithmetic fluency also increased significantly from grade 2 to grade 3, which is consistent with the finding by  Krinzinger et al. (2009)  that children's calculation ability generally improves during school. In sum, although children's arithmetic skill and math anxiety increased as they advanced from grade 2 to grade 3, the concurrent relations did not get stronger in the present study. More generally, math anxiety for young students may be linked to their recent experiences as well as to specific measures of performance. More detailed data will be important for understanding how math anxiety changes over time.
We characterize the LoRa channel in terms of multi-path fading, loss burstiness, and assess the benefits of Forward Error Correction as well as the influence of frame length. We make these observations by synthesizing extensive experimental measurements realized with The Things Network in a medium size city. We then propose to optimize the LoRaWAN Adaptive Data Rate algorithm based on this refined LoRa channel characterization and taking into account the LoRaWAN inherent macro-diversity from multi-gateway reception. Firstly, we propose ADR opt , which adjusts Spreading Factor and frame repetition number to maintain the communication below a target Packet Error Rate ceiling with optimized Time-On-Air. Secondly, we propose ADR IFECC , an extension of ADR opt in case an Inter-Frame Erasure Correction Code is available.
In this work, we start with the analysis of experimental measurements over a public LoRaWAN network with multiple reception gateways. From the insight gained into the channel characteristics, we derive methods to use the network with optimized performances in terms of reliability and Time-On-Air. This paper is organized as follows: Section 2 presents LoRa, LoRaWAN, the metrics to measure performance and then the experimental traces database construction. Section 3 presents the experimental channel characterization. Section 4 presents the transmission parameters selection for network-wide optimization. Section 5 discusses the related work. Section 6 concludes the article.
Setup and Experiments We have gathered an experimental dataset by recording LoRaWAN transmissions collected by several gateways in an urban area. We then replay the recorded frame series to assess the effect of adjusting various MAC parameters. The test-bench consists of one ED (B-L072Z-LRWAN1 LoRa ® /Sigfox™ Discovery kit. ), placed indoors on the third floor of a residential building, sending traffic to the The Thing Network (TTN) community network through a set of gateways. The device transmits series of LoRaWAN frames and varies the transmission parameters from one frame to the next. We randomize the transmission parameters in order to avoid shadow correlations and moderate the effect of possibly congested frequency channels. We present here the results from two measurements sessions. In both cases, we used three channels centered on 868.
1, 868. 3 and 868. 5 MHz, with bandwidth BW = 125 kHz. In the first session, we considered 48 combinations of (P Tx , SF) value pairs. We set the LoRaWAN coding rate to the default CR = 4 5 for intra-packet FEC. The payload was 15 Bytes resulting in LoRa frames with a Number of Symbols (NS) from 38 to 53. The experiment ran for a whole week and there were on average 4300 frames transmission attempts per series, that is, one frame every ≈2. 4 min. In the second experiment we extended the possible configurations to many more (P Tx , SF, CR) combinations with a payload such that 48 ≤ NS ≤ 50. We also extended the possible configurations for SF = 7 with CR ∈ { 4 5 ; 4 6 ; 4 7 ; 4  8 } and with 10 different frame sizes: 48 ≤ NS ≤ 298. Notice that because each SF does not encode the same amount of bits and because the FEC add redundant Bytes to the payload in a non continuous manner, some value of NS might not be feasible with some transmissions parameters combination.
Frame with up to 2 less symbols are then used. 336 transmission parameters configurations are thus tested. The experiment ran for twelves days and the dataset includes on average 940 frames transmissions attempts per series, that is, one frame every ≈ 20 min. Table  1  summarizes the choice of experimental configurations. Twelve and thirteen TTN GWs showed up within the transmission range of the device during respectively the first and the second experiment. Among them, 8 were up for both experiments. Fifteen are GWs deployed in the Grenoble urban area within 5 km of the ED. Two GWs are outside the city at 6 km and 14 km from the ED with respectively 1000 m and 2000 m higher elevation from the city. We could not retrieve the position of one of the GWs. Figure  4  shows the position of the GWs in red and their distance from the ED (in yellow).
We reject from the study the series with FER > 0. 99. In these cases, the transmission is not robust enough and only residual frames are received. The valid data represents a total of 2319 independents LoRaWAN series of frames. This set of measures captures the frame erasure patterns over a typical LoRaWAN urban network, and it is publicly available (https://gricad-gitlab. univ-grenoble-alpes. fr/ coutaudu/lora-measurements, accessed on 29 March 2021).
The solutions based on acknowledgement frames, such as Automatic Repeat reQuest (ARQ), are strongly limited by the asymmetry of LoRaWAN networks where downlink transmission opportunities are scarce  [6]. Channel coding solutions based on Inter-Frames Erasure Correction Code (IFECC) recover the losses by introducing redundancy with time diversity in the communication and can provide high reliability in LoRaWAN  [14, 15]. The systematic repetition implemented by the LoRaWAN MAC layer parameter NB Trans , is the simplest kind of IFECC. The redundancy is a duplicate of the original frame, transmitted successively, thus it is weak against burst losses. Even though, as stated in Section 3. 4, the channel erasures are close to iid, the probability to loose multiple frames in a row mechanically increases with the FER.
00 0. 25 In the following, we use an IFECC scheme based on a linear combination of packets, LoRaFFEC  [16] , which is efficient to recover the typical residual errors from a Rayleigh channel up to FER ≈ 0. 3. LoRaFFEC spreads the redundancy over many frames and so, introduces more time diversity. In practice, LoRaFFEC is computed and spread over 128 frames. Notably, the redundancy spreading is higher than the default ADR downlink transmission period, limited to ACK_LIMIT + ACK_DELAY = 96 frames. Moreover, LoRaFFEC does not require additional downlink signaling. The redundant data overhead of LoRaFFEC, can either be transmitted in separate frames or piggybacked into existing ones. Here, we choose to piggyback, as the LoRa and LoRaWAN headers overhead are then paid only once, which improves the ToA/b.
Adaptive Data Rate Various studies evaluate and improve the ADR's performances. But because the algorithm is not strictly defined by the LoRaWAN specification, various implementations exist and variations of their interpretation appear in the literature. Some studies  [17, 18]  suggest that the ADR TTN tends to overestimate the link quality because of the MAX operator used for the SNR estimation. As a consequence, they suggest to replace it by a MEAN operator. But because the packets with lowest SNR are likely to be more censored, the current path loss' estimation can be biased by both MEAN and MAX. Moreover, the SNR variance has a major influence on the ADR's operation  [18]. We think that the SNR distribution pattern and parameters estimation as described in Section 4 are key for optimized ADR decisions.
The ADR can be slow to converge, especially decreasing to more robust and lower Data Rate, because it relies on EDs to drift toward more robust configuration until a downlink is received  [19, 20]. For the same reason, the ADR does not converge to the same final configuration depending on its starting configuration. Our solution is no longer based solely on this drift to switch to a more robust configuration. In a previous work  [12] , we improved the ADR protocol by relying on the characterization of the channel as a Rayleigh channel and the use of an application layer FEC algorithm. This solution is only tailored for a single cell LoRaWAN network, which is a major weakness for dense deployments composed of few to many gateways. Our new solution is based on a more accurate estimation of the effective channel and dynamically adapts to the number of GWs in range and fully exploits the macro diversity, making it more suitable for real world deployment.
Conclusions In this paper, we establish a channel model which reflects the observations we make after generating and analyzing traffic collected on a real-word LoRaWAN deployment. The channel model includes the distribution of the received power around its average, the erasure patterns, and the influence on the demodulation floor of the frame length, as well as of LoRa Forward Error Correction. We then use this model to derive the expected PER for any transmission parameter settings in presence of an arbitrary amount of GWs. This PER prediction is the basis of ADR opt , an Adaptive Data Rate mechanism, which can be configured to match an arbitrary reliability goal in terms of Packet Error Rate. ADR opt inherently takes into account macro-diversity and the observed channel variability due to temporal fading.
We also build ADR IFECC which efficiently provides high reliability, with Data Error Rate < 0. 01 in LoRaWAN networks, even for challenging transmission conditions. It is a significant improvement over the LoRaWAN ADR implemented by The Things Network. ADR IFECC tackles the inevitable erasures of LoRa communications by using an Inter-Frame Erasure Correction Code. ADR IFECC does not necessitate any additional downlink transmissions compared to legacy LoRaWAN ADR. Both ADR opt and ADR IFECC Time on Air are bounded by the maximal effort configuration. They are designed with scalability in mind and are realistic options for current and future deployments. The ADR opt and ADR IFECC propositions are validated both by simulation and by replaying actual transmission traces.
Data extraction Tadpole movements were analyzed by tracking individual movement patterns with a custom-made 'Tadpole Video Analysis' application (available upon request from J. O. ). The program is coded in Python 2. 7 (https://www. python. org/; accessed 7 March 2021) and uses the external libraries NumPy (van der  Walt et al. , 2011) , OpenCV  (Bradski and Kaehler, 2000)  and wxPython (https://www. wxpython. org/). The tracking of tadpole movements was started immediately after the addition of the stimuli, as soon as the water surface was calm (<1 s). After the locations of tadpoles across all frames had been determined (for more details, see Supplementary Materials and Methods), the program calculated the distance to the respective center of the bowls (i. e. the location of the dragonfly larvae, heterospecifics or conspecifics) and distance traveled from the previous frame by using the known size of the bowl (100 mm radius).
We used the cumulative sum moved towards/away from the center as the response variable in a linear mixed effects model (LME, R package lmerTEST;  Kuznetsova et al. , 2017)  with type of stimulus used (stimulus group: water control, chemical, visual, chemical+visual), time of day a tadpole was tested (noon and afternoonbefore or after 14:00 h) and the interaction of stimulus group with frame as the fixed effects to account for swimming behavior across time. We made sure to order the factor levels of stimulus group to include the water control in the intercept (first level) to allow a comparison of behavior in the groups (chemical, visual and chemical+visual) with the water control. The data from all control individuals regardless of treatment (femoralis, tinctorius and dragonfly) were used for comparison in all analyses.
We included a random intercept (tadpole ID) and random slope (frame) to account for repeated measures across frames. Frame was scaled and centered for better model performance. We visually inspected Q-Q plots to ensure that model residuals conformed to the assumption of normality and transformed response variables if this assumption was not met (see provided R script for details: doi:10. 17605/OSF. IO/ ESRYN). To be able to apply data transformation, we shifted the whole dataset upwards by adding the absolute maximum value to all values. By doing so, we were able to remove negative values but kept the relative movement behavior of the tadpoles towards/away from the center. We ran one model for each treatment group (femoralis, tinctorius and dragonfly). To ensure that our results were robust and not an artefact of the time frame chosen for analysis, we ran these models across 1500 (1 min), 3000 (2 min) and 4500 frames (3 min).
Frame was scaled and centered for better model performance. We visually inspected Q-Q plots to ensure that model residuals conformed to the assumption of normality and transformed response variables if this assumption was not met (see provided R script for details: doi:10. 17605/OSF. IO/ESRYN). We ran one model for each treatment group (femoralis, tinctorius and dragonfly). To ensure that our results were robust and not an artefact of the time frame chosen for analysis, we ran these models across 1500 (1 min), 3000 (2 min) and 4500 frames (3 min). Again, we compared the cumulative distance traveled at frame 1500 (1 min), 3000 (2 min) and 4500 (3 min) across stimulus groups (water control, chemical, visual, chemical+visual) using a Kruskal-Wallis test to see whether the tadpoles' behavior persisted across frames.
These measurements, combined with the micromechanical characterisation of single bridges (see Section 2), are then used as inputs for a minimal model of cohesive granular materials. [15]  This model is thus constrained in all its parameters by observations at the microscopic scale. In Section 4, we will then simulate unconfined uniaxial testing of the modelled material, and find that the results compare favourably to in situ experimental compression tests. A. X-ray microtomography: Bead and bridge geometry X-ray microtomography data obtained in a previous study  [19]  were further analysed in the present work (sample A, see Fig. 1(c )), and complemented by data from a similar sample which featured softer bonds (sample B). Briefly, unconfined uniaxial compression tests of cohesive granular samples were performed in situ within an Xray micro-computed tomography system (GE Nanotom).
The samples were composed of monodisperse beads of diameter D = 200. 9 ± 1. 9 µm (Whitehouse Scientific), mixed with PDMS of Young's modulus E p = 1. 5 ± 0. 15 MPa (sample A) or E p = 0. 64 ± 0. 05 MPa (sample B). These materials were shaped into cylinders of 4. 25 mm diameter × 4. 05 mm height for sample A, and 4. 25 mm diameter × 4. 82 mm height for sample B. Tomography scans were performed before compression, and consisted of sets of 2000 projections with a resolution of 1132 × 1132 pixels and a voxel size of 5 µm. The samples were then compressed at a speed of 5 µm/min, and their stressstrain curves will be compared with simulations in Section 4, and Fig. 3. Beads were detected within the reconstructed sample volumes using Matlab, and particle positions determined by finding the centroid of each individual connected volume after segmentation, with a precision of about one voxel (see Tables  S1  and S2   tions and Movies S3 and S4 for illustrating their detection).