# Erratum: “Detecting Reconnection Events in Kinetic Vlasov Hybrid Simulations Using Clustering Techniques” (2021, ApJ, 908, 107)

Manuela Sisti, Francesco Finelli, Giorgio Pedrazzi, Matteo Faganello,
Francesco Califano, Francesca Delli Ponti

► To cite this version:

Manuela Sisti, Francesco Finelli, Giorgio Pedrazzi, Matteo Faganello, Francesco Califano, et al.. Erratum: “Detecting Reconnection Events in Kinetic Vlasov Hybrid Simulations Using Clustering Techniques” (2021, ApJ, 908, 107). The Astrophysical Journal, 2021, 917 (1), pp.51. 10.3847/1538-4357/ac1747. hal-03667194

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Erratum: “Detecting Reconnection Events in Kinetic Vlasov Hybrid Simulations Using Clustering Techniques” (2021, ApJ, 908, 107)

Manuela Sisti¹,² Ⓓ, Francesco Finelli², Giorgio Pedrazzi³, Matteo Faganello¹ Ⓓ, Francesco Califano² Ⓓ, and Francesca Delli Ponti³

¹Aix-Marseille University, CNRS, PIIM UMR F-7345, Marseille, EU, France; manuela.sisti@univ-amu.fr

²Dipartimento di Fisica, Università di Pisa, Italy

³HPC Department, Cineca, Bologna, Italy

Received 2021 July 19; revised 2021 July 21; published 2021 August 16

While the physical picture that emerges is correct, we regret the presence of a bug in the code for the estimation of the aspect ratio of the candidate structures found. In particular, a factor $\sqrt{2}$ was inadvertently set in the estimation of the thickness, leading to an underestimation of the AR by a factor $1/\sqrt{2}$. The revised Tables 3, 4, and 5 with the corrected values of AR are reported in the following, together with the corrected Figure 6. As anticipated the physical picture is the same, with only a slightly different value of the “optimal” AR threshold. The new “optimal” AR threshold is $\simeq 26$. In the published article we shared the link to our codes, which will become a tool, namely Unsupervised ML Reconnection, in Python language, in the context of the EU AIDA project. We share here the links to the new version of the scripts where the small bug has been corrected: https://gitlab.com/aidaspace/aidapy/-/tree/ unsuperv_rec_2/aidapy/unsupmr and, for Zenodo, https://doi.org/10.5281/zenodo.5118596 (version 2.0.0). We also take advantage of this opportunity to signal a misspelling: “Davis-Bouldin index” should be “Davies-Bouldin index.”

<table><caption>Table 3
Number of Structures Found, Precision and nMR-precision for AML, for Different AR Thresholds (from 10 to 70)</caption><thead><tr><th>Time [1/Ω<sub>ci</sub>]</th><th></th><th>20</th><th>230</th><th>247</th><th>282</th><th>494</th><th>Mean (3t)</th><th>Mean (4t)</th></tr></thead><tbody><tr><td rowspan="6">N. structures</td><td>AR > 10</td><td>35</td><td>29</td><td>19</td><td>24</td><td>32</td><td></td><td></td></tr><tr><td>AR > 12.5</td><td>0</td><td>20</td><td>17</td><td>22</td><td>30</td><td></td><td></td></tr><tr><td>AR > 20</td><td>0</td><td>18</td><td>17</td><td>21</td><td>30</td><td></td><td></td></tr><tr><td>AR > 30</td><td>0</td><td>15</td><td>17</td><td>20</td><td>23</td><td></td><td></td></tr><tr><td>AR > 50</td><td>0</td><td>14</td><td>13</td><td>14</td><td>18</td><td></td><td></td></tr><tr><td>AR > 70</td><td>0</td><td>8</td><td>10</td><td>13</td><td>9</td><td></td><td></td></tr><tr><td rowspan="6">precision</td><td>AR > 10</td><td>...</td><td>0.6</td><td>0.82</td><td>0.64</td><td>0.4</td><td>0.69</td><td>0.61</td></tr><tr><td>AR > 12.5</td><td>...</td><td>0.67</td><td>0.82</td><td>0.67</td><td>0.4</td><td>0.72</td><td>0.64</td></tr><tr><td>AR > 20</td><td>...</td><td>0.73</td><td>0.82</td><td>0.7</td><td>0.39</td><td>0.75</td><td>0.66</td></tr><tr><td>AR > 30</td><td>...</td><td>0.79</td><td>0.85</td><td>0.79</td><td>0.39</td><td>0.81</td><td>0.70</td></tr><tr><td>AR > 50</td><td>...</td><td>1</td><td>1</td><td>0.77</td><td>0.33</td><td>0.92</td><td>0.77</td></tr><tr><td>AR > 70</td><td>...</td><td>1</td><td>1</td><td>0.75</td><td>0.43</td><td>0.92</td><td>0.79</td></tr><tr><td rowspan="6">nMR-precision</td><td>AR < 10</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>AR < 12.5</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>AR < 20</td><td>1</td><td>0.93</td><td>1</td><td>1</td><td>0.67</td><td>0.98</td><td>0.9</td></tr><tr><td>AR < 30</td><td>1</td><td>0.93</td><td>0.5</td><td>0.7</td><td>0.64</td><td>0.71</td><td>0.69</td></tr><tr><td>AR < 50</td><td>1</td><td>0.81</td><td>0.55</td><td>0.64</td><td>0.61</td><td>0.67</td><td>0.65</td></tr><tr><td>AR < 70</td><td>1</td><td>0.74</td><td>0.5</td><td>0.58</td><td>0.64</td><td>0.61</td><td>0.61</td></tr></tbody></table>

Note. The results are shown for five different times of our simulation: $t \sim 20[1/\Omega_{ci}]$, $t \sim 230[1/\Omega_{ci}]$, $t \sim 247[1/\Omega_{ci}]$, $t \sim 282[1/\Omega_{ci}]$, and $t \sim 494[1/\Omega_{ci}]$. In the last two columns we report the mean value of our quality parameters for the three central times (230, 247, and 282) and for four times (230, 247, 282, and 494). In the second row we list the number of structures found at the end of the third step; in the third to eighth rows we give the number of detected structures overcoming the specified AR threshold. In the ninth to fourteenth rows we give the values of precision for different AR thresholds computed among the structures enumerated in the third to eighth rows; finally in the fifteenth to twentieth rows we give values for nMR-precision.
<table><caption>**Table 4**
Number of Structures Found, Precision and nMR-precision for A1, for Different AR Thresholds (from 10 to 70)</caption><thead><tr><th>Time [1/Ω<sub>ci</sub>]</th><th>20</th><th>230</th><th>247</th><th>282</th><th>494</th><th>Mean (3t)</th><th>Mean (4t)</th></tr></thead><tbody><tr><td>N. structures</td><td>12</td><td>46</td><td>48</td><td>52</td><td>454</td><td></td><td></td></tr><tr><td rowspan="6">N. structures</td><td>AR > 10</td><td>0</td><td>23</td><td>25</td><td>21</td><td>108</td><td></td><td></td></tr><tr><td>AR > 12.5</td><td>0</td><td>23</td><td>25</td><td>18</td><td>93</td><td></td><td></td></tr><tr><td>AR > 20</td><td>0</td><td>20</td><td>17</td><td>14</td><td>61</td><td></td><td></td></tr><tr><td>AR > 30</td><td>0</td><td>15</td><td>15</td><td>12</td><td>39</td><td></td><td></td></tr><tr><td>AR > 50</td><td>0</td><td>12</td><td>10</td><td>10</td><td>17</td><td></td><td></td></tr><tr><td>AR > 70</td><td>0</td><td>11</td><td>9</td><td>7</td><td>12</td><td></td><td></td></tr><tr><td rowspan="6">precision</td><td>AR > 10</td><td>...</td><td>0.70</td><td>0.6</td><td>0.52</td><td>0.26</td><td>0.61</td><td>0.52</td></tr><tr><td>AR > 12.5</td><td>...</td><td>0.70</td><td>0.6</td><td>0.61</td><td>0.26</td><td>0.64</td><td>0.54</td></tr><tr><td>AR > 20</td><td>...</td><td>0.75</td><td>0.71</td><td>0.71</td><td>0.28</td><td>0.72</td><td>0.61</td></tr><tr><td>AR > 30</td><td>...</td><td>0.8</td><td>0.8</td><td>0.75</td><td>0.33</td><td>0.78</td><td>0.67</td></tr><tr><td>AR > 50</td><td>...</td><td>0.83</td><td>0.9</td><td>0.8</td><td>0.41</td><td>0.84</td><td>0.73</td></tr><tr><td>AR > 70</td><td>...</td><td>0.82</td><td>1</td><td>0.86</td><td>0.42</td><td>0.89</td><td>0.77</td></tr><tr><td rowspan="6">nMR-precision</td><td>AR < 10</td><td>1</td><td>0.74</td><td>0.78</td><td>0.61</td><td>0.91</td><td>0.71</td><td>0.76</td></tr><tr><td>AR < 12.5</td><td>1</td><td>0.74</td><td>0.78</td><td>0.65</td><td>0.90</td><td>0.72</td><td>0.77</td></tr><tr><td>AR < 20</td><td>1</td><td>0.73</td><td>0.74</td><td>0.66</td><td>0.89</td><td>0.71</td><td>0.75</td></tr><tr><td>AR < 30</td><td>1</td><td>0.68</td><td>0.76</td><td>0.65</td><td>0.89</td><td>0.70</td><td>0.74</td></tr><tr><td>AR < 50</td><td>1</td><td>0.65</td><td>0.71</td><td>0.64</td><td>0.88</td><td>0.67</td><td>0.72</td></tr><tr><td>AR < 70</td><td>1</td><td>0.63</td><td>0.72</td><td>0.62</td><td>0.88</td><td>0.65</td><td>0.71</td></tr></tbody></table>

**Note.** The results are shown for five different times of our simulation: $t \sim 20[1/\Omega_{ci}]$, $t \sim 230[1/\Omega_{ci}]$, $t \sim 247[1/\Omega_{ci}]$, $t \sim 282[1/\Omega_{ci}]$, and $t \sim 494[1/\Omega_{ci}]$. In the last two columns we report the mean value of our quality parameters for the three central times (230, 247, and 282) and for four times (230, 247, 282, and 494). In the second row we list the number of structures found at the end of the third step; in the third to eighth rows we give the number of detected structures overcoming the specified AR threshold. In the ninth to fourteenth rows we give the values of precision for different AR thresholds computed among the structures enumerated in the third to eighth rows; finally in the fifteenth to twentieth rows we give values for nMR-precision.

<table><caption>**Table 5**
Number of Structures Found, Precision and nMR-precision for A2, for Different AR Thresholds (from 10 to 70)</caption><thead><tr><th>Tempo [1/Ω<sub>ci</sub>]</th><th>20</th><th>230</th><th>247</th><th>282</th><th>494</th><th>Mean (3t)</th><th>Mean (4t)</th></tr></thead><tbody><tr><td>N. structures</td><td>2</td><td>30</td><td>27</td><td>26</td><td>126</td><td></td><td></td></tr><tr><td rowspan="6">N. structures</td><td>AR > 10</td><td>0</td><td>21</td><td>20</td><td>14</td><td>56</td><td></td><td></td></tr><tr><td>AR > 12.5</td><td>0</td><td>21</td><td>15</td><td>12</td><td>54</td><td></td><td></td></tr><tr><td>AR > 20</td><td>0</td><td>18</td><td>14</td><td>11</td><td>38</td><td></td><td></td></tr><tr><td>AR > 30</td><td>0</td><td>15</td><td>10</td><td>10</td><td>27</td><td></td><td></td></tr><tr><td>AR > 50</td><td>0</td><td>12</td><td>9</td><td>9</td><td>14</td><td></td><td></td></tr><tr><td>AR > 70</td><td>0</td><td>11</td><td>6</td><td>7</td><td>9</td><td></td><td></td></tr><tr><td rowspan="6">precision</td><td>AR > 10</td><td>...</td><td>0.76</td><td>0.75</td><td>0.79</td><td>0.36</td><td>0.77</td><td>0.66</td></tr><tr><td>AR > 12.5</td><td>...</td><td>0.76</td><td>0.75</td><td>0.92</td><td>0.33</td><td>0.81</td><td>0.69</td></tr><tr><td>AR > 20</td><td>...</td><td>0.83</td><td>0.8</td><td>0.91</td><td>0.34</td><td>0.85</td><td>0.72</td></tr><tr><td>AR > 30</td><td>...</td><td>0.8</td><td>0.86</td><td>0.9</td><td>0.37</td><td>0.85</td><td>0.73</td></tr><tr><td>AR > 50</td><td>...</td><td>0.83</td><td>0.9</td><td>0.89</td><td>0.43</td><td>0.87</td><td>0.76</td></tr><tr><td>AR > 70</td><td>...</td><td>0.81</td><td>1</td><td>0.86</td><td>0.44</td><td>0.89</td><td>0.78</td></tr><tr><td rowspan="6">nMR-precision</td><td>AR < 10</td><td>1</td><td>0.89</td><td>0.43</td><td>0.58</td><td>0.84</td><td>0.62</td><td>0.68</td></tr><tr><td>AR < 12.5</td><td>1</td><td>0.89</td><td>0.43</td><td>0.64</td><td>0.82</td><td>0.65</td><td>0.69</td></tr><tr><td>AR < 20</td><td>1</td><td>0.83</td><td>0.42</td><td>0.6</td><td>0.79</td><td>0.62</td><td>0.66</td></tr><tr><td>AR < 30</td><td>1</td><td>0.67</td><td>0.46</td><td>0.56</td><td>0.79</td><td>0.56</td><td>0.62</td></tr><tr><td>AR < 50</td><td>1</td><td>0.61</td><td>0.41</td><td>0.53</td><td>0.78</td><td>0.52</td><td>0.58</td></tr><tr><td>AR < 70</td><td>1</td><td>0.58</td><td>0.44</td><td>0.47</td><td>0.77</td><td>0.50</td><td>0.56</td></tr></tbody></table>

**Note.** The results are shown for five different times of our simulation: $t \sim 20[1/\Omega_{ci}]$, $t \sim 230[1/\Omega_{ci}]$, $t \sim 247[1/\Omega_{ci}]$, $t \sim 282[1/\Omega_{ci}]$, and $t \sim 494[1/\Omega_{ci}]$. In the last two columns we report the mean value of our quality parameters for the three central times (230, 247, and 282) and for four times (230, 247, 282, and 494). In the second row we list the number of structures found at the end of the third step; in the third to eighth rows we give the number of detected structures overcoming the specified AR threshold. In the ninth to fourteenth rows we give the values of precision for different AR thresholds computed among the structures enumerated in the third to eighth rows; finally in the fifteenth to twentieth rows we give values for nMR-precision.
Precision and nMR-precision, comparison among AML, A1 and A2

Mean over phase II

<figure><img src="image_3.png" /></figure>

Mean over phase II and III

<figure><img src="image_4.png" /><figcaption>**Figure 6.** Plots of the values of precision (red, orange, and brown lines) and nMR-precision (blue, cyan, and violet lines) averaged over the three central times (left panel) and over four times (right panel), as a function of the AR threshold, for the three different methods we are analyzing: solid line, AML; dashed line, A1; dotted line, A2.</figcaption></figure>

ORCID iDs

Manuela Sisti https://orcid.org/0000-0003-3331-0606

Matteo Faganello https://orcid.org/0000-0002-5232-0108

Francesco Califano https://orcid.org/0000-0002-9626-4371