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1 | <?xml version="1.0" encoding="utf-8"?> | |||
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2 | <notebook> | |||
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3 | <name>rmt</name> | |||
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4 | <nbformat>2</nbformat> | |||
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5 | <worksheets> | |||
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6 | <worksheet> | |||
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7 | <cells> | |||
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8 | <markdowncell> | |||
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9 | <source># Eigenvalue distribution of Gaussian orthogonal random matrices</source> | |||
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10 | </markdowncell> | |||
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11 | <markdowncell> | |||
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12 | <source>The eigenvalues of random matrices obey certain statistical laws. Here we construct random matrices | |||
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13 | from the Gaussian Orthogonal Ensemble (GOE), find their eigenvalues and then investigate the nearest | |||
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14 | neighbor eigenvalue distribution $\rho(s)$.</source> | |||
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15 | </markdowncell> | |||
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16 | <codecell> | |||
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17 | <input>from rmtkernel import ensemble_diffs, normalize_diffs, GOE | |||
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18 | import numpy as np | |||
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19 | from IPython.parallel import Client</input> | |||
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20 | <language>python</language> | |||
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21 | <prompt_number>1</prompt_number> | |||
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22 | <collapsed>0</collapsed> | |||
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23 | <outputs /> | |||
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24 | </codecell> | |||
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25 | <markdowncell> | |||
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26 | <source>## Wigner's nearest neighbor eigenvalue distribution</source> | |||
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27 | </markdowncell> | |||
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28 | <markdowncell> | |||
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29 | <source>The Wigner distribution gives the theoretical result for the nearest neighbor eigenvalue distribution | |||
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30 | for the GOE: | |||
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31 | ||||
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32 | $$\rho(s) = \frac{\pi s}{2} \exp(-\pi s^2/4)$$</source> | |||
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33 | </markdowncell> | |||
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34 | <codecell> | |||
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35 | <input>def wigner_dist(s): | |||
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36 | """Returns (s, rho(s)) for the Wigner GOE distribution.""" | |||
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37 | return (np.pi*s/2.0) * np.exp(-np.pi*s**2/4.)</input> | |||
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38 | <language>python</language> | |||
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39 | <prompt_number>2</prompt_number> | |||
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40 | <collapsed>1</collapsed> | |||
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41 | <outputs /> | |||
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42 | </codecell> | |||
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43 | <codecell> | |||
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44 | <input>def generate_wigner_data(): | |||
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45 | s = np.linspace(0.0,4.0,400) | |||
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46 | rhos = wigner_dist(s) | |||
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47 | return s, rhos</input> | |||
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48 | <language>python</language> | |||
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49 | <prompt_number>3</prompt_number> | |||
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50 | <collapsed>1</collapsed> | |||
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51 | <outputs /> | |||
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52 | </codecell> | |||
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53 | <codecell> | |||
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54 | <input>s, rhos = generate_wigner_data()</input> | |||
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55 | <language>python</language> | |||
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56 | <prompt_number>4</prompt_number> | |||
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57 | <collapsed>0</collapsed> | |||
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58 | <outputs /> | |||
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59 | </codecell> | |||
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60 | <codecell> | |||
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61 | <input>plot(s, rhos) | |||
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62 | xlabel('Normalized level spacing s') | |||
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63 | ylabel('Probability $\rho(s)$')</input> | |||
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64 | <language>python</language> | |||
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65 | <prompt_number>17</prompt_number> | |||
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66 | <collapsed>0</collapsed> | |||
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67 | <outputs> | |||
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68 | <output> | |||
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69 | <output_type>pyout</output_type> | |||
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70 | <text>&lt;matplotlib.text.Text at 0x3828790&gt;</text> | |||
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71 | <prompt_number>17</prompt_number> | |||
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72 | </output> | |||
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73 | <output> | |||
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74 | <output_type>display_data</output_type> | |||
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398 | WGw0ZTk5eHpEeDkvL0RHMzMzNjdYYTR0SElQMFlRamh4T3k1NDF4c2JDenIxcTNEemMyTi8vdS8v | |||
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399 | NU5pVVF2SkU0WVEKUWdpelNCK0dFRUlJczBqQkVFSUlZUllwR0VJSUljd2lCVU1JSVlSWnBHQUlJ | |||
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400 | WVF3aXhRTUlZUVFadmwvQ0hyZjBuUWF1Ym9BQUFBQQpTVVZPUks1Q1lJST0K | |||
|
401 | </png> | |||
|
402 | </output> | |||
|
403 | </outputs> | |||
|
404 | </codecell> | |||
|
405 | <markdowncell> | |||
|
406 | <source>## Serial calculation of nearest neighbor eigenvalue distribution</source> | |||
|
407 | </markdowncell> | |||
|
408 | <markdowncell> | |||
|
409 | <source>In this section we numerically construct and diagonalize a large number of GOE random matrices | |||
|
410 | and compute the nerest neighbor eigenvalue distribution. This comptation is done on a single core.</source> | |||
|
411 | </markdowncell> | |||
|
412 | <codecell> | |||
|
413 | <input>def serial_diffs(num, N): | |||
|
414 | """Compute the nearest neighbor distribution for num NxX matrices.""" | |||
|
415 | diffs = ensemble_diffs(num, N) | |||
|
416 | normalized_diffs = normalize_diffs(diffs) | |||
|
417 | return normalized_diffs</input> | |||
|
418 | <language>python</language> | |||
|
419 | <prompt_number>6</prompt_number> | |||
|
420 | <collapsed>1</collapsed> | |||
|
421 | <outputs /> | |||
|
422 | </codecell> | |||
|
423 | <codecell> | |||
|
424 | <input>serial_nmats = 1000 | |||
|
425 | serial_matsize = 50</input> | |||
|
426 | <language>python</language> | |||
|
427 | <prompt_number>7</prompt_number> | |||
|
428 | <collapsed>1</collapsed> | |||
|
429 | <outputs /> | |||
|
430 | </codecell> | |||
|
431 | <codecell> | |||
|
432 | <input>%timeit -r1 -n1 serial_diffs(serial_nmats, serial_matsize)</input> | |||
|
433 | <language>python</language> | |||
|
434 | <prompt_number>8</prompt_number> | |||
|
435 | <collapsed>0</collapsed> | |||
|
436 | <outputs> | |||
|
437 | <output> | |||
|
438 | <output_type>stream</output_type> | |||
|
439 | <text>1 loops, best of 1: 1.19 s per loop</text> | |||
|
440 | </output> | |||
|
441 | </outputs> | |||
|
442 | </codecell> | |||
|
443 | <codecell> | |||
|
444 | <input>serial_diffs = serial_diffs(serial_nmats, serial_matsize)</input> | |||
|
445 | <language>python</language> | |||
|
446 | <prompt_number>9</prompt_number> | |||
|
447 | <collapsed>0</collapsed> | |||
|
448 | <outputs /> | |||
|
449 | </codecell> | |||
|
450 | <markdowncell> | |||
|
451 | <source>The numerical computation agrees with the predictions of Wigner, but it would be nice to get more | |||
|
452 | statistics. For that we will do a parallel computation.</source> | |||
|
453 | </markdowncell> | |||
|
454 | <codecell> | |||
|
455 | <input>hist_data = hist(serial_diffs, bins=30, normed=True) | |||
|
456 | plot(s, rhos) | |||
|
457 | xlabel('Normalized level spacing s') | |||
|
458 | ylabel('Probability $P(s)$')</input> | |||
|
459 | <language>python</language> | |||
|
460 | <prompt_number>10</prompt_number> | |||
|
461 | <collapsed>0</collapsed> | |||
|
462 | <outputs> | |||
|
463 | <output> | |||
|
464 | <output_type>pyout</output_type> | |||
|
465 | <text>&lt;matplotlib.text.Text at 0x3475bd0&gt;</text> | |||
|
466 | <prompt_number>10</prompt_number> | |||
|
467 | </output> | |||
|
468 | <output> | |||
|
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641 | M1Y0TUFZZTNxRjFFaUVzWHJVdEdMOWUveFhIT282MApiTkJTNnlpaUt1WFVnWitYd2VBWG9VYW0x | |||
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642 | bW1Fc0dqVnRtRHNQTDlUem82cUxrNFBnWVFPME9NRHJaTUlZZEdxYmNFSU94OG00eGZWCnljOUxv | |||
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643 | TnNTYUhSZTZ5UkNXS3hxV1RBeWN6TTVFSDhBZjJkL3JhTUlVMGxwRFh0ZmhTZWVCMTIrMW1tRXNF | |||
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644 | alZzbURzdTdTUGprMDYKMHVDQkJscEhFYVowNEdXb2tRRmRWMnFkUkFpTFZDMExob3hmVkZQS0Zu | |||
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645 | NzRBdnpuZ2NNWnJkTUlZWEdxWmNHUThZdHFMS2s5Ukw0QgpUMDBvbVBSV0NHR3dhbGN3a3U0a2NT | |||
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647 | ajhPZlNDRXdrbnRFNGpoTVdvZGdVajhtSWsvcTM5dFk0aHRIYlRCWDZ4b2NNL082Q3oxYUhURlgv | |||
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648 | WTJ6dG9uVklJczFMdENrYkUKeFFqNnRPNmpkUXhoRGc3bVEyWi82UGwvRk56QnIrZ2pMZTJtcHZH | |||
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652 | Q1NmeGVkQkg2eWpDSE4xdURqOTgKRHNQSFF0MGJXcWNSd2l4Vm00S3gvL0orSG0zeEtMVnExTkk2 | |||
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653 | aWpCWFp3Y1ZISjRhL2orZ3k5TTZqUkJtcDlvVWpJaUxFZmc1KzJGdgo3MURpT2ZmM1BrUTF0bnQr | |||
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654 | d1d5MmZtOXBuVVFJczZOSndZaU1qTVROelkxMjdkcXhiTm15WXN2WHJsMkxwNmNubnA2ZWpCMDds | |||
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658 | QURSMGRGRjJuVHYzcDBHRFFydVZSRVlHRWhFUkVTRnRoa1ZIMFducHAyb1kxZW5RdXNSMVVpY1A4 | |||
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659 | VFkwSEpXCnkxS25EcEhwUTBSMVkvS0NFUnNiaTZ1cnEvNjV1N3M3VVZGUnBiYi8rT09QR1RwMGFJ | |||
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660 | VzJXVGgrSVlSUjl1WkQxaURvRzB4cGh5OWwKK2hCUm5kVFFPc0Q5aElXRnNXYk5HdmJ2MzE5cW0z | |||
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661 | bno1dWwvOXZmM3g5L2Z2MWlieUl1UnpPNHh1d29TQ3F1bWdPKytncURPY0trWAovUEdrMW9tRUtK | |||
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662 | Znc4SERDdzhNcnZCNmRVc3Frbzd3cEtTbjQrL3R6NU1nUkFLWlBuODdBZ1FNSkRBd3MwdTYzMzM3 | |||
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663 | ajZhZWZadHUyCmJiUnQyN2JFZGVsME9zcUtuNVdiaGVNSGpseDUrUXIydGV6dm5nVlYxa2N1cTAx | |||
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664 | bHJNT2N0bU5PV2N6d016OFlEV09Id245MndnM1AKWW0xTS9DY2tSSVVaOHQxWkVwTWZraW9jbTRp | |||
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665 | TWpDUXVMbzZkTzNmaTYxdjBaa2FYTGwxaStQRGhyRjI3dHRSaVlhaVlLekc0T3JwaQpYOHUrUXVz | |||
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666 | Ylh5WTFBQUFXSjBsRVFWUVIxZGdWWC9ocGVVSFJxSDlGNnpSQ2FFYVRRMUtMRnk4bUtDaUluSndj | |||
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667 | WnN5WWdhT2pJeUVoCklRQUVCUVh4MWx0dmtaeWN6TlNwVXdHd3M3TWpKaWFtWE51UzZVQkVwVGcr | |||
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668 | RWhxZGg3RkQ0UE5JeUs2dmRTSWhUTTdraDZRcWt5RzcKVlFPK0dzQTBuMms4MGY0Si9Yc3M1N0NK | |||
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669 | R1I2ZXNacnRsQ2VMZ3FFdlFQMnI4TTNtZ3R1OHlpRXBZWUVzNXBDVUtlWGs1UkFWSDBXdgpWcjIw | |||
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670 | amlLc2dnNjJyZ1NiWEJnNEU3bklVMVEzVmwwd0RsODdUSnRHYlhDb0xlZktpMHFTYndjYk54VE1h | |||
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671 | dHQ5a2RacGhEQXBzejZ0CnRxSmsvRUpVaWF3R3NHNHJUTzRCY2htR3FFYXNlZzlEYnBna3FreEtL | |||
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672 | L2g2TXd5RkE1Y1BhSjFHQ0pPdzJvS1JsNS9IdnN2NzZOMnEKdDlaUmhMVzYxZ1craHllL2VaTG8r | |||
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673 | T2l5Mnd0aDRheTJZUHgyNHplYTFXdEcwM3BOdFk0aXJObForUHpKenhuNjlWQmlycFR2MUc4aApM | |||
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674 | SVhWRmd3WnZ4Q21FdmhJSUo4OStSbER2eDVLN0pWWXJlTUlVV1dzdG1ESStJVXdwU0dQRE9IVEp6 | |||
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675 | NWx5TmREcEdnSXEyVlZGKzdaCjJ6djhkL2JRZndBaFFHcEo3N1NVaTh2TStTSTJTOTlPNVdXNTk3 | |||
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676 | L0JMWDlzWWZLUGs5azZkaXRkSCt4YXhudUYwSVpjdUFmL3ZadWUKMHpISWNvRlV1WnVlTUsyaDdZ | |||
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677 | Znl5Uk9mTU9UcklSeThlbERyT0VKVUt1dThEcU4xSkZ5VThRdWhqU2ZhUDRGU2lzQjFnV3g4WnFP | |||
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678 | TQpwUW1yWVZWN0dIck9FWEJSeGkrRWRwNTBmWkkxdzlZd1lzTUkxdnkyUnVzNFFsUUtLeXdZQ2xw | |||
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679 | SFFKd1VES0d0L2cvM1ovZjQzYnk1CiswM21oYytUU1FxRnhiTytndUZ3dG1BVzBWdk9XaWNSZ2c1 | |||
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680 | Tk9oQTFPWXFmei83TXVCL0drWldicFhVa0ljck5xczZTMHVsMDBIazEKT0lmRGQ2VWRCckNrTTNr | |||
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681 | czc0d2h5OWxPNVdVcDYwL0kzdDZCdE15Yk1BeW9DM3dEWlB4M2VmMzZqVWhOVFM1ak8wSlVIamxM | |||
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682 | cXBBTQplQXN6azVaMkUzSVViTXlEeTYvQzgyMmg4UjhVbnJtblB4VmNDRE5uaFFWRHhpK0VtVkky | |||
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683 | RVBZdTdIc1ZKdldDRGh1MFRpU0VVYXpyCnROb0dRSTBzU0hwRTZ5UkNsTzd3ODNEZEM0YVBoYmJi | |||
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684 | NEdldEF3bGhHT3ZhdzNEbTd1RW9uY1pCUlBWUkE1MU9kOTlIaWE0K0NpR0gKUWVrZ0NMbklUMWdF | |||
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685 | NnlvWXJaSHhDMkZpdVJTZlRjREEyUVd5NjhHUG44SXZNSGp0WU43Zjl6NzVLci9xSXd0UlR0WlhN | |||
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686 | R1Q4UWxpYQo0eEE3SlpZdHA3Y3c0S3NCWEVtOW9uVWlJVXBrTlFYamF0cFZxQTBrZE5BNmloQkdh | |||
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687 | OTJ3TmJ2SDc4YXZ0UitlSDNueTcvMy9KaWN2ClIrdFlRaFJoTlFVajhtSWtYS0xnVEJRaExGQU5t | |||
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688 | eHE4NmZjbSt5ZnZKK3g4R0o0ZmViTHIvQzZ0WXdtaFp6WGZycEVYSStHaTFpbUUKcUxoSEdqL0N6 | |||
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689 | Ly96TXd2NkxtRHlqNU1adVhFa2wxTXVheDFMQ09zcEdCRVhJeUJPNnhSQ1ZBNmRUc2RUcms5eDRz | |||
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690 | VVR1RG01NFJYaQp4WUk5QzhqSXlTajd6VUpVRWFzb0dBbnBDY1NueHNNTnJaTUlVYm5xMk5WaHZ2 | |||
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691 | OThZcWZFRW5zMWxvZVhQc3pDL1F0SnowN1hPcHFvCmhxeWlZT3k1dEllZUxYdUNuSkVvckpSTEl4 | |||
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692 | ZStIL1U5UC8zUFQwUmRpY0pscVFzTDlpd2dOYXZFVzBvS1VTV3NvbURJL2J1RlpTdjcKNGo5N2V3 | |||
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693 | Y0F2SnA1c2ZHWmpld2V2NXVUaVNkeFdlTEMzUEM1SkdmSTVJV2k2bGxGd1lpOEdDbDNOUk1Xck95 | |||
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694 | TC8vNDZRYUc3a3p0ZgpEZnVLcU9lanVKSjZoWWVYUHN5a3paUFlkMm1mM0hkRFZCbUxuOTQ4K1U0 | |||
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695 | eXJSYTNJbWwyRXJWcTFNS2NwcjIybk8yWVV4YjV6S1cxCnVkK2Y2dlhiMS9uUHIvL2gweU9mWXFP | |||
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696 | ellaTFhKTVo1anFOcHZhWmxyRmRVUjlWMmV2TjlsL2ZoKzZBdk5XMXJhaDFGQ00wMHE5ZU0KMlQx | |||
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697 | bmMrckZVNndldXBvVGlTZG92N3c5dzlZUEkvUjBLTG41dVZwSEZGYkE0dmN3Z25jRVkxL1RuamY5 | |||
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698 | M3J3NzBadjUvSXZRY3JaagpUbG5rTTVmV3h0Zy8xYlNzTk5ZZlg4K25SejdsVE5JWkF0b0dFTmd1 | |||
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699 | a0lGdEIrSlEyOEdvZFFuclV0NDlESXN2R0Q2cmZYaS8zL3Y0Ck9mdEp3YkNLTFBLWlMydFRrVC9W | |||
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700 | K05SNGZqcnpFMXZQYkNVOExweE9UVHNSMkM2UXdIYUJlRFR4S0gxV1hXR1ZxbTNCcVB0T1hSSm4K | |||
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701 | Si9KQWpRZWtZRmhGRnZuTUpiT2pZSEM4ZEliZTZqVXpONVB3dUhDMm50bksxdE5ieVZONURHdzdr | |||
|
702 | TzRQZGNmM1FWL2FPN2JIUm1meApSNnZGZlZUYmd0SDdzOTVFVG96VVB6ZWZQM0JMMm80NVpaSFBY | |||
|
703 | SkUyeHY0NUs2VTRsWGlLSGVkMkVIMGxtcGdyTVNUZVNlVFJGby9pCjg2QVBQZy82NFB1Z0w4M3JO | |||
|
704 | emRxdmNLOGxiZGdXUHdkOS95Yy9iU09JSVRGMHVsMHVEbTU0ZWJrcG44dDhVNGlzVmRpaWI0U3pj | |||
|
705 | ZUgKUHViNUg1K250bDF0ZkI3MHdjM1JqYllPYldubjBJNTJqZHZoVk1kSkRtZFZJNXJzWVVSR1Jo | |||
|
706 | SVVGRVJ1Ymk0elpzeGcrdlRweGRxOAo5dHByckYrL25rYU5HckYyN1ZwY1hWMkx0ZEhwZE93NHU0 | |||
|
707 | UCtEL2ZYUHpmUGZ4R0dBLzRtMkU1RjIreW01SnltekdJdGV4amgvTGN2CnpYY1BJenc4SEg5Ly8v | |||
|
708 | dTJVVXB4L3VaNVlxL0c4a2ZpSDV5OWVaWXpTV2M0bTN5V25Qd2MyanEwL1c4UmNXaW5mKzVVMTZu | |||
|
709 | U0RtMFoKa3RNY1dFcE9pOXJEbURsekppRWhJYlJ1M1pxQWdBREdqQm1EbzZPamZubE1UQXg3OXV6 | |||
|
710 | aDRNR0RiTisrbmVEZ1lFSkRRMHRjVjQrVwpQVXdWdXdMQ0tmMkwySnlFWXhrNUxVRTRsdENYaG56 | |||
|
711 | QjZYUTZIblo0bUljZEhpNjI3R2JHVGM0a0Z4U1BNMGxuQ0xzUXhxcURxemgzCjh4eTNNbS9SdUha | |||
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797 | V05IMnJScFU2emRraVZMNk5peEl6NCtQcmk2dXRLalI0OFNmeS9DTXNua2cwSllxTGk0T0lZT0hj | |||
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798 | cnZ2Lzl1a3UybHA2ZFQKdDI1ZFVsSlNHREprQ0o5ODhnbnQyN2MzeWJhRmVaQXhEQ0VzbUNudk9E | |||
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799 | ZHYzanpDd3NLd3M3UGoyV2VmbFdKUkRja2VoaEJDQ0lQSQpHSVlRUWdpRFNNRVFRZ2hoRUNrWVFn | |||
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800 | Z2hEQ0lGUXdnaGhFR2tZQWdoaERDSUZBd2hoQkFHK1g4TEF4UDFCZTVmQkFBQUFBQkpSVTVFCnJr | |||
|
801 | SmdnZz09Cg== | |||
|
802 | </png> | |||
|
803 | </output> | |||
|
804 | </outputs> | |||
|
805 | </codecell> | |||
|
806 | <markdowncell> | |||
|
807 | <source>## Parallel calculation of nearest neighbor eigenvalue distribution</source> | |||
|
808 | </markdowncell> | |||
|
809 | <markdowncell> | |||
|
810 | <source>Here we perform a parallel computation, where each process constructs and diagonalizes a subset of | |||
|
811 | the overall set of random matrices.</source> | |||
|
812 | </markdowncell> | |||
|
813 | <codecell> | |||
|
814 | <input>def parallel_diffs(rc, num, N): | |||
|
815 | nengines = len(rc.targets) | |||
|
816 | num_per_engine = num/nengines | |||
|
817 | print "Running with", num_per_engine, "per engine." | |||
|
818 | ar = rc.apply_async(ensemble_diffs, num_per_engine, N) | |||
|
819 | diffs = np.array(ar.get()).flatten() | |||
|
820 | normalized_diffs = normalize_diffs(diffs) | |||
|
821 | return normalized_diffs</input> | |||
|
822 | <language>python</language> | |||
|
823 | <prompt_number>11</prompt_number> | |||
|
824 | <collapsed>1</collapsed> | |||
|
825 | <outputs /> | |||
|
826 | </codecell> | |||
|
827 | <codecell> | |||
|
828 | <input>client = Client() | |||
|
829 | view = client[:] | |||
|
830 | view.run('rmtkernel.py') | |||
|
831 | view.block = False</input> | |||
|
832 | <language>python</language> | |||
|
833 | <prompt_number>12</prompt_number> | |||
|
834 | <collapsed>1</collapsed> | |||
|
835 | <outputs /> | |||
|
836 | </codecell> | |||
|
837 | <codecell> | |||
|
838 | <input>parallel_nmats = 40*serial_nmats | |||
|
839 | parallel_matsize = 50</input> | |||
|
840 | <language>python</language> | |||
|
841 | <prompt_number>13</prompt_number> | |||
|
842 | <collapsed>1</collapsed> | |||
|
843 | <outputs /> | |||
|
844 | </codecell> | |||
|
845 | <codecell> | |||
|
846 | <input>%timeit -r1 -n1 parallel_diffs(view, parallel_nmats, parallel_matsize)</input> | |||
|
847 | <language>python</language> | |||
|
848 | <prompt_number>14</prompt_number> | |||
|
849 | <collapsed>0</collapsed> | |||
|
850 | <outputs> | |||
|
851 | <output> | |||
|
852 | <output_type>stream</output_type> | |||
|
853 | <text>Running with 10000 per engine. | |||
|
854 | 1 loops, best of 1: 14 s per loop</text> | |||
|
855 | </output> | |||
|
856 | <output> | |||
|
857 | <output_type>stream</output_type> | |||
|
858 | <text /> | |||
|
859 | </output> | |||
|
860 | </outputs> | |||
|
861 | </codecell> | |||
|
862 | <codecell> | |||
|
863 | <input>pdiffs = parallel_diffs(view, parallel_nmats, parallel_matsize)</input> | |||
|
864 | <language>python</language> | |||
|
865 | <prompt_number>15</prompt_number> | |||
|
866 | <collapsed>0</collapsed> | |||
|
867 | <outputs> | |||
|
868 | <output> | |||
|
869 | <output_type>stream</output_type> | |||
|
870 | <text>Running with 10000 per engine.</text> | |||
|
871 | </output> | |||
|
872 | </outputs> | |||
|
873 | </codecell> | |||
|
874 | <markdowncell> | |||
|
875 | <source>Again, the agreement with the Wigner distribution is excellent, but now we have better | |||
|
876 | statistics.</source> | |||
|
877 | </markdowncell> | |||
|
878 | <codecell> | |||
|
879 | <input>hist_data = hist(pdiffs, bins=30, normed=True) | |||
|
880 | plot(s, rhos) | |||
|
881 | xlabel('Normalized level spacing s') | |||
|
882 | ylabel('Probability $P(s)$')</input> | |||
|
883 | <language>python</language> | |||
|
884 | <prompt_number>16</prompt_number> | |||
|
885 | <collapsed>0</collapsed> | |||
|
886 | <outputs> | |||
|
887 | <output> | |||
|
888 | <output_type>pyout</output_type> | |||
|
889 | <text>&lt;matplotlib.text.Text at 0x376c950&gt;</text> | |||
|
890 | <prompt_number>16</prompt_number> | |||
|
891 | </output> | |||
|
892 | <output> | |||
|
893 | <output_type>display_data</output_type> | |||
|
894 | <png>aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQVl3QUFBRU1DQVlBQUFEWGlZR1NBQUFBQkhOQ1NWUUlD | |||
|
895 | QWdJZkFoa2lBQUFBQWx3U0ZsegpBQUFMRWdBQUN4SUIwdDErL0FBQUlBQkpSRUZVZUp6dDNYbGNW | |||
|
896 | UFgreC9IWElMZ2pMcWhvRm1xaGdDZ01Db2dtVG01Z3FOMVNNNjFjCjZoWmxpcmxVMXErdVdyZHVk | |||
|
897 | YStwbVJyWnRWVXJ5OHF0TWt6SDBRVEVMWGROQlJPM0ZCVlEyVG0vUDRpNWptd3pNTXlaWVQ3UCs1 | |||
|
898 | aEgKek16WDcvZk40VElmenZtZTh6MGFSVkVVaEJCQ2lFcTRxQjFBQ0NHRVk1Q0NJWVFRd2l4U01J | |||
|
899 | UVFRcGhGQ29ZUVFnaXpTTUVRUWdoaApGaWtZUWdnaHpLSkt3VEFZRFBqNStlSGo0OFBDaFF0THZa | |||
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900 | K1ZsY1gwNmRNSkNnb2lQRHljRXlkT3FKQlNDQ0hFelZRcEdGT21UQ0V1CkxvNk5HemV5YU5FaUxs | |||
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901 | MjZaUEwrRjE5OFFYNStQbnYzN3VXZGQ5N2grZWVmVnlPbUVFS0ltOWk4WUdSa1pBQVFFUkdCdDdj | |||
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902 | M2d3WU4KSWlrcHlhVE5wazJiaUk2T0JpQThQSnpqeDQvYk9xWVFRb2hiMkx4Z0pDY240K3ZyYTN6 | |||
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903 | dTcrOVBZbUtpU1p2SXlFaSsrT0lMc3JPegpXYk5tRGZ2Mzd5Y2xKY1hXVVlVUVF0ekVWZTBBWlJr | |||
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904 | MWFoUnBhV24wN2R1WHpwMDc0K1BqUTcxNjlVcTEwMmcwS3FRVFFnakhWNlZWCm9SUWJ1M3IxcWhJ | |||
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905 | VUZHUjhQbW5TSkdYZHVuWGx0cy9LeWxJQ0F3UExmRStGK0ZVeWE5WXN0U09ZUlhKYWp5TmtWQlRK | |||
|
906 | YVcyT2tyT3EKbjUwMlB5VGw0ZUVCRko4cGxacWFTbng4UEdGaFlTWnRNakl5eU12TDQ4YU5HL3py | |||
|
907 | WC85aTRNQ0J0bzRwaEJEaUZxb2NrcG8vZno0eApNVEhrNStjVEd4dUxwNmNuY1hGeEFNVEV4SERv | |||
|
908 | MENIR2p4OVBVVkVSNGVIaHZQLysrMnJFRkVJSWNSTlZDa2Jmdm4wNWZQaXd5V3N4Ck1USEdyOFBE | |||
|
909 | d3psNjlLaXRZOVVZblU2bmRnU3pTRTdyY1lTTUlEbXR6VkZ5VnBYbXIrTlpEa21qMFZSdDRrWUlJ | |||
|
910 | WnhZVlQ4N1pXa1EKSVlRUVpwR0NJWVFRd2l4U01JUVFRcGhGQ29ZUVFnaXpTTUVRUWdoaEZpa1lR | |||
|
911 | Z2doekNJRlF3Z2hoRm1rWUFnaGhEQ0xGQXdoaEJCbQprWUloaEJEQ0xGSXdoQkJDbUVVS2hnTnEw | |||
|
912 | cVE1R28ybTBrZVRKczNWamlxRXFFVms4VUVIVkh5blFYTytiK2ZjUGtLSWlzbmlnMElJCklXcVVG | |||
|
913 | QXdoaEJCbVVhVmdHQXdHL1B6ODhQSHhZZUhDaGFYZXo4N09adHk0Y1dpMVd2cjI3Y3ZxMWF0VlND | |||
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914 | bUVFT0ptcXN4aGFMVmEKRml4WWdMZTNONUdSa1d6YnRnMVBUMC9qKysrLy96Nzc5dTFqOGVMRm5E | |||
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915 | cDFpbjc5K25IOCtQRy9qdDNmRkY3bU1DcHI2WlRiUndoUgpNWWVadzhqSXlBQWdJaUlDYjI5dkJn | |||
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916 | MGFSRkpTa2trYkR3OFBzckt5eU0vUDUvTGx5elJzMkxCVXNSQkNDR0ZiTnIrbmQzSnlNcjYrCnZz | |||
|
917 | Ym4vdjcrSkNZbUVoMGRiWHh0OU9qUnJGMjdGazlQVHdvS0NraElTQ2kzdjltelp4dS8xdWwwdGY2 | |||
|
918 | ZXVrSUlZU205WG85ZXI2OTIKUHpZdkdPWjQ3NzMzY0hWMTVkeTVjK3pmdjUvbzZHaE9uVHFGaTB2 | |||
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919 | cEhhS2JDNFlRUW9qU2J2MWplczZjT1ZYcXgrYUhwRUpDUWpoeQo1SWp4K2NHREIrblpzNmRKRzRQ | |||
|
920 | QndNTVBQMHpEaGcwSkN3dWpiZHUySER0MnpOWlJhd0ZYdWNCUENHRTFOaThZSGg0ZVFIRlJTRTFO | |||
|
921 | CkpUNCtuckN3TUpNMi9mdjNaKzNhdFJRVkZYSHk1RWt1WDc1c2NoaExtS3VBNHNueGloOVpXVmRV | |||
|
922 | U3lpRWNCeXFISkthUDM4K01URXgKNU9mbkV4c2JpNmVuSjNGeGNRREV4TVR3MEVNUGNlalFJWHIw | |||
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923 | NkVITGxpMVpzR0NCR2pHRkVFTGNSSllHc1JOTm1qUzM4Qzk5ODA2cgpsZE52aFJDM3F1cG5weFFN | |||
|
924 | TzJIK3RSVmdTU0dRZ2lHRXVKWERYSWNoaEJEQ01VbkJFRUlJWVJhN3ZBNURtRXVCSm1lZzBaK1E0 | |||
|
925 | d0U1CnpTQzdHY1dIb29RUXdycWtZRGlhQnVrUUFIVHREVjYvUWE0N1hHOE45VEtoNFNXNDVnVkho | |||
|
926 | OEhSb1hBYUtES25VMWV6bGw1eGQyOUcKWnVibGFuNERRZ2hISlpQZWRxTFNTVyszNjNEUExBaitF | |||
|
927 | SDdQZ045K2dOTzlJTmZqcGtZS3ROa0RuZGRBNTlWUWJ5OXMvQm9PRGFmaQp2UTZaSEJmQ21jaFpV | |||
|
928 | ZzZ1d29KeDU4OHc1Q2s0SFE0YjVoWHZVWmp6QWQ5QkE1R0JrTmNZTnJ3RFowTExHOTI4L3FSZ0NG | |||
|
929 | RXJTTUZ3CmNHVVdERTBoREk2RlR1dGgzUkk0UHJqa2pkSnR5KzRWTkFVUStDbjBmd2tTbjRWZm42 | |||
|
930 | ZjAzb1lVRENHY2lSUU1CMWVxWUxqa3d3T1AKUXNPTDhPWDNrT2QrYzJzc3ZnNmp5V2tZTlJ5dWRJ | |||
|
931 | RFZ5eUMvVVpYNnF5M2JXd2huSnRkaDFDYXVPY1VmN203WFljWDZXNHBGRldYZQpEaDhaSUw4aC9E | |||
|
932 | MGNQUDZvZnA5Q0NLY2lCY1BlMU1tRjBjTWd2d0Y4OVMwVTFMZGUzd1gxaS9jdWZoc0w0L3BCNDNQ | |||
|
933 | VzYxc0lVZXZKCmFiWDJKdXJaNHIyQVZTdEFxVk1EQTJoZys0emlRMTVqQjhESGVyaFJBOE1JSVdv | |||
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934 | ZEtSajJKT2dqNkxBSmxpYlhVTEc0eWJZWG9lNDEKZURRU1BnRnlhblk0SVlUamswTlM5cUlOTVBC | |||
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935 | NStPbzd5RzFpbXpFMy9STk85WUdIS1M0ZVFnaFJBU2tZZGlEOVJqbzhDS3hmQWhmOQpiVGl5cHZp | |||
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936 | NmpvdkE4REdnTWV1eWNDR0VrMUtsWUJnTUJ2ejgvUER4OFdIaHdvV2wzdi9QZi82RFZxdEZxOVhT | |||
|
937 | dFd0WFhGMWR1WHIxCnFncEpiU1AycDFnNEFod2FZZnZCRlJkWVQvR1NJM2UvYWZ2eGhSQU9RNVhy | |||
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938 | TUxSYUxRc1dMTURiMjV2SXlFaTJiZHVHcDZkbm1XM1gKclZ2SC9QbnoyYmh4WTZuM2FzTjFHQnVP | |||
|
939 | YitEcDlVK1Q4bHdLNUt0M1B3emMwK0RKSHZEZFozQnlRTG50SEgxN0N5RWM2RHFNakl3TQpBQ0lp | |||
|
940 | SXZEMjltYlFvRUVrSlNXVjIzN0ZpaFdNSGozYVZ2RnM2a2IrRFNiK01KRkY5eTZDZkpYRFpOMEcz | |||
|
941 | eTZIK3g4dHZzaFBDQ0Z1CllmT0NrWnljaksrdnIvRzV2NzgvaVltSlpiYTljZU1HR3pac1lQanc0 | |||
|
942 | YmFLWjFPdkdWNGpwRzBJZzMwR1Y5N1lGbEw2UWRJVWVIQWsKMU1sVE80MFF3czdZOVdtMWE5ZXU1 | |||
|
943 | ZTY3NzZacDA2Ymx0cGs5ZTdieGE1MU9oMDZucS9sZ1ZyRC93bjcrdS91LzdIdDZuOXBSVEcxNwpB | |||
|
944 | ZG9sd3NEbjRLY0ZhcWNSUWxpQlhxOUhyOWRYdXgrYnoyRmtaR1NnMCtuWXMyY1BBSk1uVHlZcUtv | |||
|
945 | cm82T2hTYmUrLy8zNUdqUnJGClF3ODlWR1pmampxSG9TZ0t1azkwakFrWVEweVBHRUQ5ZTNxYnRL | |||
|
946 | dC9CU1oyaFc4L2gxU2RTVHRIM041Q0NGTU9NNGZoNFZGOC93YUQKd1VCcWFpcng4ZkdFaFlXVmFw | |||
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947 | ZVJrWUhCWU9DKysrNnpkY1FhRjM4eW5ndlhMdkQzNEwrckhhVnNPYzFnL1dJWTl2Zmk5YXlNaW0r | |||
|
948 | MApaTTZqU1pQbXFzVVhRdFFNVlU2cm5UOS9QakV4TVF3WU1JQ0pFeWZpNmVsSlhGd2NjWEZ4eGpi | |||
|
949 | ZmYvODlrWkdSTkdqUVFJMklOVVpSCkZGN1ovQXF6ZGJPcDQxTERWM05YeDlGaGtCWUcvVjY1NmNV | |||
|
950 | Q2l2ZEVLbjlrWlYyeGNXQWhSRTJUNWMxdGJQMng5Y3o4WlNhL1BmVWIKTHByLzFXdTdPaVJWb3VF | |||
|
951 | bGVMb3JyRnhWZkhjL3Mvc3I3dFBSZmpaQ09BdUhPU1RsekJSRjRSLzZmekJITjhla1dOaXRHNTd3 | |||
|
952 | NDBLNAo3N0hpSmRlRkVFN05BVDYxYW8vdmozeVBvaWpjNzN1LzJsSE1kMmdFL0JrQWZlZW9uVVFJ | |||
|
953 | b1RJcEdEWlNwQlR4RC8wL2VQV2VWLzg2Ci9PUkExaThDN1RKb3EzWVFJWVNhcEdEWXlOY0h2NmFS | |||
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954 | V3lPaWZVcWZQbXozcnJlR24rZkNNSXJ2TXk2RWNFb3k2VjNEbWpScFR0YTEKS3pBUitBazRVVkZy | |||
|
955 | TzV2ME5xSEFCQmZZRndlN25qU3JUM3YvMlFqaHJHVFMyMDVsWlYyQk8zK0VnaUE0VVVUNXA2TGFP | |||
|
956 | dzM4Q056egpENmhmZTFjT0ZrS1VUd3FHTFlRdWhCMlRLZjVMM29HZEI0NE9oWWpYMUU0aWhGQ0JG | |||
|
957 | SXlhMWh5NExSbjIxNUlWZHpmOUU0SStnUmJICjFFNGloTEF4S1JnMUxRVFk4eGdVMUpJcjFxKzNM | |||
|
958 | bDZnY05CMHRaTUlJV3hNQ2tZTnVwWjNEUUtCNUtmVmptSmRTYkhnZVFUdTNLQjIKRWlHRURVbkJx | |||
|
959 | RUdmNy9zY1RnRVozbXBIc2E3Q2VzV24yVVpOQlJlMTcvd2toTEFWS1JnMVJGRVUzdHZ4SHBSL00w | |||
|
960 | SEhkblFvWkxhRApIdStyblVRSVlTTlNNR3JJNXRUTnhWK2txaHFqQm1uZ3AzblE5elZva0s1MkdD | |||
|
961 | R0VEVWpCcUNFTGR5eGtVdWdrdFdQVXJJdGQ0T0NECm9KTjFwb1J3QmxJd2FrQmFaaHFHVXdZZTZm | |||
|
962 | YUkybEZxbm40V2RGME9IcWZVVGlLRXFHRlNNR3JBOG4zTEdlRS9nc1oxRzZzZHBlYmQKYUFuSkU2 | |||
|
963 | SHZxMm9uRVVMVU1GVUtoc0Znd00vUER4OGZIeFl1WEZobW0rVGtaRUpDUXZEejgwT24wOWsyWURV | |||
|
964 | b2lzSm4rejdqa2E1TwpzSGRSSW1FNmRGNGpGL01KVWN1cHN2aWdWcXRsd1lJRmVIdDdFeGtaeWJa | |||
|
965 | dDIvRDA5RFMrcnlnSzNicDFZOTY4ZVF3WU1JQkxseTZaCnZGL0NIaGNmL08zOGI5ejM1WDJjbkhJ | |||
|
966 | U0Y0MkxCWGZTczhNNzdsblNyczhiMEdvL3JQckMyTmJlZmpaQ2lHSU9zL2hnUmtZR0FCRVIKRVho | |||
|
967 | N2V6Tm8wQ0NTa2t6UFBkMjVjeWZkdW5WandJQUJBR1VXQzN2MTJiN1BlS1RiSTQ1eFJ6MXJTb3FG | |||
|
968 | RHB1aDlUNjFrd2doYW9qTgpQOVdTazVQeDlmVTFQdmYzOXljeE1kR2t6WVlORzlCb05QVHAwNGVo | |||
|
969 | UTRleVlZTmpYRkZjV0ZUSWl2MHJlTGpydzJwSHNiMjh4ckJ0Ckp0enppdHBKaEJBMXhGWHRBR1hK | |||
|
970 | eWNsaDc5NjliTnk0a1JzM2JqQnc0RUFPSERoQWd3YWwxMk9hUFh1MjhXdWRUcWZxZk1lbWxFMjAK | |||
|
971 | ZFcrTFgwcy8xVEtvYXVkVEVENFhia3VDTTJxSEVVS1UwT3YxNlBYNmF2ZGo4NElSRWhMQ2M4ODla | |||
|
972 | M3grOE9CQm9xS2lUTnFFaDRlVAptNXVMbDVjWEFEMTY5TUJnTUJBWkdWbXF2NXNMaHRvKzMvKzVj | |||
|
973 | NXhLVzU2QyttQjRCZnE5REorcEhVWUlVZUxXUDZibnpLbmF0Vk1XClRYb1hGUldSa0pCQWFtb3FG | |||
|
974 | eTllcEduVHBuVHAwb1h1M2J2ajRtTCswYTJTU2U4NzdyaURxS2lvVXBQZTZlbnBEQjQ4R0wxZVQw | |||
|
975 | NU8KRGoxNzltVDM3dDAwYm14Nm1xbzlUWHBmejd0T3UzbnRPUExNRVZvM2JtMTgzV2ttdlV1NDVN | |||
|
976 | TWtYMWh6Q2xJcnY1MnJ1M3N6TWpNdgptekcyRU1KYXF2clphZFllUmw1ZUh2UG16YU93c0pDbVRa | |||
|
977 | dlNzV05IdW5UcFFscGFHdHUzYjJmVnFsVzBhdFdLS1ZPbVVLZE9uVXI3Cm16OS9QakV4TWVUbjV4 | |||
|
978 | TWJHNHVucHlkeGNYRUF4TVRFMEtKRkN5Wk1tRUNQSGoxbzJiSWxyNzc2YXFsaVlXOVdIMTFOejNZ | |||
|
979 | OVRZcUYKVXlweUEvMXM2RGNXbGhWUjJVMmpzckljL0taU1FqaVJTdmN3Y25OeldiRmlCVU9HREtG | |||
|
980 | bHk1Ymx0anQ1OGlTLy9QSUxUenp4aE5WRApsc2VlOWpEdVhYNHZEM2Q5bUllN21VNTRPOTBlQm9D | |||
|
981 | bUVKNTJoZmoxOFB1OWxmWnBMejlESVp4RlZUODdWYmtPdzFyc3BXQmN1SGFCCnp1OTE1c3kwTXpT | |||
|
982 | cTI4amtQYWNzR0FCK0dvalFRdHd1S3Q3THNJK2ZvUkRPeEdiWFlSdzVjb1FmZnZpQnk1Y3ZjL2p3 | |||
|
983 | WVlzSHJJMisKUFBBbHd6b1BLMVVzbk5waFFOR0EzN2RxSnhGQ1dFbVZDb2FYbHhjOWUvWmsvZnIx | |||
|
984 | ZlBhWm5BN2o5R2RIbFdmVFA2SGZLOFdIcUlRUQpEcy9pZ25IMjdGazJiOTZNVnF0bHhvd1p0Rzd0 | |||
|
985 | M0pPOHY2Zi9UbHBtR3YwNjlGTTdpdjA1SGdYWnpTRGdLN1dUQ0NHc3dPS0NNVzdjCk9IeDlmVm15 | |||
|
986 | WkFuUFBQTU1lL2Z1cllsY0R1UDdJOTl6WCtmN2NIV3h5MnNnVmFZcHZpNmp6eHVnS1ZJN2pCQ2lt | |||
|
987 | cW8xNlgzbHloV2EKTm0zNjE4U3U3ZG5EcEhmdlpiMTV1Yy9MRFBZWlhPYjdUanZwYld5cndCT2hz | |||
|
988 | TzFGT1B4QW1lM1UvaGtLNFd4cWJOSTdOemVYbzBlUApsdmxlczJiTlRJckYxcTFiTFE3Z3lDNWN1 | |||
|
989 | OENCUHcvSTRhZ0thY0R3TWtUOEUvT0xqUkRDSGxWYU1PclZxMGQ2ZWpydnZmZGVtV2RGClpXWm1z | |||
|
990 | blhyVm1KalkybldyRm1OaExSWDY0NnRZOUNkZzZqbldrL3RLUGJ0MkZCd0tRQ2ZIOVZPSW9Tb0Jy | |||
|
991 | TU92Qjg1Y29SWFhubUYKYWRPbVViZHVYUjU1NUJGeWNuTEl6TXpFeTh1THlNaElGaXhZb05xaEti | |||
|
992 | V3NQcnFhQjdzOHFIWU0rNmU0Z09IL0lPSTErSDB3bFYzOQpMWVN3VDJZVmpMMTc5M0xod2dXeXNy | |||
|
993 | SjQ5OTEzR1RCZ0FIMzY5S25wYkhidGV0NTE5S2w2UHZuYkoycEhjUXlIUnNBOXM2RERKa2pwCnIz | |||
|
994 | WWFJVVFWbUhXV1ZMZHUzYWhidHk0dFdyUmcxcXhaN05tenA2WnoyYjM0ay9HRTNCWkNzd2JPZFJp | |||
|
995 | dXlwUTZzUFdsditZeWhCQ08KeUt5Q2taQ1F3SkVqUjRyL2dZc0wzdDdlTlJyS0Vhdyt1cHI3T3Qr | |||
|
996 | bmRnekhzbjgwTkQwRmQyeFRPNGtRb2dyTU9xMVdwOVBSdUhGagpEaDQ4U051MmJXbmF0Q2xqeG95 | |||
|
997 | aFY2OWU3Tnk1azVFalI5b2lheWxxblZaYldGU0kxMXd2ZGo2eEUrK21GUmRQT2EzMkZzRkx3WDhW | |||
|
998 | CmZQNlRzWjJjVml1RWJkWG80b01IRHg2a1M1Y3VRUEdxdEVsSlNTUW5KNU9VbE1UKy9mdkp6TXkw | |||
|
999 | UExFVnFGVXd0cDdheXVRZko3UDMKcWNvdldwU0NjWXM2dVJEckExK3Rnck1oU01FUXd2WlVXNjEy | |||
|
1000 | M3J4NVRKMDZ0VHBkVkpsYUJXUEd6ek5ZT0hjUmVUL25tUGt2cEdDWQpDSDBQT3NiRGw2dVJnaUdF | |||
|
1001 | N2FsV01Bb0xDODI2YVZKTlVLTmdLSXBDcC9jNmNmeGZ4K0djSFg0WTIwVzdTdHE2WnNPVWpzV0hw | |||
|
1002 | UzRFClNjRVF3c1pzdHJ6NXJhcFNMQXdHQTM1K2Z2ajQrTEJ3NGNKUzcrdjFlanc4UE5CcXRXaTFX | |||
|
1003 | djc1VC9zNXMrYndwY1BrRnVUQ09iV1QKT0xDQ0JwQXd2WGlOS1NHRXcxQmx4YndwVTZZUUZ4ZUh0 | |||
|
1004 | N2Mza1pHUmpCNDkydVNlM2dCOSsvWmx6Wm8xYXNTcjBPb2pxeG5XZVJpTApXS1IyRk1lMjh5bVk4 | |||
|
1005 | alo0VnQ1VUNHRWZMTnJET0hQbVRMVUh6TWpJQUNBaUlnSnZiMjhHRFJwRVVsSlNxWGIyZXBoQ1Rx | |||
|
1006 | ZTFrcnpHCmtEZ0ZuUHY2VHlFY2lrVUZZK0RBZ1F3ZVBKaVZLMWVTbjU5ZnBRR1RrNVB4OWZVMVB2 | |||
|
1007 | ZjM5eWN4TWRHa2pVYWpZZnYyN1FRRkJURnQKMmpST25EaFJwYkdzN1Z6V09ZNm1INlZ2Kzc1cVI2 | |||
|
1008 | a2Rka3dDSHpoeDJUNSt2a0tJaWxsMFNPclFvVU5zMzc2ZFpjdVc4Znp6enpOMAo2RkFtVEpoQWNI | |||
|
1009 | Q3dWVU1GQndkeit2UnAzTnpjK09TVFQ1Z3laUXJyMXEwcnMrM3MyYk9OWCt0ME9uUTZuVld6M0d6 | |||
|
1010 | dHNiVkUzUlZGCjNUcDFhMndNcDVMckFjbnc1cTl2c25Ub1VyWFRDRkZyNmZWNjlIcDk5VHRTcXVq | |||
|
1011 | SEgzOVUyclJwbzdScTFVcnAxYXVYa3BDUVlOYS8KdTNyMXFoSVVGR1I4UG1uU0pHWGR1blhsdGk4 | |||
|
1012 | cUtsSmF0V3FsNU9Ua2xIcXZHdkdyNU43bDl5cGY3UC9DT0RZb1pqeXMzVTdOc1dzZwpZNE02Q2kr | |||
|
1013 | ZzRGRnk4NHl5SCs3dXpXejZzeGFpTnF2cVo2ZEZoNlRTMHRKNC9mWFhDUWdJWU5teVpYejg4Y2Vj | |||
|
1014 | TzNlT3hZc1g4OWhqCmo1blZoNGVIQjFCOHBsUnFhaXJ4OGZHRWhZV1p0TGx3NFlKeERtUHQyclYw | |||
|
1015 | NjlhTmV2WFVYVUw4ZXQ1MXRwN2F5dUM3eXI1UmtxaWkKN0VMWS9SejBta1FGOVlLc3JDc3FoaFJD | |||
|
1016 | Z0lXSHBBWVBIc3lFQ1JQUTYvVW1aelVGQmdieTFGTlBtZDNQL1BuemlZbUpJVDgvbjlqWQpXRHc5 | |||
|
1017 | UFltTGl3TWdKaWFHYjc3NWhpVkxsdURxNmtxM2J0MllPM2V1SlRGcmhPR1VBVzBiTFI3MVBkU09V | |||
|
1018 | dnRzbnc2VC9Jb1hKN3pXClJ1MDBRb2h5V0hUaDNvNGRPd2dORGEzME5WdXg1WVY3MHpaTW8xbjla | |||
|
1019 | cnpTOXhYajJIWjVVWnhkdEt0Q24xRlRvTWdOZnY1UHVlMXMKOWJNV29yYXp5WVY3WmUxRnhNVEVX | |||
|
1020 | RHlvSTlwNGNpTUQ3eHlvZG96YWEvdHpvRjBHRFMrcG5VUUlVUTZ6RGtrbEp5ZXpZOGNPTGw2OAp5 | |||
|
1021 | T0xGaTQyVjZlTEZpMDV4VzliejE4NXpPdk0wUGRyMlVEdEs3WlhaRGc0K0NEM253YWJYMVU0amhD | |||
|
1022 | aURXWHNZR1JrWm5ENTltdno4CmZFNmZQazFhV2hwcGFXbDRlWG54MFVjZjFYUkcxVzA4dVpGNzJ0 | |||
|
1023 | K0RxNHNxRjhZN2oyMHZRSS8zb2I1TWNBdGhqeXlhd3poMjdCaWQKT25XcXlUd1dzZFVjeHJqdng5 | |||
|
1024 | SHp0cDQ4SGZLMHlkZ09NejlnODNiVjZQTnY0K0h5bldCNHBWUTdtY01Rd2pwcWRMWGE2T2hvMXE5 | |||
|
1025 | ZgpUL3YyN2YvNm9EUWQrT1RKa3hZUGJBMjJLQmlLb25EYk83ZGhtR0RncnVaM21ZenRjQi9HTm10 | |||
|
1026 | WGpUNWJISVBIZXNPQ2s1RG5idEpPCkNvWVExbEhWejA2empyRXNYNzRjZ0owN2QxbzhnS003ZFBF | |||
|
1027 | UTlWenJjV2V6TzlXTzRoelNPOEhKQVJDeUJINTlYdTAwUW9pYm1GVXcKbWpadENsQnFSVmxuRUg4 | |||
|
1028 | eW5vRWRCNWJhc3hJMWFPdExNSFpnOFZwVCtRM1ZUaU9FK0l0WkJlUENoUXRsZm1BcWlvSkdvNkZW | |||
|
1029 | cTFaVwpEMll2NGsvR016NXd2Tm94bk11ZlhlRjBMK2orQVNRK3EzWWFJY1JmekpyRDhQSHhLVzU4 | |||
|
1030 | UzlFb0tSakhqaDJybVhTVnFPazVqTHpDClBEemY5aVJsU2dvdEdyWW9OYmJEelEvWXJKMFYrdlRh | |||
|
1031 | QXc5SHc0SVR4VGRja2prTUlheW1SaS9jNjlTcEU3Ly8vanQ1ZVhuazUrZVQKbDVkbi9McXF5NXc3 | |||
|
1032 | Z29UVENYVDI3RnlxV0FnYk9LK0ZNNkhRWFZheEZjSmVtTFdIa1pHUmdZZUhCNWN1bGI0S1Y2UFIw | |||
|
1033 | S0tGT2grbwpOYjJIOGZLbWx5bFNpbmlqZitsYmljb2VoZzM2YkxNYlJnK0ZkNDlEUVVQWnd4RENT | |||
|
1034 | bXIwTEttU0ZXYWRiZEk3L21ROGIvWi9VKzBZCnp1dGNNSnp0VWJ5WFVmcW1qRUlJRzdQNDB1Vkxs | |||
|
1035 | eTZ4WWNNR05Cb05rWkdScXUxZDFMUXIyVmM0ZlBFd3ZXN3ZwWFlVNTdabFZ2RmUKeGk2MWd3Z2hM | |||
|
1036 | RnA4Y1BueTVZU0hoNU9Ra01EMjdkc0pEdzgzWHFOUjIyeEsyVVR2TzNwVHoxWGQrM0E0dlpLOURP | |||
|
1037 | dmUxRkVJVVFVVwo3V0g4KzkvL1p1dldyWGg1ZVFIRnA5dEdSa2J5OE1NUDEwZzROVzFNMmNqQWpy | |||
|
1038 | STZyVjNZOGc4WXZZYWNnaHpxdTlaWE80MFFUc3VpClBZem16WnVUbloxdGZKNmRuVTN6NXMydEhz | |||
|
1039 | b2V4SitJWjBESEFXckhFQURudXNNNVdMcEx6cGdTUWsxbUZZekpreWN6ZWZKa1dyWnMKU2ZmdTNi | |||
|
1040 | bnZ2dnNZTm13WXdjSEJ0R3paMHVKQkRRWURmbjUrK1BqNHNIRGh3bkxiSlNjbjQrcnF5cmZmZm12 | |||
|
1041 | eEdOV1JjaVdGYTNuWAo2TnFxcTAzSEZSWFF3MXUvdmtWT1FZN2FTWVJ3V21ZZGt1cmV2YnZ4b3Iz | |||
|
1042 | QmcvOTNUK3NISG5pZ1NrdG1USmt5aGJpNE9MeTl2WW1NCmpHVDA2TkdsenNBcUxDemtoUmRlSUNv | |||
|
1043 | cXl1YW5VOGFmTE42N2tPVkE3TWc1MExiUjh1SHVENWtVT2tudE5FSTRKYk1LeHZqeDQ2MDIKWUVa | |||
|
1044 | R0JnQVJFUkVBREJvMGlLU2tKS0tqbzAzYUxWeTRrQkVqUnBDY25HeTFzYzBWZnpLZUlUNURiRDZ1 | |||
|
1045 | cU5pc3ZyUDQyNWQvNCsvQgpmNWU1RENGVVlORWNSbloyTnF0WHIyYml4SW1NSGoyYU1XUEdNR2JN | |||
|
1046 | R0lzR1RFNU94dGZYMS9qYzM5K2Z4TVJFa3pabnpweGg5ZXJWClBQMTA4ZjBuYlBtWGZtRlJJWnRT | |||
|
1047 | TnNuOGhSM3EwYllIMmpaYS9ydjd2MnBIRWNJcFdYU1cxTXN2djR4R28ySERoZzA4Ly96ekxGKysK | |||
|
1048 | bkx2dnZ0dnFvWjU5OWxuZWZQTk40OVdJRlIyU21qMTd0dkZyblU2SFRxZXIxdGk3eiszR3E3RVh0 | |||
|
1049 | elc1clZyOWlKcFJzcGZ4ZVBEagpzcGNoaEpuMGVqMTZ2YjdhL1ZoMHg3M2c0R0IyNzk1Tmx5NWRP | |||
|
1050 | SGp3SUJrWkdRd1lNTUNpdzBZWkdSbm9kRHIyN05rREZFK29SMFZGCm1SeVM2dGl4bzdGSVhMcDBp | |||
|
1051 | WVlORzdKMDZWS0dEUnRtR3I0R2xnWjVZK3NiL0huOVQrWkh6YSt3blN3Tll2dXhTMzdXUTFZTVlm | |||
|
1052 | QmQKZzNrbTlCa3pzd2doYmxhaml3K1djSE56QTZCSGp4NnNXN2VPQ3hjdWtKTmoyVmtySmN1TUdB | |||
|
1053 | d0dVbE5UaVkrUEp5d3N6S1ROeVpNbgpTVWxKSVNVbGhSRWpSckJreVpKU3hhS21iRHk1VVE1SDJT | |||
|
1054 | VlhOQm9OR28yRzljK3RaOUtYazlDNGFveXZsVHlhTkttZHAza0xZUThzCk9pVDF6RFBQY09YS0Zh | |||
|
1055 | Wk9uY3JNbVRNNWMrWU1yNzc2cXNXRHpwOC9uNWlZR1BMejg0bU5qY1hUMDVPNHVEZ0FZbUppTE83 | |||
|
1056 | UFd2SUsKODloeFpnZDk3dWlqV2daUm5nS01leUpuZ1F2UkVCd055Uk5OV21WbHlabHRRdFFVaXc1 | |||
|
1057 | SndmL1drZ0tJakl4VWRVRkNheCtTU2ppZAp3RE0vUE1QdW1OMW1qVjJiRHZjNFhNYmJkc0NEdzR0 | |||
|
1058 | WHNpMnNaOUpPVnJVVm9tSTJPU1IxODFwU2lZbUo5T3JWcTFhdEpXVTRaYUNQCnQreGRPSVF6b1hD | |||
|
1059 | aEcyaVhxWjFFQ0tkaDBSNUdVRkFRUC8zMFU2bTFwUGJ1M1Z0akFTdGk3VDJNNkJYUlBCYjBHTVA5 | |||
|
1060 | aDVzMWRxMzkKNjczYTdXdzBkcGw3R2JLSElVUmxiTEtIVVp2WGtpb3NLdVRYUDM3bDdqdXNmNXF3 | |||
|
1061 | cUNGblFvdnYveTE3R1VMWWhGbVQzcE1uVHdZdwpyaVZWY3UzRnRtM2JHRGl3ZHF6b3V2L1AvWGcx | |||
|
1062 | OXFKMTQ5WnFSeEdXME0rQ0IwZkNuc2R1bWNzUVFsaGJsZGFTS3ZtNnFtdEoyYU90CnA3WVM0UjFC | |||
|
1063 | a3liTnljcTZvblljWWE0ellmQm5GOUIrQkR1ZlVqdU5FTFdheFdkSkFlemF0UXVOUmtOd3NMcDN0 | |||
|
1064 | YkhtSE1iSXIwY3kKck5Nd3hnYU5SZVlIcXR2T3htTzNTNFNSRDhLN3YwTmhmWm5ERUtJU05wbkRN | |||
|
1065 | QmdNZE9yVWlaZGVlb2tYWDN5UlRwMDZzWFhyVm9zSAp0VGVLb21BNFpTRENPMEx0S0tJcTBuckNu | |||
|
1066 | d0hRSTA3dEpFTFVhaFpkdVBmMjIyK3paczBhNCtLQlI0OGVaZnIwNmZUcDQ5aW5vdjUrCitYZnF1 | |||
|
1067 | OWJIdTZtMzJsRkVWVzE4RXg0ZENPcWNzQ2VFVTdCb0QrUHk1Y3UwYmR2VytMeE5telpjdm56WjZx | |||
|
1068 | RnN6WERLSUZkM083b0wKM2VCNEZQUldPNGdRdFpkRmV4aVBQdm9vMGRIUmpCdzVFa1ZSK1BiYmJ4 | |||
|
1069 | azdkbXhOWmJNWk9SeFZTMngrRFdJKzVXeldXZHE2dDYyOAp2UkRDSW1aUGVpdUt3cmx6NXpoLy9q | |||
|
1070 | enIxcTFEbzlFd1pNZ1F0RnB0VFdjc2w3VW12VHNzNk1BUFkzN0FyNldmaWhmazJlbUVjcFhhCnFU | |||
|
1071 | ajJRQTFQVEg2Q0Q0WitZRWFmUWppbnFuNTJXbFF3dW5idHlvRURCeXdlcEtaWW8yQ2N6amhOOEFm | |||
|
1072 | Qi9EbmpUK09LcC9KaFhOMTIKS281ZFgwUExWMXV5WmZ3Vy9GcjZtZEd2RU02bnhzK1MwbWcwaElX | |||
|
1073 | RnNYNzllb3NIc1dkYi95aSsvcUsyWEUvaTlITGcrZDdQOCtJdgpMNnFkUkloYXg2Sko3NlNrSklZ | |||
|
1074 | T0hZcVhseGRhclJhdFZxdjZ0UmpWSlJQZXRjK2swRW5zT2IrSFgvLzRWZTBvUXRRcUZrMTZyMTY5 | |||
|
1075 | CnV0WmRGR1U0WmVESjdrK3FIVU5ZVVgzWCtyeDJ6MnM4Ri84Y3Z6NzJxK3c5Q21FbFp1MWg1T2Zu | |||
|
1076 | czI3ZE9wWXVYY3JwMDZmcDJMRWoKZDkxMWwvSGhxQzVldjhpWnJETUV0ZzVVTzRxd3NvZTdQc3ox | |||
|
1077 | L090OGYrUjd0YU1JVVd1WVZUQmVldWtsbGl4WlFzdVdMWG4xMVZlWgpQNy9pKzExWHhtQXc0T2Zu | |||
|
1078 | aDQrUER3c1hMaXoxL3VyVnF3a01EQ1FvS0lqbzZHaUw3aGx1aVcxL2JLUFg3YjJvNDFLblJ2b1g2 | |||
|
1079 | cW5qClVvZTNCcnpGaTcrOFNFRlJnZHB4aEtnZEZETUVCd2NyZVhsNWlxSW95cFVyVjVTSWlBaHov | |||
|
1080 | bG01Z29LQ2xDMWJ0aWlwcWFsSzU4NmQKbFlzWEw1cThmKzNhTmVQWGVyMWU2ZE9uVDVuOW1CbS9Y | |||
|
1081 | TS8rOUt6eWh1R05VbjJDWXNaRHJYYVNzYkoySllxS2lwUituL1JUM2s5Kwp2MXIvUHhHaXRxbnFa | |||
|
1082 | NmRaZXhoRlJVVzR1YmtCMExScFV6SXpNNnRjb0RJeU1nQ0lpSWpBMjl1YlFZTUdrWlNVWk5LbVVh | |||
|
1083 | TkdKdTNyCjE2OWY1ZkVxc3ZYVVZybkRYaTJtMFdoNGU4RGJ6Tmt5aCt0NTE5V09JNFRETTJ2U2U5 | |||
|
1084 | KytmYmk3dXh1ZloyZG5HNTlyTkJxTENraHkKY3JKeExTb0FmMzkvRWhNVGlZNk9ObW4zM1hmZk1Y | |||
|
1085 | WHFWSzVkdThhdVhidks3Vy8yN05uR3IzVTZIVHFkenF3Y21ibVpITGwwaEpDMgpJV1puRjQ3QXRm | |||
|
1086 | UWs5M0JvdktZeEdFeGZkbmR2Um1hbTR5OXRJMFJsOUhvOWVyMisydjJZVlRBS0N3dXJQWkNsN3Iv | |||
|
1087 | L2Z1Ni8vMzYrCit1b3IvdmEzdjdGbno1NHkyOTFjTUN5eC9mUjJ1cmZ0VGoxWHVlbE83VkpBcVF2 | |||
|
1088 | OE5wMkVKMEpoMXlHNDNzcjRjbGFXbkQwbG5NT3QKZjB6UG1UT25TdjFZZEIyR05ZU0VoSERreUJI | |||
|
1089 | ajg0TUhEOUt6Wjg5eTI0OGFOWXF6WjgrYTNCcldHa291MkJOTzRFcEgyUGN3NkdhcgpuVVFJaDJi | |||
|
1090 | aTNkZEpBQUFjV1VsRVFWVHpndUhoNFFFVW55bVZtcHBLZkh3OFlXRmhKbTFPbkRoaHZON2poeDkr | |||
|
1091 | b0h2MzdqUm8wTUNxCk9ReW5ERVRjSVFYRGFXeVpCWDdmUXB2ZGFpY1J3bUZaZE9HZXRjeWZQNStZ | |||
|
1092 | bUJqeTgvT0pqWTNGMDlPVHVMamltOS9FeE1Td2F0VXEKUHYzMFU5emMzTkJxdGJ6OTl0dFdIVCtu | |||
|
1093 | SUljOTUvWVFmbnU0VmZzVmRpeTdPZnp5QnR6N0RDejdGY3c3MzBNSWNaTXEzYUxWWGxSMQpBUzNE | |||
|
1094 | S1FNemZwN0JqaWQybE5tbkxPeFgzWFpxamwxQk8wMFJQTlliZGo4QmV4NERySGVMWHlFY2lVMXUw | |||
|
1095 | VnBiR0U0WjVIUmFaNlM0CndBK0xvUDlMMEVET2poTENVazVaTUxiK3NWWG1MNXpWdVdBNE5BTDZ2 | |||
|
1096 | YXgyRWlFY2p0TVZqSUtpQWhKT0ozRDNIWGVySFVXb1pkTnIKNFBzZHRGRTdpQkNPeGVrS3hwNXpl | |||
|
1097 | N2pENHc1YU5HeWhkaFNobHB4bThNdS9JQnFLbENLMTB3amhNSnl1WUNTa0pkRDdqdDVxeHhCcQor | |||
|
1098 | MjBzRk1HeVBjdlVUaUtFdzNES2doSGVUazZuZFhxS0Mvd0EvN2ZwLzBpL2thNTJHaUVjZ3RNVmpN | |||
|
1099 | UzBSSHEySy8vS2N1RkV6c09vCkxxUDR2MDMvcDNZU0lSeUNVeFdNODlmT2s1R1RRYWNXbmRTT0l1 | |||
|
1100 | ekVxL2U4eXVxanEwaytVelAzWEJHaU5uR3FncEdVbGtSWXV6QmMKTkU3MWJZc0tOSzNmbExjR3ZN | |||
|
1101 | WEVIeVpTV0dUN1JUYUZjQ1JPOWNtWmtKWkF6OXZrY0pRdzlXaTNSMm5vMXBCM2s5NVZPNG9RZHMy | |||
|
1102 | cApDb2JNWDRpeWFEUWFsZzFieHV0YlgrZm9wYU5xeHhIQ2JqbE53U2dvS21EWHVWMkUzaGFxZGhS | |||
|
1103 | aGgrNXNmaWR6ZEhNWXYzcThISm9TCm9oeE9VVENhTkdtTzIyMXVYRHR6amVZTm02UFJhTXA5Q09m | |||
|
1104 | MWRNalROSEJ0d055RXVXcEhFY0l1T1VYQnlNcTZBdTBXUTlvRWlsY3kKcmVnaG5KV0x4b1ZsOXkz | |||
|
1105 | ajM5di96Y0UvRDZvZFJ3aTc0eFFGQTRCMmlaQW04eGVpWXUyYnR1ZjFmcTh6N3Z0eDVCZm1xeDFI | |||
|
1106 | Q0x1aQpTc0V3R0F6NCtmbmg0K1BEd29VTFM3Mi9mUGx5QWdNRENRd01aTXlZTVJ3N2RxejZnMHJC | |||
|
1107 | RUdaNkl2Z0pXalJzd1Z1L3ZxVjJGQ0hzCmlpbzNVTkpxdFN4WXNBQnZiMjhpSXlQWnRtMGJucDZl | |||
|
1108 | eHZjVEVoTHc5L2ZIdzhPRFR6NzVoSTBiTi9MWlo1K1Y2c2ZjbTRCb0dtcmcKV1hkNDh3b29kU3By | |||
|
1109 | amQzZCtNZHV4cTV0R2QyQWdyTGZhZ0xFQUorQys0MW1aR2JLL1RORTdlRXdOMURLeU1nQUlDSWlB | |||
|
1110 | bTl2YndZTgpHa1JTVXBKSm0vRHdjT085djZPam85bXlaVXYxQm0wSG5Ba3hvMWdJNTFKQXVYTlpt | |||
|
1111 | UXJFZndUM0I1SjE0NHFhSVlXd0d6WXZHTW5KCnlmajYraHFmKy92N2s1aVlXRzc3RHo3NGdLRkRo | |||
|
1112 | MVp2MEhiSTRTaGh1YjNqSU9OMmtIdHRDUUdBcTlvQktySng0MFkrLy94enRtL2YKWG02YjJiTm5H | |||
|
1113 | Ny9XNlhUb2RMclNqZG9CU2JKQ3JiQ1VCdForQURGdDBhZnEwYlhYcVIxSWlDclI2L1hvOWZwcTky | |||
|
1114 | UHpPWXlNakF4MApPaDE3OXV3QllQTGt5VVJGUlJFZEhXM1NidCsrZlR6d3dBUDg5Tk5QM0hYWFhX | |||
|
1115 | WDJaYzV4dUNLbGlEb3YxWUYzLzRRYkxjMUk2QWpICjNpVmo5ZHRaMExhamhqWVQyN0RyeVYyMGNa | |||
|
1116 | ZmI5QW5INXpCekdDVnpFd2FEZ2RUVVZPTGo0d2tMQ3pOcDg4Y2ZmekI4K0hDV0wxOWUKYnJFdzEr | |||
|
1117 | R0xoK0VHWmhZTEljcHdFbUs2eHpCNjFXZ0tpc3FaSkJmQ0NhaHlXdTM4K2ZPSmlZbGh3SUFCVEp3 | |||
|
1118 | NEVVOVBUK0xpNG9pTAppd1BnMVZkZjVmTGx5enoxMUZOb3RWcENRNnUrbkVkaVdpS2tXU3U1Y0ZZ | |||
|
1119 | dlI3eE0zVHAxZVdYeksycEhFVUkxcXB4V2F5M203Rlk5CnNmWUpQbnp0UTBoMndrTXBrdEZxZlNx | |||
|
1120 | S3dzWHJGK24rUVhjV1J5OW1TS2NoWm80aGhQMXhtRU5TdHBad09rSDJNSVJWdEd6VWtpOUgKZk1u | |||
|
1121 | amF4NG45V3FxMm5HRXNMbGFYVEF5Y2pLS2Y3RXZxSjFFMUJhOWJ1L0ZDNzFmWU9UWEk4a3R5RlU3 | |||
|
1122 | amhBMlZhc0xSdkxaWklMYgpCRU9SMmtsRWJUSzE1MVJ1YjNJNzAzNmVwbllVSVd5cVZoZU1oTk1K | |||
|
1123 | Y3NNa1lRV3VKa3ZndTdpNDhOMjQ3MWk4WVRHYXdQKzkzcVJKCmM3V0RDbEdqYW5YQlNEd2pkOWdU | |||
|
1124 | MWxER0VpSzVDbnk1RHlKYmd2Y1dRQ2xlUmwrSVdxeldGZ3hGVWVTV3JLSm0vZGtWVmkySGtTT2gK | |||
|
1125 | NVNHMTB3aFI0MnB0d1RoKytUaU42emFtclh0YnRhT0kydXprUUloL0d4NitGeHFySFVhSW1sVnJD | |||
|
1126 | MFpDbXN4ZkNCdjViUnpzZmh3ZQpocXpjTExYVENGRmphbTNCU0V4THBPZHRVakNFalJoZWhyUHc0 | |||
|
1127 | RGNQeXAzNlJLMVZ1d3VHN0dFSW05SEFldENnNGVuMVQxZnBLbG9oCjdGMnRMQmpYODY1ek5QMW84 | |||
|
1128 | VFVZUXRoS0Vhd2N1Wkk5NS9md1Q4TS8xVTRqaE5YVnlvS3g4K3hPdXJicVNqM1hlbXBIRVU2bWNk | |||
|
1129 | M0cKckIrem5tVjdsN0ZveHlLMTR3aGhWWFo5QTZXcWtzTlJRazFlamIzWU5IWVQvVDd0UjE1aEhs | |||
|
1130 | UERwNm9kU1FpcnFKVjdHSWxuRWdsdgpKM2ZZRStycDBLd0RXOFp2WWZIT3hmeHI2Ny9VamlPRVZk | |||
|
1131 | UzZnaUVYN0FsN2NZZkhIV3dadjRWUDkzM0tMUDBzbVFnWERxL1dGWXhUCkdhZUE0bDlXSWRUVzFy | |||
|
1132 | MHQrbkY2dmozOExTLys4cUlVRGVIUVZDa1lCb01CUHo4L2ZIeDhXTGh3WWFuM2p4dzVRbmg0T1BY | |||
|
1133 | cjEyZnUKM0xrVzlWMnlkNkhSYUt3VlY0aHFhZDI0Tlp2SGJXYkRpUTFNKzNtYUZBM2hzRlFwR0ZP | |||
|
1134 | bVRDRXVMbzZOR3pleWFORWlMbDI2WlBKKwppeFl0V0xod0lUTm16TEM0NzhRMG1iOFE5c2V6b1Nl | |||
|
1135 | YnhtN2kxejkrWmVJUEV5a3NLbFE3a2hBV3MzbkJ5TWpJQUNBaUlnSnZiMjhHCkRScEVVbEtTU1p1 | |||
|
1136 | V0xWdlNvMGNQM056Y0xPNWZsZ1FSNmpGZEJ2M1dSL09HelVtZW5NelNWUjh5NUlzaFhNMjVxblpn | |||
|
1137 | SVN4aTg0S1IKbkp5TXI2K3Y4Ym0vdnorSmlZbFc2VHVuSUljRGZ4NmdlNXZ1VnVsUENNdVVzUXg2 | |||
|
1138 | R2N1aUYzNVN3RjNON3lMc3d6Q09YanFxWGx3aApMT1R3MTJITW5qM2IrSFZMLzViNGV2clNxRzRq | |||
|
1139 | OVFJSlVaa2lXRGg0SVV0M0xhWFBSMzM0NUcrZk1OaG5zTnFwUkMybTErdlI2L1hWCjdzZm1CU01r | |||
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1140 | SklUbm5udk8rUHpnd1lORVJVVlZ1YitiQzhhOGhIbjBiQ3lIbzRSamVLTDdFL2kxOUdQazF5T1pI | |||
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1141 | ajZkNmVIVDVXUU4KVVNOME9oMDZuYzc0Zk02Y09WWHF4K2FIcER3OFBJRGlNNlZTVTFPSmo0OG5M | |||
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1142 | Q3lzekxhV25rMlNrSllnSzlRS2gzTDNIWGVUOVBjawpWdXhmd2Rqdng1SlRrS04ySkNIS3BWRlVP | |||
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1143 | TWR2eTVZdFBQWFVVK1RuNXhNYkcwdHNiQ3h4Y1hFQXhNVEVjUDc4ZVVKQ1Fzak16TVRGCnhRVjNk | |||
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1144 | M2NPSFRwRTQ4YW1kNmpSYURRbVJlV09lWGZ3eTloZjhHbmhVNnBkOFRGa2M1amJWcTEyYW80dEdh | |||
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1145 | M1Y3dFpmdXh2NU4zaHMKOVdNY1N6L0dwL2QvU2tDckFEUDZFYUpxYnYzc05QdmZxVkV3ck9YbWIv | |||
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1146 | cE01aGtDM3cvazRuTVhTKzNXUzhHd2RUczF4M2FNakdYOQoyaW1Ld29lN1ArU2xUUzh4STN3R00z | |||
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1147 | ck5vSTVMSFRQNkU4SXlUbHN3alB3QUxiQ2l2TmIyL3lFaUdXM1pUczJ4Sy81bFRiMmF5b1RWCkU4 | |||
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1148 | Z3R5T1hqdjMxTXB4YWR6T2hUQ1BOVnRXRFVncVZCL2pwZHNkME1TSHZ0Zjg5TkhrSTRqdlpOMi9Q | |||
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1149 | TDJGOTRLT0FoZXYyM0YrOG0KdlV1UlVxUjJMQ0ZxUThINFM3dEVTSk1KYjFFN3VHaGNpQTJMWmZ2 | |||
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1150 | ajIvbnl3SmYwLzdRL3h5OGZWenVXY0hLMW8yQzQ1RU9iUFhBbQpWTzBrUWxoVnB4YWQyRHBoSzlF | |||
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1151 | KzBmVDhzQ2RUTjB6bGN2Wmx0V01KSjFVN0NrYnJmWENsQStRMlVUdUpFR2FvZUFtUm14OU5talNu | |||
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1152 | Cmprc2RadlNhd2NHSkI4a3R5S1h6ZTUxNUorRWRjZ3R5MWY1R2hKT3BIUVhqOWdRNUhDVWNpQmxM | |||
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1153 | aVB6MXlNcTZZdnhYclJ1M1puSDAKWWd6akRlaFQ5Zmd0OG1QbHdaV3krcTJ3bVZwd2xwUUNEendD | |||
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1154 | S2YxZ3oyUGx0Y1FSenB5UmpMWnNwK2JZbG1VczcxZDBjOHBtWnNUUAp3TTNGamYvcjgzOUVkNHJH | |||
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1155 | UlZNNy9nWVVOY3VKVDZ0VklQWXUrR0lOWFBRdnJ5VzE3VU5FTWxhM25acGpXNmRnQUJRcFJhdzh1 | |||
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1156 | SkovCmIvODMxL091TTdYblZCNE5mSlNHYmczTjdGODRvNm9XRElkZmZKQkdmMExEUzNESnQvSzJR | |||
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1157 | amdjVjdQV2wycnMzcFIxKzc1bmJzSmMKWHRuOENrLzFlSXBuUXA2aGRlUFdOc2dvbklYajc3L2Vs | |||
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1158 | bFI4ZHBUaStOK0tFS1daTjk5eExlc3FmZHYzWmMzb05XeWRzSldMTnk3aQp1OGlYOGQrUFoxUEtK | |||
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1159 | cmxoazdBS3h6OGsxZThsS0hJRmZVV3JMOWErd3hTU3NicnQxQnk3WmpMZStxdDg2Y1lsUHQ3N01W | |||
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1160 | OGMrSUp6CldlY1lGVENLTVFGajZORzJoNnlLNitTY2R3NWpiRC9ZUGdPT1YzUS9BZWY5RUpHTTlq | |||
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1161 | aTJiUXJHelk1Y09zSVhCNzVneGY3aXRYUEcKZEIzRDZJRFIrSHJLb1Z4bjVMd0Y0MFYzbUo4SzJj | |||
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1162 | MHJhb216Zm9oSVJuc2MyL1lGbzRTaUtPdzh1NU12RG56Qmx3ZStwRW05Smd6bwpPSUQrSGZxamE2 | |||
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1163 | K2pXWU5tWnVZU2pzeDVDOGFrenZEZWtjcGE0cXdmSXBMUkhzZXVpWXh1Rk05M1ZNemR2Um1abWNW | |||
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1164 | WGloY3BSZngyCi9qYzJudHpJTHltLzhPdnBYL0h6OURNV2tONTM5S2ErYTMwemN3cEg0cndGNDIv | |||
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1165 | ajRQdVBLMnVKYzM2SVNFYjdIRnZkak9YOXl1Y1cKNUpLWWxzakdsSTM4Y3ZJWDl2KzVuKzV0dWhQ | |||
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1166 | Y0pwZ2dyeUNDdklMdzgvVERyWTZibWRtRnZYTGVndEZqQ2V4OHFyS1d5SWVJTGR1cApPYlprckt5 | |||
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1167 | ZHViL3ltYm1aSkp4T1lPLzV2ZXk5c0plOTUvZHk2dW9wZkQxOWpRVWt5Q3VJd05hQmVOVDNNS3RQ | |||
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1168 | WVI4Y3FtQVlEQVppClltSW9LQ2dnTmphV3laTW5sMnJ6NG9zdjh0VlhYOUdzV1RPV0wxK09yMi9w | |||
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1169 | eVRtTlJnTmVlK0I4VUNVanF2MGhzaG5RV2FrL1M4ZTIKcEoyZWluUGFRMGFvT0tka3JKamxoNjV1 | |||
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1170 | ZGozdk9nZitQR0JTUlBaZjJFOTkxL3A0Ti9XbWZkUDJ4UStQNHYrV3ZOYWtYdlhXZWRQcgo5U2Iz | |||
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1171 | cExaWGpwTFRvUzdjbXpKbENuRnhjWGg3ZXhNWkdjbm8wYVB4OVBRMHZyOWp4dzYyYnQzS3pwMDcy | |||
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1172 | YkJoQXpObXpHRGR1blZsCmQvYW5JOXpLVWsvbEJjTWU2SkdjMXFMSFBqT1dYTmRSWXZaZkQxTlpX | |||
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1173 | V1dmZHR1b2JpUEMyb1VSMWk3TStKcWlLRnk4Y1pIVXE2bWMKdW5xSzFLdXBIRWsvd2s4bmZqSytW | |||
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1174 | cmRPWGRvM2JjL3RIcmZqMmRDVEZnMWEwS0pCQzVvM2FFNkxocVcvcnVkYXoyUmNSL2tnZHBTYwpW | |||
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1175 | V1h6Z3BHUmtRRkFSRVFFQUlNR0RTSXBLWW5vNkdoam02U2tKRWFNR0VIejVzMFpQWG8wTDcvOGN2 | |||
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1176 | a2RGam4reGVwQzJCL3pyakF2CjVnYmtWOWppZXNQcjVMWXQ0T1UxTDVOK0k1MzA3T0xIc2N2SFNM | |||
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1177 | K1J6dVhzeThXdi9mVzFXeDIzNHFMU3NMaVFuRGx3aHFPcmpsTGYKdFQ0TlhCdlF3SzFCOFg5di92 | |||
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1178 | cXYvOVozclYvcXRaTC8xbk90UngxTkhlcTQxTUZGNDBJZHpWLy8vZXU1cUpqTlAyMlRrNU5ORGkv | |||
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1179 | NQorL3VUbUpob1VqQjI3TmpCbzQ4K2FuemVzbVZMVHB3NHdaMTMzbW5UckVJNHIxdjNSQ3BpeHVH | |||
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1180 | d0czRGp1QnZEL1lkWDJsdGo5NmFjCnZmZ0g2ZGwvRlpJYjZmeDN4MzhaMm1rbzJmblpaQmRrazUy | |||
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1181 | ZlRVNUJEdGZ6cjNNcCs1TEo2emUvZit0cnVZVzVGQllWVXFRVVVhajgKOWQraVFncVY0aXZoeXlv | |||
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1182 | aVpUMHY3NzMwNUhTK1hmSnRtVzFkTkM1b0tDN0NOeGRqdFY2ckNydjg4MXhSbEZMSDE4ci9SczNk | |||
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1183 | QUpacwpLR3YzT2Vldmg3WDZzNlN0cGUwcXkya1BHYUhpbkpMUnNuYmw1YXlKakpXN2xuV1ZKdlZM | |||
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1184 | ejNsOHRlZ3JxNDFSbnFLLy9sY2RGMys0CmFLVTA5c2ZtQlNNa0pJVG5ubnZPK1B6Z3dZTkVSVVda | |||
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1185 | dEFrTEMrUFFvVU5FUmtZQ2NQSGlSVHAyN0ZpcUx3Yyt3VXNJSVJ5T3pRL2EKZVhnVW4zNW5NQmhJ | |||
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1186 | VFUwbFBqNmVzTEF3a3paaFlXR3NXcldLOVBSMFZxeFlnWitmbjYxakNpR0V1SVVxaDZUbXo1OVBU | |||
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1187 | RXdNK2ZuNQp4TWJHNHVucFNWeGNIQUF4TVRHRWhvWnk5OTEzMDZOSEQ1bzNiODdubjMrdVJrd2ho | |||
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1188 | QkEzVSt6Y2xpMWJGRjlmWCtXdXUrNVMzbjMzCjNUTGJ6Snc1VStuUW9ZTVNIQnlzSEQ1ODJNWUpp | |||
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1189 | MVdXYy9QbXpVcVRKazJVb0tBZ0pTZ29TSG50dGRkc25uSENoQWxLcTFhdGxJQ0EKZ0hMYjJNTzJy | |||
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1190 | Q3luUFd4TFJWR1VQLzc0UTlIcGRJcS92Ny9TdDI5Zlpmbnk1V1cyVTN1Ym1wTlQ3VzJhbloydGhJ | |||
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1191 | YUdLb0dCZ1VwWQpXSmp5emp2dmxObE83VzFwVGs2MXQrWE5DZ29LbEtDZ0lHWElrQ0Zsdm0vcDly | |||
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1192 | VDdnaEVVRktSczJiSkZTVTFOVlRwMzdxeGN2SGpSCjVQMmtwQ1NsZCsvZVNucDZ1ckppeFFvbE9q | |||
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1193 | cmFMbk51M3J4WkdUcDBxQ3JaU2hnTUJtWDM3dDNsZmhEYnk3YXNMS2M5YkV0RlVaUnoKNTg0cGUv | |||
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1194 | YnNVUlJGVVM1ZXZLaDA2TkJCeWN6TU5HbGpEOXZVbkp6MnNFMnZYNyt1S0lxaTVPVGtLRjI2ZEZG | |||
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1195 | Ky8vMTNrL2Z0WVZzcQpTdVU1N1dGYmxwZzdkNjR5WnN5WU12TlVaWHZhOVluSE4xK3o0ZTN0YmJ4 | |||
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1196 | bTQyYTNYck54K1BCaHU4d0o2ay9TOStuVGgyYk55bCtOCjFCNjJKVlNlRTlUZmxnQmVYbDRFQlJX | |||
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1197 | dk11RHA2VW1YTGwzWXVYT25TUnQ3MktibTVBVDF0Mm5EaHNXM2xiMTI3Um9GQlFYVXEyZDYKOFo0 | |||
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1198 | OWJFdW9QQ2VvdnkwQjB0TFMrT0dISC9qNzMvOWVacDZxYkUrN0xoamxYYk54c3gwN2R1RHYvNzk3 | |||
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1199 | ZVpkY3MyRkw1dVRVYURScwozNzZkb0tBZ3BrMmJadk9NNXJDSGJXa09lOXlXeDQ4ZjUrREJnNFNH | |||
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1200 | aHBxOGJtL2J0THljOXJCTmk0cUtDQXdNcEhYcjFreWFOSW5iCmI3L2Q1SDE3MlphVjViU0hiUWt3 | |||
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1201 | ZGVwVS92M3ZmK1BpVXZiSGZGVzJwMTBYREhNb0ZsMnpvWjdnNEdCT256NU5jbkl5L3Y3K1RKa3kK | |||
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1202 | UmUxSXBjaTJySnFzckN4R2pSckZ2SG56YU5Tb2tjbDc5clJOSzhwcEQ5dlV4Y1dGMzM3N2plUEhq | |||
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1203 | N040OFdMMjdObGo4cjY5Yk12SwpjdHJEdGx5M2JoMnRXclZDcTlXV3U3ZFRsZTFwMXdVakpDU0VJ | |||
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1204 | MGYrZDYrTGd3Y1Awck5uVDVNMkpkZHNsQ2p2bW8yYVpFNU9kM2QzCkdqWnNpSnViRzQ4Ly9qakp5 | |||
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1205 | Y25rNXViYU5HZGw3R0ZibXNPZXRtVitmajdEaHcvbjBVY2Y1Yjc3N2l2MXZyMXMwOHB5MnRNMmJk | |||
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1206 | KysKUGZmZWUyK3B3N3Iyc2kxTGxKZlRIcmJsOXUzYldiTm1EUjA2ZEdEMDZORnMyclNKc1dQSG1y | |||
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1207 | U3B5dmEwNjRMaEtOZHNtSlB6d29VTAp4bXErZHUxYXVuWHJWdWF4VHpYWnc3WTBoNzFzUzBWUmVQ | |||
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1208 | enh4d2tJQ09EWlo1OHRzNDA5YkZOemNxcTlUUzlkdXNUVnExY0JTRTlQCjUrZWZmeTVWMk94aFc1 | |||
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1209 | cVRVKzF0Q2ZER0cyOXcrdlJwVWxKUytQTExMK25YcngrZmZ2cXBTWnVxYkUrN1hCcmtabzV5elVa | |||
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1210 | bE9iLzUKNWh1V0xGbUNxNnNyM2JwMVkrN2N1VGJQT0hyMGFMWnMyY0tsUzVlNC9mYmJtVE5uRHZu | |||
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1211 | NStjYU05ckl0Szh0cEQ5c1M0TmRmZitYegp6eituVzdkdWFMVmFvUGdYOVk4Ly9qQm10WWR0YWs1 | |||
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1212 | T3RiZnB1WFBuR0RkdUhJV0ZoWGg1ZVRGanhnemF0R2xqZDcvcjV1UlVlMXVXCnBlUlFVM1czcDBQ | |||
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1213 | ZlFFa0lJWVR0MlBVaEtTR0VFUFpEQ29ZUVFnaXpTTUVRUWdoaEZpa1lRZ2doekNJRlExaVZpNHNM | |||
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1214 | TTJiTU1ENy8KejMvK3c1dzU1dHc4eW5wME9oMjdkKzhHSURvNm1zek16R3IxcDlmckdUcDBxTm12 | |||
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1215 | MThSWU5lbnMyYk9NSERuU3BtTUt4eVFGUTFoVgozYnAxK2U2NzcwaFBUd2NzdnhLM3NMQ3cyaGx1 | |||
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1216 | SG5QOSt2VTBhVkw2N20zaWY5cTJiY3ZYWDMrdGRnemhBS1JnQ0t0eWMzUGp5U2VmClpONjhlYVhl | |||
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1217 | TzN2MkxGT21UQ0V3TUpDcFU2ZHk0Y0lGQU1hUEg4KzBhZE1JQ3d2amhSZGVZTUtFQ1V5ZlBwM1Ew | |||
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1218 | RkE2ZCs3TW5qMTcKZVBMSkorblNwUXV6Wjg4MjlqZHg0a1JDUWtMbzFhc1hTNWN1TFROUCsvYnRT | |||
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1219 | VTlQNS8zMzMwZXIxYUxWYXVuUW9RUDkrdlVEaXRjQgpHenQyTEdGaFljeWNPZE40Ulc1eWNqTDkr | |||
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1220 | L2RIcTlXeVljT0dTci92N094czNubm5IZnIyN1V0MGREUjZ2UjZBOFBCd2s2dHBTL1orCmNuSnl5 | |||
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1221 | bXhmbnRPblR6TjQ4R0NDZ29JSURBemt4SWtUcEthbTR1L3Z6K09QUDQ2Zm54OXo1c3d4NW4vdHRk | |||
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1222 | Y0lEUTBsSkNTRU45NTQKdzZTZjZkT25vOVZxNmQ2OU95a3BLYVNtcHRLMWExY0FQdjc0WXg1NjZD | |||
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1223 | SHV2ZmRlQWdJQ2VQZmRkNDMvOXFlZmZpSThQSnpRMEZDZQpmZlpaSmsrZVhDcm4zcjE3NmQrL1Aw | |||
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1224 | RkJRUVFIQjNQdDJyVkt0NTF3SU5WWk9sZUlXelZ1M0ZqSnpNeFUycmR2cjJSa1pDai8rYzkvCmxO | |||
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1225 | bXpaeXVLb2loVHAwNVYzbjc3YlVWUkZPV05OOTVRbm4vK2VVVlJGR1hjdUhGSzM3NTlqVXR1ang4 | |||
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1226 | L1hoazhlTENTbTV1cmZQengKeDByanhvMFZ2VjZ2NU9ibUtuNStmc2FsNHk5ZnZxd29pcUxrNXVZ | |||
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1227 | cVlXRmh5clZyMXhSRlVSU2RUcWZzMnJWTFVSUkZhZCsrdlpLZQpubTdNbDUrZnIvVHAwMGRadDI2 | |||
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1228 | ZHNlM1ZxMWNWUlZHVTU1OS9Ydm55eXk4VlJWR1VidDI2S1VsSlNjcTFhOWVVcUtpb01wZUgzcng1 | |||
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1229 | CnMvRStBeDk5OUpHeVlNRUNSVkVVNWZ6NTgwcG9hS2lpS0lveWI5NDhaZGFzV1lxaUtNclpzMmVW | |||
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1230 | enAwN1Y5ais1ajV2Tm12V0xPWEQKRHo4MGZnL1oyZGxLU2txS290Rm9sRysvL1ZiSnljbFJIbmpn | |||
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1231 | QWVXYmI3NHgyVFlGQlFYSzBLRkRsU05IamhpMzlhSkZpNHpiN2NhTgpHMHBLU29weEtmbVBQdnBJ | |||
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1232 | YWRXcWxYTDI3RmtsTXpOVGFkZXVuWktYbDZmazUrY3I3ZHUzVjFKU1VwVDA5SFFsT0RoWW1UeDVj | |||
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1233 | cW1jCjQ4YU5Velp1M0tnb1N2RXk0QVVGQmFYYUNNY2xleGpDNnR6ZDNSazdkcXpKWDZjQVAvNzRJ | |||
|
1234 | NDg5OWhnQWp6LytPR3ZYcmdXS0R5R04KR0RFQ2QzZDNZOXNSSTBaUXQyNWR3c1BEYWRxMEtYMzc5 | |||
|
1235 | cVZ1M2Jwb3RWcmpTc0R4OGZGRVIwZWoxV281ZWZJa216WnRxalJiYkd3cwovZnYzSnpvNm1sMjdk | |||
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1236 | bkhnd0FGME9oMWFyWloxNjlaaE1CZzRjK1lNaXFJUUdocEtvMGFOR0RWcVZLWExWYTlhdFlxbFM1 | |||
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1237 | ZWkxV3FKCmlvcml3b1VMcEtTazhPQ0REL0xOTjk4QXNITGxTdU5jUVZudFQ1NDhXVzcvSVNFaHpK | |||
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1238 | OC9uN2ZlZW92TGx5OVR2MzU5b0hoWm12dnYKdjU5Njllb3hldlJvZnZycEp3QjI3dHpKOE9IRDZk | |||
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1239 | YXRHN3QzNytibm4zOG1MeStQelpzMzg4UVRUd0RGaHc4Yk5HaFFhcXhCZ3diUgpwazBiM04zZDhm | |||
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1240 | ZjNaL2Z1M1NRbUp0SzFhMWZhdDI5UDgrYk5HVFpzV0puYkpEdzhuSmt6Wi9MZWUrOVJVRkJBblRw | |||
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1241 | MUt2MlpDTWRoCjkwdURDTWYwN0xQUEVod2N6SVFKRTB4ZUwrK0R0MDJiTmliUFM5Ym5xbHUzTGsy | |||
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1242 | Yk5qVytYcmR1WGZMeThzakt5bUxtekpsczNicVYKMjI2N2pmdnZ2NThyVjY1VW1Pbmpqei9tOU9u | |||
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1243 | VExGNjhHQ2hlcGpvZ0lJRE5temVidEV0TFN6UHZtN3hKVVZFUml4WXRJaUlpb3RSNwpMVnEwWVAv | |||
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1244 | Ky9heGN1ZEs0TkVONTdVdVc2N2hWZEhRMDNidDM1L1BQUDZkMzc5NTgvZlhYSnR1bFJNbjh6ZVRK | |||
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1245 | ay9ubW0yOElDQWhnCjZ0U3BYTGx5QlkxR1UrWUtwYmU2ZFh2bjVPVGc2dXBxTWpkVVhoOHhNVEVN | |||
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1246 | SERqUXVCUkpVbElTclZ1M3JuQTg0VGhrRDBQVWlHYk4KbXZIZ2d3L3kzLy8rMS9oQmMrKzk5L0xK | |||
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1247 | SjU5UVZGVEVzbVhMR0Rac1dKWDZWaFNGcTFldjR1Ym1ocGVYRjhlT0hlT1hYMzZwOE4vcwoycldM | |||
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1248 | dVhQbjh0bG5ueGxmQ3drSjRjS0ZDOFk5bHV2WHIvUDc3Ny9UcmwwNzZ0U3BRM0p5TXRldlgyZmx5 | |||
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1249 | cFdWWmhvelpneHhjWEZrClpXVUJtQ3g1UFdyVUtONTY2eTB5TXpNSkNBaW90SDFaVWxKU2pHc1g5 | |||
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1250 | ZS9mM3pndmtwR1J3ZmZmZjA5dWJpNWZmZlVWVVZGUjVPVGsKa0pXVlJmdjI3VGx6NWd5clY2OEdp | |||
|
1251 | dWVYN3JubkhwWXVYWXFpS09UbTVwS2RuVjNwOTZiUmFPalpzeWY3OSs4bk5UV1Z5NWN2czI3ZAp1 | |||
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1252 | akpQYURoeDRnUWRPM2JrSC8vNEI3Nit2blp4cnhKaFBWSXdoRlhkL0NFeWZmcDBMbDI2Wkh3K1k4 | |||
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1253 | WU0vdmpqRDdSYUxSY3VYR0RhCnRHbGwvcnRibjVmMTN1MjMzODd3NGNNSkNBaGcwcVJKNVo2S1d2 | |||
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1254 | Slg5YUpGaTdoeTVRcjMzSE1QV3EyV0o1OThFb0RQUHZ1TUpVdVcKMEsxYk4zcjE2c1hSbzBjQitP | |||
|
1255 | Q0REM2p4eFJlNSsrNjdDUXdNTFBQRFVhUFJHRjhmTVdJRW9hR2hSRVpHRWhBUXdLeFpzNHp0Um93 | |||
|
1256 | WQp3VmRmZmNXRER6NW84bHBaN1cvdTgyWXJWNjRrSUNDQWtKQVFidHk0WWV6TDE5ZVhOV3ZXRUJR | |||
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1257 | VVJFQkFBTkhSMGRTdlg1K1pNMmNTCkdocktxRkdqdVBmZWU0Mzl2UDc2Nnh3L2ZwekF3RUI2OSs1 | |||
|
1258 | dFBQR2daTXp5eHE5VHB3N3Z2ZmNlbzBhTklpb3FpcTVkdTlLaFE0ZFMKN1JZc1dFRFhybDBKRFEz | |||
|
1259 | RjE5ZVhYcjE2bGZsekVZNUpGaDhVd2tHbHBxWXlkT2hROXUvZmI1UHhybCsvVHFOR2pjakl5R0RJ | |||
|
1260 | a0NGOAorT0dIZE83YzJTWmpDL3NnY3hoQ09EQmIzbkZ1OXV6WmJOeTRFVGMzTng1NTVCRXBGazVJ | |||
|
1261 | OWpDRUVFS1lSZVl3aEJCQ21FVUtoaEJDCkNMTkl3UkJDQ0dFV0tSaENDQ0hNSWdWRENDR0VXYVJn | |||
|
1262 | Q0NHRU1Ndi9BMkdrMllXcWd3ZTFBQUFBQUVsRlRrU3VRbUNDCg== | |||
|
1263 | </png> | |||
|
1264 | </output> | |||
|
1265 | </outputs> | |||
|
1266 | </codecell> | |||
|
1267 | </cells> | |||
|
1268 | </worksheet> | |||
|
1269 | </worksheets> | |||
|
1270 | </notebook> |
@@ -1,56 +1,146 b'' | |||||
1 | #------------------------------------------------------------------------------- |
|
1 | # <nbformat>2</nbformat> | |
2 | # Driver code that the client runs. |
|
2 | ||
3 | #------------------------------------------------------------------------------- |
|
3 | # <markdowncell> | |
4 | # To run this code start a controller and engines using: |
|
4 | ||
5 | # ipcluster -n 2 |
|
5 | # # Eigenvalue distribution of Gaussian orthogonal random matrices | |
6 | # Then run the scripts by doing irunner rmt.ipy or by starting ipython and |
|
6 | ||
7 | # doing run rmt.ipy. |
|
7 | # <markdowncell> | |
8 |
|
8 | |||
9 | from rmtkernel import * |
|
9 | # The eigenvalues of random matrices obey certain statistical laws. Here we construct random matrices | |
10 | import numpy |
|
10 | # from the Gaussian Orthogonal Ensemble (GOE), find their eigenvalues and then investigate the nearest | |
|
11 | # neighbor eigenvalue distribution $\rho(s)$. | |||
|
12 | ||||
|
13 | # <codecell> | |||
|
14 | ||||
|
15 | from rmtkernel import ensemble_diffs, normalize_diffs, GOE | |||
|
16 | import numpy as np | |||
11 | from IPython.parallel import Client |
|
17 | from IPython.parallel import Client | |
12 |
|
18 | |||
|
19 | # <markdowncell> | |||
13 |
|
20 | |||
14 | def wignerDistribution(s): |
|
21 | # ## Wigner's nearest neighbor eigenvalue distribution | |
|
22 | ||||
|
23 | # <markdowncell> | |||
|
24 | ||||
|
25 | # The Wigner distribution gives the theoretical result for the nearest neighbor eigenvalue distribution | |||
|
26 | # for the GOE: | |||
|
27 | # | |||
|
28 | # $$\rho(s) = \frac{\pi s}{2} \exp(-\pi s^2/4)$$ | |||
|
29 | ||||
|
30 | # <codecell> | |||
|
31 | ||||
|
32 | def wigner_dist(s): | |||
15 | """Returns (s, rho(s)) for the Wigner GOE distribution.""" |
|
33 | """Returns (s, rho(s)) for the Wigner GOE distribution.""" | |
16 |
return (n |
|
34 | return (np.pi*s/2.0) * np.exp(-np.pi*s**2/4.) | |
17 |
|
35 | |||
|
36 | # <codecell> | |||
18 |
|
37 | |||
19 |
def generate |
|
38 | def generate_wigner_data(): | |
20 |
s = n |
|
39 | s = np.linspace(0.0,4.0,400) | |
21 |
rhos = wigner |
|
40 | rhos = wigner_dist(s) | |
22 | return s, rhos |
|
41 | return s, rhos | |
23 |
|
||||
24 |
|
42 | |||
25 | def serialDiffs(num, N): |
|
43 | # <codecell> | |
26 | diffs = ensembleDiffs(num, N) |
|
44 | ||
27 | normalizedDiffs = normalizeDiffs(diffs) |
|
45 | s, rhos = generate_wigner_data() | |
28 | return normalizedDiffs |
|
46 | ||
|
47 | # <codecell> | |||
|
48 | ||||
|
49 | plot(s, rhos) | |||
|
50 | xlabel('Normalized level spacing s') | |||
|
51 | ylabel('Probability $\rho(s)$') | |||
|
52 | ||||
|
53 | # <markdowncell> | |||
|
54 | ||||
|
55 | # ## Serial calculation of nearest neighbor eigenvalue distribution | |||
|
56 | ||||
|
57 | # <markdowncell> | |||
|
58 | ||||
|
59 | # In this section we numerically construct and diagonalize a large number of GOE random matrices | |||
|
60 | # and compute the nerest neighbor eigenvalue distribution. This comptation is done on a single core. | |||
|
61 | ||||
|
62 | # <codecell> | |||
|
63 | ||||
|
64 | def serial_diffs(num, N): | |||
|
65 | """Compute the nearest neighbor distribution for num NxX matrices.""" | |||
|
66 | diffs = ensemble_diffs(num, N) | |||
|
67 | normalized_diffs = normalize_diffs(diffs) | |||
|
68 | return normalized_diffs | |||
|
69 | ||||
|
70 | # <codecell> | |||
|
71 | ||||
|
72 | serial_nmats = 1000 | |||
|
73 | serial_matsize = 50 | |||
|
74 | ||||
|
75 | # <codecell> | |||
|
76 | ||||
|
77 | %timeit -r1 -n1 serial_diffs(serial_nmats, serial_matsize) | |||
29 |
|
78 | |||
|
79 | # <codecell> | |||
30 |
|
80 | |||
31 | def parallelDiffs(rc, num, N): |
|
81 | serial_diffs = serial_diffs(serial_nmats, serial_matsize) | |
|
82 | ||||
|
83 | # <markdowncell> | |||
|
84 | ||||
|
85 | # The numerical computation agrees with the predictions of Wigner, but it would be nice to get more | |||
|
86 | # statistics. For that we will do a parallel computation. | |||
|
87 | ||||
|
88 | # <codecell> | |||
|
89 | ||||
|
90 | hist_data = hist(serial_diffs, bins=30, normed=True) | |||
|
91 | plot(s, rhos) | |||
|
92 | xlabel('Normalized level spacing s') | |||
|
93 | ylabel('Probability $P(s)$') | |||
|
94 | ||||
|
95 | # <markdowncell> | |||
|
96 | ||||
|
97 | # ## Parallel calculation of nearest neighbor eigenvalue distribution | |||
|
98 | ||||
|
99 | # <markdowncell> | |||
|
100 | ||||
|
101 | # Here we perform a parallel computation, where each process constructs and diagonalizes a subset of | |||
|
102 | # the overall set of random matrices. | |||
|
103 | ||||
|
104 | # <codecell> | |||
|
105 | ||||
|
106 | def parallel_diffs(rc, num, N): | |||
32 | nengines = len(rc.targets) |
|
107 | nengines = len(rc.targets) | |
33 | num_per_engine = num/nengines |
|
108 | num_per_engine = num/nengines | |
34 | print "Running with", num_per_engine, "per engine." |
|
109 | print "Running with", num_per_engine, "per engine." | |
35 |
ar = rc.apply_async(ensemble |
|
110 | ar = rc.apply_async(ensemble_diffs, num_per_engine, N) | |
36 |
|
|
111 | diffs = np.array(ar.get()).flatten() | |
37 |
|
112 | normalized_diffs = normalize_diffs(diffs) | ||
38 |
|
113 | return normalized_diffs | ||
39 | # Main code |
|
114 | ||
40 | if __name__ == '__main__': |
|
115 | # <codecell> | |
41 | rc = Client() |
|
116 | ||
42 | view = rc[:] |
|
117 | client = Client() | |
43 | print "Distributing code to engines..." |
|
118 | view = client[:] | |
44 |
|
|
119 | view.run('rmtkernel.py') | |
45 |
|
|
120 | view.block = False | |
46 |
|
121 | |||
47 | # Simulation parameters |
|
122 | # <codecell> | |
48 | nmats = 100 |
|
123 | ||
49 | matsize = 30 |
|
124 | parallel_nmats = 40*serial_nmats | |
50 | # tic = time.time() |
|
125 | parallel_matsize = 50 | |
51 | %timeit -r1 -n1 serialDiffs(nmats,matsize) |
|
126 | ||
52 | %timeit -r1 -n1 parallelDiffs(view, nmats, matsize) |
|
127 | # <codecell> | |
53 |
|
128 | |||
54 | # Uncomment these to plot the histogram |
|
129 | %timeit -r1 -n1 parallel_diffs(view, parallel_nmats, parallel_matsize) | |
55 | # import pylab |
|
130 | ||
56 | # pylab.hist(parallelDiffs(rc,matsize,matsize)) |
|
131 | # <codecell> | |
|
132 | ||||
|
133 | pdiffs = parallel_diffs(view, parallel_nmats, parallel_matsize) | |||
|
134 | ||||
|
135 | # <markdowncell> | |||
|
136 | ||||
|
137 | # Again, the agreement with the Wigner distribution is excellent, but now we have better | |||
|
138 | # statistics. | |||
|
139 | ||||
|
140 | # <codecell> | |||
|
141 | ||||
|
142 | hist_data = hist(pdiffs, bins=30, normed=True) | |||
|
143 | plot(s, rhos) | |||
|
144 | xlabel('Normalized level spacing s') | |||
|
145 | ylabel('Probability $P(s)$') | |||
|
146 |
@@ -1,44 +1,42 b'' | |||||
1 | #------------------------------------------------------------------------------- |
|
1 | #------------------------------------------------------------------------------- | |
2 | # Core routines for computing properties of symmetric random matrices. |
|
2 | # Core routines for computing properties of symmetric random matrices. | |
3 | #------------------------------------------------------------------------------- |
|
3 | #------------------------------------------------------------------------------- | |
4 |
|
4 | |||
5 | import numpy |
|
5 | import numpy as np | |
6 |
ra = n |
|
6 | ra = np.random | |
7 |
la = n |
|
7 | la = np.linalg | |
8 |
|
8 | |||
9 | def GOE(N): |
|
9 | def GOE(N): | |
10 | """Creates an NxN element of the Gaussian Orthogonal Ensemble""" |
|
10 | """Creates an NxN element of the Gaussian Orthogonal Ensemble""" | |
11 | m = ra.standard_normal((N,N)) |
|
11 | m = ra.standard_normal((N,N)) | |
12 | m += m.T |
|
12 | m += m.T | |
13 | return m |
|
13 | return m/2 | |
14 |
|
14 | |||
15 |
|
15 | |||
16 |
def center |
|
16 | def center_eigenvalue_diff(mat): | |
17 | """Compute the eigvals of mat and then find the center eigval difference.""" |
|
17 | """Compute the eigvals of mat and then find the center eigval difference.""" | |
18 | N = len(mat) |
|
18 | N = len(mat) | |
19 |
evals = n |
|
19 | evals = np.sort(la.eigvals(mat)) | |
20 | diff = evals[N/2] - evals[N/2-1] |
|
20 | diff = np.abs(evals[N/2] - evals[N/2-1]) | |
21 |
return diff |
|
21 | return diff | |
22 |
|
22 | |||
23 |
|
23 | |||
24 |
def ensemble |
|
24 | def ensemble_diffs(num, N): | |
25 |
"""Return |
|
25 | """Return num eigenvalue diffs for the NxN GOE ensemble.""" | |
26 | ensemble.""" |
|
26 | diffs = np.empty(num) | |
27 | diffs = numpy.empty(num) |
|
|||
28 | for i in xrange(num): |
|
27 | for i in xrange(num): | |
29 | mat = GOE(N) |
|
28 | mat = GOE(N) | |
30 |
diffs[i] = center |
|
29 | diffs[i] = center_eigenvalue_diff(mat) | |
31 | return diffs |
|
30 | return diffs | |
32 |
|
31 | |||
33 |
|
32 | |||
34 |
def normalize |
|
33 | def normalize_diffs(diffs): | |
35 | """Normalize an array of eigenvalue diffs.""" |
|
34 | """Normalize an array of eigenvalue diffs.""" | |
36 | return diffs/diffs.mean() |
|
35 | return diffs/diffs.mean() | |
37 |
|
36 | |||
38 |
|
37 | |||
39 |
def normalized |
|
38 | def normalized_ensemble_diffs(num, N): | |
40 |
"""Return |
|
39 | """Return num *normalized* eigenvalue diffs for the NxN GOE ensemble.""" | |
41 | GOE ensemble.""" |
|
40 | diffs = ensemble_diffs(num, N) | |
42 | diffs = ensembleDiffs(num, N) |
|
41 | return normalize_diffs(diffs) | |
43 | return normalizeDiffs(diffs) |
|
|||
44 |
|
42 |
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