350:
The minimum possible value of the
Fowlkes–Mallows index is 0, which corresponds to the worst binary classification possible, where all the elements have been misclassified. And the maximum possible value of the Fowlkes–Mallows index is 1, which corresponds to the best binary classification possible,
2098:
making
Fowlkes–Mallows index a much more accurate representation for unrelated data. This index also performs well if noise is added to an existing dataset and their similarity compared. Fowlkes and Mallows showed that the value of the index decreases as the component of the noise increases. The
2073:
Since the index is directly proportional to the number of true positives, a higher index means greater similarity between the two clusterings used to determine the index. One basic way to test the validity of this index is to compare two clusterings that are unrelated to each other. Fowlkes and
1888:
183:
2099:
index also showed similarity even when the noisy dataset had a different number of clusters than the clusters of the original dataset. Thus making it a reliable tool for measuring similarity between two clusters.
1195:
1087:
651:
979:
874:
43:
or a clustering and a benchmark classification. A higher value for the
Fowlkes–Mallows index indicates a greater similarity between the clusters and the benchmark classifications. It was invented by
2317:
2074:
Mallows showed that on using two unrelated clusterings, the value of this index approaches zero as the number of total data points chosen for clustering increase; whereas the value for the
1759:
1350:
529:
531:
clusters for each tree (by either selecting clusters at a particular height of the tree or setting different strength of the hierarchical clustering). For each value of
1774:
687:
69:
2109:
Chicco, Davide; Jurman, Giuseppe (2023). "A statistical comparison between
Matthews correlation coefficient (MCC), prevalence threshold, and Fowlkes–Mallows index".
1673:
1646:
1594:
1567:
1515:
1488:
1436:
1409:
1271:
1224:
781:
734:
485:
458:
431:
404:
2041:
1999:
335:
293:
1967:
1940:
1913:
1619:
1540:
1461:
1382:
263:
236:
209:
2096:
1311:
1291:
1244:
805:
754:
707:
549:
377:
2314:
1093:
985:
557:
885:
2167:
1358:
can also be defined based on the number of points that are common or uncommon in the two hierarchical clusterings. If we define
813:
2341:
2222:
Halkidi, Maria; Batistakis, Yannis; Vazirgiannis, Michalis (1 January 2001). "On
Clustering Validation Techniques".
2325:
40:
2195:
Fowlkes, E. B.; Mallows, C. L. (1 September 1983). "A Method for
Comparing Two Hierarchical Clusterings".
1685:
2049:
343:
1316:
2061:
2013:
490:
307:
28:
27:
method that is used to determine the similarity between two clusterings (clusters obtained after a
2346:
2144:
2007:
301:
36:
1883:{\displaystyle FM={\sqrt {PPV\cdot TPR}}={\sqrt {{\frac {TP}{TP+FP}}\cdot {\frac {TP}{TP+FN}}}}}
178:{\displaystyle FM={\sqrt {PPV\cdot TPR}}={\sqrt {{\frac {TP}{TP+FP}}\cdot {\frac {TP}{TP+FN}}}}}
2136:
659:
2291:
2262:
2231:
2204:
2172:
2126:
2118:
63:, when results of two clustering algorithms are used to evaluate the results, is defined as
32:
24:
1651:
1624:
1572:
1545:
1493:
1466:
1414:
1387:
1249:
1202:
759:
712:
463:
436:
409:
382:
2321:
1970:
1943:
266:
239:
2020:
1978:
314:
272:
1949:
1922:
1895:
1601:
1522:
1443:
1364:
245:
218:
191:
2081:
2057:
1296:
1276:
1229:
790:
739:
692:
534:
362:
2335:
2148:
1916:
212:
48:
2267:
2250:
2296:
2283:
2235:
2122:
2075:
1384:
as the number of pairs of points that are present in the same cluster in both
44:
2140:
1463:
as the number of pairs of points that are present in the same cluster in
2162:
1542:
as the number of pairs of points that are present in the same cluster in
2131:
1621:
as the number of pairs of points that are in different clusters in both
1246:
and the similarity between the two clusterings can be shown by plotting
2208:
1190:{\displaystyle Q_{k}=\sum _{j=1}^{k}(\sum _{i=1}^{k}m_{i,j})^{2}-n}
1082:{\displaystyle P_{k}=\sum _{i=1}^{k}(\sum _{j=1}^{k}m_{i,j})^{2}-n}
646:{\displaystyle M=\qquad (i=1,\ldots ,k{\text{ and }}j=1,\ldots ,k)}
1679:
It can be shown that the four counts have the following property
974:{\displaystyle T_{k}=\sum _{i=1}^{k}\sum _{j=1}^{k}m_{i,j}^{2}-n}
869:{\displaystyle B_{k}={\frac {T_{k}}{\sqrt {P_{k}Q_{k}}}}}
351:
where all the elements have been perfectly classified.
2251:"Comparing clusterings—an information based distance"
2084:
2023:
1981:
1952:
1925:
1898:
1777:
1688:
1654:
1627:
1604:
1575:
1548:
1525:
1496:
1469:
1446:
1417:
1390:
1367:
1319:
1299:
1279:
1252:
1232:
1205:
1096:
988:
888:
816:
793:
762:
742:
715:
695:
662:
560:
537:
493:
466:
439:
412:
385:
365:
317:
275:
248:
221:
194:
72:
2190:
2188:
2090:
2035:
1993:
1961:
1934:
1907:
1882:
1753:
1667:
1640:
1613:
1588:
1561:
1534:
1509:
1482:
1455:
1430:
1403:
1376:
1344:
1305:
1285:
1265:
1238:
1218:
1189:
1081:
973:
868:
799:
775:
748:
728:
701:
681:
645:
543:
523:
479:
452:
425:
398:
371:
329:
287:
257:
230:
203:
177:
2197:Journal of the American Statistical Association
8:
2224:Journal of Intelligent Information Systems
1226:can then be calculated for every value of
551:, the following table can then be created
2295:
2266:
2130:
2083:
2022:
1980:
1951:
1924:
1897:
1849:
1817:
1815:
1787:
1776:
1743:
1687:
1659:
1653:
1632:
1626:
1603:
1580:
1574:
1553:
1547:
1524:
1501:
1495:
1474:
1468:
1445:
1422:
1416:
1395:
1389:
1366:
1330:
1318:
1298:
1278:
1257:
1251:
1231:
1210:
1204:
1175:
1159:
1149:
1138:
1125:
1114:
1101:
1095:
1067:
1051:
1041:
1030:
1017:
1006:
993:
987:
959:
948:
938:
927:
917:
906:
893:
887:
857:
847:
836:
830:
821:
815:
792:
767:
761:
741:
720:
714:
694:
667:
661:
614:
574:
559:
536:
492:
471:
465:
444:
438:
417:
411:
390:
384:
364:
359:Consider two hierarchical clusterings of
316:
274:
247:
220:
193:
144:
112:
110:
82:
71:
2315:Implementation of Fowlkes–Mallows index
2184:
1768:for two clusterings can be defined as
2078:for the same data quickly approaches
16:Evaluation method in cluster analysis
7:
1754:{\displaystyle TP+FP+FN+TN=n(n-1)/2}
2284:"Classification assessment methods"
14:
2288:Applied Computing and Informatics
2111:Journal of Biomedical Informatics
2056:The Fowlkes–Mallows index is the
1345:{\displaystyle 0\leq B_{k}\leq 1}
689:is of objects common between the
47:statisticians Edward Fowlkes and
2255:Journal of Multivariate Analysis
2168:Matthews correlation coefficient
31:), and also a metric to measure
589:
524:{\displaystyle k=2,\ldots ,n-1}
1740:
1728:
1172:
1131:
1064:
1023:
640:
590:
586:
567:
1:
39:could be either between two
2363:
2268:10.1016/j.jmva.2006.11.013
787:for the specific value of
2297:10.1016/j.aci.2018.08.003
2282:Tharwat A (August 2018).
2123:10.1016/j.jbi.2023.104426
2045:positive predictive rate
339:positive predictive rate
41:hierarchical clusterings
2249:MEILA, M (1 May 2007).
2236:10.1023/A:1012801612483
682:{\displaystyle m_{i,j}}
2092:
2037:
1995:
1963:
1936:
1909:
1884:
1755:
1669:
1642:
1615:
1590:
1563:
1536:
1511:
1484:
1457:
1432:
1405:
1378:
1346:
1307:
1287:
1267:
1240:
1220:
1191:
1154:
1130:
1083:
1046:
1022:
975:
943:
922:
870:
801:
777:
750:
730:
703:
683:
647:
545:
525:
487:can be cut to produce
481:
454:
427:
400:
373:
331:
289:
259:
232:
205:
179:
2093:
2038:
1996:
1964:
1937:
1910:
1885:
1766:Fowlkes–Mallows index
1756:
1670:
1668:{\displaystyle A_{2}}
1643:
1641:{\displaystyle A_{1}}
1616:
1591:
1589:{\displaystyle A_{1}}
1564:
1562:{\displaystyle A_{2}}
1537:
1512:
1510:{\displaystyle A_{2}}
1485:
1483:{\displaystyle A_{1}}
1458:
1433:
1431:{\displaystyle A_{2}}
1406:
1404:{\displaystyle A_{1}}
1379:
1356:Fowlkes–Mallows index
1347:
1308:
1288:
1268:
1266:{\displaystyle B_{k}}
1241:
1221:
1219:{\displaystyle B_{k}}
1192:
1134:
1110:
1084:
1026:
1002:
976:
923:
902:
871:
802:
785:Fowlkes–Mallows index
778:
776:{\displaystyle A_{2}}
751:
731:
729:{\displaystyle A_{1}}
704:
684:
648:
546:
526:
482:
480:{\displaystyle A_{2}}
455:
453:{\displaystyle A_{1}}
428:
426:{\displaystyle A_{2}}
401:
399:{\displaystyle A_{1}}
374:
332:
290:
260:
233:
206:
180:
61:Fowlkes–Mallows index
37:measure of similarity
21:Fowlkes–Mallows index
2082:
2062:precision and recall
2021:
1979:
1950:
1923:
1896:
1775:
1686:
1652:
1625:
1602:
1573:
1546:
1523:
1494:
1467:
1444:
1415:
1388:
1365:
1317:
1297:
1277:
1250:
1230:
1203:
1094:
986:
886:
814:
791:
760:
740:
713:
693:
660:
558:
535:
491:
464:
437:
410:
383:
363:
315:
273:
246:
219:
192:
70:
29:clustering algorithm
2342:Clustering criteria
2036:{\displaystyle PPV}
1994:{\displaystyle TPR}
964:
807:is then defined as
330:{\displaystyle PPV}
288:{\displaystyle TPR}
25:external evaluation
2320:2016-06-03 at the
2088:
2033:
2003:true positive rate
1991:
1962:{\displaystyle FN}
1959:
1935:{\displaystyle FP}
1932:
1908:{\displaystyle TP}
1905:
1880:
1751:
1665:
1638:
1614:{\displaystyle TN}
1611:
1586:
1559:
1535:{\displaystyle FN}
1532:
1507:
1480:
1456:{\displaystyle FP}
1453:
1428:
1401:
1377:{\displaystyle TP}
1374:
1342:
1303:
1283:
1263:
1236:
1216:
1187:
1079:
971:
944:
866:
797:
773:
746:
726:
699:
679:
643:
541:
521:
477:
450:
423:
396:
369:
327:
297:true positive rate
285:
258:{\displaystyle FN}
255:
231:{\displaystyle FP}
228:
204:{\displaystyle TP}
201:
175:
33:confusion matrices
2091:{\displaystyle 1}
1969:is the number of
1942:is the number of
1915:is the number of
1878:
1876:
1844:
1810:
1306:{\displaystyle k}
1286:{\displaystyle k}
1239:{\displaystyle k}
864:
863:
800:{\displaystyle k}
749:{\displaystyle j}
702:{\displaystyle i}
617:
544:{\displaystyle k}
372:{\displaystyle n}
265:is the number of
238:is the number of
211:is the number of
173:
171:
139:
105:
2354:
2302:
2301:
2299:
2279:
2273:
2272:
2270:
2246:
2240:
2239:
2230:(2/3): 107–145.
2219:
2213:
2212:
2192:
2173:Confusion matrix
2152:
2134:
2097:
2095:
2094:
2089:
2047:, also known as
2042:
2040:
2039:
2034:
2000:
1998:
1997:
1992:
1968:
1966:
1965:
1960:
1941:
1939:
1938:
1933:
1914:
1912:
1911:
1906:
1889:
1887:
1886:
1881:
1879:
1877:
1875:
1858:
1850:
1845:
1843:
1826:
1818:
1816:
1811:
1788:
1760:
1758:
1757:
1752:
1747:
1674:
1672:
1671:
1666:
1664:
1663:
1647:
1645:
1644:
1639:
1637:
1636:
1620:
1618:
1617:
1612:
1595:
1593:
1592:
1587:
1585:
1584:
1568:
1566:
1565:
1560:
1558:
1557:
1541:
1539:
1538:
1533:
1516:
1514:
1513:
1508:
1506:
1505:
1489:
1487:
1486:
1481:
1479:
1478:
1462:
1460:
1459:
1454:
1437:
1435:
1434:
1429:
1427:
1426:
1410:
1408:
1407:
1402:
1400:
1399:
1383:
1381:
1380:
1375:
1351:
1349:
1348:
1343:
1335:
1334:
1312:
1310:
1309:
1304:
1292:
1290:
1289:
1284:
1272:
1270:
1269:
1264:
1262:
1261:
1245:
1243:
1242:
1237:
1225:
1223:
1222:
1217:
1215:
1214:
1196:
1194:
1193:
1188:
1180:
1179:
1170:
1169:
1153:
1148:
1129:
1124:
1106:
1105:
1088:
1086:
1085:
1080:
1072:
1071:
1062:
1061:
1045:
1040:
1021:
1016:
998:
997:
980:
978:
977:
972:
963:
958:
942:
937:
921:
916:
898:
897:
875:
873:
872:
867:
865:
862:
861:
852:
851:
842:
841:
840:
831:
826:
825:
806:
804:
803:
798:
782:
780:
779:
774:
772:
771:
755:
753:
752:
747:
735:
733:
732:
727:
725:
724:
708:
706:
705:
700:
688:
686:
685:
680:
678:
677:
652:
650:
649:
644:
618:
615:
585:
584:
550:
548:
547:
542:
530:
528:
527:
522:
486:
484:
483:
478:
476:
475:
459:
457:
456:
451:
449:
448:
432:
430:
429:
424:
422:
421:
405:
403:
402:
397:
395:
394:
379:objects labeled
378:
376:
375:
370:
341:, also known as
336:
334:
333:
328:
294:
292:
291:
286:
264:
262:
261:
256:
237:
235:
234:
229:
210:
208:
207:
202:
184:
182:
181:
176:
174:
172:
170:
153:
145:
140:
138:
121:
113:
111:
106:
83:
2362:
2361:
2357:
2356:
2355:
2353:
2352:
2351:
2332:
2331:
2322:Wayback Machine
2311:
2306:
2305:
2281:
2280:
2276:
2248:
2247:
2243:
2221:
2220:
2216:
2209:10.2307/2288117
2194:
2193:
2186:
2181:
2159:
2117:(104426): 1–7.
2108:
2105:
2103:Further reading
2080:
2079:
2071:
2019:
2018:
1977:
1976:
1971:false negatives
1948:
1947:
1944:false positives
1921:
1920:
1894:
1893:
1859:
1851:
1827:
1819:
1773:
1772:
1684:
1683:
1655:
1650:
1649:
1628:
1623:
1622:
1600:
1599:
1576:
1571:
1570:
1549:
1544:
1543:
1521:
1520:
1497:
1492:
1491:
1470:
1465:
1464:
1442:
1441:
1418:
1413:
1412:
1391:
1386:
1385:
1363:
1362:
1326:
1315:
1314:
1295:
1294:
1275:
1274:
1253:
1248:
1247:
1228:
1227:
1206:
1201:
1200:
1171:
1155:
1097:
1092:
1091:
1063:
1047:
989:
984:
983:
889:
884:
883:
853:
843:
832:
817:
812:
811:
789:
788:
763:
758:
757:
738:
737:
716:
711:
710:
691:
690:
663:
658:
657:
616: and
570:
556:
555:
533:
532:
489:
488:
467:
462:
461:
440:
435:
434:
413:
408:
407:
386:
381:
380:
361:
360:
357:
313:
312:
271:
270:
267:false negatives
244:
243:
240:false positives
217:
216:
190:
189:
154:
146:
122:
114:
68:
67:
57:
17:
12:
11:
5:
2360:
2358:
2350:
2349:
2344:
2334:
2333:
2330:
2329:
2310:
2309:External links
2307:
2304:
2303:
2274:
2261:(5): 873–895.
2241:
2214:
2183:
2182:
2180:
2177:
2176:
2175:
2170:
2165:
2158:
2155:
2154:
2153:
2104:
2101:
2087:
2070:
2067:
2066:
2065:
2058:geometric mean
2054:
2032:
2029:
2026:
2005:, also called
1990:
1987:
1984:
1974:
1958:
1955:
1931:
1928:
1917:true positives
1904:
1901:
1890:
1874:
1871:
1868:
1865:
1862:
1857:
1854:
1848:
1842:
1839:
1836:
1833:
1830:
1825:
1822:
1814:
1809:
1806:
1803:
1800:
1797:
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1791:
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1780:
1762:
1761:
1750:
1746:
1742:
1739:
1736:
1733:
1730:
1727:
1724:
1721:
1718:
1715:
1712:
1709:
1706:
1703:
1700:
1697:
1694:
1691:
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1676:
1662:
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1635:
1631:
1610:
1607:
1597:
1583:
1579:
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1552:
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1528:
1518:
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1500:
1477:
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1128:
1123:
1120:
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1109:
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1015:
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1009:
1005:
1001:
996:
992:
981:
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967:
962:
957:
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951:
947:
941:
936:
933:
930:
926:
920:
915:
912:
909:
905:
901:
896:
892:
877:
876:
860:
856:
850:
846:
839:
835:
829:
824:
820:
796:
770:
766:
756:th cluster of
745:
723:
719:
709:th cluster of
698:
676:
673:
670:
666:
654:
653:
642:
639:
636:
633:
630:
627:
624:
621:
613:
610:
607:
604:
601:
598:
595:
592:
588:
583:
580:
577:
573:
569:
566:
563:
540:
520:
517:
514:
511:
508:
505:
502:
499:
496:
474:
470:
447:
443:
420:
416:
393:
389:
368:
356:
353:
326:
323:
320:
299:, also called
284:
281:
278:
254:
251:
227:
224:
213:true positives
200:
197:
186:
185:
169:
166:
163:
160:
157:
152:
149:
143:
137:
134:
131:
128:
125:
120:
117:
109:
104:
101:
98:
95:
92:
89:
86:
81:
78:
75:
56:
53:
49:Collin Mallows
15:
13:
10:
9:
6:
4:
3:
2:
2359:
2348:
2345:
2343:
2340:
2339:
2337:
2327:
2323:
2319:
2316:
2313:
2312:
2308:
2298:
2293:
2289:
2285:
2278:
2275:
2269:
2264:
2260:
2256:
2252:
2245:
2242:
2237:
2233:
2229:
2225:
2218:
2215:
2210:
2206:
2202:
2198:
2191:
2189:
2185:
2178:
2174:
2171:
2169:
2166:
2164:
2161:
2160:
2156:
2150:
2146:
2142:
2138:
2133:
2128:
2124:
2120:
2116:
2112:
2107:
2106:
2102:
2100:
2085:
2077:
2068:
2063:
2059:
2055:
2052:
2051:
2046:
2030:
2027:
2024:
2016:
2015:
2010:
2009:
2004:
1988:
1985:
1982:
1975:
1972:
1956:
1953:
1945:
1929:
1926:
1918:
1902:
1899:
1891:
1872:
1869:
1866:
1863:
1860:
1855:
1852:
1846:
1840:
1837:
1834:
1831:
1828:
1823:
1820:
1812:
1807:
1804:
1801:
1798:
1795:
1792:
1789:
1784:
1781:
1778:
1771:
1770:
1769:
1767:
1764:and that the
1748:
1744:
1737:
1734:
1731:
1725:
1722:
1719:
1716:
1713:
1710:
1707:
1704:
1701:
1698:
1695:
1692:
1689:
1682:
1681:
1680:
1660:
1656:
1633:
1629:
1608:
1605:
1598:
1581:
1577:
1554:
1550:
1529:
1526:
1519:
1502:
1498:
1475:
1471:
1450:
1447:
1440:
1423:
1419:
1396:
1392:
1371:
1368:
1361:
1360:
1359:
1357:
1353:
1339:
1336:
1331:
1327:
1323:
1320:
1300:
1280:
1258:
1254:
1233:
1211:
1207:
1184:
1181:
1176:
1166:
1163:
1160:
1156:
1150:
1145:
1142:
1139:
1135:
1126:
1121:
1118:
1115:
1111:
1107:
1102:
1098:
1090:
1076:
1073:
1068:
1058:
1055:
1052:
1048:
1042:
1037:
1034:
1031:
1027:
1018:
1013:
1010:
1007:
1003:
999:
994:
990:
982:
968:
965:
960:
955:
952:
949:
945:
939:
934:
931:
928:
924:
918:
913:
910:
907:
903:
899:
894:
890:
882:
881:
880:
858:
854:
848:
844:
837:
833:
827:
822:
818:
810:
809:
808:
794:
786:
768:
764:
743:
721:
717:
696:
674:
671:
668:
664:
637:
634:
631:
628:
625:
622:
619:
611:
608:
605:
602:
599:
596:
593:
581:
578:
575:
571:
564:
561:
554:
553:
552:
538:
518:
515:
512:
509:
506:
503:
500:
497:
494:
472:
468:
445:
441:
418:
414:
391:
387:
366:
354:
352:
348:
346:
345:
340:
324:
321:
318:
310:
309:
304:
303:
298:
282:
279:
276:
268:
252:
249:
241:
225:
222:
214:
198:
195:
167:
164:
161:
158:
155:
150:
147:
141:
135:
132:
129:
126:
123:
118:
115:
107:
102:
99:
96:
93:
90:
87:
84:
79:
76:
73:
66:
65:
64:
62:
55:Preliminaries
54:
52:
50:
46:
42:
38:
34:
30:
26:
22:
2287:
2277:
2258:
2254:
2244:
2227:
2223:
2217:
2203:(383): 553.
2200:
2196:
2132:10281/430040
2114:
2110:
2072:
2048:
2044:
2012:
2006:
2002:
1765:
1763:
1678:
1355:
1354:
1199:
878:
784:
655:
433:. The trees
358:
349:
342:
338:
306:
300:
296:
187:
60:
58:
20:
18:
2008:sensitivity
1569:but not in
1490:but not in
1293:. For each
302:sensitivity
2336:Categories
2179:References
2076:Rand index
2069:Discussion
355:Definition
2347:Bell Labs
2149:259240662
2050:precision
1847:⋅
1799:⋅
1735:−
1337:≤
1324:≤
1182:−
1136:∑
1112:∑
1074:−
1028:∑
1004:∑
966:−
925:∑
904:∑
632:…
606:…
516:−
507:…
344:precision
142:⋅
94:⋅
51:in 1983.
45:Bell Labs
2318:Archived
2163:F1 score
2157:See also
2141:37352899
1313:we have
2043:is the
2001:is the
1892:where
1273:versus
337:is the
295:is the
188:where
35:. This
2147:
2139:
2017:, and
2014:recall
1946:, and
879:where
783:. The
656:where
311:, and
308:recall
242:, and
23:is an
2145:S2CID
2137:PMID
1648:and
1411:and
736:and
460:and
406:and
59:The
19:The
2324:in
2292:doi
2263:doi
2232:doi
2205:doi
2127:hdl
2119:doi
2115:144
2060:of
2011:or
305:or
2338::
2290:.
2286:.
2259:98
2257:.
2253:.
2228:17
2226:.
2201:78
2199:.
2187:^
2143:.
2135:.
2125:.
2113:.
1919:,
1352:.
347:.
269:.
215:,
2328:.
2326:R
2300:.
2294::
2271:.
2265::
2238:.
2234::
2211:.
2207::
2151:.
2129::
2121::
2086:1
2064:.
2053:.
2031:V
2028:P
2025:P
1989:R
1986:P
1983:T
1973:.
1957:N
1954:F
1930:P
1927:F
1903:P
1900:T
1873:N
1870:F
1867:+
1864:P
1861:T
1856:P
1853:T
1841:P
1838:F
1835:+
1832:P
1829:T
1824:P
1821:T
1813:=
1808:R
1805:P
1802:T
1796:V
1793:P
1790:P
1785:=
1782:M
1779:F
1749:2
1745:/
1741:)
1738:1
1732:n
1729:(
1726:n
1723:=
1720:N
1717:T
1714:+
1711:N
1708:F
1705:+
1702:P
1699:F
1696:+
1693:P
1690:T
1675:.
1661:2
1657:A
1634:1
1630:A
1609:N
1606:T
1596:.
1582:1
1578:A
1555:2
1551:A
1530:N
1527:F
1517:.
1503:2
1499:A
1476:1
1472:A
1451:P
1448:F
1438:.
1424:2
1420:A
1397:1
1393:A
1372:P
1369:T
1340:1
1332:k
1328:B
1321:0
1301:k
1281:k
1259:k
1255:B
1234:k
1212:k
1208:B
1185:n
1177:2
1173:)
1167:j
1164:,
1161:i
1157:m
1151:k
1146:1
1143:=
1140:i
1132:(
1127:k
1122:1
1119:=
1116:j
1108:=
1103:k
1099:Q
1077:n
1069:2
1065:)
1059:j
1056:,
1053:i
1049:m
1043:k
1038:1
1035:=
1032:j
1024:(
1019:k
1014:1
1011:=
1008:i
1000:=
995:k
991:P
969:n
961:2
956:j
953:,
950:i
946:m
940:k
935:1
932:=
929:j
919:k
914:1
911:=
908:i
900:=
895:k
891:T
859:k
855:Q
849:k
845:P
838:k
834:T
828:=
823:k
819:B
795:k
769:2
765:A
744:j
722:1
718:A
697:i
675:j
672:,
669:i
665:m
641:)
638:k
635:,
629:,
626:1
623:=
620:j
612:k
609:,
603:,
600:1
597:=
594:i
591:(
587:]
582:j
579:,
576:i
572:m
568:[
565:=
562:M
539:k
519:1
513:n
510:,
504:,
501:2
498:=
495:k
473:2
469:A
446:1
442:A
419:2
415:A
392:1
388:A
367:n
325:V
322:P
319:P
283:R
280:P
277:T
253:N
250:F
226:P
223:F
199:P
196:T
168:N
165:F
162:+
159:P
156:T
151:P
148:T
136:P
133:F
130:+
127:P
124:T
119:P
116:T
108:=
103:R
100:P
97:T
91:V
88:P
85:P
80:=
77:M
74:F
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