36:
150:. A score of zero (0%) reflects a fully integrated environment; a score of 1 (100%) reflects full segregation. In terms of black–white segregation, a score of .60 means that 60 percent of blacks would have to exchange places with whites in other units to achieve an even geographic distribution.Index of dissimilarity is invariant to relative size of group.
3164:
140:
measure of the evenness with which two groups are distributed across component geographic areas that make up a larger area. A group is evenly distributed when each geographic unit has the same percentage of group members as the total population. The index score can also be interpreted as the
1758:
2611:
1541:
1458:
2866:
260:
145:
of one of the two groups included in the calculation that would have to move to different geographic areas in order to produce a distribution that matches that of the larger area. The index of dissimilarity can be used as a measure of
1753:
Consider a city consisting of four blocks of 2 people each. One block consists of 2 rich people. One block consists of 2 poor people. Two blocks consist of 1 rich and 1 poor person. What is the index of dissimilarity for this city?
2998:
2741:
1743:
1328:
2256:
2139:
513:
3007:
2449:
2306:
1201:
1088:
3173:
When the Index of
Dissimilarity is zero, this means that the community we are studying has zero segregation. For example, if we are studying the segregation of rich and poor people in a city, then if
928:
4093:
3654:
3280:
312:(whether demographic or not) and because of its simple properties is useful for input into multidimensional scaling and clustering programs. It has been used extensively in the study of
2478:
4047:
3608:
3526:
1652:
1621:
1259:
3921:
3842:
1464:
1381:
3752:
3705:
3443:
3365:
3324:
1914:
1861:
816:
711:
612:
2787:
2765:
1807:
1785:
1374:
1352:
1225:
636:
537:
2794:
2019:
1968:
3798:
164:
3405:
2895:
1590:
997:
843:
741:
365:
3234:
3197:
2658:
2638:
2471:
1563:
1110:
970:
950:
461:
2902:
1761:
Our fictional city has 4 blocks: one block containing 2 rich people; another containing 2 poor people; and two blocks containing 1 rich and 1 poor person.
2665:
1667:
3159:{\displaystyle D={\frac {1}{2}}|{\hat {\mathbf {r} }}-{\hat {\mathbf {p} }}|_{1}={\frac {1}{2}}\sum _{i=1}^{N}|{\frac {r_{i}}{R}}-{\frac {p_{i}}{P}}|}
1266:
2145:
2028:
468:
100:
2313:
72:
435:
The formula for the Index of
Dissimilarity can be made much more compact and meaningful by considering it from the perspective of
2263:
1117:
1004:
53:
4336:
850:
79:
4054:
3615:
3241:
285:= the total population in group A in the large geographic entity for which the index of dissimilarity is being calculated.
304:= the total population in group B in the large geographic entity for which the index of dissimilarity is being calculated.
17:
3002:
Thus we prove that the linear algebra formula for the index of dissimilarity is equivalent to the basic formula for it:
86:
716:
119:
3203:
There are no blocks in the city which are "rich blocks", and there are no blocks in the city which are "poor blocks"
68:
4140:
2606:{\displaystyle D={\frac {1}{2}}|{\hat {\mathbf {r} }}-{\hat {\mathbf {p} }}|_{1}={\frac {1}{2}}(|0.5|+|-0.5|)=0.5}
4104:
57:
3927:
3532:
3450:
1626:
1595:
1233:
3849:
1536:{\displaystyle {\hat {\mathbf {p} }}={\frac {\mathbf {p} }{|\mathbf {p} |_{1}}}={\frac {\mathbf {p} }{P}}}
1453:{\displaystyle {\hat {\mathbf {r} }}={\frac {\mathbf {r} }{|\mathbf {r} |_{1}}}={\frac {\mathbf {r} }{R}}}
3803:
3284:
For example, suppose you have a city with 2 blocks. Each block has 4 rich people and 100 poor people:
745:
of a vector is simply the sum of (the magnitude of) each entry in that vector. That is, for a vector
2861:{\displaystyle D={\frac {1}{2}}\left|{\frac {\mathbf {r} }{R}}-{\frac {\mathbf {p} }{P}}\right|_{1}}
93:
3711:
3664:
3410:
3330:
3289:
1867:
1814:
748:
643:
544:
147:
2770:
2748:
1790:
1768:
1357:
1335:
1208:
619:
520:
1974:
1923:
255:{\displaystyle D={\frac {1}{2}}\sum _{i=1}^{N}\left|{\frac {a_{i}}{A}}-{\frac {b_{i}}{B}}\right|}
46:
4355:
3759:
4170:
3372:
3236:
in the linear algebraic formula, we get the necessary condition for having zero segregation:
2873:
1568:
975:
821:
719:
343:
309:
8:
3213:
3176:
324:
Consider the following distribution of white and black population across neighborhoods.
4218:
4114:
2643:
2623:
2456:
1548:
1095:
955:
935:
446:
2993:{\displaystyle D={\frac {1}{2}}\sum _{i=1}^{N}|{\frac {r_{i}}{R}}-{\frac {p_{i}}{P}}|}
4333:
4301:
4262:
4223:
4205:
4158:
4293:
4254:
4213:
4197:
1918:
Next, let's calculate the total number of rich people and poor people in our city:
439:. Suppose we are studying the distribution of rich and poor people in a city (e.g.
4340:
4109:
2736:{\displaystyle D={\frac {1}{2}}|{\hat {\mathbf {r} }}-{\hat {\mathbf {p} }}|_{1}}
1738:{\displaystyle D={\frac {1}{2}}|{\hat {\mathbf {r} }}-{\hat {\mathbf {p} }}|_{1}}
313:
1323:{\displaystyle {\hat {\mathbf {v} }}={\frac {\mathbf {v} }{|\mathbf {v} |_{1}}}}
952:
as the total number of rich people in our city, than a compact way to calculate
3206:
There is a homogeneous distribution of rich and poor people throughout the city
2251:{\displaystyle {\hat {\mathbf {p} }}={\frac {\mathbf {p} }{P}}={\frac {1}{4}}=}
2134:{\displaystyle {\hat {\mathbf {r} }}={\frac {\mathbf {r} }{R}}={\frac {1}{4}}=}
436:
4185:
508:{\displaystyle \{{\text{block 1}},{\text{block 2}},\ldots ,{\text{block N}}\}}
4349:
4318:
4305:
4266:
4209:
4201:
316:
to compare distributions of origin (or destination) occupational categories.
4227:
4119:
1228:
137:
4242:
4184:
Massey, Douglas S.; Rothwell, Jonathan; Domina, Thurston (2009-10-26).
4297:
4258:
35:
4141:"Housing Patterns: Appendix B: Measures of Residential Segregation"
4281:
4190:
The Annals of the
American Academy of Political and Social Science
1545:
We finally return to the formula for the Index of
Dissimilarity (
638:
which shows the number of poor people in each block of our city:
539:
which shows the number of rich people in each block of our city:
142:
4243:"Segregation and Diversity Measures in Population Distribution"
440:
2444:{\displaystyle {\hat {\mathbf {r} }}-{\hat {\mathbf {p} }}=-=}
1227:
by its norm, we get what is called the normalized vector or
265:
where (comparing a black and white population, for example):
3659:
As another example, suppose you have a city with 3 blocks:
2301:{\displaystyle {\hat {\mathbf {r} }}-{\hat {\mathbf {p} }}}
1757:
1196:{\displaystyle P=|\mathbf {p} |_{1}=\sum _{i=1}^{N}|p_{i}|}
1083:{\displaystyle R=|\mathbf {r} |_{1}=\sum _{i=1}^{N}|r_{i}|}
2897:-norm, we know that we can replace it with the summation:
923:{\displaystyle |\mathbf {v} |_{1}=\sum _{i=1}^{N}|v_{i}|}
4186:"The Changing Bases of Segregation in the United States"
4088:{\displaystyle \mathbf {\hat {r}} =\mathbf {\hat {p}} }
3649:{\displaystyle \mathbf {\hat {r}} =\mathbf {\hat {p}} }
3275:{\displaystyle \mathbf {\hat {r}} =\mathbf {\hat {p}} }
4280:
Massey, Douglas S.; Denton, Nancy A. (December 1988).
1112:
as the total number of poor people in our city, then:
4057:
3930:
3852:
3806:
3762:
3714:
3667:
3618:
3535:
3453:
3413:
3375:
3333:
3292:
3244:
3216:
3179:
3010:
2905:
2876:
2797:
2773:
2751:
2668:
2646:
2626:
2481:
2459:
2316:
2266:
2148:
2031:
1977:
1926:
1870:
1817:
1793:
1771:
1670:
1629:
1598:
1571:
1551:
1467:
1384:
1360:
1338:
1269:
1236:
1211:
1120:
1098:
1007:
978:
958:
938:
853:
824:
751:
722:
646:
622:
547:
523:
471:
449:
346:
167:
158:
The basic formula for the index of dissimilarity is:
4183:
2620:We can prove that the Linear Algebraic formula for
60:. Unsourced material may be challenged and removed.
4334:http://enceladus.isr.umich.edu/race/calculate.html
4087:
4041:
3915:
3836:
3792:
3746:
3699:
3648:
3602:
3520:
3437:
3399:
3359:
3318:
3274:
3228:
3191:
3158:
2992:
2889:
2860:
2781:
2759:
2735:
2652:
2632:
2605:
2465:
2443:
2300:
2250:
2133:
2013:
1962:
1908:
1855:
1801:
1779:
1737:
1646:
1615:
1584:
1557:
1535:
1452:
1368:
1346:
1322:
1253:
1219:
1195:
1104:
1082:
991:
964:
944:
922:
837:
810:
735:
705:
630:
606:
531:
507:
455:
359:
254:
4079:
4064:
3937:
3859:
3640:
3625:
3542:
3460:
3266:
3251:
2660:. Let's start with the Linear Algebraic formula:
2023:Next, let's normalize the rich and poor vectors:
4347:
2453:Finally, let's find the index of dissimilarity (
308:The index of dissimilarity is applicable to any
2615:
430:
4279:
4095:, thus this city also has zero segregation.
1592:-norm of the difference between the vectors
502:
472:
4282:"The Dimensions of Residential Segregation"
3407:, and the total number of poor people is
4217:
3369:Then, the total number of rich people is
120:Learn how and when to remove this message
1756:
3656:, thus this city has zero segregation.
14:
4348:
2640:is identical to the basic formula for
1748:
1565:); it is simply equal to one-half the
4240:
4042:{\displaystyle \mathbf {\hat {p}} ==}
3603:{\displaystyle \mathbf {\hat {p}} ==}
3521:{\displaystyle \mathbf {\hat {r}} ==}
2745:Let's replace the normalized vectors
1647:{\displaystyle {\hat {\mathbf {p} }}}
1616:{\displaystyle {\hat {\mathbf {r} }}}
1254:{\displaystyle {\hat {\mathbf {v} }}}
3916:{\displaystyle \mathbf {\hat {r}} =}
2870:Finally, from the definition of the
2260:We can now calculate the difference
1765:Firstly, let's find the rich vector
319:
58:adding citations to reliable sources
29:
3168:
294:= the population of group B in the
275:= the population of group A in the
24:
4138:
25:
4367:
4327:
3837:{\displaystyle P=100+200+300=600}
1332:Let us normalize the rich vector
616:Similarly, let's create a vector
4076:
4061:
3934:
3856:
3716:
3669:
3637:
3622:
3539:
3457:
3335:
3294:
3263:
3248:
3053:
3036:
2838:
2823:
2775:
2753:
2711:
2694:
2524:
2507:
2338:
2321:
2288:
2271:
2169:
2153:
2052:
2036:
1872:
1819:
1795:
1773:
1713:
1696:
1634:
1603:
1524:
1499:
1488:
1472:
1441:
1416:
1405:
1389:
1362:
1340:
1301:
1290:
1274:
1241:
1213:
1133:
1020:
860:
753:
648:
624:
549:
525:
153:
34:
45:needs additional citations for
4312:
4273:
4234:
4177:
4132:
4036:
3994:
3988:
3946:
3910:
3868:
3741:
3723:
3694:
3676:
3597:
3585:
3579:
3551:
3515:
3503:
3497:
3469:
3354:
3342:
3313:
3301:
3152:
3110:
3065:
3057:
3040:
3028:
2986:
2944:
2723:
2715:
2698:
2686:
2594:
2590:
2579:
2571:
2563:
2559:
2536:
2528:
2511:
2499:
2438:
2411:
2405:
2381:
2375:
2351:
2342:
2325:
2292:
2275:
2245:
2221:
2215:
2191:
2157:
2128:
2104:
2098:
2074:
2040:
1903:
1879:
1850:
1826:
1725:
1717:
1700:
1688:
1662:(in Linear Algebraic notation)
1638:
1607:
1505:
1494:
1476:
1422:
1411:
1393:
1307:
1296:
1278:
1245:
1189:
1174:
1139:
1128:
1076:
1061:
1026:
1015:
916:
901:
866:
855:
805:
760:
700:
655:
601:
556:
13:
1:
4125:
3800:rich people in our city, and
3747:{\displaystyle \mathbf {p} =}
3700:{\displaystyle \mathbf {r} =}
3438:{\displaystyle P=100+100=200}
3360:{\displaystyle \mathbf {p} =}
3319:{\displaystyle \mathbf {r} =}
1909:{\displaystyle \mathbf {p} =}
1856:{\displaystyle \mathbf {r} =}
811:{\displaystyle \mathbf {v} =}
706:{\displaystyle \mathbf {p} =}
607:{\displaystyle \mathbf {r} =}
443:). Suppose our city contains
2782:{\displaystyle \mathbf {p} }
2760:{\displaystyle \mathbf {r} }
2616:Equivalence between formulae
1802:{\displaystyle \mathbf {p} }
1780:{\displaystyle \mathbf {r} }
1369:{\displaystyle \mathbf {p} }
1347:{\displaystyle \mathbf {r} }
1220:{\displaystyle \mathbf {v} }
631:{\displaystyle \mathbf {p} }
532:{\displaystyle \mathbf {r} }
7:
4105:Kullback–Leibler divergence
4098:
2014:{\displaystyle P=0+2+1+1=4}
1963:{\displaystyle R=2+0+1+1=4}
10:
4372:
4319:Wolfram MathWorld: L1 Norm
4241:White, Michael J. (1986).
431:Linear algebra perspective
3793:{\displaystyle R=1+2+3=6}
4202:10.1177/0002716209343558
1205:When we divide a vector
1092:Similarly, if we denote
69:"Index of dissimilarity"
3400:{\displaystyle R=4+4=8}
279:area, e.g. census tract
4089:
4043:
3917:
3838:
3794:
3748:
3701:
3650:
3604:
3522:
3439:
3401:
3361:
3320:
3276:
3230:
3193:
3160:
3108:
2994:
2942:
2891:
2862:
2783:
2761:
2737:
2654:
2634:
2607:
2467:
2445:
2302:
2252:
2135:
2015:
1964:
1910:
1857:
1803:
1781:
1762:
1739:
1658:Index of Dissimilarity
1648:
1617:
1586:
1559:
1537:
1454:
1370:
1348:
1324:
1255:
1221:
1197:
1172:
1106:
1084:
1059:
993:
966:
946:
924:
899:
839:
812:
737:
707:
632:
608:
533:
517:Let's create a vector
509:
457:
361:
256:
204:
134:index of dissimilarity
4090:
4044:
3918:
3839:
3795:
3749:
3702:
3651:
3605:
3523:
3440:
3402:
3362:
3321:
3277:
3231:
3194:
3161:
3088:
2995:
2922:
2892:
2890:{\displaystyle L^{1}}
2863:
2784:
2762:
2738:
2655:
2635:
2608:
2468:
2446:
2303:
2253:
2136:
2016:
1965:
1911:
1858:
1804:
1782:
1760:
1740:
1649:
1618:
1587:
1585:{\displaystyle L^{1}}
1560:
1538:
1455:
1371:
1349:
1325:
1256:
1222:
1198:
1152:
1107:
1085:
1039:
994:
992:{\displaystyle L^{1}}
967:
947:
925:
879:
840:
838:{\displaystyle L^{1}}
813:
738:
736:{\displaystyle L^{1}}
708:
633:
609:
534:
510:
458:
362:
360:{\displaystyle D_{i}}
257:
184:
4055:
3928:
3850:
3804:
3760:
3712:
3665:
3616:
3533:
3451:
3411:
3373:
3331:
3290:
3242:
3214:
3177:
3008:
2903:
2874:
2795:
2771:
2749:
2666:
2644:
2624:
2479:
2457:
2314:
2264:
2146:
2029:
1975:
1924:
1868:
1815:
1791:
1769:
1668:
1627:
1596:
1569:
1549:
1465:
1382:
1358:
1354:and the poor vector
1336:
1267:
1234:
1209:
1118:
1096:
1005:
976:
972:would be to use the
956:
936:
851:
822:
749:
720:
644:
620:
545:
521:
469:
447:
344:
310:categorical variable
165:
54:improve this article
4139:Bureau, US Census.
3844:poor people. Thus:
3229:{\displaystyle D=0}
3192:{\displaystyle D=0}
328:
27:Demographic measure
18:Dissimilarity index
4339:2011-05-17 at the
4169:has generic name (
4115:self-dissimilarity
4085:
4039:
3913:
3834:
3790:
3744:
3697:
3646:
3600:
3518:
3435:
3397:
3357:
3316:
3272:
3226:
3189:
3156:
2990:
2887:
2858:
2779:
2757:
2733:
2650:
2630:
2603:
2463:
2441:
2298:
2248:
2131:
2011:
1960:
1906:
1853:
1799:
1777:
1763:
1735:
1644:
1613:
1582:
1555:
1533:
1450:
1366:
1344:
1320:
1251:
1217:
1193:
1102:
1080:
989:
962:
942:
920:
835:
808:
733:
703:
628:
604:
529:
505:
453:
357:
327:
252:
4082:
4067:
3940:
3862:
3643:
3628:
3545:
3463:
3269:
3254:
3199:, it means that:
3149:
3129:
3086:
3060:
3043:
3025:
2983:
2963:
2920:
2845:
2830:
2812:
2718:
2701:
2683:
2653:{\displaystyle D}
2633:{\displaystyle D}
2557:
2531:
2514:
2496:
2466:{\displaystyle D}
2345:
2328:
2295:
2278:
2189:
2176:
2160:
2072:
2059:
2043:
1749:Numerical example
1720:
1703:
1685:
1641:
1610:
1558:{\displaystyle D}
1531:
1516:
1479:
1448:
1433:
1396:
1318:
1281:
1248:
1105:{\displaystyle P}
965:{\displaystyle R}
945:{\displaystyle R}
500:
486:
478:
456:{\displaystyle N}
428:
427:
320:Numerical Example
245:
225:
182:
130:
129:
122:
104:
16:(Redirected from
4363:
4321:
4316:
4310:
4309:
4277:
4271:
4270:
4247:Population Index
4238:
4232:
4231:
4221:
4181:
4175:
4174:
4168:
4164:
4162:
4154:
4152:
4151:
4136:
4094:
4092:
4091:
4086:
4084:
4083:
4075:
4069:
4068:
4060:
4048:
4046:
4045:
4040:
4032:
4018:
4004:
3984:
3970:
3956:
3942:
3941:
3933:
3922:
3920:
3919:
3914:
3906:
3892:
3878:
3864:
3863:
3855:
3843:
3841:
3840:
3835:
3799:
3797:
3796:
3791:
3753:
3751:
3750:
3745:
3719:
3706:
3704:
3703:
3698:
3672:
3655:
3653:
3652:
3647:
3645:
3644:
3636:
3630:
3629:
3621:
3609:
3607:
3606:
3601:
3575:
3561:
3547:
3546:
3538:
3527:
3525:
3524:
3519:
3493:
3479:
3465:
3464:
3456:
3444:
3442:
3441:
3436:
3406:
3404:
3403:
3398:
3366:
3364:
3363:
3358:
3338:
3325:
3323:
3322:
3317:
3297:
3281:
3279:
3278:
3273:
3271:
3270:
3262:
3256:
3255:
3247:
3235:
3233:
3232:
3227:
3198:
3196:
3195:
3190:
3169:Zero segregation
3165:
3163:
3162:
3157:
3155:
3150:
3145:
3144:
3135:
3130:
3125:
3124:
3115:
3113:
3107:
3102:
3087:
3079:
3074:
3073:
3068:
3062:
3061:
3056:
3051:
3045:
3044:
3039:
3034:
3031:
3026:
3018:
2999:
2997:
2996:
2991:
2989:
2984:
2979:
2978:
2969:
2964:
2959:
2958:
2949:
2947:
2941:
2936:
2921:
2913:
2896:
2894:
2893:
2888:
2886:
2885:
2867:
2865:
2864:
2859:
2857:
2856:
2851:
2847:
2846:
2841:
2836:
2831:
2826:
2821:
2813:
2805:
2788:
2786:
2785:
2780:
2778:
2766:
2764:
2763:
2758:
2756:
2742:
2740:
2739:
2734:
2732:
2731:
2726:
2720:
2719:
2714:
2709:
2703:
2702:
2697:
2692:
2689:
2684:
2676:
2659:
2657:
2656:
2651:
2639:
2637:
2636:
2631:
2612:
2610:
2609:
2604:
2593:
2582:
2574:
2566:
2558:
2550:
2545:
2544:
2539:
2533:
2532:
2527:
2522:
2516:
2515:
2510:
2505:
2502:
2497:
2489:
2472:
2470:
2469:
2464:
2450:
2448:
2447:
2442:
2347:
2346:
2341:
2336:
2330:
2329:
2324:
2319:
2307:
2305:
2304:
2299:
2297:
2296:
2291:
2286:
2280:
2279:
2274:
2269:
2257:
2255:
2254:
2249:
2190:
2182:
2177:
2172:
2167:
2162:
2161:
2156:
2151:
2140:
2138:
2137:
2132:
2073:
2065:
2060:
2055:
2050:
2045:
2044:
2039:
2034:
2020:
2018:
2017:
2012:
1969:
1967:
1966:
1961:
1915:
1913:
1912:
1907:
1875:
1862:
1860:
1859:
1854:
1822:
1808:
1806:
1805:
1800:
1798:
1787:and poor vector
1786:
1784:
1783:
1778:
1776:
1744:
1742:
1741:
1736:
1734:
1733:
1728:
1722:
1721:
1716:
1711:
1705:
1704:
1699:
1694:
1691:
1686:
1678:
1653:
1651:
1650:
1645:
1643:
1642:
1637:
1632:
1622:
1620:
1619:
1614:
1612:
1611:
1606:
1601:
1591:
1589:
1588:
1583:
1581:
1580:
1564:
1562:
1561:
1556:
1542:
1540:
1539:
1534:
1532:
1527:
1522:
1517:
1515:
1514:
1513:
1508:
1502:
1497:
1491:
1486:
1481:
1480:
1475:
1470:
1459:
1457:
1456:
1451:
1449:
1444:
1439:
1434:
1432:
1431:
1430:
1425:
1419:
1414:
1408:
1403:
1398:
1397:
1392:
1387:
1375:
1373:
1372:
1367:
1365:
1353:
1351:
1350:
1345:
1343:
1329:
1327:
1326:
1321:
1319:
1317:
1316:
1315:
1310:
1304:
1299:
1293:
1288:
1283:
1282:
1277:
1272:
1260:
1258:
1257:
1252:
1250:
1249:
1244:
1239:
1226:
1224:
1223:
1218:
1216:
1202:
1200:
1199:
1194:
1192:
1187:
1186:
1177:
1171:
1166:
1148:
1147:
1142:
1136:
1131:
1111:
1109:
1108:
1103:
1089:
1087:
1086:
1081:
1079:
1074:
1073:
1064:
1058:
1053:
1035:
1034:
1029:
1023:
1018:
998:
996:
995:
990:
988:
987:
971:
969:
968:
963:
951:
949:
948:
943:
929:
927:
926:
921:
919:
914:
913:
904:
898:
893:
875:
874:
869:
863:
858:
844:
842:
841:
836:
834:
833:
817:
815:
814:
809:
804:
803:
785:
784:
772:
771:
756:
742:
740:
739:
734:
732:
731:
712:
710:
709:
704:
699:
698:
680:
679:
667:
666:
651:
637:
635:
634:
629:
627:
613:
611:
610:
605:
600:
599:
581:
580:
568:
567:
552:
538:
536:
535:
530:
528:
514:
512:
511:
506:
501:
498:
487:
484:
479:
476:
462:
460:
459:
454:
366:
364:
363:
358:
356:
355:
329:
326:
261:
259:
258:
253:
251:
247:
246:
241:
240:
231:
226:
221:
220:
211:
203:
198:
183:
175:
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
4371:
4370:
4366:
4365:
4364:
4362:
4361:
4360:
4346:
4345:
4341:Wayback Machine
4330:
4325:
4324:
4317:
4313:
4298:10.2307/2579183
4278:
4274:
4259:10.2307/3644339
4239:
4235:
4182:
4178:
4166:
4165:
4156:
4155:
4149:
4147:
4137:
4133:
4128:
4110:Isolation index
4101:
4074:
4073:
4059:
4058:
4056:
4053:
4052:
4051:Again, because
4028:
4014:
4000:
3980:
3966:
3952:
3932:
3931:
3929:
3926:
3925:
3902:
3888:
3874:
3854:
3853:
3851:
3848:
3847:
3805:
3802:
3801:
3761:
3758:
3757:
3715:
3713:
3710:
3709:
3668:
3666:
3663:
3662:
3635:
3634:
3620:
3619:
3617:
3614:
3613:
3571:
3557:
3537:
3536:
3534:
3531:
3530:
3489:
3475:
3455:
3454:
3452:
3449:
3448:
3412:
3409:
3408:
3374:
3371:
3370:
3334:
3332:
3329:
3328:
3293:
3291:
3288:
3287:
3261:
3260:
3246:
3245:
3243:
3240:
3239:
3215:
3212:
3211:
3178:
3175:
3174:
3171:
3151:
3140:
3136:
3134:
3120:
3116:
3114:
3109:
3103:
3092:
3078:
3069:
3064:
3063:
3052:
3050:
3049:
3035:
3033:
3032:
3027:
3017:
3009:
3006:
3005:
2985:
2974:
2970:
2968:
2954:
2950:
2948:
2943:
2937:
2926:
2912:
2904:
2901:
2900:
2881:
2877:
2875:
2872:
2871:
2852:
2837:
2835:
2822:
2820:
2819:
2815:
2814:
2804:
2796:
2793:
2792:
2774:
2772:
2769:
2768:
2752:
2750:
2747:
2746:
2727:
2722:
2721:
2710:
2708:
2707:
2693:
2691:
2690:
2685:
2675:
2667:
2664:
2663:
2645:
2642:
2641:
2625:
2622:
2621:
2618:
2589:
2578:
2570:
2562:
2549:
2540:
2535:
2534:
2523:
2521:
2520:
2506:
2504:
2503:
2498:
2488:
2480:
2477:
2476:
2458:
2455:
2454:
2337:
2335:
2334:
2320:
2318:
2317:
2315:
2312:
2311:
2287:
2285:
2284:
2270:
2268:
2267:
2265:
2262:
2261:
2181:
2168:
2166:
2152:
2150:
2149:
2147:
2144:
2143:
2064:
2051:
2049:
2035:
2033:
2032:
2030:
2027:
2026:
1976:
1973:
1972:
1925:
1922:
1921:
1871:
1869:
1866:
1865:
1818:
1816:
1813:
1812:
1794:
1792:
1789:
1788:
1772:
1770:
1767:
1766:
1751:
1746:
1729:
1724:
1723:
1712:
1710:
1709:
1695:
1693:
1692:
1687:
1677:
1669:
1666:
1665:
1660:
1633:
1631:
1630:
1628:
1625:
1624:
1602:
1600:
1599:
1597:
1594:
1593:
1576:
1572:
1570:
1567:
1566:
1550:
1547:
1546:
1523:
1521:
1509:
1504:
1503:
1498:
1493:
1492:
1487:
1485:
1471:
1469:
1468:
1466:
1463:
1462:
1440:
1438:
1426:
1421:
1420:
1415:
1410:
1409:
1404:
1402:
1388:
1386:
1385:
1383:
1380:
1379:
1361:
1359:
1356:
1355:
1339:
1337:
1334:
1333:
1311:
1306:
1305:
1300:
1295:
1294:
1289:
1287:
1273:
1271:
1270:
1268:
1265:
1264:
1240:
1238:
1237:
1235:
1232:
1231:
1212:
1210:
1207:
1206:
1188:
1182:
1178:
1173:
1167:
1156:
1143:
1138:
1137:
1132:
1127:
1119:
1116:
1115:
1097:
1094:
1093:
1075:
1069:
1065:
1060:
1054:
1043:
1030:
1025:
1024:
1019:
1014:
1006:
1003:
1002:
983:
979:
977:
974:
973:
957:
954:
953:
937:
934:
933:
915:
909:
905:
900:
894:
883:
870:
865:
864:
859:
854:
852:
849:
848:
829:
825:
823:
820:
819:
799:
795:
780:
776:
767:
763:
752:
750:
747:
746:
727:
723:
721:
718:
717:
694:
690:
675:
671:
662:
658:
647:
645:
642:
641:
623:
621:
618:
617:
595:
591:
576:
572:
563:
559:
548:
546:
543:
542:
524:
522:
519:
518:
497:
483:
475:
470:
467:
466:
448:
445:
444:
433:
351:
347:
345:
342:
341:
322:
314:social mobility
292:
273:
236:
232:
230:
216:
212:
210:
209:
205:
199:
188:
174:
166:
163:
162:
156:
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
4369:
4359:
4358:
4344:
4343:
4329:
4328:External links
4326:
4323:
4322:
4311:
4272:
4253:(2): 198–221.
4233:
4176:
4130:
4129:
4127:
4124:
4123:
4122:
4117:
4112:
4107:
4100:
4097:
4081:
4078:
4072:
4066:
4063:
4038:
4035:
4031:
4027:
4024:
4021:
4017:
4013:
4010:
4007:
4003:
3999:
3996:
3993:
3990:
3987:
3983:
3979:
3976:
3973:
3969:
3965:
3962:
3959:
3955:
3951:
3948:
3945:
3939:
3936:
3912:
3909:
3905:
3901:
3898:
3895:
3891:
3887:
3884:
3881:
3877:
3873:
3870:
3867:
3861:
3858:
3833:
3830:
3827:
3824:
3821:
3818:
3815:
3812:
3809:
3789:
3786:
3783:
3780:
3777:
3774:
3771:
3768:
3765:
3756:Then, we have
3743:
3740:
3737:
3734:
3731:
3728:
3725:
3722:
3718:
3696:
3693:
3690:
3687:
3684:
3681:
3678:
3675:
3671:
3642:
3639:
3633:
3627:
3624:
3599:
3596:
3593:
3590:
3587:
3584:
3581:
3578:
3574:
3570:
3567:
3564:
3560:
3556:
3553:
3550:
3544:
3541:
3517:
3514:
3511:
3508:
3505:
3502:
3499:
3496:
3492:
3488:
3485:
3482:
3478:
3474:
3471:
3468:
3462:
3459:
3434:
3431:
3428:
3425:
3422:
3419:
3416:
3396:
3393:
3390:
3387:
3384:
3381:
3378:
3356:
3353:
3350:
3347:
3344:
3341:
3337:
3315:
3312:
3309:
3306:
3303:
3300:
3296:
3268:
3265:
3259:
3253:
3250:
3225:
3222:
3219:
3208:
3207:
3204:
3188:
3185:
3182:
3170:
3167:
3154:
3148:
3143:
3139:
3133:
3128:
3123:
3119:
3112:
3106:
3101:
3098:
3095:
3091:
3085:
3082:
3077:
3072:
3067:
3059:
3055:
3048:
3042:
3038:
3030:
3024:
3021:
3016:
3013:
2988:
2982:
2977:
2973:
2967:
2962:
2957:
2953:
2946:
2940:
2935:
2932:
2929:
2925:
2919:
2916:
2911:
2908:
2884:
2880:
2855:
2850:
2844:
2840:
2834:
2829:
2825:
2818:
2811:
2808:
2803:
2800:
2777:
2755:
2730:
2725:
2717:
2713:
2706:
2700:
2696:
2688:
2682:
2679:
2674:
2671:
2649:
2629:
2617:
2614:
2602:
2599:
2596:
2592:
2588:
2585:
2581:
2577:
2573:
2569:
2565:
2561:
2556:
2553:
2548:
2543:
2538:
2530:
2526:
2519:
2513:
2509:
2501:
2495:
2492:
2487:
2484:
2462:
2440:
2437:
2434:
2431:
2428:
2425:
2422:
2419:
2416:
2413:
2410:
2407:
2404:
2401:
2398:
2395:
2392:
2389:
2386:
2383:
2380:
2377:
2374:
2371:
2368:
2365:
2362:
2359:
2356:
2353:
2350:
2344:
2340:
2333:
2327:
2323:
2294:
2290:
2283:
2277:
2273:
2247:
2244:
2241:
2238:
2235:
2232:
2229:
2226:
2223:
2220:
2217:
2214:
2211:
2208:
2205:
2202:
2199:
2196:
2193:
2188:
2185:
2180:
2175:
2171:
2165:
2159:
2155:
2130:
2127:
2124:
2121:
2118:
2115:
2112:
2109:
2106:
2103:
2100:
2097:
2094:
2091:
2088:
2085:
2082:
2079:
2076:
2071:
2068:
2063:
2058:
2054:
2048:
2042:
2038:
2010:
2007:
2004:
2001:
1998:
1995:
1992:
1989:
1986:
1983:
1980:
1959:
1956:
1953:
1950:
1947:
1944:
1941:
1938:
1935:
1932:
1929:
1905:
1902:
1899:
1896:
1893:
1890:
1887:
1884:
1881:
1878:
1874:
1852:
1849:
1846:
1843:
1840:
1837:
1834:
1831:
1828:
1825:
1821:
1797:
1775:
1750:
1747:
1732:
1727:
1719:
1715:
1708:
1702:
1698:
1690:
1684:
1681:
1676:
1673:
1656:
1640:
1636:
1609:
1605:
1579:
1575:
1554:
1530:
1526:
1520:
1512:
1507:
1501:
1496:
1490:
1484:
1478:
1474:
1447:
1443:
1437:
1429:
1424:
1418:
1413:
1407:
1401:
1395:
1391:
1364:
1342:
1314:
1309:
1303:
1298:
1292:
1286:
1280:
1276:
1247:
1243:
1215:
1191:
1185:
1181:
1176:
1170:
1165:
1162:
1159:
1155:
1151:
1146:
1141:
1135:
1130:
1126:
1123:
1101:
1078:
1072:
1068:
1063:
1057:
1052:
1049:
1046:
1042:
1038:
1033:
1028:
1022:
1017:
1013:
1010:
986:
982:
961:
941:
918:
912:
908:
903:
897:
892:
889:
886:
882:
878:
873:
868:
862:
857:
832:
828:
818:, we have the
807:
802:
798:
794:
791:
788:
783:
779:
775:
770:
766:
762:
759:
755:
730:
726:
702:
697:
693:
689:
686:
683:
678:
674:
670:
665:
661:
657:
654:
650:
626:
603:
598:
594:
590:
587:
584:
579:
575:
571:
566:
562:
558:
555:
551:
527:
504:
496:
493:
490:
482:
474:
452:
437:Linear algebra
432:
429:
426:
425:
422:
419:
416:
410:
409:
406:
403:
400:
396:
395:
392:
389:
386:
382:
381:
378:
375:
372:
368:
367:
354:
350:
339:
336:
333:
321:
318:
306:
305:
299:
290:
286:
280:
271:
263:
262:
250:
244:
239:
235:
229:
224:
219:
215:
208:
202:
197:
194:
191:
187:
181:
178:
173:
170:
155:
152:
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
4368:
4357:
4356:Index numbers
4354:
4353:
4351:
4342:
4338:
4335:
4332:
4331:
4320:
4315:
4307:
4303:
4299:
4295:
4291:
4287:
4286:Social Forces
4283:
4276:
4268:
4264:
4260:
4256:
4252:
4248:
4244:
4237:
4229:
4225:
4220:
4215:
4211:
4207:
4203:
4199:
4195:
4191:
4187:
4180:
4172:
4160:
4146:
4142:
4135:
4131:
4121:
4118:
4116:
4113:
4111:
4108:
4106:
4103:
4102:
4096:
4070:
4049:
4033:
4029:
4025:
4022:
4019:
4015:
4011:
4008:
4005:
4001:
3997:
3991:
3985:
3981:
3977:
3974:
3971:
3967:
3963:
3960:
3957:
3953:
3949:
3943:
3923:
3907:
3903:
3899:
3896:
3893:
3889:
3885:
3882:
3879:
3875:
3871:
3865:
3845:
3831:
3828:
3825:
3822:
3819:
3816:
3813:
3810:
3807:
3787:
3784:
3781:
3778:
3775:
3772:
3769:
3766:
3763:
3754:
3738:
3735:
3732:
3729:
3726:
3720:
3707:
3691:
3688:
3685:
3682:
3679:
3673:
3660:
3657:
3631:
3610:
3594:
3591:
3588:
3582:
3576:
3572:
3568:
3565:
3562:
3558:
3554:
3548:
3528:
3512:
3509:
3506:
3500:
3494:
3490:
3486:
3483:
3480:
3476:
3472:
3466:
3446:
3432:
3429:
3426:
3423:
3420:
3417:
3414:
3394:
3391:
3388:
3385:
3382:
3379:
3376:
3367:
3351:
3348:
3345:
3339:
3326:
3310:
3307:
3304:
3298:
3285:
3282:
3257:
3237:
3223:
3220:
3217:
3205:
3202:
3201:
3200:
3186:
3183:
3180:
3166:
3146:
3141:
3137:
3131:
3126:
3121:
3117:
3104:
3099:
3096:
3093:
3089:
3083:
3080:
3075:
3070:
3046:
3022:
3019:
3014:
3011:
3003:
3000:
2980:
2975:
2971:
2965:
2960:
2955:
2951:
2938:
2933:
2930:
2927:
2923:
2917:
2914:
2909:
2906:
2898:
2882:
2878:
2868:
2853:
2848:
2842:
2832:
2827:
2816:
2809:
2806:
2801:
2798:
2790:
2743:
2728:
2704:
2680:
2677:
2672:
2669:
2661:
2647:
2627:
2613:
2600:
2597:
2586:
2583:
2575:
2567:
2554:
2551:
2546:
2541:
2517:
2493:
2490:
2485:
2482:
2474:
2460:
2451:
2435:
2432:
2429:
2426:
2423:
2420:
2417:
2414:
2408:
2402:
2399:
2396:
2393:
2390:
2387:
2384:
2378:
2372:
2369:
2366:
2363:
2360:
2357:
2354:
2348:
2331:
2309:
2281:
2258:
2242:
2239:
2236:
2233:
2230:
2227:
2224:
2218:
2212:
2209:
2206:
2203:
2200:
2197:
2194:
2186:
2183:
2178:
2173:
2163:
2141:
2125:
2122:
2119:
2116:
2113:
2110:
2107:
2101:
2095:
2092:
2089:
2086:
2083:
2080:
2077:
2069:
2066:
2061:
2056:
2046:
2024:
2021:
2008:
2005:
2002:
1999:
1996:
1993:
1990:
1987:
1984:
1981:
1978:
1970:
1957:
1954:
1951:
1948:
1945:
1942:
1939:
1936:
1933:
1930:
1927:
1919:
1916:
1900:
1897:
1894:
1891:
1888:
1885:
1882:
1876:
1863:
1847:
1844:
1841:
1838:
1835:
1832:
1829:
1823:
1810:
1759:
1755:
1745:
1730:
1706:
1682:
1679:
1674:
1671:
1663:
1659:
1655:
1577:
1573:
1552:
1543:
1528:
1518:
1510:
1482:
1460:
1445:
1435:
1427:
1399:
1377:
1330:
1312:
1284:
1262:
1230:
1203:
1183:
1179:
1168:
1163:
1160:
1157:
1153:
1149:
1144:
1124:
1121:
1113:
1099:
1090:
1070:
1066:
1055:
1050:
1047:
1044:
1040:
1036:
1031:
1011:
1008:
1000:
984:
980:
959:
939:
932:If we denote
930:
910:
906:
895:
890:
887:
884:
880:
876:
871:
846:
830:
826:
800:
796:
792:
789:
786:
781:
777:
773:
768:
764:
757:
744:
728:
724:
713:
695:
691:
687:
684:
681:
676:
672:
668:
663:
659:
652:
639:
614:
596:
592:
588:
585:
582:
577:
573:
569:
564:
560:
553:
540:
515:
494:
491:
488:
480:
464:
450:
442:
438:
423:
420:
417:
415:
412:
411:
407:
404:
401:
398:
397:
393:
390:
387:
384:
383:
379:
376:
373:
370:
369:
352:
348:
340:
337:
334:
332:Neighborhood
331:
330:
325:
317:
315:
311:
303:
300:
297:
293:
287:
284:
281:
278:
274:
268:
267:
266:
248:
242:
237:
233:
227:
222:
217:
213:
206:
200:
195:
192:
189:
185:
179:
176:
171:
168:
161:
160:
159:
154:Basic formula
151:
149:
144:
139:
135:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
4314:
4289:
4285:
4275:
4250:
4246:
4236:
4196:(1): 74–90.
4193:
4189:
4179:
4148:. Retrieved
4144:
4134:
4120:Hoover index
4050:
3924:
3846:
3755:
3708:
3661:
3658:
3611:
3529:
3447:
3368:
3327:
3286:
3283:
3238:
3209:
3172:
3004:
3001:
2899:
2869:
2791:
2744:
2662:
2619:
2475:
2452:
2310:
2259:
2142:
2025:
2022:
1971:
1920:
1917:
1864:
1811:
1764:
1752:
1664:
1661:
1657:
1544:
1461:
1378:
1331:
1263:
1204:
1114:
1091:
1001:
931:
847:
714:
640:
615:
541:
516:
465:
434:
413:
323:
307:
301:
295:
288:
282:
276:
269:
264:
157:
133:
131:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
4167:|last=
1229:Unit vector
148:segregation
138:demographic
4292:(2): 281.
4150:2022-04-28
4145:Census.gov
4126:References
3210:If we set
143:percentage
80:newspapers
4306:0037-7732
4267:0032-4701
4210:0002-7162
4080:^
4065:^
3938:^
3860:^
3641:^
3626:^
3543:^
3461:^
3267:^
3252:^
3132:−
3090:∑
3058:^
3047:−
3041:^
2966:−
2924:∑
2833:−
2716:^
2705:−
2699:^
2584:−
2529:^
2518:−
2512:^
2421:−
2379:−
2343:^
2332:−
2326:^
2293:^
2282:−
2276:^
2158:^
2041:^
1718:^
1707:−
1701:^
1639:^
1608:^
1477:^
1394:^
1279:^
1246:^
1154:∑
1041:∑
881:∑
790:⋯
715:Now, the
685:⋯
586:⋯
492:…
228:−
186:∑
110:July 2018
4350:Category
4337:Archived
4228:24298193
4159:cite web
4099:See also
3612:Because
3445:. Thus:
463:blocks:
4219:3844132
999:-norm:
845:-norm:
499:block N
485:block 2
477:block 1
94:scholar
4304:
4265:
4226:
4216:
4208:
2789:with:
441:London
338:Black
335:White
96:
89:
82:
75:
67:
743:-norm
424:0.12
414:Total
408:0.03
394:0.03
380:0.06
136:is a
101:JSTOR
87:books
4302:ISSN
4263:ISSN
4224:PMID
4206:ISSN
4171:help
2767:and
2403:0.25
2397:0.25
2373:0.25
2367:0.25
2243:0.25
2237:0.25
2126:0.25
2120:0.25
1623:and
418:300
402:100
388:100
374:100
298:area
132:The
73:news
4294:doi
4255:doi
4214:PMC
4198:doi
4194:626
3986:600
3978:300
3972:600
3964:200
3958:600
3950:100
3832:600
3826:300
3820:200
3814:100
3739:300
3733:200
3727:100
3595:0.5
3589:0.5
3577:200
3569:100
3563:200
3555:100
3513:0.5
3507:0.5
3433:200
3427:100
3421:100
3352:100
3346:100
2601:0.5
2587:0.5
2568:0.5
2473:):
2424:0.5
2415:0.5
2391:0.5
2355:0.5
2231:0.5
2108:0.5
421:25
405:10
391:10
56:by
4352::
4300:.
4290:67
4288:.
4284:.
4261:.
4251:52
4249:.
4245:.
4222:.
4212:.
4204:.
4192:.
4188:.
4163::
4161:}}
4157:{{
4143:.
2308::
1809::
1654::
1376::
1261::
399:C
385:B
377:5
371:A
4308:.
4296::
4269:.
4257::
4230:.
4200::
4173:)
4153:.
4077:p
4071:=
4062:r
4037:]
4034:6
4030:/
4026:3
4023:,
4020:6
4016:/
4012:2
4009:,
4006:6
4002:/
3998:1
3995:[
3992:=
3989:]
3982:/
3975:,
3968:/
3961:,
3954:/
3947:[
3944:=
3935:p
3911:]
3908:6
3904:/
3900:3
3897:,
3894:6
3890:/
3886:2
3883:,
3880:6
3876:/
3872:1
3869:[
3866:=
3857:r
3829:=
3823:+
3817:+
3811:=
3808:P
3788:6
3785:=
3782:3
3779:+
3776:2
3773:+
3770:1
3767:=
3764:R
3742:]
3736:,
3730:,
3724:[
3721:=
3717:p
3695:]
3692:3
3689:,
3686:2
3683:,
3680:1
3677:[
3674:=
3670:r
3638:p
3632:=
3623:r
3598:]
3592:,
3586:[
3583:=
3580:]
3573:/
3566:,
3559:/
3552:[
3549:=
3540:p
3516:]
3510:,
3504:[
3501:=
3498:]
3495:8
3491:/
3487:4
3484:,
3481:8
3477:/
3473:4
3470:[
3467:=
3458:r
3430:=
3424:+
3418:=
3415:P
3395:8
3392:=
3389:4
3386:+
3383:4
3380:=
3377:R
3355:]
3349:,
3343:[
3340:=
3336:p
3314:]
3311:4
3308:,
3305:4
3302:[
3299:=
3295:r
3264:p
3258:=
3249:r
3224:0
3221:=
3218:D
3187:0
3184:=
3181:D
3153:|
3147:P
3142:i
3138:p
3127:R
3122:i
3118:r
3111:|
3105:N
3100:1
3097:=
3094:i
3084:2
3081:1
3076:=
3071:1
3066:|
3054:p
3037:r
3029:|
3023:2
3020:1
3015:=
3012:D
2987:|
2981:P
2976:i
2972:p
2961:R
2956:i
2952:r
2945:|
2939:N
2934:1
2931:=
2928:i
2918:2
2915:1
2910:=
2907:D
2883:1
2879:L
2854:1
2849:|
2843:P
2839:p
2828:R
2824:r
2817:|
2810:2
2807:1
2802:=
2799:D
2776:p
2754:r
2729:1
2724:|
2712:p
2695:r
2687:|
2681:2
2678:1
2673:=
2670:D
2648:D
2628:D
2598:=
2595:)
2591:|
2580:|
2576:+
2572:|
2564:|
2560:(
2555:2
2552:1
2547:=
2542:1
2537:|
2525:p
2508:r
2500:|
2494:2
2491:1
2486:=
2483:D
2461:D
2439:]
2436:0
2433:,
2430:0
2427:,
2418:,
2412:[
2409:=
2406:]
2400:,
2394:,
2388:,
2385:0
2382:[
2376:]
2370:,
2364:,
2361:0
2358:,
2352:[
2349:=
2339:p
2322:r
2289:p
2272:r
2246:]
2240:,
2234:,
2228:,
2225:0
2222:[
2219:=
2216:]
2213:1
2210:,
2207:1
2204:,
2201:2
2198:,
2195:0
2192:[
2187:4
2184:1
2179:=
2174:P
2170:p
2164:=
2154:p
2129:]
2123:,
2117:,
2114:0
2111:,
2105:[
2102:=
2099:]
2096:1
2093:,
2090:1
2087:,
2084:0
2081:,
2078:2
2075:[
2070:4
2067:1
2062:=
2057:R
2053:r
2047:=
2037:r
2009:4
2006:=
2003:1
2000:+
1997:1
1994:+
1991:2
1988:+
1985:0
1982:=
1979:P
1958:4
1955:=
1952:1
1949:+
1946:1
1943:+
1940:0
1937:+
1934:2
1931:=
1928:R
1904:]
1901:1
1898:,
1895:1
1892:,
1889:2
1886:,
1883:0
1880:[
1877:=
1873:p
1851:]
1848:1
1845:,
1842:1
1839:,
1836:0
1833:,
1830:2
1827:[
1824:=
1820:r
1796:p
1774:r
1731:1
1726:|
1714:p
1697:r
1689:|
1683:2
1680:1
1675:=
1672:D
1635:p
1604:r
1578:1
1574:L
1553:D
1529:P
1525:p
1519:=
1511:1
1506:|
1500:p
1495:|
1489:p
1483:=
1473:p
1446:R
1442:r
1436:=
1428:1
1423:|
1417:r
1412:|
1406:r
1400:=
1390:r
1363:p
1341:r
1313:1
1308:|
1302:v
1297:|
1291:v
1285:=
1275:v
1242:v
1214:v
1190:|
1184:i
1180:p
1175:|
1169:N
1164:1
1161:=
1158:i
1150:=
1145:1
1140:|
1134:p
1129:|
1125:=
1122:P
1100:P
1077:|
1071:i
1067:r
1062:|
1056:N
1051:1
1048:=
1045:i
1037:=
1032:1
1027:|
1021:r
1016:|
1012:=
1009:R
985:1
981:L
960:R
940:R
917:|
911:i
907:v
902:|
896:N
891:1
888:=
885:i
877:=
872:1
867:|
861:v
856:|
831:1
827:L
806:]
801:N
797:v
793:,
787:,
782:2
778:v
774:,
769:1
765:v
761:[
758:=
754:v
729:1
725:L
701:]
696:N
692:p
688:,
682:,
677:2
673:p
669:,
664:1
660:p
656:[
653:=
649:p
625:p
602:]
597:N
593:r
589:,
583:,
578:2
574:r
570:,
565:1
561:r
557:[
554:=
550:r
526:r
503:}
495:,
489:,
481:,
473:{
451:N
353:i
349:D
302:B
296:i
291:i
289:b
283:A
277:i
272:i
270:a
249:|
243:B
238:i
234:b
223:A
218:i
214:a
207:|
201:N
196:1
193:=
190:i
180:2
177:1
172:=
169:D
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
