2208:
521:, given the surface area of the lake covered by ice. However, melting the ice in a region of the lake by pouring salt onto it, will not cause bears to come out of hibernation. Nor will waking the bears by physically disturbing them cause the ice to melt. In this case the two quantities
1969:
causes the reaction to occur producing more product, or more reactant, respectively. It is standard to draw “harpoon-type” arrows in place of an equals sign, ⇌, to denote the reversible nature of the reaction and the dynamic causal relationship between reactants and products.
2183:
A causal diagram consists of a set of nodes which may or may not be interlinked by arrows. Arrows between nodes denote causal relationships with the arrow pointing from the cause to the effect. There exist several forms of causal diagrams including
51:
In nature and human societies, many phenomena have causal relationships where one phenomenon A (a cause) impacts another phenomenon B (an effect). Establishing causal relationships is the aim of many scientific studies across fields ranging from
3529:
4267:
3460:
4859:
4809:
4647:
4385:
3166:
75:
or many chemistry and mathematics textbooks. Mathematical conventions are also used, such as plotting an independent variable on a horizontal axis and a dependent variable on a vertical axis, or the notation
5556:
5506:
5249:
5174:
4597:
4435:
3876:
3583:
3320:
3270:
2860:
4120:
4070:
3826:
3633:
3013:
5037:
3773:
4016:
899:
4332:
5764:
2275:
2351:
2313:
1842:. Suppose an individual in this economy always keeps half of their value in the form of cows and the other half in the form of barrels of oil. Then, increasing their number of cows
2049:
3465:
1942:
1800:
1494:
5450:
5414:
5378:
5315:
4209:
1165:
990:
942:
109:
5342:
5279:
4951:
1194:
1019:
971:
5614:
5585:
5095:
5066:
4980:
4919:
4890:
4756:
4727:
4678:
4544:
4515:
4466:
4204:
4175:
3959:
3907:
3716:
3664:
3381:
3352:
3196:
3092:
3063:
2939:
2890:
2807:
2778:
2714:
2685:
2636:
2607:
2578:
2549:
2520:
2491:
2419:
2390:
1898:
1869:
1668:
1639:
1610:
1581:
1552:
1523:
1430:
1401:
1364:
1295:
1266:
1065:
844:
752:
658:
629:
577:
548:
519:
490:
461:
432:
403:
374:
345:
288:
219:
1145:
775:
706:
4146:
3930:
3687:
815:
4698:
4486:
3401:
3216:
3112:
3034:
2959:
2910:
2749:
2656:
2462:
2442:
2173:
2153:
2133:
2113:
2093:
2073:
1840:
1820:
1756:
1736:
1716:
1696:
1450:
1335:
1315:
1237:
1214:
1125:
1105:
1085:
1039:
922:
795:
726:
686:
600:
316:
259:
239:
190:
149:
129:
5950:{{Hitchcock, Christopher, "Causal Models", The Stanford Encyclopedia of Philosophy (Spring 2023 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = <
5558:) is one of pure correlation unless both expressions are proven to be bi-directional causal equalities. In that case, the overall causal relationship between
1981:, and specifically the do operator, is used to describe causal relationships in the language of probability. A notation used in do-calculus is, for instance:
158:
The following examples illustrate various types of causal relationships. These are followed by different notations used to represent causal relationships.
5755:
2226:
can be used to describe the graph structure of
Bayesian networks. Three possible patterns allowed in a 3-node directed acyclic graph (DAG) include:
3406:
5633:
Marshall, BarryJ; Warren, J.Robin (June 1984). "Unidentified curved bacilli in the stomach of patients with gastritis and peptic ulceration".
5900:
5875:
5850:
5825:
5797:
5963:
Van Horne N. and
Mukherjee M. Improved description of trapped ions as a modular electromechanical system, J. Appl. Phys. 135, 154401 (2024)
1758:. If a marketplace exists where cows can be traded for chickens which can in turn be traded for barrels of oil, one can write an equation
4814:
4764:
4602:
4340:
3121:
5935:
5511:
5461:
5179:
5104:
4552:
4390:
3831:
3538:
3275:
3225:
2815:
4075:
4025:
3781:
3588:
2968:
4985:
71:
To describe causal relationships between phenomena, non-quantitative visual notations are common, such as arrows, e.g. in the
3721:
5678:"Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment : A New Violation of Bell's Inequalities"
3964:
851:
4272:
290:
denote two quantities with an a priori unknown causal relationship, which can be related by a mathematical expression.
2248:
2212:
2201:
2324:
2286:
2197:
1957:
In chemistry, many chemical reactions are reversible and described using equations which tend towards a dynamic
68:. It is also a subject of accident analysis, and can be considered a prerequisite for effective policy making.
33:
5768:
5458:
It should be assumed that a relationship between two equations with identical senses of causality (such as
29:
23:
5726:
2189:
668:
Suppose an ideal solar-powered system is built such that if it is sunny and the sun provides an intensity
1987:
5951:
5731:
5689:
1958:
3462:. If a bi-directional causal relationship may exist, but this is not yet established, the notation
2193:
1966:
3524:{\displaystyle a\left(s\right)~{\overset {\curvearrowleft ?\curvearrowright }{=}}~b\left(s\right)}
5717:
Fischer, Stanley; Easterly, William (1990). "The economics of the government budget constraint".
5658:
4262:{\displaystyle a\left(s\right)~{\overset {\curvearrowright \curvearrowleft }{=}}~b\left(s\right)}
2207:
2200:(WBGs). The image below shows a partial why-because graph used to analyze the capsizing of the
1903:
1871:
by offering them 4 cows, will eventually lead to an increase in their number of barrels of oil
1761:
1455:
5979:
5931:
5896:
5871:
5846:
5821:
5793:
5650:
5419:
5383:
5347:
5284:
151:". Causal relationships are also described using quantitative mathematical expressions. (See
5736:
5697:
5642:
2223:
2185:
1150:
975:
927:
79:
5320:
5257:
4924:
1170:
995:
947:
5590:
5561:
5071:
5042:
4956:
4895:
4866:
4732:
4703:
4654:
4520:
4491:
4442:
4180:
4151:
3935:
3883:
3692:
3640:
3357:
3328:
3172:
3068:
3039:
2915:
2866:
2783:
2754:
2690:
2661:
2612:
2583:
2554:
2525:
2496:
2467:
2395:
2366:
1874:
1845:
1644:
1615:
1586:
1557:
1528:
1499:
1406:
1377:
1340:
1271:
1242:
1044:
820:
731:
634:
605:
553:
524:
495:
466:
437:
408:
379:
350:
321:
264:
195:
61:
5866:
Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey; Madura, Jeffry D. (2007).
5816:
Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey; Madura, Jeffry D. (2007).
1130:
757:
691:
5693:
4128:
3912:
3669:
800:
5757:
Analysing
Aviation Accidents Using WB-Analysis - an Application of Multimodal Reasoning
4683:
4471:
3386:
3201:
3097:
3019:
2944:
2895:
2734:
2641:
2447:
2427:
2158:
2138:
2118:
2098:
2078:
2058:
1825:
1805:
1741:
1721:
1701:
1681:
1496:
to describe an equivalent carcinogenicity between how many cigarettes a person smokes,
1435:
1320:
1300:
1222:
1199:
1110:
1090:
1070:
1024:
907:
780:
711:
671:
585:
301:
244:
224:
175:
134:
114:
72:
5646:
1297:) will not result in turning on the sun to illuminate the solar panel (an increase in
492:. This equation may be used to successfully calculate the number of hibernating bears
5973:
5662:
1978:
5925:
846:. More generally, we assume the system is described by the following expression:
5921:
5820:(9th ed.). Pearson Prentice Hall Upper Saddle River, NJ. pp. 573–650.
2422:
580:
5702:
5677:
5792:(5th ed.). Pearson Prentice Hall Upper Saddle River, NJ. p. 44,45.
2638:. The following table contains notation representing a variety of ways that
65:
5870:(9th ed.). Pearson Prentice Hall Upper Saddle River, NJ. p. 575.
5740:
5254:
Mismatched indices indicate that for any arbitrary causal relation between
3455:{\displaystyle a(s)~{\overset {\curvearrowleft \curvearrowright }{=}}~b(s)}
5654:
2363:
Various forms of causal relationships exist. For instance, two quantities
1219:
In this example, the fact that it is sunny and there is a light intensity
131:" is a dependent variable which is a function of an independent variable "
2135:. It specifies that there is no unidirectional causal relationship where
45:
1962:
57:
53:
2444:, but not by each other. Imagine a garbage strike in a large city,
5952:
https://plato.stanford.edu/archives/spr2023/entries/causal-models/
4854:{\displaystyle s~{\overset {\leftrightarrow }{=}}~b\left(s\right)}
4804:{\displaystyle s~{\overset {\leftrightarrow }{=}}~a\left(s\right)}
4642:{\displaystyle s~{\overset {\leftrightarrow }{=}}~b\left(s\right)}
4380:{\displaystyle s~{\overset {\leftrightarrow }{=}}~a\left(s\right)}
3161:{\displaystyle s~{\overset {\leftrightarrow }{=}}~a\left(s\right)}
2206:
5676:
Aspect, Alain; Grangier, Philippe; Roger, GĂ©rard (12 July 1982).
298:
Imagine the number of days of weather below one degrees
Celsius,
1698:
one owns has value measured in a standard currency of chickens,
5551:{\displaystyle s~{\overset {\rightarrow }{=}}~b\left(s\right)}
5501:{\displaystyle s~{\overset {\rightarrow }{=}}~a\left(s\right)}
5244:{\displaystyle s_{2}~{\overset {arb.}{=}}~b\left(s_{2}\right)}
5169:{\displaystyle s_{1}~{\overset {arb.}{=}}~a\left(s_{1}\right)}
4592:{\displaystyle s~{\overset {\rightarrow }{=}}~a\left(s\right)}
4430:{\displaystyle s~{\overset {\rightarrow }{=}}~b\left(s\right)}
3871:{\displaystyle s~{\overset {\rightarrow }{=}}~b\left(s\right)}
3578:{\displaystyle s~{\overset {\rightarrow }{=}}~a\left(s\right)}
3315:{\displaystyle s~{\overset {\rightarrow }{=}}~b\left(s\right)}
3265:{\displaystyle s~{\overset {\rightarrow }{=}}~a\left(s\right)}
2855:{\displaystyle s~{\overset {\rightarrow }{=}}~a\left(s\right)}
4115:{\displaystyle s~{\overset {\leftarrow }{=}}~b\left(s\right)}
4065:{\displaystyle s~{\overset {\leftarrow }{=}}~a\left(s\right)}
3821:{\displaystyle s~{\overset {\leftarrow }{=}}~a\left(s\right)}
3628:{\displaystyle s~{\overset {\leftarrow }{=}}~b\left(s\right)}
3008:{\displaystyle s~{\overset {\leftarrow }{=}}~a\left(s\right)}
5765:
Association for the
Advancement of Artificial Intelligence
5032:{\displaystyle a(s)~{\overset {\leftrightarrow }{=}}~b(s)}
1268:, not the other way around; lifting the stone (increasing
1900:, or vice-versa. In this case, the mathematical equality
1678:
Consider a barter-based economy where the number of cows
5868:
General
Chemistry Principles & Modern Applications
5818:
General
Chemistry Principles & Modern Applications
3768:{\displaystyle b(s)~{\overset {\rightarrow }{=}}~a(s)}
1738:
one owns has value which can be measured in chickens,
1674:
Bartering example: a bidirectional causal relationship
5593:
5564:
5514:
5464:
5422:
5386:
5350:
5323:
5287:
5260:
5182:
5107:
5074:
5045:
4988:
4959:
4927:
4898:
4869:
4817:
4767:
4735:
4706:
4686:
4657:
4605:
4555:
4523:
4494:
4474:
4445:
4393:
4343:
4275:
4212:
4183:
4154:
4131:
4078:
4028:
4011:{\displaystyle b(s)~{\overset {\leftarrow }{=}}~a(s)}
3967:
3938:
3915:
3886:
3834:
3784:
3724:
3695:
3672:
3643:
3591:
3541:
3468:
3409:
3389:
3360:
3331:
3278:
3228:
3204:
3175:
3124:
3100:
3071:
3042:
3022:
2971:
2947:
2918:
2898:
2869:
2818:
2786:
2757:
2737:
2693:
2664:
2644:
2615:
2586:
2557:
2528:
2499:
2470:
2450:
2430:
2398:
2369:
2327:
2289:
2251:
2161:
2141:
2121:
2101:
2081:
2061:
1990:
1906:
1877:
1848:
1828:
1808:
1764:
1744:
1724:
1704:
1684:
1647:
1618:
1589:
1560:
1531:
1502:
1458:
1438:
1409:
1380:
1343:
1323:
1303:
1274:
1245:
1225:
1202:
1173:
1153:
1133:
1113:
1093:
1073:
1047:
1027:
998:
978:
950:
930:
910:
854:
823:
803:
783:
760:
734:
714:
694:
674:
664:
Physics example: a unidirectional causal relationship
637:
608:
588:
556:
527:
498:
469:
440:
411:
382:
353:
324:
304:
267:
247:
227:
198:
178:
137:
117:
82:
5927:
The Book of Why: The New
Science of Cause and Effect
3218:
are mutually dependent, or bi-directionally causal.
1127:
represents the acceleration due to Earth's gravity (
894:{\displaystyle I\times A\times t=m\times g\times h~}
4327:{\displaystyle b(s)~{\overset {>-<}{=}}~a(s)}
2580:and vice-versa, one can write an equation relating
1525:, and how many grams of asbestos a person inhales,
434:and vice-versa, one can write an equation relating
5608:
5579:
5550:
5500:
5444:
5408:
5372:
5336:
5309:
5273:
5243:
5168:
5089:
5060:
5031:
4974:
4945:
4913:
4884:
4853:
4803:
4750:
4721:
4692:
4672:
4641:
4591:
4538:
4509:
4480:
4460:
4429:
4379:
4326:
4261:
4198:
4169:
4140:
4114:
4064:
4010:
3953:
3924:
3901:
3870:
3820:
3767:
3710:
3681:
3658:
3627:
3577:
3523:
3454:
3395:
3375:
3346:
3314:
3264:
3210:
3190:
3160:
3106:
3086:
3057:
3028:
3007:
2953:
2933:
2904:
2884:
2854:
2801:
2772:
2743:
2708:
2679:
2650:
2630:
2601:
2572:
2543:
2514:
2485:
2456:
2436:
2413:
2384:
2345:
2307:
2269:
2211:Partial Why–because graph of the capsizing of the
2167:
2147:
2127:
2107:
2087:
2067:
2043:
1936:
1892:
1863:
1834:
1814:
1794:
1750:
1730:
1710:
1690:
1662:
1633:
1604:
1575:
1546:
1517:
1488:
1444:
1424:
1395:
1358:
1329:
1309:
1289:
1260:
1231:
1208:
1188:
1159:
1139:
1119:
1099:
1079:
1059:
1033:
1013:
984:
965:
936:
916:
893:
838:
809:
789:
769:
746:
720:
700:
680:
652:
623:
602:(the outdoor temperature), but not by each other.
594:
571:
542:
513:
484:
455:
426:
397:
368:
339:
310:
282:
253:
233:
213:
184:
143:
123:
103:
2095:”. The expression above describes the case where
1370:Medicine example: two causes for a single outcome
1802:to describe the value relationship between cows
294:Ecosystem example: correlation without causation
1944:describes a bidirectional causal relationship.
221:denotes a function of the independent variable
2464:, causes an increase in the smell of garbage,
1216:represents the height the rock is lifted (m).
660:are related by correlation without causation.
1718:. Additionally, the number of barrels of oil
347:, and it causes bears to go into hibernation
8:
5754:Ladkin, Peter; Loer, Karsten (April 1998).
2270:{\displaystyle X\rightarrow Y\rightarrow Z}
2346:{\displaystyle X\rightarrow Y\leftarrow Z}
2308:{\displaystyle X\leftarrow Y\rightarrow Z}
2055:which can be read as: “the probability of
5730:
5701:
5592:
5563:
5521:
5513:
5471:
5463:
5433:
5421:
5397:
5385:
5361:
5349:
5328:
5322:
5298:
5286:
5265:
5259:
5231:
5196:
5187:
5181:
5156:
5121:
5112:
5106:
5073:
5044:
5004:
4987:
4958:
4926:
4897:
4868:
4824:
4816:
4774:
4766:
4734:
4705:
4685:
4656:
4612:
4604:
4562:
4554:
4522:
4493:
4473:
4444:
4400:
4392:
4350:
4342:
4291:
4274:
4230:
4211:
4182:
4153:
4130:
4085:
4077:
4035:
4027:
3983:
3966:
3937:
3914:
3885:
3841:
3833:
3791:
3783:
3740:
3723:
3694:
3671:
3642:
3598:
3590:
3548:
3540:
3486:
3467:
3425:
3408:
3388:
3359:
3330:
3285:
3277:
3235:
3227:
3203:
3174:
3131:
3123:
3099:
3070:
3041:
3021:
2978:
2970:
2946:
2917:
2897:
2868:
2825:
2817:
2785:
2756:
2736:
2692:
2663:
2643:
2614:
2585:
2556:
2527:
2498:
2469:
2449:
2429:
2397:
2368:
2326:
2288:
2250:
2160:
2140:
2120:
2100:
2080:
2060:
2000:
1989:
1905:
1876:
1847:
1827:
1807:
1763:
1743:
1723:
1703:
1683:
1646:
1617:
1588:
1559:
1530:
1501:
1457:
1437:
1408:
1379:
1342:
1322:
1302:
1273:
1244:
1224:
1201:
1177:
1172:
1152:
1132:
1112:
1092:
1072:
1051:
1046:
1041:is the surface area of the solar panel (m
1026:
1002:
997:
977:
954:
949:
929:
909:
853:
822:
802:
782:
759:
738:
733:
713:
693:
673:
636:
607:
587:
555:
526:
497:
468:
439:
410:
381:
352:
323:
303:
266:
246:
226:
197:
177:
136:
116:
81:
2721:
2228:
5625:
1670:, but they both have a common outcome.
34:question marks, boxes, or other symbols
5916:
5914:
5912:
5895:(11th ed.). Pearson. p. 19.
5845:(11th ed.). Pearson. p. 20.
2493:and an increase in the rat population
192:denotes an independent variable, and
7:
5811:
5809:
5783:
5781:
777:seconds, an electric motor raises a
16:Notation to express cause and effect
2115:is independent of anything done to
1432:, are both known causes of cancer,
1317:). The causal relationship between
924:represents intensity of sunlight (J
48:used to express cause and effect.
14:
318:, causes ice to form on a lake,
5924:; Mackenzie, Dana (2018-05-15).
5719:The World Bank Research Observer
2044:{\displaystyle P(Y|do(X))=P(Y)~}
5788:Bruice, Paula Yurkanis (2007).
1961:. In these reactions, adding a
5603:
5597:
5574:
5568:
5526:
5476:
5439:
5426:
5403:
5390:
5367:
5354:
5304:
5291:
5084:
5078:
5055:
5049:
5026:
5020:
5009:
4998:
4992:
4969:
4963:
4937:
4931:
4908:
4902:
4879:
4873:
4829:
4779:
4745:
4739:
4716:
4710:
4667:
4661:
4617:
4567:
4533:
4527:
4504:
4498:
4455:
4449:
4405:
4355:
4321:
4315:
4285:
4279:
4193:
4187:
4164:
4158:
4090:
4040:
4005:
3999:
3988:
3977:
3971:
3948:
3942:
3896:
3890:
3846:
3796:
3762:
3756:
3745:
3734:
3728:
3705:
3699:
3653:
3647:
3603:
3553:
3449:
3443:
3419:
3413:
3370:
3364:
3341:
3335:
3290:
3240:
3185:
3179:
3136:
3081:
3075:
3065:. The independent variable is
3052:
3046:
2983:
2941:. The independent variable is
2928:
2922:
2879:
2873:
2830:
2796:
2790:
2767:
2761:
2731:Defined relationships between
2716:may be related to each other.
2703:
2697:
2674:
2668:
2625:
2619:
2596:
2590:
2567:
2561:
2538:
2532:
2509:
2503:
2480:
2474:
2408:
2402:
2379:
2373:
2337:
2331:
2299:
2293:
2261:
2255:
2035:
2029:
2020:
2017:
2011:
2001:
1994:
1931:
1925:
1916:
1910:
1887:
1881:
1858:
1852:
1789:
1783:
1774:
1768:
1657:
1651:
1628:
1622:
1599:
1593:
1570:
1564:
1541:
1535:
1512:
1506:
1483:
1477:
1468:
1462:
1419:
1413:
1390:
1384:
1353:
1347:
1284:
1278:
1255:
1249:
833:
827:
647:
641:
618:
612:
566:
560:
537:
531:
508:
502:
479:
473:
450:
444:
421:
415:
392:
386:
363:
357:
334:
328:
277:
271:
208:
202:
152:
98:
92:
1:
5647:10.1016/S0140-6736(84)91816-6
5097:are bi-directionally causal.
4700:are bi-directionally causal.
4488:are bi-directionally causal.
5616:is bi-directionally causal.
3094:. The dependent variable is
2912:. The dependent variable is
1452:. One can write an equation
1403:, and exposure to asbestos,
1239:, causes the stone to rise
111:to denote that a quantity "
5996:
5891:B. George, George (2007).
5841:B. George, George (2007).
5703:10.1103/PhysRevLett.49.91
2723:Causal equality notation
2213:Herald of Free Enterprise
2202:Herald of Free Enterprise
1937:{\displaystyle C(y)=B(y)}
1795:{\displaystyle C(y)=B(y)}
1489:{\displaystyle f(y)=g(y)}
5445:{\displaystyle b(s_{2})}
5409:{\displaystyle a(s_{1})}
5373:{\displaystyle b(s_{2})}
5310:{\displaystyle a(s_{1})}
2421:can both be caused by a
2359:Causal equality notation
5682:Physical Review Letters
2190:directed acyclic graphs
1974:Statistics: Do notation
172:the convention whereby
5610:
5581:
5552:
5502:
5446:
5410:
5374:
5338:
5311:
5275:
5245:
5170:
5091:
5062:
5033:
4976:
4947:
4915:
4886:
4855:
4805:
4752:
4723:
4694:
4674:
4643:
4593:
4540:
4511:
4482:
4462:
4431:
4381:
4328:
4263:
4200:
4171:
4142:
4125:Uncertainty/bicausal:
4116:
4066:
4012:
3955:
3926:
3903:
3872:
3822:
3769:
3712:
3683:
3660:
3629:
3579:
3525:
3456:
3397:
3377:
3348:
3316:
3266:
3212:
3192:
3162:
3108:
3088:
3059:
3030:
3009:
2955:
2935:
2906:
2886:
2856:
2803:
2774:
2745:
2710:
2681:
2652:
2632:
2603:
2574:
2545:
2516:
2487:
2458:
2438:
2415:
2386:
2347:
2309:
2271:
2215:
2169:
2149:
2129:
2109:
2089:
2069:
2045:
1938:
1894:
1865:
1836:
1816:
1796:
1752:
1732:
1712:
1692:
1664:
1635:
1606:
1577:
1548:
1519:
1490:
1446:
1426:
1397:
1360:
1331:
1311:
1291:
1262:
1233:
1210:
1190:
1161:
1160:{\displaystyle \cdot }
1141:
1121:
1107:represents mass (kg),
1101:
1081:
1061:
1035:
1015:
986:
985:{\displaystyle \cdot }
967:
938:
937:{\displaystyle \cdot }
918:
895:
840:
811:
791:
771:
748:
722:
702:
682:
654:
625:
596:
573:
544:
515:
486:
457:
428:
399:
370:
341:
312:
284:
255:
235:
215:
186:
169:not necessarily assume
145:
125:
105:
104:{\displaystyle y=f(x)}
22:This article contains
5611:
5582:
5553:
5503:
5447:
5411:
5375:
5339:
5337:{\displaystyle s_{2}}
5312:
5276:
5274:{\displaystyle s_{1}}
5246:
5171:
5092:
5063:
5034:
4977:
4948:
4946:{\displaystyle a(s)~}
4916:
4887:
4856:
4806:
4753:
4724:
4695:
4675:
4644:
4594:
4541:
4512:
4483:
4463:
4432:
4382:
4329:
4264:
4201:
4172:
4143:
4117:
4067:
4013:
3956:
3932:which in turn causes
3927:
3904:
3873:
3823:
3770:
3713:
3689:which in turn causes
3684:
3661:
3630:
3580:
3526:
3457:
3398:
3378:
3349:
3317:
3267:
3213:
3193:
3163:
3109:
3089:
3060:
3031:
3010:
2956:
2936:
2907:
2887:
2857:
2804:
2775:
2746:
2711:
2682:
2653:
2633:
2604:
2575:
2546:
2517:
2488:
2459:
2439:
2416:
2387:
2348:
2310:
2272:
2210:
2170:
2150:
2130:
2110:
2090:
2070:
2046:
1939:
1895:
1866:
1837:
1817:
1797:
1753:
1733:
1713:
1693:
1665:
1636:
1607:
1578:
1549:
1520:
1491:
1447:
1427:
1398:
1361:
1332:
1312:
1292:
1263:
1234:
1211:
1191:
1189:{\displaystyle ^{-2}}
1162:
1142:
1122:
1102:
1087:represents time (s),
1082:
1062:
1036:
1016:
1014:{\displaystyle ^{-2}}
987:
968:
966:{\displaystyle ^{-1}}
939:
919:
896:
841:
812:
792:
772:
749:
723:
703:
683:
655:
626:
597:
579:are both caused by a
574:
545:
516:
487:
458:
429:
400:
371:
342:
313:
285:
256:
236:
216:
187:
146:
126:
106:
5763:. Spring Symposion.
5741:10.1093/wbro/5.2.127
5609:{\displaystyle a(s)}
5591:
5580:{\displaystyle b(s)}
5562:
5512:
5462:
5420:
5384:
5348:
5321:
5285:
5258:
5180:
5105:
5090:{\displaystyle a(s)}
5072:
5061:{\displaystyle b(s)}
5043:
4986:
4975:{\displaystyle b(s)}
4957:
4925:
4914:{\displaystyle a(s)}
4896:
4885:{\displaystyle b(s)}
4867:
4815:
4765:
4751:{\displaystyle b(s)}
4733:
4722:{\displaystyle a(s)}
4704:
4684:
4673:{\displaystyle b(s)}
4655:
4603:
4553:
4539:{\displaystyle a(s)}
4521:
4510:{\displaystyle b(s)}
4492:
4472:
4461:{\displaystyle a(s)}
4443:
4391:
4341:
4273:
4210:
4199:{\displaystyle b(s)}
4181:
4170:{\displaystyle a(s)}
4152:
4129:
4076:
4026:
3965:
3954:{\displaystyle b(s)}
3936:
3913:
3902:{\displaystyle a(s)}
3884:
3832:
3782:
3722:
3711:{\displaystyle a(s)}
3693:
3670:
3659:{\displaystyle b(s)}
3641:
3589:
3539:
3466:
3407:
3387:
3376:{\displaystyle b(s)}
3358:
3347:{\displaystyle a(s)}
3329:
3276:
3226:
3202:
3191:{\displaystyle a(s)}
3173:
3122:
3098:
3087:{\displaystyle a(s)}
3069:
3058:{\displaystyle a(s)}
3040:
3020:
2969:
2945:
2934:{\displaystyle a(s)}
2916:
2896:
2885:{\displaystyle a(s)}
2867:
2816:
2802:{\displaystyle b(s)}
2784:
2773:{\displaystyle a(s)}
2755:
2735:
2728:Symbolic expression
2709:{\displaystyle b(s)}
2691:
2680:{\displaystyle a(s)}
2662:
2642:
2631:{\displaystyle a(s)}
2613:
2602:{\displaystyle b(s)}
2584:
2573:{\displaystyle a(s)}
2555:
2544:{\displaystyle b(s)}
2526:
2515:{\displaystyle b(s)}
2497:
2486:{\displaystyle a(s)}
2468:
2448:
2428:
2423:confounding variable
2414:{\displaystyle b(s)}
2396:
2385:{\displaystyle a(s)}
2367:
2325:
2287:
2249:
2194:causal loop diagrams
2159:
2139:
2119:
2099:
2079:
2059:
1988:
1959:chemical equilibrium
1904:
1893:{\displaystyle B(y)}
1875:
1864:{\displaystyle C(y)}
1846:
1826:
1806:
1762:
1742:
1722:
1702:
1682:
1663:{\displaystyle f(y)}
1645:
1634:{\displaystyle g(y)}
1616:
1605:{\displaystyle g(y)}
1587:
1576:{\displaystyle f(y)}
1558:
1547:{\displaystyle g(y)}
1529:
1518:{\displaystyle f(y)}
1500:
1456:
1436:
1425:{\displaystyle g(y)}
1407:
1396:{\displaystyle f(y)}
1378:
1359:{\displaystyle h(I)}
1341:
1321:
1301:
1290:{\displaystyle h(I)}
1272:
1261:{\displaystyle h(I)}
1243:
1223:
1200:
1171:
1151:
1131:
1111:
1091:
1071:
1060:{\displaystyle ^{2}}
1045:
1025:
996:
976:
948:
928:
908:
852:
839:{\displaystyle h(I)}
821:
801:
781:
758:
747:{\displaystyle ^{2}}
732:
712:
708:watts incident on a
692:
672:
653:{\displaystyle g(y)}
635:
624:{\displaystyle f(y)}
606:
586:
581:confounding variable
572:{\displaystyle g(y)}
554:
543:{\displaystyle f(y)}
525:
514:{\displaystyle g(y)}
496:
485:{\displaystyle f(y)}
467:
456:{\displaystyle g(y)}
438:
427:{\displaystyle f(y)}
409:
398:{\displaystyle g(y)}
380:
369:{\displaystyle g(y)}
351:
340:{\displaystyle f(y)}
322:
302:
283:{\displaystyle f(y)}
265:
245:
225:
214:{\displaystyle f(y)}
196:
176:
135:
115:
80:
5694:1982PhRvL..49...91A
5641:(8390): 1311–1315.
5452:cannot be related.
3383:are both caused by
2724:
2231:
1822:and barrels of oil
1366:is unidirectional.
1140:{\displaystyle 9.8}
770:{\displaystyle 10~}
701:{\displaystyle 100}
5606:
5577:
5548:
5498:
5442:
5406:
5370:
5334:
5307:
5271:
5241:
5166:
5087:
5058:
5029:
4972:
4943:
4911:
4882:
4851:
4801:
4748:
4719:
4690:
4670:
4639:
4589:
4536:
4507:
4478:
4458:
4427:
4377:
4324:
4259:
4237:↷ ↶
4196:
4167:
4141:{\displaystyle s~}
4138:
4112:
4062:
4008:
3951:
3925:{\displaystyle s~}
3922:
3899:
3868:
3818:
3765:
3708:
3682:{\displaystyle s~}
3679:
3656:
3625:
3575:
3521:
3452:
3432:↶ ↷
3393:
3373:
3344:
3312:
3262:
3208:
3188:
3158:
3104:
3084:
3055:
3026:
3005:
2951:
2931:
2902:
2882:
2852:
2799:
2770:
2741:
2722:
2706:
2677:
2648:
2628:
2599:
2570:
2541:
2512:
2483:
2454:
2434:
2411:
2382:
2343:
2305:
2267:
2230:Junction patterns
2229:
2216:
2198:why-because graphs
2165:
2145:
2125:
2105:
2085:
2075:given that you do
2065:
2041:
1953:Chemical reactions
1934:
1890:
1861:
1832:
1812:
1792:
1748:
1728:
1708:
1688:
1660:
1631:
1602:
1573:
1544:
1515:
1486:
1442:
1422:
1393:
1356:
1327:
1307:
1287:
1258:
1229:
1206:
1186:
1157:
1137:
1117:
1097:
1077:
1057:
1031:
1011:
982:
963:
934:
914:
891:
836:
810:{\displaystyle 50}
807:
787:
767:
744:
718:
698:
678:
650:
621:
592:
569:
540:
511:
482:
453:
424:
395:
366:
337:
308:
280:
251:
231:
211:
182:
166:What follows does
141:
121:
101:
24:special characters
5902:978-0-321-18558-7
5877:978-0-13-149330-8
5852:978-0-321-18558-7
5827:978-0-13-149330-8
5799:978-0-13-196316-0
5790:Organic chemistry
5533:
5529:
5520:
5483:
5479:
5470:
5456:
5455:
5219:
5215:
5195:
5144:
5140:
5120:
5016:
5012:
5003:
4942:
4836:
4832:
4823:
4786:
4782:
4773:
4693:{\displaystyle s}
4624:
4620:
4611:
4574:
4570:
4561:
4481:{\displaystyle s}
4412:
4408:
4399:
4362:
4358:
4349:
4311:
4307:
4290:
4244:
4240:
4229:
4148:can be caused by
4137:
4097:
4093:
4084:
4047:
4043:
4034:
3995:
3991:
3982:
3921:
3853:
3849:
3840:
3803:
3799:
3790:
3752:
3748:
3739:
3678:
3610:
3606:
3597:
3560:
3556:
3547:
3506:
3502:
3485:
3439:
3435:
3424:
3396:{\displaystyle s}
3297:
3293:
3284:
3247:
3243:
3234:
3211:{\displaystyle s}
3143:
3139:
3130:
3107:{\displaystyle s}
3029:{\displaystyle s}
2990:
2986:
2977:
2954:{\displaystyle s}
2905:{\displaystyle s}
2837:
2833:
2824:
2744:{\displaystyle s}
2651:{\displaystyle s}
2457:{\displaystyle s}
2437:{\displaystyle s}
2356:
2355:
2224:Junction patterns
2219:Junction patterns
2186:Ishikawa diagrams
2168:{\displaystyle Y}
2148:{\displaystyle X}
2128:{\displaystyle X}
2108:{\displaystyle Y}
2088:{\displaystyle X}
2068:{\displaystyle Y}
2040:
1835:{\displaystyle B}
1815:{\displaystyle C}
1751:{\displaystyle y}
1731:{\displaystyle B}
1711:{\displaystyle y}
1691:{\displaystyle C}
1445:{\displaystyle y}
1330:{\displaystyle I}
1310:{\displaystyle I}
1232:{\displaystyle I}
1209:{\displaystyle h}
1120:{\displaystyle g}
1100:{\displaystyle m}
1080:{\displaystyle t}
1034:{\displaystyle A}
917:{\displaystyle I}
890:
790:{\displaystyle 2}
766:
721:{\displaystyle 1}
681:{\displaystyle I}
595:{\displaystyle y}
311:{\displaystyle y}
254:{\displaystyle y}
234:{\displaystyle y}
185:{\displaystyle y}
144:{\displaystyle x}
124:{\displaystyle y}
30:rendering support
5987:
5964:
5961:
5955:
5948:
5942:
5941:
5918:
5907:
5906:
5893:Thomas' calculus
5888:
5882:
5881:
5863:
5857:
5856:
5843:Thomas' calculus
5838:
5832:
5831:
5813:
5804:
5803:
5785:
5776:
5775:
5773:
5767:. Archived from
5762:
5751:
5745:
5744:
5734:
5732:10.1.1.1009.4220
5714:
5708:
5707:
5705:
5673:
5667:
5666:
5630:
5615:
5613:
5612:
5607:
5586:
5584:
5583:
5578:
5557:
5555:
5554:
5549:
5547:
5531:
5530:
5522:
5518:
5507:
5505:
5504:
5499:
5497:
5481:
5480:
5472:
5468:
5451:
5449:
5448:
5443:
5438:
5437:
5415:
5413:
5412:
5407:
5402:
5401:
5379:
5377:
5376:
5371:
5366:
5365:
5343:
5341:
5340:
5335:
5333:
5332:
5316:
5314:
5313:
5308:
5303:
5302:
5280:
5278:
5277:
5272:
5270:
5269:
5250:
5248:
5247:
5242:
5240:
5236:
5235:
5217:
5216:
5214:
5197:
5193:
5192:
5191:
5175:
5173:
5172:
5167:
5165:
5161:
5160:
5142:
5141:
5139:
5122:
5118:
5117:
5116:
5096:
5094:
5093:
5088:
5067:
5065:
5064:
5059:
5038:
5036:
5035:
5030:
5014:
5013:
5005:
5001:
4981:
4979:
4978:
4973:
4952:
4950:
4949:
4944:
4940:
4920:
4918:
4917:
4912:
4891:
4889:
4888:
4883:
4860:
4858:
4857:
4852:
4850:
4834:
4833:
4825:
4821:
4810:
4808:
4807:
4802:
4800:
4784:
4783:
4775:
4771:
4757:
4755:
4754:
4749:
4728:
4726:
4725:
4720:
4699:
4697:
4696:
4691:
4679:
4677:
4676:
4671:
4648:
4646:
4645:
4640:
4638:
4622:
4621:
4613:
4609:
4598:
4596:
4595:
4590:
4588:
4572:
4571:
4563:
4559:
4545:
4543:
4542:
4537:
4516:
4514:
4513:
4508:
4487:
4485:
4484:
4479:
4467:
4465:
4464:
4459:
4436:
4434:
4433:
4428:
4426:
4410:
4409:
4401:
4397:
4386:
4384:
4383:
4378:
4376:
4360:
4359:
4351:
4347:
4333:
4331:
4330:
4325:
4309:
4308:
4306:
4292:
4288:
4268:
4266:
4265:
4260:
4258:
4242:
4241:
4239:
4231:
4227:
4226:
4205:
4203:
4202:
4197:
4176:
4174:
4173:
4168:
4147:
4145:
4144:
4139:
4135:
4121:
4119:
4118:
4113:
4111:
4095:
4094:
4086:
4082:
4071:
4069:
4068:
4063:
4061:
4045:
4044:
4036:
4032:
4017:
4015:
4014:
4009:
3993:
3992:
3984:
3980:
3960:
3958:
3957:
3952:
3931:
3929:
3928:
3923:
3919:
3908:
3906:
3905:
3900:
3877:
3875:
3874:
3869:
3867:
3851:
3850:
3842:
3838:
3827:
3825:
3824:
3819:
3817:
3801:
3800:
3792:
3788:
3774:
3772:
3771:
3766:
3750:
3749:
3741:
3737:
3717:
3715:
3714:
3709:
3688:
3686:
3685:
3680:
3676:
3665:
3663:
3662:
3657:
3634:
3632:
3631:
3626:
3624:
3608:
3607:
3599:
3595:
3584:
3582:
3581:
3576:
3574:
3558:
3557:
3549:
3545:
3530:
3528:
3527:
3522:
3520:
3504:
3503:
3501:
3487:
3483:
3482:
3461:
3459:
3458:
3453:
3437:
3436:
3434:
3426:
3422:
3402:
3400:
3399:
3394:
3382:
3380:
3379:
3374:
3353:
3351:
3350:
3345:
3321:
3319:
3318:
3313:
3311:
3295:
3294:
3286:
3282:
3271:
3269:
3268:
3263:
3261:
3245:
3244:
3236:
3232:
3217:
3215:
3214:
3209:
3197:
3195:
3194:
3189:
3167:
3165:
3164:
3159:
3157:
3141:
3140:
3132:
3128:
3113:
3111:
3110:
3105:
3093:
3091:
3090:
3085:
3064:
3062:
3061:
3056:
3035:
3033:
3032:
3027:
3014:
3012:
3011:
3006:
3004:
2988:
2987:
2979:
2975:
2960:
2958:
2957:
2952:
2940:
2938:
2937:
2932:
2911:
2909:
2908:
2903:
2891:
2889:
2888:
2883:
2861:
2859:
2858:
2853:
2851:
2835:
2834:
2826:
2822:
2808:
2806:
2805:
2800:
2779:
2777:
2776:
2771:
2750:
2748:
2747:
2742:
2725:
2715:
2713:
2712:
2707:
2686:
2684:
2683:
2678:
2657:
2655:
2654:
2649:
2637:
2635:
2634:
2629:
2608:
2606:
2605:
2600:
2579:
2577:
2576:
2571:
2550:
2548:
2547:
2542:
2521:
2519:
2518:
2513:
2492:
2490:
2489:
2484:
2463:
2461:
2460:
2455:
2443:
2441:
2440:
2435:
2420:
2418:
2417:
2412:
2391:
2389:
2388:
2383:
2352:
2350:
2349:
2344:
2314:
2312:
2311:
2306:
2276:
2274:
2273:
2268:
2232:
2174:
2172:
2171:
2166:
2154:
2152:
2151:
2146:
2134:
2132:
2131:
2126:
2114:
2112:
2111:
2106:
2094:
2092:
2091:
2086:
2074:
2072:
2071:
2066:
2050:
2048:
2047:
2042:
2038:
2004:
1943:
1941:
1940:
1935:
1899:
1897:
1896:
1891:
1870:
1868:
1867:
1862:
1841:
1839:
1838:
1833:
1821:
1819:
1818:
1813:
1801:
1799:
1798:
1793:
1757:
1755:
1754:
1749:
1737:
1735:
1734:
1729:
1717:
1715:
1714:
1709:
1697:
1695:
1694:
1689:
1669:
1667:
1666:
1661:
1640:
1638:
1637:
1632:
1611:
1609:
1608:
1603:
1582:
1580:
1579:
1574:
1554:. Here, neither
1553:
1551:
1550:
1545:
1524:
1522:
1521:
1516:
1495:
1493:
1492:
1487:
1451:
1449:
1448:
1443:
1431:
1429:
1428:
1423:
1402:
1400:
1399:
1394:
1365:
1363:
1362:
1357:
1336:
1334:
1333:
1328:
1316:
1314:
1313:
1308:
1296:
1294:
1293:
1288:
1267:
1265:
1264:
1259:
1238:
1236:
1235:
1230:
1215:
1213:
1212:
1207:
1195:
1193:
1192:
1187:
1185:
1184:
1166:
1164:
1163:
1158:
1146:
1144:
1143:
1138:
1126:
1124:
1123:
1118:
1106:
1104:
1103:
1098:
1086:
1084:
1083:
1078:
1066:
1064:
1063:
1058:
1056:
1055:
1040:
1038:
1037:
1032:
1020:
1018:
1017:
1012:
1010:
1009:
991:
989:
988:
983:
972:
970:
969:
964:
962:
961:
943:
941:
940:
935:
923:
921:
920:
915:
900:
898:
897:
892:
888:
845:
843:
842:
837:
816:
814:
813:
808:
796:
794:
793:
788:
776:
774:
773:
768:
764:
754:solar panel for
753:
751:
750:
745:
743:
742:
727:
725:
724:
719:
707:
705:
704:
699:
687:
685:
684:
679:
659:
657:
656:
651:
630:
628:
627:
622:
601:
599:
598:
593:
578:
576:
575:
570:
549:
547:
546:
541:
520:
518:
517:
512:
491:
489:
488:
483:
462:
460:
459:
454:
433:
431:
430:
425:
404:
402:
401:
396:
375:
373:
372:
367:
346:
344:
343:
338:
317:
315:
314:
309:
289:
287:
286:
281:
260:
258:
257:
252:
240:
238:
237:
232:
220:
218:
217:
212:
191:
189:
188:
183:
150:
148:
147:
142:
130:
128:
127:
122:
110:
108:
107:
102:
5995:
5994:
5990:
5989:
5988:
5986:
5985:
5984:
5970:
5969:
5968:
5967:
5962:
5958:
5949:
5945:
5938:
5930:. Basic Books.
5920:
5919:
5910:
5903:
5890:
5889:
5885:
5878:
5865:
5864:
5860:
5853:
5840:
5839:
5835:
5828:
5815:
5814:
5807:
5800:
5787:
5786:
5779:
5771:
5760:
5753:
5752:
5748:
5716:
5715:
5711:
5675:
5674:
5670:
5632:
5631:
5627:
5622:
5589:
5588:
5560:
5559:
5537:
5510:
5509:
5487:
5460:
5459:
5429:
5418:
5417:
5393:
5382:
5381:
5357:
5346:
5345:
5324:
5319:
5318:
5294:
5283:
5282:
5261:
5256:
5255:
5227:
5223:
5201:
5183:
5178:
5177:
5152:
5148:
5126:
5108:
5103:
5102:
5070:
5069:
5041:
5040:
4984:
4983:
4955:
4954:
4923:
4922:
4894:
4893:
4865:
4864:
4840:
4813:
4812:
4790:
4763:
4762:
4731:
4730:
4702:
4701:
4682:
4681:
4653:
4652:
4628:
4601:
4600:
4578:
4551:
4550:
4519:
4518:
4490:
4489:
4470:
4469:
4441:
4440:
4416:
4389:
4388:
4366:
4339:
4338:
4296:
4271:
4270:
4248:
4235:
4216:
4208:
4207:
4179:
4178:
4150:
4149:
4127:
4126:
4101:
4074:
4073:
4051:
4024:
4023:
3963:
3962:
3934:
3933:
3911:
3910:
3882:
3881:
3857:
3830:
3829:
3807:
3780:
3779:
3720:
3719:
3691:
3690:
3668:
3667:
3639:
3638:
3614:
3587:
3586:
3564:
3537:
3536:
3510:
3491:
3472:
3464:
3463:
3430:
3405:
3404:
3385:
3384:
3356:
3355:
3327:
3326:
3301:
3274:
3273:
3251:
3224:
3223:
3200:
3199:
3171:
3170:
3147:
3120:
3119:
3096:
3095:
3067:
3066:
3038:
3037:
3018:
3017:
2994:
2967:
2966:
2943:
2942:
2914:
2913:
2894:
2893:
2865:
2864:
2841:
2814:
2813:
2782:
2781:
2753:
2752:
2733:
2732:
2719:
2689:
2688:
2660:
2659:
2640:
2639:
2611:
2610:
2582:
2581:
2553:
2552:
2551:does not cause
2524:
2523:
2522:. Even though
2495:
2494:
2466:
2465:
2446:
2445:
2426:
2425:
2394:
2393:
2365:
2364:
2361:
2323:
2322:
2285:
2284:
2247:
2246:
2221:
2181:
2179:Causal diagrams
2157:
2156:
2137:
2136:
2117:
2116:
2097:
2096:
2077:
2076:
2057:
2056:
1986:
1985:
1976:
1955:
1950:
1902:
1901:
1873:
1872:
1844:
1843:
1824:
1823:
1804:
1803:
1760:
1759:
1740:
1739:
1720:
1719:
1700:
1699:
1680:
1679:
1676:
1643:
1642:
1614:
1613:
1585:
1584:
1556:
1555:
1527:
1526:
1498:
1497:
1454:
1453:
1434:
1433:
1405:
1404:
1376:
1375:
1372:
1339:
1338:
1319:
1318:
1299:
1298:
1270:
1269:
1241:
1240:
1221:
1220:
1198:
1197:
1174:
1169:
1168:
1149:
1148:
1129:
1128:
1109:
1108:
1089:
1088:
1069:
1068:
1048:
1043:
1042:
1023:
1022:
999:
994:
993:
974:
973:
951:
946:
945:
926:
925:
906:
905:
850:
849:
819:
818:
799:
798:
779:
778:
756:
755:
735:
730:
729:
710:
709:
690:
689:
670:
669:
666:
633:
632:
604:
603:
584:
583:
552:
551:
523:
522:
494:
493:
465:
464:
436:
435:
407:
406:
405:does not cause
378:
377:
349:
348:
320:
319:
300:
299:
296:
263:
262:
243:
242:
223:
222:
194:
193:
174:
173:
164:
133:
132:
113:
112:
78:
77:
62:social sciences
42:Causal notation
39:
38:
37:
28:Without proper
17:
12:
11:
5:
5993:
5991:
5983:
5982:
5972:
5971:
5966:
5965:
5956:
5943:
5936:
5908:
5901:
5883:
5876:
5858:
5851:
5833:
5826:
5805:
5798:
5777:
5774:on 2022-12-21.
5746:
5725:(2): 127–142.
5709:
5668:
5624:
5623:
5621:
5618:
5605:
5602:
5599:
5596:
5576:
5573:
5570:
5567:
5546:
5543:
5540:
5536:
5528:
5525:
5517:
5496:
5493:
5490:
5486:
5478:
5475:
5467:
5454:
5453:
5441:
5436:
5432:
5428:
5425:
5405:
5400:
5396:
5392:
5389:
5369:
5364:
5360:
5356:
5353:
5331:
5327:
5306:
5301:
5297:
5293:
5290:
5268:
5264:
5252:
5239:
5234:
5230:
5226:
5222:
5213:
5210:
5207:
5204:
5200:
5190:
5186:
5164:
5159:
5155:
5151:
5147:
5138:
5135:
5132:
5129:
5125:
5115:
5111:
5099:
5098:
5086:
5083:
5080:
5077:
5057:
5054:
5051:
5048:
5028:
5025:
5022:
5019:
5011:
5008:
5000:
4997:
4994:
4991:
4971:
4968:
4965:
4962:
4939:
4936:
4933:
4930:
4910:
4907:
4904:
4901:
4881:
4878:
4875:
4872:
4862:
4849:
4846:
4843:
4839:
4831:
4828:
4820:
4799:
4796:
4793:
4789:
4781:
4778:
4770:
4759:
4758:
4747:
4744:
4741:
4738:
4718:
4715:
4712:
4709:
4689:
4669:
4666:
4663:
4660:
4650:
4637:
4634:
4631:
4627:
4619:
4616:
4608:
4587:
4584:
4581:
4577:
4569:
4566:
4558:
4547:
4546:
4535:
4532:
4529:
4526:
4506:
4503:
4500:
4497:
4477:
4457:
4454:
4451:
4448:
4438:
4425:
4422:
4419:
4415:
4407:
4404:
4396:
4375:
4372:
4369:
4365:
4357:
4354:
4346:
4335:
4334:
4323:
4320:
4317:
4314:
4305:
4302:
4299:
4295:
4287:
4284:
4281:
4278:
4257:
4254:
4251:
4247:
4238:
4234:
4225:
4222:
4219:
4215:
4195:
4192:
4189:
4186:
4166:
4163:
4160:
4157:
4134:
4123:
4110:
4107:
4104:
4100:
4092:
4089:
4081:
4060:
4057:
4054:
4050:
4042:
4039:
4031:
4020:
4019:
4007:
4004:
4001:
3998:
3990:
3987:
3979:
3976:
3973:
3970:
3950:
3947:
3944:
3941:
3918:
3898:
3895:
3892:
3889:
3879:
3866:
3863:
3860:
3856:
3848:
3845:
3837:
3816:
3813:
3810:
3806:
3798:
3795:
3787:
3776:
3775:
3764:
3761:
3758:
3755:
3747:
3744:
3736:
3733:
3730:
3727:
3707:
3704:
3701:
3698:
3675:
3655:
3652:
3649:
3646:
3636:
3623:
3620:
3617:
3613:
3605:
3602:
3594:
3573:
3570:
3567:
3563:
3555:
3552:
3544:
3533:
3532:
3519:
3516:
3513:
3509:
3500:
3497:
3494:
3490:
3481:
3478:
3475:
3471:
3451:
3448:
3445:
3442:
3433:
3429:
3421:
3418:
3415:
3412:
3392:
3372:
3369:
3366:
3363:
3343:
3340:
3337:
3334:
3323:
3310:
3307:
3304:
3300:
3292:
3289:
3281:
3260:
3257:
3254:
3250:
3242:
3239:
3231:
3220:
3219:
3207:
3187:
3184:
3181:
3178:
3168:
3156:
3153:
3150:
3146:
3138:
3135:
3127:
3116:
3115:
3103:
3083:
3080:
3077:
3074:
3054:
3051:
3048:
3045:
3025:
3015:
3003:
3000:
2997:
2993:
2985:
2982:
2974:
2963:
2962:
2950:
2930:
2927:
2924:
2921:
2901:
2881:
2878:
2875:
2872:
2862:
2850:
2847:
2844:
2840:
2832:
2829:
2821:
2810:
2809:
2798:
2795:
2792:
2789:
2769:
2766:
2763:
2760:
2740:
2729:
2705:
2702:
2699:
2696:
2676:
2673:
2670:
2667:
2647:
2627:
2624:
2621:
2618:
2598:
2595:
2592:
2589:
2569:
2566:
2563:
2560:
2540:
2537:
2534:
2531:
2511:
2508:
2505:
2502:
2482:
2479:
2476:
2473:
2453:
2433:
2410:
2407:
2404:
2401:
2381:
2378:
2375:
2372:
2360:
2357:
2354:
2353:
2342:
2339:
2336:
2333:
2330:
2320:
2316:
2315:
2304:
2301:
2298:
2295:
2292:
2282:
2278:
2277:
2266:
2263:
2260:
2257:
2254:
2244:
2240:
2239:
2236:
2220:
2217:
2180:
2177:
2164:
2144:
2124:
2104:
2084:
2064:
2053:
2052:
2037:
2034:
2031:
2028:
2025:
2022:
2019:
2016:
2013:
2010:
2007:
2003:
1999:
1996:
1993:
1975:
1972:
1954:
1951:
1949:
1946:
1933:
1930:
1927:
1924:
1921:
1918:
1915:
1912:
1909:
1889:
1886:
1883:
1880:
1860:
1857:
1854:
1851:
1831:
1811:
1791:
1788:
1785:
1782:
1779:
1776:
1773:
1770:
1767:
1747:
1727:
1707:
1687:
1675:
1672:
1659:
1656:
1653:
1650:
1630:
1627:
1624:
1621:
1601:
1598:
1595:
1592:
1572:
1569:
1566:
1563:
1543:
1540:
1537:
1534:
1514:
1511:
1508:
1505:
1485:
1482:
1479:
1476:
1473:
1470:
1467:
1464:
1461:
1441:
1421:
1418:
1415:
1412:
1392:
1389:
1386:
1383:
1371:
1368:
1355:
1352:
1349:
1346:
1326:
1306:
1286:
1283:
1280:
1277:
1257:
1254:
1251:
1248:
1228:
1205:
1183:
1180:
1176:
1156:
1136:
1116:
1096:
1076:
1054:
1050:
1030:
1008:
1005:
1001:
981:
960:
957:
953:
933:
913:
887:
884:
881:
878:
875:
872:
869:
866:
863:
860:
857:
835:
832:
829:
826:
806:
786:
763:
741:
737:
717:
697:
677:
665:
662:
649:
646:
643:
640:
620:
617:
614:
611:
591:
568:
565:
562:
559:
539:
536:
533:
530:
510:
507:
504:
501:
481:
478:
475:
472:
452:
449:
446:
443:
423:
420:
417:
414:
394:
391:
388:
385:
376:. Even though
365:
362:
359:
356:
336:
333:
330:
327:
307:
295:
292:
279:
276:
273:
270:
250:
230:
210:
207:
204:
201:
181:
163:
160:
140:
120:
100:
97:
94:
91:
88:
85:
73:nitrogen cycle
32:, you may see
20:
19:
18:
15:
13:
10:
9:
6:
4:
3:
2:
5992:
5981:
5978:
5977:
5975:
5960:
5957:
5953:
5947:
5944:
5939:
5937:9780465097616
5933:
5929:
5928:
5923:
5917:
5915:
5913:
5909:
5904:
5898:
5894:
5887:
5884:
5879:
5873:
5869:
5862:
5859:
5854:
5848:
5844:
5837:
5834:
5829:
5823:
5819:
5812:
5810:
5806:
5801:
5795:
5791:
5784:
5782:
5778:
5770:
5766:
5759:
5758:
5750:
5747:
5742:
5738:
5733:
5728:
5724:
5720:
5713:
5710:
5704:
5699:
5695:
5691:
5687:
5683:
5679:
5672:
5669:
5664:
5660:
5656:
5652:
5648:
5644:
5640:
5636:
5629:
5626:
5619:
5617:
5600:
5594:
5571:
5565:
5544:
5541:
5538:
5534:
5523:
5515:
5494:
5491:
5488:
5484:
5473:
5465:
5434:
5430:
5423:
5398:
5394:
5387:
5362:
5358:
5351:
5329:
5325:
5299:
5295:
5288:
5266:
5262:
5253:
5251:
5237:
5232:
5228:
5224:
5220:
5211:
5208:
5205:
5202:
5198:
5188:
5184:
5162:
5157:
5153:
5149:
5145:
5136:
5133:
5130:
5127:
5123:
5113:
5109:
5101:
5100:
5081:
5075:
5052:
5046:
5023:
5017:
5006:
4995:
4989:
4966:
4960:
4934:
4928:
4905:
4899:
4876:
4870:
4863:
4861:
4847:
4844:
4841:
4837:
4826:
4818:
4797:
4794:
4791:
4787:
4776:
4768:
4761:
4760:
4742:
4736:
4729:is caused by
4713:
4707:
4687:
4664:
4658:
4651:
4649:
4635:
4632:
4629:
4625:
4614:
4606:
4585:
4582:
4579:
4575:
4564:
4556:
4549:
4548:
4530:
4524:
4517:is caused by
4501:
4495:
4475:
4452:
4446:
4439:
4437:
4423:
4420:
4417:
4413:
4402:
4394:
4373:
4370:
4367:
4363:
4352:
4344:
4337:
4336:
4318:
4312:
4303:
4300:
4297:
4293:
4282:
4276:
4255:
4252:
4249:
4245:
4236:
4232:
4223:
4220:
4217:
4213:
4190:
4184:
4161:
4155:
4132:
4124:
4122:
4108:
4105:
4102:
4098:
4087:
4079:
4058:
4055:
4052:
4048:
4037:
4029:
4022:
4021:
4002:
3996:
3985:
3974:
3968:
3945:
3939:
3916:
3893:
3887:
3880:
3878:
3864:
3861:
3858:
3854:
3843:
3835:
3814:
3811:
3808:
3804:
3793:
3785:
3778:
3777:
3759:
3753:
3742:
3731:
3725:
3702:
3696:
3673:
3650:
3644:
3637:
3635:
3621:
3618:
3615:
3611:
3600:
3592:
3571:
3568:
3565:
3561:
3550:
3542:
3535:
3534:
3531:can be used.
3517:
3514:
3511:
3507:
3498:
3495:
3492:
3488:
3479:
3476:
3473:
3469:
3446:
3440:
3431:
3427:
3416:
3410:
3390:
3367:
3361:
3338:
3332:
3325:Correlation:
3324:
3322:
3308:
3305:
3302:
3298:
3287:
3279:
3258:
3255:
3252:
3248:
3237:
3229:
3222:
3221:
3205:
3182:
3176:
3169:
3154:
3151:
3148:
3144:
3133:
3125:
3118:
3117:
3101:
3078:
3072:
3049:
3043:
3036:is caused by
3023:
3016:
3001:
2998:
2995:
2991:
2980:
2972:
2965:
2964:
2948:
2925:
2919:
2899:
2892:is caused by
2876:
2870:
2863:
2848:
2845:
2842:
2838:
2827:
2819:
2812:
2811:
2793:
2787:
2764:
2758:
2738:
2730:
2727:
2726:
2720:
2717:
2700:
2694:
2671:
2665:
2645:
2622:
2616:
2593:
2587:
2564:
2558:
2535:
2529:
2506:
2500:
2477:
2471:
2451:
2431:
2424:
2405:
2399:
2376:
2370:
2358:
2340:
2334:
2328:
2321:
2318:
2317:
2302:
2296:
2290:
2283:
2280:
2279:
2264:
2258:
2252:
2245:
2242:
2241:
2237:
2234:
2233:
2227:
2225:
2218:
2214:
2209:
2205:
2203:
2199:
2195:
2191:
2187:
2178:
2176:
2162:
2142:
2122:
2102:
2082:
2062:
2032:
2026:
2023:
2014:
2008:
2005:
1997:
1991:
1984:
1983:
1982:
1980:
1973:
1971:
1968:
1964:
1960:
1952:
1947:
1945:
1928:
1922:
1919:
1913:
1907:
1884:
1878:
1855:
1849:
1829:
1809:
1786:
1780:
1777:
1771:
1765:
1745:
1725:
1705:
1685:
1673:
1671:
1654:
1648:
1625:
1619:
1596:
1590:
1567:
1561:
1538:
1532:
1509:
1503:
1480:
1474:
1471:
1465:
1459:
1439:
1416:
1410:
1387:
1381:
1369:
1367:
1350:
1344:
1324:
1304:
1281:
1275:
1252:
1246:
1226:
1217:
1203:
1181:
1178:
1175:
1154:
1134:
1114:
1094:
1074:
1052:
1049:
1028:
1006:
1003:
1000:
979:
958:
955:
952:
931:
911:
902:
885:
882:
879:
876:
873:
870:
867:
864:
861:
858:
855:
847:
830:
824:
804:
784:
761:
739:
736:
715:
695:
675:
663:
661:
644:
638:
615:
609:
589:
582:
563:
557:
534:
528:
505:
499:
476:
470:
447:
441:
418:
412:
389:
383:
360:
354:
331:
325:
305:
293:
291:
274:
268:
248:
228:
205:
199:
179:
171:
170:
161:
159:
156:
154:
138:
118:
95:
89:
86:
83:
74:
69:
67:
63:
59:
55:
49:
47:
43:
35:
31:
27:
25:
5959:
5946:
5926:
5922:Pearl, Judea
5892:
5886:
5867:
5861:
5842:
5836:
5817:
5789:
5769:the original
5756:
5749:
5722:
5718:
5712:
5688:(2): 91–94.
5685:
5681:
5671:
5638:
5634:
5628:
5457:
5176:
4811:
4599:
4387:
4072:
3828:
3585:
3272:
2718:
2362:
2222:
2182:
2054:
1977:
1956:
1677:
1373:
1218:
903:
848:
797:kg stone by
667:
297:
168:
167:
165:
157:
70:
50:
41:
40:
21:
1979:Do-calculus
241:. Instead,
5635:The Lancet
5620:References
155:section.)
5727:CiteSeerX
5527:→
5477:→
5010:↔
4830:↔
4780:↔
4618:↔
4568:→
4406:→
4356:↔
4301:−
4091:←
4041:←
3989:←
3847:→
3797:←
3746:→
3604:←
3554:→
3499:↷
3493:↶
3291:→
3241:→
3137:↔
2984:←
2831:→
2338:←
2332:→
2319:Collider
2300:→
2294:←
2262:→
2256:→
1948:Notations
1374:Smoking,
1179:−
1155:⋅
1004:−
980:⋅
956:−
932:⋅
883:×
877:×
865:×
859:×
153:Notations
66:economics
5980:Notation
5974:Category
5663:10066001
2235:Pattern
1963:reactant
817:meters,
162:Examples
46:notation
5690:Bibcode
5655:6145023
4953:causes
4892:causes
3909:causes
3666:causes
2155:causes
1967:product
1641:causes
1583:causes
1196:), and
58:physics
54:biology
5954:>}}
5934:
5899:
5874:
5849:
5824:
5796:
5729:
5661:
5653:
5532:
5519:
5508:, and
5482:
5469:
5218:
5194:
5143:
5119:
5015:
5002:
4941:
4835:
4822:
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4772:
4623:
4610:
4573:
4560:
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4310:
4289:
4243:
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4083:
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4033:
3994:
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3296:
3283:
3246:
3233:
3142:
3129:
2989:
2976:
2836:
2823:
2243:Chain
2238:Model
2196:, and
2039:
904:where
889:
765:
5772:(PDF)
5761:(PDF)
5659:S2CID
4269:, or
2281:Fork
1965:or a
5932:ISBN
5897:ISBN
5872:ISBN
5847:ISBN
5822:ISBN
5794:ISBN
5651:PMID
5587:and
5416:and
5344:and
5281:and
5068:and
4921:and
4680:and
4468:and
4304:<
4298:>
3354:and
3198:and
2780:and
2687:and
2609:and
2392:and
1612:nor
1337:and
631:and
550:and
463:and
261:and
64:and
56:and
5737:doi
5698:doi
5643:doi
5639:323
5317:or
4177:or
1135:9.8
1067:),
1021:),
696:100
688:of
60:to
44:is
5976::
5911:^
5808:^
5780:^
5735:.
5721:.
5696:.
5686:49
5684:.
5680:.
5657:.
5649:.
5637:.
5380:,
5039:.
4982::
4206::
4018:.
3961::
3718::
3403::
3114:.
2961:.
2751:,
2658:,
2204:.
2192:,
2188:,
2175:.
901:,
805:50
762:10
5940:.
5905:.
5880:.
5855:.
5830:.
5802:.
5743:.
5739::
5723:5
5706:.
5700::
5692::
5665:.
5645::
5604:)
5601:s
5598:(
5595:a
5575:)
5572:s
5569:(
5566:b
5545:)
5542:s
5539:(
5535:b
5524:=
5516:s
5495:)
5492:s
5489:(
5485:a
5474:=
5466:s
5440:)
5435:2
5431:s
5427:(
5424:b
5404:)
5399:1
5395:s
5391:(
5388:a
5368:)
5363:2
5359:s
5355:(
5352:b
5330:2
5326:s
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5300:1
5296:s
5292:(
5289:a
5267:1
5263:s
5238:)
5233:2
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5225:(
5221:b
5212:.
5209:b
5206:r
5203:a
5199:=
5189:2
5185:s
5163:)
5158:1
5154:s
5150:(
5146:a
5137:.
5134:b
5131:r
5128:a
5124:=
5114:1
5110:s
5085:)
5082:s
5079:(
5076:a
5056:)
5053:s
5050:(
5047:b
5027:)
5024:s
5021:(
5018:b
5007:=
4999:)
4996:s
4993:(
4990:a
4970:)
4967:s
4964:(
4961:b
4938:)
4935:s
4932:(
4929:a
4909:)
4906:s
4903:(
4900:a
4880:)
4877:s
4874:(
4871:b
4848:)
4845:s
4842:(
4838:b
4827:=
4819:s
4798:)
4795:s
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4788:a
4777:=
4769:s
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4743:s
4740:(
4737:b
4717:)
4714:s
4711:(
4708:a
4688:s
4668:)
4665:s
4662:(
4659:b
4636:)
4633:s
4630:(
4626:b
4615:=
4607:s
4586:)
4583:s
4580:(
4576:a
4565:=
4557:s
4534:)
4531:s
4528:(
4525:a
4505:)
4502:s
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4496:b
4476:s
4456:)
4453:s
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4447:a
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4421:s
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4414:b
4403:=
4395:s
4374:)
4371:s
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4364:a
4353:=
4345:s
4322:)
4319:s
4316:(
4313:a
4294:=
4286:)
4283:s
4280:(
4277:b
4256:)
4253:s
4250:(
4246:b
4233:=
4224:)
4221:s
4218:(
4214:a
4194:)
4191:s
4188:(
4185:b
4165:)
4162:s
4159:(
4156:a
4133:s
4109:)
4106:s
4103:(
4099:b
4088:=
4080:s
4059:)
4056:s
4053:(
4049:a
4038:=
4030:s
4006:)
4003:s
4000:(
3997:a
3986:=
3978:)
3975:s
3972:(
3969:b
3949:)
3946:s
3943:(
3940:b
3917:s
3897:)
3894:s
3891:(
3888:a
3865:)
3862:s
3859:(
3855:b
3844:=
3836:s
3815:)
3812:s
3809:(
3805:a
3794:=
3786:s
3763:)
3760:s
3757:(
3754:a
3743:=
3735:)
3732:s
3729:(
3726:b
3706:)
3703:s
3700:(
3697:a
3674:s
3654:)
3651:s
3648:(
3645:b
3622:)
3619:s
3616:(
3612:b
3601:=
3593:s
3572:)
3569:s
3566:(
3562:a
3551:=
3543:s
3518:)
3515:s
3512:(
3508:b
3496:?
3489:=
3480:)
3477:s
3474:(
3470:a
3450:)
3447:s
3444:(
3441:b
3428:=
3420:)
3417:s
3414:(
3411:a
3391:s
3371:)
3368:s
3365:(
3362:b
3342:)
3339:s
3336:(
3333:a
3309:)
3306:s
3303:(
3299:b
3288:=
3280:s
3259:)
3256:s
3253:(
3249:a
3238:=
3230:s
3206:s
3186:)
3183:s
3180:(
3177:a
3155:)
3152:s
3149:(
3145:a
3134:=
3126:s
3102:s
3082:)
3079:s
3076:(
3073:a
3053:)
3050:s
3047:(
3044:a
3024:s
3002:)
2999:s
2996:(
2992:a
2981:=
2973:s
2949:s
2929:)
2926:s
2923:(
2920:a
2900:s
2880:)
2877:s
2874:(
2871:a
2849:)
2846:s
2843:(
2839:a
2828:=
2820:s
2797:)
2794:s
2791:(
2788:b
2768:)
2765:s
2762:(
2759:a
2739:s
2704:)
2701:s
2698:(
2695:b
2675:)
2672:s
2669:(
2666:a
2646:s
2626:)
2623:s
2620:(
2617:a
2597:)
2594:s
2591:(
2588:b
2568:)
2565:s
2562:(
2559:a
2539:)
2536:s
2533:(
2530:b
2510:)
2507:s
2504:(
2501:b
2481:)
2478:s
2475:(
2472:a
2452:s
2432:s
2409:)
2406:s
2403:(
2400:b
2380:)
2377:s
2374:(
2371:a
2341:Z
2335:Y
2329:X
2303:Z
2297:Y
2291:X
2265:Z
2259:Y
2253:X
2163:Y
2143:X
2123:X
2103:Y
2083:X
2063:Y
2051:,
2036:)
2033:Y
2030:(
2027:P
2024:=
2021:)
2018:)
2015:X
2012:(
2009:o
2006:d
2002:|
1998:Y
1995:(
1992:P
1932:)
1929:y
1926:(
1923:B
1920:=
1917:)
1914:y
1911:(
1908:C
1888:)
1885:y
1882:(
1879:B
1859:)
1856:y
1853:(
1850:C
1830:B
1810:C
1790:)
1787:y
1784:(
1781:B
1778:=
1775:)
1772:y
1769:(
1766:C
1746:y
1726:B
1706:y
1686:C
1658:)
1655:y
1652:(
1649:f
1629:)
1626:y
1623:(
1620:g
1600:)
1597:y
1594:(
1591:g
1571:)
1568:y
1565:(
1562:f
1542:)
1539:y
1536:(
1533:g
1513:)
1510:y
1507:(
1504:f
1484:)
1481:y
1478:(
1475:g
1472:=
1469:)
1466:y
1463:(
1460:f
1440:y
1420:)
1417:y
1414:(
1411:g
1391:)
1388:y
1385:(
1382:f
1354:)
1351:I
1348:(
1345:h
1325:I
1305:I
1285:)
1282:I
1279:(
1276:h
1256:)
1253:I
1250:(
1247:h
1227:I
1204:h
1182:2
1167:s
1147:m
1115:g
1095:m
1075:t
1053:2
1029:A
1007:2
992:m
959:1
944:s
912:I
886:h
880:g
874:m
871:=
868:t
862:A
856:I
834:)
831:I
828:(
825:h
785:2
740:2
728:m
716:1
676:I
648:)
645:y
642:(
639:g
619:)
616:y
613:(
610:f
590:y
567:)
564:y
561:(
558:g
538:)
535:y
532:(
529:f
509:)
506:y
503:(
500:g
480:)
477:y
474:(
471:f
451:)
448:y
445:(
442:g
422:)
419:y
416:(
413:f
393:)
390:y
387:(
384:g
364:)
361:y
358:(
355:g
335:)
332:y
329:(
326:f
306:y
278:)
275:y
272:(
269:f
249:y
229:y
209:)
206:y
203:(
200:f
180:y
139:x
119:y
99:)
96:x
93:(
90:f
87:=
84:y
36:.
26:.
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