2890:
1618:
2838:
2850:
112:. Clay tablets from circa 2000 BCE include the exercise "Given an interest rate of 1/60 per month (no compounding), come the doubling time." This yields an annual interest rate of 12/60 = 20%, and hence a doubling time of 100% growth/20% growth per year = 5 years. Further, repaying double the initial amount of a loan, after a fixed time, was common commercial practice of the period: a common
2902:
2862:
1617:
1416:
When applied to the constant growth in consumption of a resource, the total amount consumed in one doubling period equals the total amount consumed in all previous periods. This enabled U.S. President Jimmy Carter to note in a speech in 1977 that in each of the previous two decades the world had used
99:
As an example, Canada's net population growth was 2.7 percent in the year 2022, dividing 72 by 2.7 gives an approximate doubling time of about 27 years. Thus if that growth rate were to remain constant, Canada's population would double from its 2023 figure of about 39 million to about 78 million by
246:
1573:
1956:
116:
loan of 1900 BCE consisted of loaning 2 minas of gold, getting back 4 in five years, and an
Egyptian proverb of the time was "If wealth is placed where it bears interest, it comes back to you redoubled."
1789:
1413:
For example, with an annual growth rate of 4.8% the doubling time is 14.78 years, and a doubling time of 10 years corresponds to a growth rate between 7% and 7.5% (actually about 7.18%).
322:
1708:
1856:
1824:
1417:
more oil than in all of previous history (The roughly exponential growth in world oil consumption between 1950 and 1970 had a doubling period of under a decade).
1900:
1878:
2137:
151:
1454:
2251:
2220:
1912:
2818:
125:
Examining the doubling time can give a more intuitive sense of the long-term impact of growth than simply viewing the percentage growth rate.
2293:
2802:
1624:
73:
by the exponent of growth, or approximated by dividing 70 by the percentage growth rate (more roughly but roundly, dividing 72; see the
2103:
2942:
2631:
1719:
2927:
2792:
2906:
2797:
2244:
1627:
Graphs comparing doubling times and half lives of exponential growths (bold lines) and decay (faint lines), and their 70/
2922:
1649:
Cell doubling time can be calculated in the following way using growth rate (amount of doubling in one unit of time)
2880:
2646:
2498:
2144:
2866:
1599:
2932:
2842:
2237:
2072:
2526:
47:
2085:
260:
2854:
2546:
2349:
109:
70:
2217:
2937:
2823:
2536:
2406:
2007:
2889:
1658:
1636:
2686:
2661:
2616:
2464:
2459:
2421:
2396:
2040:
59:
2561:
2454:
85:
66:
and has a constant doubling time or period, which can be calculated directly from the growth rate.
43:
2849:
2894:
2691:
2626:
2606:
2596:
2556:
2541:
2516:
2474:
2469:
2323:
2313:
2308:
2030:
63:
2756:
2671:
2611:
2581:
2506:
2364:
2359:
2283:
2025:
1588:
89:
51:
35:
2751:
2621:
2483:
2434:
2416:
2189:
2181:
2012:
1834:
2721:
2706:
2681:
2656:
2576:
2571:
2531:
2449:
2444:
2439:
2354:
2303:
2260:
2224:
2064:
1800:
241:{\displaystyle T_{d}=t{\frac {\ln(2)}{\ln(1+{\frac {r}{100}})}}\approx t{\frac {70}{r}}}
17:
2776:
2771:
2766:
2736:
2711:
2701:
2696:
2666:
2591:
2586:
2551:
2511:
2479:
2401:
2386:
2318:
2288:
2212:
2194:
2169:
1885:
1863:
1568:{\displaystyle T_{d}=(t_{2}-t_{1})\cdot {\frac {\ln(2)}{\ln({\frac {q_{2}}{q_{1}}})}}.}
2916:
2761:
2676:
2636:
2521:
2328:
88:(a natural unit of scale) for the exponential growth equation, and its converse for
2741:
2641:
2566:
2115:
2086:"The Daily — Canada's population estimates: Record-high population growth in 2022"
2731:
2726:
2716:
2651:
2391:
2278:
34:
is the time it takes for a population to double in size/value. It is applied to
2746:
2601:
2045:
1448:, and assuming a constant growth rate, the doubling time can be calculated as
78:
74:
2075:, 2008, page 33 (box "Hint on reinforcing feedback loops and doubling time").
2411:
2298:
2185:
2035:
2017:
1605:
1592:
93:
39:
1951:{\displaystyle {\text{doubling time}}={\frac {\ln(2)}{\text{growth rate}}}}
2901:
251:
Some doubling times calculated with this formula are shown in this table.
113:
2218:
http://geography.about.com/od/populationgeography/a/populationgrow.htm
1587:
for a material undergoing a constant negative relative growth rate or
2268:
55:
62:(not the absolute growth rate) is constant, the quantity undergoes
2229:
1961:
The following is the known doubling time for the following cells:
2104:
Why the “Miracle of
Compound Interest” leads to Financial Crises
350:= doubling period (time it takes for object to double in number)
2233:
58:, and many other things that tend to grow over time. When the
1784:{\displaystyle r={\frac {\ln \left(N(t)/N_{0}\right)}{t}}}
108:
The notion of doubling time dates to interest on loans in
1639:, hover over a graph to highlight it and its complement.
2127:
Miriam
Lichtheim, Ancient Egyptian Literature, II:135.
2878:
1915:
1888:
1866:
1837:
1803:
1722:
1661:
1457:
263:
154:
2811:
2785:
2497:
2373:
2337:
2267:
1950:
1894:
1872:
1850:
1818:
1783:
1702:
1567:
316:
240:
2174:Proceedings of the National Academy of Sciences
1420:Given two measurements of a growing quantity,
2245:
8:
2168:Bearzi, Claudia; et al. (August 2007).
69:This time can be calculated by dividing the
2379:
2252:
2238:
2230:
2193:
1924:
1916:
1914:
1887:
1865:
1842:
1836:
1802:
1764:
1755:
1729:
1721:
1691:
1681:
1660:
1548:
1538:
1532:
1503:
1491:
1478:
1462:
1456:
306:
297:
293:
283:
262:
228:
206:
171:
159:
153:
2099:
2097:
2095:
1963:
1308:
1206:
1104:
1002:
900:
798:
696:
594:
492:
390:
2885:
2057:
317:{\displaystyle N(t)=N_{0}2^{t/T_{d}}}
7:
2861:
136:, the formula for the doubling time
2803:Systems theory in political science
338:) = the number of objects at time
27:Time required to double a quantity
25:
2900:
2888:
2860:
2848:
2837:
2836:
1703:{\displaystyle N(t)=N_{0}e^{rt}}
1616:
1858:= the number of cells at time 0
1598:The equivalent concept in base-
2793:Systems theory in anthropology
1939:
1933:
1826:= the number of cells at time
1813:
1807:
1752:
1746:
1671:
1665:
1556:
1529:
1518:
1512:
1497:
1471:
273:
267:
254:Simple doubling time formula:
216:
197:
186:
180:
128:For a constant growth rate of
1:
2798:Systems theory in archaeology
2116:Have we caught your interest?
2069:Thinking in Systems: A Primer
359:= initial number of objects
79:derivations of this formula
2959:
2170:"Human cardiac stem cells"
1645:Cell culture doubling time
1583:The equivalent concept to
2832:
2430:
2382:
2294:Coupled human–environment
1995:29 ± 10 hours
1902:= time (usually in hours)
2213:Doubling Time Calculator
2073:Chelsea Green Publishing
1989:Cardiac/heart stem cell
18:Population doubling time
2943:Mathematics in medicine
2627:Charles A. S. Hall
2186:10.1073/pnas.0706760104
1635:approximations. In the
84:The doubling time is a
2907:Business and economics
2547:Ludwig von Bertalanffy
1978:Mesenchymal Stem Cell
1952:
1896:
1874:
1852:
1820:
1785:
1704:
1569:
318:
242:
110:Babylonian mathematics
71:natural logarithm of 2
2928:Temporal exponentials
2824:Principia Cybernetica
2537:Anthony Stafford Beer
2407:Sociotechnical system
2008:Albert Allen Bartlett
1953:
1897:
1875:
1853:
1851:{\displaystyle N_{0}}
1821:
1786:
1705:
1570:
319:
243:
132: % within time
2687:Mihajlo D. Mesarovic
2662:Edward Norton Lorenz
2617:Jay Wright Forrester
2422:World-systems theory
2397:Earth system science
2041:Relative growth rate
1913:
1886:
1864:
1835:
1819:{\displaystyle N(t)}
1801:
1720:
1659:
1455:
261:
152:
145: is given by
60:relative growth rate
2562:Kenneth E. Boulding
2180:(35): 14068–14073.
2138:"Life Technologies"
2106:, by Michael Hudson
386:
86:characteristic unit
44:resource extraction
2923:Population ecology
2692:James Grier Miller
2647:Faina M. Kirillova
2607:Heinz von Foerster
2597:Edsger W. Dijkstra
2557:Alexander Bogdanov
2542:Richard E. Bellman
2517:William Ross Ashby
2223:2006-08-28 at the
2031:Exponential growth
1948:
1892:
1870:
1848:
1816:
1781:
1700:
1565:
369:
314:
238:
64:exponential growth
2876:
2875:
2757:Manuela M. Veloso
2672:Humberto Maturana
2612:Stephanie Forrest
2582:C. West Churchman
2507:Russell L. Ackoff
2493:
2492:
2365:Positive feedback
2360:Negative feedback
2026:Exponential decay
1999:
1998:
1946:
1945:
1919:
1895:{\displaystyle t}
1873:{\displaystyle r}
1779:
1589:exponential decay
1560:
1554:
1411:
1410:
1407:
1406:
1305:
1304:
1203:
1202:
1101:
1100:
999:
998:
897:
896:
795:
794:
693:
692:
591:
590:
489:
488:
236:
220:
214:
90:exponential decay
56:malignant tumours
52:compound interest
36:population growth
16:(Redirected from
2950:
2905:
2904:
2893:
2892:
2884:
2864:
2863:
2852:
2840:
2839:
2752:Francisco Varela
2484:Systems thinking
2417:Urban metabolism
2380:
2254:
2247:
2240:
2231:
2200:
2199:
2197:
2165:
2159:
2158:
2156:
2155:
2149:
2143:. Archived from
2142:
2134:
2128:
2125:
2119:
2113:
2107:
2101:
2090:
2089:
2088:. 22 March 2023.
2082:
2076:
2062:
2013:Binary logarithm
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1620:
1579:Related concepts
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189:
172:
164:
163:
77:for details and
54:, the volume of
21:
2958:
2957:
2953:
2952:
2951:
2949:
2948:
2947:
2933:Economic growth
2913:
2912:
2911:
2899:
2887:
2879:
2877:
2872:
2828:
2807:
2781:
2722:Anatol Rapoport
2707:Talcott Parsons
2682:Donella Meadows
2657:Allenna Leonard
2577:Mary Cartwright
2572:Kathleen Carley
2532:Gregory Bateson
2527:Béla H. Bánáthy
2489:
2426:
2375:
2369:
2355:Limiting factor
2350:Leverage points
2333:
2271:
2263:
2261:Systems science
2258:
2225:Wayback Machine
2209:
2204:
2203:
2167:
2166:
2162:
2153:
2151:
2147:
2140:
2136:
2135:
2131:
2126:
2122:
2118:by John H. Webb
2114:
2110:
2102:
2093:
2084:
2083:
2079:
2065:Donella Meadows
2063:
2059:
2054:
2004:
1926:
1911:
1910:
1906:Doubling time:
1884:
1883:
1862:
1861:
1838:
1833:
1832:
1799:
1798:
1760:
1742:
1738:
1731:
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1717:
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1677:
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1522:
1505:
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1474:
1458:
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1452:
1447:
1440:
1433:
1426:
1322:
1220:
1118:
1016:
914:
812:
710:
608:
506:
404:
380:given constant
379:
371:Doubling times
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2800:
2795:
2789:
2787:
2783:
2782:
2780:
2779:
2777:Anthony Wilden
2774:
2772:Jennifer Wilby
2769:
2767:Norbert Wiener
2764:
2759:
2754:
2749:
2744:
2739:
2737:Claude Shannon
2734:
2729:
2724:
2719:
2714:
2712:Ilya Prigogine
2709:
2704:
2702:Howard T. Odum
2699:
2697:Radhika Nagpal
2694:
2689:
2684:
2679:
2674:
2669:
2667:Niklas Luhmann
2664:
2659:
2654:
2649:
2644:
2639:
2634:
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2624:
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2614:
2609:
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2599:
2594:
2592:George Dantzig
2589:
2587:Manfred Clynes
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2559:
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2552:Margaret Boden
2549:
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2512:Victor Aladjev
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548:
545:
541:
540:
537:
533:
532:
529:
525:
524:
521:
517:
516:
513:
509:
508:
504:
500:
490:
487:
486:
483:
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463:
462:
459:
455:
454:
451:
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446:
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439:
438:
435:
431:
430:
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423:
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419:
415:
414:
411:
407:
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402:
398:
375:
367:
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356:
351:
346:
342:
325:
324:
309:
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296:
292:
286:
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269:
266:
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235:
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227:
224:
218:
213:
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205:
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199:
196:
193:
188:
185:
182:
179:
176:
170:
167:
162:
158:
140:
122:
119:
105:
102:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2955:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
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2908:
2903:
2898:
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2891:
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2847:
2845:
2844:
2835:
2834:
2831:
2825:
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2820:
2817:
2816:
2814:
2812:Organizations
2810:
2804:
2801:
2799:
2796:
2794:
2791:
2790:
2788:
2784:
2778:
2775:
2773:
2770:
2768:
2765:
2763:
2762:Kevin Warwick
2760:
2758:
2755:
2753:
2750:
2748:
2745:
2743:
2740:
2738:
2735:
2733:
2730:
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2725:
2723:
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2718:
2715:
2713:
2710:
2708:
2705:
2703:
2700:
2698:
2695:
2693:
2690:
2688:
2685:
2683:
2680:
2678:
2677:Margaret Mead
2675:
2673:
2670:
2668:
2665:
2663:
2660:
2658:
2655:
2653:
2650:
2648:
2645:
2643:
2640:
2638:
2637:Lydia Kavraki
2635:
2633:
2630:
2628:
2625:
2623:
2622:Barbara Grosz
2620:
2618:
2615:
2613:
2610:
2608:
2605:
2603:
2600:
2598:
2595:
2593:
2590:
2588:
2585:
2583:
2580:
2578:
2575:
2573:
2570:
2568:
2565:
2563:
2560:
2558:
2555:
2553:
2550:
2548:
2545:
2543:
2540:
2538:
2535:
2533:
2530:
2528:
2525:
2523:
2522:Ruzena Bajcsy
2520:
2518:
2515:
2513:
2510:
2508:
2505:
2504:
2502:
2500:
2496:
2485:
2481:
2478:
2476:
2473:
2471:
2468:
2466:
2463:
2461:
2458:
2456:
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2443:
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2433:
2432:
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2415:
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2405:
2403:
2400:
2398:
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2384:
2381:
2378:
2372:
2366:
2363:
2361:
2358:
2356:
2353:
2351:
2348:
2346:
2345:Doubling time
2343:
2342:
2340:
2336:
2330:
2327:
2325:
2322:
2320:
2317:
2315:
2312:
2310:
2307:
2305:
2302:
2300:
2297:
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2250:
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2241:
2236:
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2222:
2219:
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2211:
2210:
2206:
2196:
2191:
2187:
2183:
2179:
2175:
2171:
2164:
2161:
2150:on 2015-04-02
2146:
2139:
2133:
2130:
2124:
2121:
2117:
2112:
2109:
2105:
2100:
2098:
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2081:
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2066:
2061:
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2047:
2044:
2042:
2039:
2037:
2034:
2032:
2029:
2027:
2024:
2022:
2020:
2016:
2014:
2011:
2009:
2006:
2005:
2001:
1994:
1991:
1988:
1987:
1983:
1980:
1977:
1976:
1972:
1969:
1966:
1965:
1962:
1936:
1930:
1927:
1921:
1918:doubling time
1909:
1908:
1907:
1889:
1882:
1880:= growth rate
1867:
1860:
1843:
1839:
1831:
1829:
1810:
1804:
1797:
1796:
1795:
1776:
1771:
1765:
1761:
1756:
1749:
1743:
1739:
1735:
1732:
1726:
1723:
1716:
1715:
1714:
1695:
1692:
1688:
1682:
1678:
1674:
1668:
1662:
1655:
1654:
1653:
1652:Growth rate:
1650:
1644:
1638:
1634:
1630:
1625:
1619:
1612:
1610:
1608:
1603:
1602:
1596:
1594:
1590:
1586:
1585:doubling time
1578:
1562:
1549:
1545:
1539:
1535:
1526:
1523:
1515:
1509:
1506:
1500:
1492:
1488:
1484:
1479:
1475:
1468:
1463:
1459:
1451:
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1449:
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1437:
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1423:
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1414:
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1399:
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1383:
1382:
1378:
1375:
1374:
1370:
1367:
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1362:
1359:
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1354:
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1346:
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1335:
1334:
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1327:
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1317:
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1307:
1300:
1297:
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1268:
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1205:
1198:
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1190:
1187:
1186:
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1179:
1178:
1174:
1171:
1170:
1166:
1163:
1162:
1158:
1155:
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1134:
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1126:
1123:
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1110:
1107:
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1103:
1096:
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1080:
1077:
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1032:
1029:
1028:
1024:
1021:
1020:
1017:
1011:
1008:
1005:
1004:
1001:
994:
991:
990:
986:
983:
982:
978:
975:
974:
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967:
966:
962:
959:
958:
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951:
950:
946:
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942:
938:
935:
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930:
927:
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922:
919:
918:
915:
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906:
903:
902:
899:
892:
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888:
884:
881:
880:
876:
873:
872:
868:
865:
864:
860:
857:
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849:
848:
844:
841:
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836:
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828:
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813:
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797:
790:
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723:
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714:
711:
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702:
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688:
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684:
680:
677:
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672:
669:
668:
664:
661:
660:
656:
653:
652:
648:
645:
644:
640:
637:
636:
632:
629:
628:
624:
621:
620:
616:
613:
612:
609:
603:
600:
597:
596:
593:
586:
583:
582:
578:
575:
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570:
567:
566:
562:
559:
558:
554:
551:
550:
546:
543:
542:
538:
535:
534:
530:
527:
526:
522:
519:
518:
514:
511:
510:
507:
501:
498:
495:
494:
491:
484:
481:
480:
476:
473:
472:
468:
465:
464:
460:
457:
456:
452:
449:
448:
444:
441:
440:
436:
433:
432:
428:
425:
424:
420:
417:
416:
412:
409:
408:
405:
399:
396:
393:
392:
389:
388:
385:
383:
378:
374:
364:
361:
355:
352:
349:
343:
341:
337:
333:
330:
329:
328:
307:
303:
298:
294:
290:
284:
280:
276:
270:
264:
257:
256:
255:
252:
233:
230:
225:
222:
211:
208:
203:
200:
194:
191:
183:
177:
174:
168:
165:
160:
156:
148:
147:
146:
143:
139:
135:
131:
126:
120:
118:
115:
111:
103:
101:
97:
95:
91:
87:
82:
80:
76:
72:
67:
65:
61:
57:
53:
49:
45:
41:
37:
33:
32:doubling time
19:
2938:Epidemiology
2865:
2853:
2841:
2786:Applications
2742:Katia Sycara
2642:James J. Kay
2632:Mike Jackson
2567:Murray Bowen
2465:Pharmacology
2460:Neuroscience
2344:
2177:
2173:
2163:
2152:. Retrieved
2145:the original
2132:
2123:
2111:
2080:
2068:
2060:
2018:
1984:21–23 hours
1960:
1905:
1827:
1793:
1712:
1651:
1648:
1632:
1628:
1606:
1600:
1597:
1584:
1582:
1442:
1435:
1428:
1421:
1419:
1415:
1412:
1318:
1312:
1216:
1210:
1114:
1108:
1012:
1006:
910:
904:
808:
802:
706:
700:
604:
598:
502:
496:
400:
394:
381:
376:
372:
370:
362:
353:
344:
339:
335:
331:
326:
253:
250:
141:
137:
133:
129:
127:
124:
107:
98:
83:
68:
31:
29:
2895:Mathematics
2732:Peter Senge
2727:John Seddon
2717:Qian Xuesen
2652:George Klir
2455:Engineering
2392:Cybernetics
2374:Theoretical
2324:Recommender
2314:Multi-agent
2309:Information
1967:Cell types
1944:growth rate
1637:SVG version
121:Examination
48:consumption
2917:Categories
2747:Eric Trist
2602:Fred Emery
2499:Scientists
2475:Psychology
2470:Philosophy
2299:Ecological
2284:Biological
2154:2015-03-12
2052:References
2046:Rule of 72
75:rule of 72
50:of goods,
2412:Systemics
2036:Half-life
1931:
1736:
1593:half-life
1527:
1510:
1501:⋅
1485:−
984: 9.5
976: 9.0
968: 8.5
960: 8.0
952: 7.5
944: 7.0
936: 6.5
928: 6.0
920: 5.5
890: 5.0
882: 4.9
874: 4.8
866: 4.7
858: 4.6
850: 4.5
842: 4.4
834: 4.3
826: 4.2
818: 4.1
788: 4.0
780: 3.9
772: 3.8
764: 3.7
756: 3.6
748: 3.5
740: 3.4
732: 3.3
724: 3.2
716: 3.1
686: 3.0
678: 2.9
670: 2.8
662: 2.7
654: 2.6
646: 2.5
638: 2.4
630: 2.3
622: 2.2
614: 2.1
584: 2.0
576: 1.9
568: 1.8
560: 1.7
552: 1.6
544: 1.5
536: 1.4
528: 1.3
520: 1.2
512: 1.1
482: 1.0
474: 0.9
466: 0.8
458: 0.7
450: 0.6
442: 0.5
434: 0.4
426: 0.3
418: 0.2
410: 0.1
223:≈
195:
178:
94:half-life
40:inflation
2843:Category
2445:Dynamics
2435:Analysis
2338:Concepts
2304:Economic
2221:Archived
2021:-folding
2002:See also
1609:-folding
1441:at time
1427:at time
384:% growth
114:Assyrian
100:2050.
2881:Portals
2867:Commons
2450:Ecology
2440:Biology
2319:Nervous
2289:Complex
2195:1955818
1970:Source
1631:and 72/
1591:is the
453:115.87
445:138.98
437:173.63
429:231.40
421:346.92
413:693.49
104:History
92:is the
2855:Portal
2480:Theory
2376:fields
2329:Social
2269:System
2192:
1992:Human
1981:Mouse
1794:where
947:10.24
939:11.01
931:11.90
923:12.95
893:14.21
885:14.49
877:14.78
869:15.09
861:15.41
853:15.75
845:16.10
837:16.46
829:16.85
821:17.25
791:17.67
783:18.12
775:18.59
767:19.08
759:19.60
751:20.15
743:20.73
735:21.35
727:22.01
719:22.70
689:23.45
681:24.25
673:25.10
665:26.02
657:27.00
649:28.07
641:29.23
633:30.48
625:31.85
617:33.35
587:35.00
579:36.83
571:38.85
563:41.12
555:43.67
547:46.56
539:49.86
531:53.66
523:58.11
515:63.64
485:69.66
477:77.36
469:86.99
461:99.36
365:= time
327:where
2272:types
2148:(PDF)
2141:(PDF)
1403:1.71
1395:1.74
1387:1.77
1379:1.80
1371:1.83
1363:1.87
1355:1.90
1347:1.94
1339:1.98
1331:2.02
1301:2.06
1293:2.10
1285:2.15
1277:2.20
1269:2.25
1261:2.31
1253:2.37
1245:2.43
1237:2.50
1229:2.57
1199:2.64
1191:2.72
1183:2.81
1175:2.90
1167:3.00
1159:3.11
1151:3.22
1143:3.35
1135:3.49
1127:3.64
1097:3.80
1089:3.98
1081:4.19
1073:4.41
1065:4.67
1057:4.96
1049:5.29
1041:5.67
1033:6.12
1025:6.64
995:7.27
987:7.64
979:8.04
971:8.50
963:9.01
955:9.58
2819:List
1434:and
1400:50.0
1392:49.0
1384:48.0
1376:47.0
1368:46.0
1360:45.0
1352:44.0
1344:43.0
1336:42.0
1328:41.0
1298:40.0
1290:39.0
1282:38.0
1274:37.0
1266:36.0
1258:35.0
1250:34.0
1242:33.0
1234:32.0
1226:31.0
1196:30.0
1188:29.0
1180:28.0
1172:27.0
1164:26.0
1156:25.0
1148:24.0
1140:23.0
1132:22.0
1124:21.0
1094:20.0
1086:19.0
1078:18.0
1070:17.0
1062:16.0
1054:15.0
1046:14.0
1038:13.0
1030:12.0
1022:11.0
992:10.0
30:The
2279:Art
2190:PMC
2182:doi
2178:104
1713:or
1604:is
212:100
81:).
2919::
2188:.
2176:.
2172:.
2094:^
2071:,
2067:,
1928:ln
1733:ln
1611:.
1595:.
1524:ln
1507:ln
231:70
192:ln
175:ln
96:.
46:,
42:,
38:,
2883::
2486:)
2482:(
2253:e
2246:t
2239:v
2198:.
2184::
2157:.
2019:e
1940:)
1937:2
1934:(
1922:=
1890:t
1868:r
1844:0
1840:N
1828:t
1814:)
1811:t
1808:(
1805:N
1777:t
1772:)
1766:0
1762:N
1757:/
1753:)
1750:t
1747:(
1744:N
1740:(
1727:=
1724:r
1696:t
1693:r
1689:e
1683:0
1679:N
1675:=
1672:)
1669:t
1666:(
1663:N
1633:t
1629:t
1607:e
1601:e
1563:.
1557:)
1550:1
1546:q
1540:2
1536:q
1530:(
1519:)
1516:2
1513:(
1498:)
1493:1
1489:t
1480:2
1476:t
1472:(
1469:=
1464:d
1460:T
1446:2
1443:t
1439:2
1436:q
1432:1
1429:t
1425:1
1422:q
1321:d
1319:T
1315:%
1313:r
1219:d
1217:T
1213:%
1211:r
1117:d
1115:T
1111:%
1109:r
1015:d
1013:T
1009:%
1007:r
913:d
911:T
907:%
905:r
811:d
809:T
805:%
803:r
709:d
707:T
703:%
701:r
607:d
605:T
601:%
599:r
505:d
503:T
499:%
497:r
403:d
401:T
397:%
395:r
382:r
377:d
373:T
363:t
357:0
354:N
347:d
345:T
340:t
336:t
334:(
332:N
308:d
304:T
299:/
295:t
291:2
285:0
281:N
277:=
274:)
271:t
268:(
265:N
234:r
226:t
217:)
209:r
204:+
201:1
198:(
187:)
184:2
181:(
169:t
166:=
161:d
157:T
142:d
138:T
134:t
130:r
20:)
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