{"id":"https://openalex.org/W4367339646","doi":"https://doi.org/10.7554/elife.84757.sa0","title":"Editor's evaluation: Patterning precision under non-linear morphogen decay and molecular noise","display_name":"Editor's evaluation: Patterning precision under non-linear morphogen decay and molecular noise","publication_year":2023,"publication_date":"2023-02-08","ids":{"openalex":"https://openalex.org/W4367339646","doi":"https://doi.org/10.7554/elife.84757.sa0"},"language":"en","primary_location":{"id":"doi:10.7554/elife.84757.sa0","doi":"https://doi.org/10.7554/elife.84757.sa0","is_oa":true,"landing_page_url":"https://doi.org/10.7554/elife.84757.sa0","pdf_url":null,"source":{"id":"https://openalex.org/S1336409049","display_name":"eLife","issn_l":"2050-084X","issn":["2050-084X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-a","jufo-2","ki-jl-2","medline","norway-2","oarl","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311710","host_organization_name":"eLife Sciences Publications Ltd","host_organization_lineage":["https://openalex.org/P4310311710"],"host_organization_lineage_names":["eLife Sciences Publications Ltd"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"peer-review"},"volume":null,"type":"peer-review","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.7554/elife.84757.sa0","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001252579","display_name":"Gordon J Berman","orcid":"https://orcid.org/0000-0003-3588-7820","observed_orcids":["https://orcid.org/0000-0003-3588-7820"]},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gordon J Berman","raw_affiliation_strings":["Emory University"],"raw_orcid":"https://orcid.org/0000-0003-3588-7820","affiliations":[{"raw_affiliation_string":"Emory University","institution_ids":["https://openalex.org/I150468666"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001252579"],"corresponding_institution_ids":["https://openalex.org/I150468666"],"apc_list":{"value":3000,"currency":"USD","value_usd":2500},"apc_paid":{"value":3000,"currency":"USD","value_usd":2500},"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10268","display_name":"Developmental Biology and Gene Regulation","score":0.8428000211715698,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10268","display_name":"Developmental Biology and Gene Regulation","score":0.8428000211715698,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.10890000313520432,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.0032999999821186066,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/morphogen-gradients","display_name":"morphogen gradients","score":0.9750000238418579},{"id":"https://openalex.org/keywords/molecular-noise","display_name":"molecular noise","score":0.968999981880188},{"id":"https://openalex.org/keywords/stochastic-gene-expression","display_name":"stochastic gene expression","score":0.6150000095367432},{"id":"https://openalex.org/keywords/developmental-patterning","display_name":"developmental patterning","score":0.6039999723434448},{"id":"https://openalex.org/keywords/reaction-diffusion","display_name":"reaction-diffusion","score":0.6700000166893005}],"concepts":[{"id":"https://openalex.org/C2778386714","wikidata":"https://www.wikidata.org/wiki/Q417084","display_name":"Morphogen","level":3,"score":0.9835400581359863},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5932671427726746},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4617934226989746},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43855413794517517},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20957505702972412},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.19689086079597473},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.09886425733566284},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.7554/elife.84757.sa0","doi":"https://doi.org/10.7554/elife.84757.sa0","is_oa":true,"landing_page_url":"https://doi.org/10.7554/elife.84757.sa0","pdf_url":null,"source":{"id":"https://openalex.org/S1336409049","display_name":"eLife","issn_l":"2050-084X","issn":["2050-084X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-a","jufo-2","ki-jl-2","medline","norway-2","oarl","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311710","host_organization_name":"eLife Sciences Publications Ltd","host_organization_lineage":["https://openalex.org/P4310311710"],"host_organization_lineage_names":["eLife Sciences Publications Ltd"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"peer-review"}],"best_oa_location":{"id":"doi:10.7554/elife.84757.sa0","doi":"https://doi.org/10.7554/elife.84757.sa0","is_oa":true,"landing_page_url":"https://doi.org/10.7554/elife.84757.sa0","pdf_url":null,"source":{"id":"https://openalex.org/S1336409049","display_name":"eLife","issn_l":"2050-084X","issn":["2050-084X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-a","jufo-2","ki-jl-2","medline","norway-2","oarl","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311710","host_organization_name":"eLife Sciences Publications Ltd","host_organization_lineage":["https://openalex.org/P4310311710"],"host_organization_lineage_names":["eLife Sciences Publications Ltd"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"peer-review"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4367174557","https://openalex.org/W2144762520","https://openalex.org/W2097893691","https://openalex.org/W7097470620","https://openalex.org/W3098890656","https://openalex.org/W2034960511","https://openalex.org/W4282038144","https://openalex.org/W7098955669","https://openalex.org/W7096310988","https://openalex.org/W2061082789"],"abstract_inverted_index":{"Full":[0],"text":[1],"Figures":[2],"and":[3,25,77,155,177,239,319,333,389,465,532,547,551,578,638,650,686,734,819,822,828,849,869,994,1032,1075,1092,1168,1197,1330,1339,1426,1428,1445,1479,1627,1707,1727,1733,1752,1837,1879,1888,1906,1919,1930,1946,2019,2024,2031,2064,2146,2170,2172,2349,2511,2813,2931,2989,3050,3139,3222,3237,3337,3384,3387,3413,3499,3589,3628,3680,3786,3879,3945,3948,3958,3971,4084,4147,4200,4239,4309,4448,4471],"data":[4,2570,3274,3726,4463],"Side":[5],"by":[6,52,293,359,455,559,645,958,1121,1185,1202,1354,1406,1416,1472,1581,1673,1695,1886,2004,2992,3087,3095,3105,3111,3125,3486,4001,4065,4304,4352],"side":[7],"Abstract":[8,29],"Editor's":[9,148],"evaluation":[10,149],"Introduction":[11,219],"Results":[12,1294],"Discussion":[13,3982],"Methods":[14],"Appendix":[15,689],"1":[16,325],"Data":[17],"availability":[18],"References":[19],"Decision":[20,211],"letter":[21,212],"Author":[22],"response":[23],"Article":[24],"author":[26],"information":[27,291,349,1671,4074],"Metrics":[28],"Morphogen":[30,554,3651],"gradients":[31,74,170,230,295,345,448,480,495,665,918,976,996,1002,1060,1112,1251,1276,1415,1649,2430,2901,2979,3015,3057,3566,3701,3837,3881,3888,4012,4029,4077,4112,4130,4257,4391],"can":[32,296,813,1463,3715,4193,4396,4404,4414],"instruct":[33],"cells":[34,241,1345,1532,1583,1595,2068,2411,3666,3906,4080,4192,4351],"about":[35,200,2657,2774],"their":[36,243,1068,1122,1517,1543,1548,1601,1606,2176,3845,4108,4195,4202],"position":[37,933,1816,1835,2770,3435],"in":[38,58,117,143,168,174,180,275,280,282,377,407,482,497,519,525,541,662,697,714,793,816,824,840,895,939,982,1039,1044,1142,1148,1159,1165,1194,1221,1279,1360,1377,1396,1441,1519,1608,1616,1763,1806,1868,1901,1998,2015,2058,2070,2104,2136,2194,2226,2251,2292,2314,2332,2344,2382,2453,2458,2542,2558,2617,2637,2709,2738,2755,2797,2806,2960,2995,3038,3173,3229,3262,3293,3301,3312,3329,3358,3392,3403,3410,3467,3504,3513,3582,3614,3624,3660,3766,3779,3826,3855,3996,4006,4038,4071,4081,4197,4204,4236,4260,4274,4306,4344,4374,4400,4425,4456,4464,4475],"a":[39,121,136,189,363,369,416,438,474,538,584,639,677,983,1107,1146,1280,1319,1325,1331,1355,1394,1511,1552,1560,1564,1749,1787,1792,1883,1924,1931,2200,2216,2258,2289,2392,2407,2416,2422,2555,2662,2685,2821,2847,3024,3089,3096,3112,3174,3211,3243,3248,3369,3398,3661,3669,3682,3749,3771,3931,3960,3989,4007,4024,4051,4066,4088,4100,4121,4322,4353],"patterned":[40,836,957,1268,1404,4089],"tissue.":[41],"Non-linear":[42,426,489,655,691,2388,3983],"morphogen":[43,60,79,126,140,169,206,229,250,277,294,335,344,393,526,572,747,817,829,865,874,922,944,969,1041,1090,1150,1250,1264,1314,1356,1398,1414,1504,1540,1598,1675,1865,1899,2016,2050,2400,2978,2997,3003,3020,3085,3169,3214,3231,3394,3411,3422,3457,3502,3509,3524,3556,3565,3591,3606,3670,3684,3742,3773,3892,3926,3936,3965,3974,3984,4011,4039,4059,4092,4169,4210,4214,4261,4497],"decay":[44,86,116,141,167,401,427,490,504,579,607,612,641,692,755,945,1007,1042,1308,2207,2243,2282,2307,2389,2419,2433,2448,2475,2546,2563,2588,2609,2742,2808,2845,2853,2888,2950,3021,3047,3441,3450,3704,3746,3802,3875,3913,3927,3977,3985,4093,4144,4170,4215,4222,4246],"has":[45,799,1024,1034,1573,2319,2463,4440],"been":[46,751,800,1026,2084,4441],"suggested":[47,908],"to":[48,56,67,92,124,158,192,221,339,403,415,430,437,470,493,502,591,614,809,834,862,871,926,1014,1052,1064,1079,1287,1302,1402,1483,1496,1500,1509,1523,1622,1652,1658,1664,1685,1716,1944,1951,1957,1992,2037,2048,2188,2198,2391,2398,2446,2487,2515,2537,2653,2656,2675,2734,2800,2827,2835,2953,2968,2985,3032,3042,3059,3242,3400,3436,3462,3483,3551,3574,3578,3638,3656,3698,3748,3754,3822,3930,3959,4079,4103,4138,4150,4209,4234,4327,4341,4366,4453,4486],"increase":[49,2438,3290,3328,3340,3817],"gradient":[50,316,409,616,678,748,792,826,845,1156,1296,1460,1578,1783,1900,1933,1965,2206,2221,2245,2309,2324,2922,2987,3114,3135,3165,3238,3314,3343,3406,3427,4424,4462,4498],"precision":[51,145,509,1311,1579,1667,2246,2635,2991,3940,4070,4141,4301,4330,4455],"reducing":[53,3844],"the":[54,59,70,88,93,95,106,108,125,128,162,184,193,201,248,265,276,283,289,300,307,311,340,347,382,408,423,459,498,507,563,609,621,634,646,651,658,719,790,794,825,832,835,852,857,863,872,884,888,910,931,937,943,972,974,989,995,1001,1015,1040,1055,1065,1085,1095,1104,1127,1130,1143,1149,1173,1190,1210,1222,1245,1260,1263,1267,1272,1274,1284,1304,1310,1347,1366,1378,1391,1403,1442,1473,1484,1488,1502,1520,1524,1539,1557,1570,1577,1582,1592,1597,1609,1623,1628,1632,1654,1666,1669,1674,1764,1769,1777,1794,1798,1807,1814,1832,1838,1846,1852,1860,1864,1869,1872,1876,1897,1902,1940,1947,1959,1970,1977,1984,1989,2005,2039,2043,2049,2059,2074,2088,2093,2098,2105,2147,2152,2164,2182,2189,2204,2211,2219,2227,2286,2293,2315,2335,2345,2362,2366,2399,2413,2427,2435,2442,2459,2467,2471,2479,2481,2483,2488,2493,2495,2506,2516,2538,2559,2573,2593,2598,2602,2654,2670,2676,2682,2690,2707,2710,2716,2722,2726,2735,2751,2756,2768,2778,2790,2793,2801,2807,2829,2842,2860,2867,2871,2882,2890,2916,2921,2928,2961,2964,2996,3002,3006,3011,3043,3068,3071,3074,3081,3084,3121,3126,3134,3156,3161,3168,3199,3203,3230,3277,3291,3294,3302,3305,3313,3317,3326,3330,3334,3338,3342,3352,3356,3359,3380,3393,3404,3416,3421,3426,3430,3433,3455,3464,3468,3484,3488,3493,3497,3500,3505,3520,3532,3542,3548,3579,3605,3625,3639,3647,3673,3676,3687,3707,3712,3729,3755,3767,3791,3794,3818,3823,3853,3856,3858,3869,3871,3908,3922,3935,3969,3997,4058,4072,4082,4104,4125,4151,4164,4182,4187,4198,4237,4242,4252,4270,4275,4293,4307,4312,4338,4349,4372,4381,4408,4426,4431,4476,4489],"sensitivity":[55,3431],"variability":[57,468,1188,1234,1481,2057,2264,2313,2994,3228,3251,3254,3292,3357,3391,3586,4037],"source.":[61,1128,2401,2443,3162],"Here,":[62,1363],"we":[63,82,589,1179,1241,1567,1874,1922,2035,3078,3289,3324,3545,4018,4336,4364,4384,4434],"use":[64,152,2036,2287],"cell-based":[65],"simulations":[66,157,2053,2138,2975],"quantitatively":[68,3576],"compare":[69],"positional":[71,89,109,301,1049,1056,1109,1246,1289,1655,1670,1839,2183,2327,2358,2395,2436,2468,2484,2496,2507,2533,2594,2643,2691,2717,2752,2794,2849,2868,2884,2955,3034,3039,3122,3140,3245,3331,3353,3521,3549,3580,3713,3751,3819,4178,4271,4339],"error":[72,90,110,1057,1247,1656,1840,2328,2359,2396,2437,2469,2485,2497,2508,2534,2595,2644,2692,2718,2753,2795,2850,2869,3123,3209,3246,3332,3354,3522,3550,3581,3714,3735,3752,3820,4272,4340],"of":[73,132,139,165,204,270,288,310,331,422,440,510,521,535,562,596,608,620,699,854,936,1058,1067,1088,1106,1111,1145,1176,1209,1248,1271,1283,1306,1312,1324,1327,1334,1390,1466,1487,1631,1668,1730,1791,1863,1871,1882,1896,1927,1964,2008,2042,2067,2092,2163,2203,2218,2241,2253,2261,2288,2295,2305,2334,2353,2365,2370,2384,2409,2418,2429,2527,2544,2548,2561,2601,2639,2664,2681,2740,2782,2810,2820,2913,2946,2963,2976,3010,3064,3073,3083,3155,3202,3213,3224,3364,3420,3432,3470,3604,3616,3632,3793,3863,3873,3904,3911,3924,3934,3962,4015,4044,4069,4087,4124,4241,4311,4331,4371,4437,4496],"for":[75,100,114,351,694,721,726,916,1022,1101,1172,1437,1454,1647,1756,1803,1822,1976,1988,2097,2168,2280,2350,2376,2378,2473,2509,2512,2586,2607,2632,2695,2702,2747,2935,3045,3260,3333,3341,3439,3448,3475,3563,3629,3719,3834,3847,3955,3993,4173],"linear":[76,332,503,602,754,855,2254,2474,2562,2587,2703,2844,2969,3449,3476,3976,4143,4168,4224,4294],"non-linear":[78,85,115,205,334,605,882,947,1006,1257,1292,1307,2242,2281,2306,2432,2501,2545,2608,2640,2696,2741,2852,2887,2949,3019,3046,3440,3471,3539,3745,3801,3874,3912,3925,4287],"decay.":[80,1258,1293,2502,2641,2704,2970,3477,4288],"While":[81,3128],"confirm":[83],"that":[84,119,161,419,588,681,909,912,1003,1100,1218,1244,1370,1492,1569,2250,2276,2621,2981,3016,3769,3781,4075,4098,4113,4185,4229,4255,4269,4321,4347,4491],"reduces":[87],"close":[91,2397,2486,2536,2652,2733,2798,3041,3637,3753,3821,3932],"source,":[94,107,973,1273,2494,2683,2843,3012,3498,3640,3648,3870,3937,4060,4244],"reduction":[96],"is":[97,111,188,304,395,420,442,517,537,583,676,718,859,946,1061,1084,1200,1215,1224,1365,1619,1641,1645,1693,1721,1774,1801,1820,1827,1842,2002,2102,2257,2330,2712,2763,2771,2831,2875,2983,3048,3170,3361,3460,3526,3529,3587,3811,3876,3928,3941,4048,4063,4094,4148,4162,4171,4181,4206,4216,4223,4231,4247,4302,4325,4430,4451,4483],"very":[98,3146,3963,4398],"small":[99,2834,3131,4052],"physiological":[101,137,2012,3381,3595],"noise":[102,464,524,1138,2013,2762,3409],"levels.":[103,3596],"Far":[104,2491],"from":[105,183,514,831,971,1005,1126,1434,1494,1699,1745,2412,2431,2441,2492,2575,2646,2669,2725,2777,2825,2841,2927,3018,3279,3304,3496,3646,3672,3731,3868,4035,4392],"much":[112],"larger":[113,2556,3026,3244],"tissues":[118,955,2620,4097],"pose":[120,4099],"flux":[122,3097,3184],"barrier":[123,4102],"at":[127,381,386,397,633,636,919,1372,1386,1559,2215,2340,2406,2425,2520,2661,2957,3067,3160,3177,3197,3198,3217,3257,3316,3594,3621,3641,3649,3675,3686,3702,3841,3890,3972,4107],"boundary.":[129],"In":[130,851,950,1129,1259,1563,2046,2566,2971,3270,3722,3897,3917,4096],"light":[131],"this":[133,515,913,940,1182,1237,1639,2277,3480,3861,4021,4061,4450],"new":[134],"data,":[135],"role":[138,3402],"dynamics":[142,555],"patterning":[144,353,460,499,1023,1096,1102,1332,1728,1808,2154,2346,2529,2624,2861,2990,3007,3417,3465,3612,3864,3915,3939,3995,4230,4300,4329,4454],"appears":[146],"unlikely.":[147],"The":[150,286,392,433,598,1458,1614,1995,2062,2142,2326,2357,2477,2532,2642,3036,3759,3836,3851,4041,4177,4422],"authors":[151],"analytic":[153],"calculations":[154],"numerical":[156,4378],"convincingly":[159],"show":[160,2374],"purported":[163],"benefits":[164],"nonlinear":[166],"may":[171,1533,3949,4296],"be":[172,297,978,1116,1464,1993,2199,2836,3375,3552,3716,3952,4297,4342,4397,4415],"marginal":[173],"some":[175],"cases":[176],"completely":[178],"reversed":[179],"others":[181],"(far":[182],"concentration":[185,236,251,355,573,587,1017,1091,1513,1615,1625,1637,1790,1796,3685],"source).":[186],"This":[187,838,1098,1199,1643,1719,1825,2909,4136,4158,4227],"valuable":[190],"contribution":[191],"field,":[194],"as":[195,306,717,1163,1192,1467,1537,2181,2224,2265,2267,2415,2451,2585,2615,2721,2765,2767,2870,2907,3103,3210,3953,3988,4032,4299,4383,4402,4468],"it":[196,373,1033,1986,2982],"questions":[197],"common":[198],"assumptions":[199],"biological":[202,1177],"function":[203,2417,3212],"decays":[207],"during":[208],"development.":[209],"https://doi.org/10.7554/eLife.84757.sa0":[210],"Reviews":[213],"on":[214,246,657,683,887,1309,1576,1776,1811,1845,1894,2087,2175,2244,2308,2323,2466,2903,3519,3541,3555,3914,4362,4380],"Sciety":[215],"eLife's":[216],"review":[217],"process":[218,1644],"According":[220,338],"Wolpert\u2019s":[222],"famous":[223],"French":[224,341,1525],"flag":[225,342,1526],"model":[226,1214,1297,1317,1611,1684,3768],"(Wolpert,":[227],"1969),":[228],"encode":[231],"readout":[232,262,284,312,476,484,932,1571,1789,1815,1834,2342,2522,2723,2769,2958,3219,3434],"positions":[233,263,313,485,2343,2523,2959,3220,3623],"x\u03b8":[234],"via":[235,354,1551,3297,3307,3320],"thresholds":[237,257,356],"C\u03b8=C\u2062(x\u03b8),":[238],"differentiating":[240],"base":[242],"fate":[244,1518,4203],"decisions":[245],"whether":[247,1037,2783,3080,4449],"local":[249,1089],"lies":[252,365],"above":[253,366,3247],"or":[254,367,604,709,867,1118,1152,1554,1604,2788,3110,3188,3311,3346,3695,4355,4377],"below":[255,368],"such":[256,1536,2180,3366,4467],"(Figure":[258,618,666,847,1018,1337,1891,2283,2610,2672,2743,2854,2877,3093,3101,3117,3137,3142,3299,3309,3322,3534,3757,3776,3784,3895,4134,4145,4225,4359],"1A).":[259],"Thus,":[260,2158],"these":[261,1812,3514],"mark":[264],"boundary":[266,1382,1800,2424,2541,2679,2874,2896,2966,3065,3098,3157,3319,3348,3367,3678,3689,4160,4357],"locations":[267],"between":[268,843,1154,2022,2505],"domains":[269,1729],"different":[271,315,483,844,960,1155,1469,2341,2351,2447,3218,3507,3622,3630],"cell":[272,364,384,466,700,1220,1429,1439,1495,1545,1549,1602,1618,1634,1697,1704,1799,1805,2060,2191,2213,2262,2317,2337,2367,2518,2604,2613,2650,2659,2666,2823,3618,3832],"fates.":[273],"Variations":[274],"profile":[278],"result":[279,481,1004,3017],"variations":[281,4235],"positions.":[285],"accuracy":[287,1290,3040,3466,3613,4189],"spatial":[290,348,1503,2634,2917,3090,3370,3611,3772,3807,3848,4073,4126,4140,4188],"carried":[292,2085],"quantified":[298],"with":[299,571,629,706,881,891,965,1113,1256,1291,1421,1702,1737,1748,2361,2380,2500,2597,2803,2816,2886,2942,3183,3531,3664,3668,3681,4023,4115,4142,4190,4282,4286,4386,4418],"error,":[302,2184,4179],"which":[303,812,1397,1515,1974,2034,2193,2920,3528,3711,4180,4191,4412],"defined":[305],"standard":[308,1086,1708,1753,1880,2582,3286,3738],"deviation":[309,1087,1709,1754,1881],"over":[314,1542,1600,1605,2919,3023,3710,4120,4407,4411],"realizations":[317],"(Vetter":[318,1444,2030,3386,3944],"Iber,":[320,548,1076,1446,1920,2032,3388,3946],"2022):":[321],"(1)":[322],"\u03c3x=stddev\u2061[x\u03b8].":[323],"Figure":[324,1166,1195,1452,1677,2298,2811,3148,3597,3657],"Download":[326,1679,2300,3150,3599],"asset":[327,329,1680,1682,2301,2303,3151,3153,3600,3602],"Open":[328,1681,2302,3152,3601],"Comparison":[330],"gradients.":[336,405,432,472,1315,1676,1688,1849,4334],"(A)":[337,2311],"model,":[343,1191,4026],"provide":[346,4078],"required":[350,4326],"tissue":[352,511,1223,1269,1405,1521,2873,3204,3626,3849,3994,4090],"C\u03b8,":[357,372,478],"numbered":[358],"\u03b8=1,2,3":[360],"etc.":[361],"If":[362,2705],"certain":[370,3249],"threshold":[371,477,1624,1640,3250],"switches":[374],"fate,":[375],"resulting":[376,894,975,981,1158,1359],"domain":[378,500,1322,1443,1692,2347,2472,2530,2678,2862,2892,3008,3076,3092,3176,3372,3663,3775],"boundaries":[379,452],"forming":[380],"respective":[383],"borders":[385],"x=x\u03b8":[387],"(blue":[388,1766],"red":[390],"lines).":[391,3537],"source":[394,635,833,1326,1344,1379,1726,1765,2414,2489,2655,2671,2711,2727,2802,3044,3069,3086,3175,3306,3318,3360,3371,3423,3607,3662,3674,3677,3688,3756,3774,3799,3824,4314,4373],"located":[396],"x=x0=0.":[398],"(B)":[399,2356],"Linear":[400,611],"leads":[402,429,469,492,613,925,2390,2952,3241,3747,4137],"exponential":[404,615,987,2220,2930,3029,3056,3880,4129,4390],"Changes":[406,3512],"amplitude":[410,631,868,1151,3115,3239,3315,3428,3437,3503],"C0":[411,441,632],"(different":[412],"colours)":[413],"lead":[414,3058,3697],"shift":[417,434,858,885,914,990,1110],"\u0394\u2062x":[418,435,842],"independent":[421,595,935,2162,2577,3281,3733],"amplitude.":[424,3344],"(C)":[425,2387],"(n=2)":[428],"power-law":[431,664,917,962,1275,2933,3014,3887,4111,4256],"due":[436,1482],"change":[439,1969],"amplitude-dependent.":[443],"(D,":[444],"E)":[445],"Noisy":[446,1295],"example":[447],"obtained":[449,3610],"numerically.":[450],"Cell":[451,1711],"are":[453,556,807,956,1400,1507,1529,1713,1735,1742,1975,2027,2125,2161,2185,2629,2786,3130,3144,3654,4013,4435],"denoted":[454,1471],"black":[456],"ticks":[457],"along":[458,1797,2073,2470],"axis.":[461,1097],"Molecular":[462,3408],"kinetic":[463,1187,1207,1230,1422,1490,2044],"area":[467,1705,2100,2263],"noisy":[471,1249,1313,1687,1782,1848,2977,4028,4333],"For":[473,789,986,3740],"fixed":[475,2201,2210,2290,2521,3113,3256],"variable":[479,1059,1229,1413,4485],"x\u03b8,j":[486,1630,1817],"(inset":[487],"plots).":[488],"(E)":[491,2503],"shallower":[494,1011,2900],"further":[496,1125,2772,4494],"compared":[501,1621,2967],"(D).":[505],"How":[506],"observed":[508,2616],"patterns":[512],"arising":[513],"principle":[516],"achieved,":[518],"spite":[520],"natural":[522],"molecular":[523,810,1137],"production,":[527,2017,3843],"transport,":[528,702],"decay,":[529,656,856,883,2018,2255,2697,3472,3540],"internalization,":[530],"turnover":[531],"other":[533,659,951,3543,4465],"sources":[534],"variability,":[536,3216],"key":[539],"question":[540],"developmental":[542],"biology":[543],"(Lander,":[544],"2011;":[545,772,2113,4515],"Vetter":[546,1074,1918],"2022;":[549,1447,1451],"Iber":[550],"Vetter,":[552],"2022).":[553,1587,2272],"often":[557],"described":[558],"reaction-diffusion":[560,1211,1770],"equations":[561],"form":[564,622,1144],"(Lander":[565,623,1028],"et":[566,624,669,730,738,742,758,762,766,770,774,778,782,786,803,905,1029,1071,1134,1449,1585,1911,1915,2078,2111,2115,2119,2129,2233,2237,2270,2590,2626,3107,3568,4003,4155,4264,4445,4480,4501,4505,4509,4513,4517,4521,4525],"al.,":[567,625,670,731,739,743,759,763,767,771,775,779,783,787,804,906,1030,1072,1135,1450,1586,1912,1916,2079,2112,2116,2120,2130,2234,2238,2271,2591,2627,3108,3569,4004,4156,4265,4446,4481,4502,4506,4510,4514,4518,4522],"2009).":[568],"(2)":[569],"\u2202C\u2202t=D\u0394C\u2212dCn/Crefn\u22121":[570],"C,":[574],"diffusion":[575,647,1301,1348,2143,4101],"coefficient":[576,648,2007],"D,":[577,2145],"rate":[580,653,1373,1943,1950,2461,3178,3233,3296,3336,3459],"d.":[581,654],"Cref":[582],"constant":[585,2720],"reference":[586],"introduce":[590],"make":[592],"all":[593,1206,1648,2071,2137,2567,2618,2784,3723,3827,3918],"units":[594,1956,2333,2383,3615],"n.":[597,2371,2943],"exponent":[599],"n":[600,685],"models":[601,3900,3919,4346],"(n=1)":[603,756],"(n>1)":[606],"morphogen.":[610],"profiles":[617,749],"1B)":[619],"2002).":[626],"(3)":[627],"C(x)=C0e\u2212x/\u03bb,\u03bb=Dd":[628],"an":[630,1407,3797,4290,4368],"x=0,":[637],"characteristic":[640],"length":[642,679,1328,1335,1731,1934,2155],"\u03bb,":[643],"set":[644,1939,2151],"D":[649,2169],"degradation":[652,1942,2148,3412,3525],"hand,":[660,3544],"results":[661,713,839,1971,2160,4250],"shifted":[663,1160,2932,3013,3886,4110,4393],"1C;":[667],"Eldar":[668,3106,4002],"2003)":[671,907,3570],"(4)":[672],"C(x)=C0(1+xm\u03bbm)\u2212m,m=2n\u22121":[673],"where":[674,1082,1594,1818,1953,2684,3377,3584,3590,3938,4010,4438],"\u03bbm":[675],"scale":[680],"depends":[682,886],"D/d,":[684],"C0/Cref":[687],"(see":[688],"1).":[690,949,4135],"would":[693,1043,1967,1981,3119],"instance":[695],"arise":[696,4034],"case":[698,720,853,1593,2252,2543,2560,2638,2739,3469,4295,4433],"lineage":[701],"when":[703,942,2759,3167,3355,3809,4091,4213,4221],"ligands":[704],"interact":[705],"receptor":[707,715],"clusters,":[708],"if":[710,953,1262,3001,3523,4245,4316],"ligand":[711],"binding":[712],"upregulation,":[716],"several":[722,1530,3831],"morphogens,":[723],"most":[724,2123],"prominently":[725],"Hedgehog":[727,1898,4470],"(Hh)":[728],"(Eldar":[729,904,1133,3567,4154,4263],"2003;":[732],"Nahmad":[733],"Stathopoulos,":[735],"2009;":[736,740],"Wartlick":[737,769,773,4512,4516],"Balaskas":[741],"2012).":[744],"Most":[745,2081,4493],"reported":[746,801,1972,2095,2186,4442],"have":[750,1499,2083,3516,4019],"fitted":[752],"assuming":[753],"(Gregor":[757,1070,4500],"2007;":[760,768,1073,1913,4503,4511],"Gregor":[761,4504],"2008;":[764,4507],"Kicheva":[765,4508],"2014;":[776,2235,4519],"Cohen":[777,1914,2236,4520],"2015;":[780,1917,4523],"Zagorski":[781,4524],"2017;":[784],"Mateus":[785],"2020).":[788],"FGF8":[791,4423],"developing":[795,2228,4427],"mouse":[796,1907,2229,4428],"brain,":[797],"n\u22484":[798],"(Chan":[802,4444],"2017).":[805],"Embryos":[806],"subject":[808],"noise,":[811],"cause":[814],"fluctuations":[815,4259,4280],"production":[818,1357,1371,1949,2460,2708,2761,2791,2998,3091,3232,3295,3335,3395,3458,3491,3510,3592,3652,3810,3815,4262,4279],"transport":[820,2020],"rates,":[821],"consequently,":[823],"amplitudes":[827,3696],"fluxes":[830],"cells.":[837,1738],"shifts":[841,897],"realisations":[846,1461],"1B":[848,1167],"C).":[850],"only":[860,1141,1375,1590,1760,1982,2173,2706,2760,2789,3804,4165,4281,4315,4432],"related":[861],"relative":[864,1013,2187,2514,3490],"influx":[866,923,938,1153,3235,3303,3495,3671],"not":[870,992,1253,1968,3447,3474,3572,3783,3951,4163,4285],"absolute":[873,889,2165],"levels":[875,2014,3816,3894,4212],"(Appendix":[876,898,948,3442,3451],"1,":[877,899,3443,3452],"Equation":[878,900,1419,2947,3444,3453,4387],"11).":[879],"However,":[880,1000,2815],"levels,":[890,3744],"higher":[892,1016,1048],"influxes":[893,970,3694],"smaller":[896,1108,2482,2848,3750],"12).":[901],"Previous":[902],"research":[903],"circumstance":[911],"vanishes":[915],"sufficiently":[920],"large":[921],"values":[924,1963,2096,2124,2166,3382],"more":[927,3060,3806,3859,3883,3979,4132,4232],"robust":[928,3061,3956,4233],"patterning,":[929],"because":[930],"becomes":[934],"limit":[941],"words,":[952],"two":[954,959,2410,2658],"noise-free":[961],"gradients,":[963,988,1162,1873,3030],"both":[964,1387],"high":[966,2633,3741,3812,3891,3942],"(but":[967],"different)":[968],"will":[977,991,997],"nearly":[979],"identical,":[980],"reproducible":[984],"pattern.":[985],"disappear,":[993],"thus":[998,2925,2951,3350,3950],"differ.":[999],"also":[1008,2054,2606,2636,3889],"possess":[1009],"significantly":[1010,1254,3025],"tails,":[1012],"1C).":[1019],"Their":[1020],"usefulness":[1021,3846],"therefore":[1025,1589,2133,2630,3051],"questioned":[1027],"2009),":[1031],"remained":[1035],"unclear":[1036],"nonlinearity":[1038],"fact":[1045],"help":[1046],"achieving":[1047],"accuracy.":[1050],"Indeed,":[1051],"first":[1053,1633],"order,":[1054],"inversely":[1062],"proportional":[1063],"magnitude":[1066],"slope":[1069],"2022)":[1077,3947],"according":[1078,1522,1657],"(5)":[1080],"\u03c3x\u2248|\u2202C\u2202x|\u22121\u03c3C,":[1081],"\u03c3C":[1083],"x":[1093],"denotes":[1094,1851],"suggests":[1099],"precision,":[1103],"benefit":[1105,3872,3923],"n>1":[1114,2510,4439],"might":[1115],"offset":[1117],"even":[1119,2746],"overcompensated":[1120],"flatter":[1123],"shape":[1124],"previous":[1131],"analysis":[1132,4047],"2003),":[1136],"was":[1139,1352,2196,2688,3255,3986],"considered":[1140,3920],"fold-change":[1147],"realisations,":[1157],"deterministic":[1161,1183,3564,4008],"shown":[1164],"C.":[1169],"To":[1170,1341,1785,1858],"account":[1171],"intrinsic":[1174],"stochasticity":[1175],"systems,":[1178,4466],"now":[1180,2274],"extend":[1181],"view":[1184,4254],"incorporating":[1186],"into":[1189,1205,1510,3968,4030],"depicted":[1193],"1D":[1196,1338,1610,1690],"E.":[1198],"achieved":[1201],"introducing":[1203],"randomness":[1204],"parameters":[1208,1423,1491,1740,1857,1966,2785,3515],"equation.":[1212],"Our":[1213,1316,4318],"cell-based,":[1216],"meaning":[1217],"each":[1219,1438,1617,1757,1804,1823,1999,2569,3273,3725],"assigned":[1225],"its":[1226,1659],"own":[1227],"specific":[1228,1962],"parameters,":[1231],"emulating":[1232],"inter-cellular":[1233],"(Methods).":[1235],"With":[1236,2421,3379,3538,3796],"quantitative":[1238,3132,4046],"statistical":[1239],"tool,":[1240],"demonstrate":[1242],"numerically":[1243,1417],"does":[1252],"improve":[1255],"contrary,":[1261],"cannot":[1265,3004],"leave":[1266],"opposite":[1270,2680,3009,4276],"become":[1277],"shallow":[1278],"substantial":[1281,4067,4122],"part":[1282],"domain,":[1285,1779,3800,4127],"leading":[1286,3031],"reduced":[1288],"We":[1298,1411,1588,1937,2132,2209,2247,2273,3478,4267],"simulated":[1299,3508],"steady-state":[1300,2153],"study":[1303,4319],"impact":[1305,1575,2260,2322,3072,3910],"uses":[1318],"one-dimensional":[1320],"cellular":[1321,1691,1778],"composed":[1323],"Ls":[1329,1732],"region":[1333],"Lp":[1336,1734],"E).":[1340],"represent":[1342,2581,3285,3737],"morphogen-secreting":[1343,3665,3905,4243,4313,4350],"explicitly,":[1346],"equation":[1349,1771],"(Equation":[1350,1661,1772,3180],"2)":[1351],"extended":[1353],"term,":[1358],"(6)":[1361],"0=D\u22022C\u2202x2\u2212dCn/Crefn\u22121+pH(\u2212x).":[1362],"H\u2062(x)":[1364],"Heaviside":[1367],"function,":[1368],"ensuring":[1369],"p":[1374,3179],"occurs":[1376,2911],"(x<0).":[1380],"Zero-flux":[1381],"conditions":[1383,3349],"were":[1384,3195],"used":[1385,1923,2134,3104],"outer":[1388],"ends":[1389],"tissue,":[1392,3970],"mimicking":[1393],"situation":[1395],"molecules":[1399],"restricted":[1401,3929],"impermeable":[1408],"boundary:":[1409],"\u2202C\u2202x(\u2212Ls)=0=\u2202C\u2202x(Lp).":[1410],"generated":[1412],"solving":[1418],"6":[1420],"pi,":[1424],"di":[1425],"Di,":[1427],"areas":[1430,1698,1712,2066,2318],"Ai":[1431],"independently":[1432,1744],"drawn":[1433,1743],"log-normal":[1435,1700,1746],"distributions":[1436,1701,1747],"i=1,\u2026,N":[1440],"Adelmann":[1448],"2,":[1453],"details":[1455],"see":[1456],"Methods).":[1457],"individual":[1459],"Cj\u2062(x)":[1462],"thought":[1465],"representing":[1468],"embryos,":[1470],"index":[1474],"j.":[1475],"They":[1476],"exhibit":[1477],"inter-":[1478],"intra-tissue":[1480],"stochastic":[1485,1861,4025,4323],"nature":[1486,1862],"three":[1489,3506,3828],"vary":[1493,2069],"cell.":[1497,1758],"Cells":[1498],"convert":[1501],"distribution":[1505,2040],"they":[1506,4033,4403,4413],"exposed":[1508],"single":[1512,1561,2822],"value,":[1514],"determines":[1516,3429],"model.":[1527,3127],"There":[1528],"ways":[1531],"achieve":[1534],"this,":[1535,4363],"averaging":[1538],"signal":[1541,1558,1599],"entire":[1544],"surface,":[1546,1603],"beyond":[1547],"surface":[1550],"cilium,":[1553],"reading":[1555],"out":[1556,2086,3840,4119],"point.":[1562],"recent":[1565],"study,":[1566],"found":[1568,2103,2225],"mechanism":[1572,3992],"little":[1574],"perceived":[1580],"(Adelmann":[1584,2269,2589,2625],"analysed":[1591],"average":[1596,1795,1833,1941,1948,2190,2205,2212,3456,3617],"diameter":[1607,2214,2338,2605,2651,2824],"here,":[1612,1973,3921],"respectively.":[1613],"then":[1620,1714,2880],"C\u03b8":[1626],"location":[1629,4196],"whose":[1635],"sensed":[1636],"subceeds":[1638],"recorded.":[1642],"repeated":[1646,1722,1828],"j,":[1650],"allowing":[1651],"compute":[1653],"definition":[1660],"1),":[1662],"\u03c3x=stddevj\u2061{x\u03b8,j}":[1663],"quantify":[1665,2986,4328],"conveyed":[1672],"2":[1678],"Numerical":[1683],"simulate":[1686],"A":[1689,2894],"constructed":[1694],"drawing":[1696],"mean":[1703,1750,1877,1925,1932,2336,2517,2574,2603,3278,3489,3494,3501,3730],"\u03bcA":[1706],"\u03c3A.":[1710],"converted":[1715],"diameters":[1717,2660,2667,3619],"(\u03b4i).":[1718],"procedure":[1720],"N":[1723],"times":[1724],"until":[1725],"filled":[1736],"Kinetic":[1739,3253],"k=p,d,D":[1741],"\u03bck":[1751],"\u03c3k":[1755],"Production":[1759,3659],"takes":[1761,1987],"place":[1762],"cells).":[1767],"Then,":[1768],"6)":[1773,3181],"solved":[1775],"generating":[1780],"one":[1781,2649],"Cj\u2062(x).":[1784],"determine":[1786,4194],"unique":[1788],"cell,":[1793],"computed":[1802],"domain.":[1809],"Based":[1810,1893,4361],"concentrations":[1813],"Cj\u2062(x\u03b8,j)=C\u03b8":[1819],"recorded":[1821],"gradient.":[1824],"step":[1826],"1000":[1829,1847],"times.":[1830],"Lastly,":[1831],"\u03bcx":[1836],"\u03c3x":[1841,2329],"calculated":[1843],"based":[1844],"PDF":[1850],"probability":[1853],"density":[1854],"function.":[1855],"Model":[1856],"define":[1859,2038],"kinetics":[1866,4310],"involved":[1867],"formation":[1870],"express":[1875],"value":[1878],"parameter":[1884,3708],"q":[1885,2001],"\u03bcq":[1887],"\u03c3q,":[1889],"respectively":[1890],"2).":[1892],"measurements":[1895],"Drosophila":[1903],"wing":[1904],"disc":[1905],"neural":[1908,2107,2230,4477],"tube":[1909,2108,2231,4478],"(Kicheva":[1910,2232],"2022),":[1921,2033,2121,2592,2628,3389],"diffusivity":[1926,3414],"\u03bcD=0.033":[1928],"\u00b5m2/s":[1929],"\u03bc\u03bb=20":[1935],"\u00b5m.":[1936,2385],"furthermore":[1938],"\u03bcd=\u03bcD/\u03bc\u03bb2,":[1945],"\u03bcp=\u03bcd\u2062Cref,":[1952],"Cref=1":[1954],"arb.":[1955],"normalise":[1958],"concentrations.":[1960],"Other":[1961],"steady":[1978,1990],"state,":[1979],"but":[1980,2026,2122,2729,2915,3446,3473,4218,4284],"alter":[1983],"timescale":[1985],"state":[1991],"reached.":[1994],"noise-to-signal":[1996],"ratio":[1997],"quantity":[2000,4184],"given":[2003],"corresponding":[2006],"variation,":[2009],"CVq=\u03c3q/\u03bcq.":[2010],"Reported":[2011],"differ":[2021],"morphogens":[2023],"tissues,":[2025],"around":[2028],"CVp,d,D\u22480.3":[2029],"widths":[2041,2063],"parameters.":[2045],"addition":[2047],"kinetics,":[2051],"our":[2052,2159,2296,2973,4045],"include":[2055,4367],"cell-to-cell":[2056,3585,4036],"areas.":[2061],"cross-sectional":[2065,2316],"layers":[2072],"apical-basal":[2075],"axis":[2076],"(G\u00f3mez":[2077],"2021).":[2080],"quantifications":[2082],"apical":[2089,2099],"surface.":[2090],"One":[2091],"highest":[2094],"CV":[2101],"vertebrate":[2106],"(CVA\u22480.9)":[2109],"(Escudero":[2110],"Guerrero":[2114],"2019;":[2117],"Bocanegra-Moreno":[2118],"considerably":[2126],"lower":[2127,2394],"(Kokic":[2128],"2019).":[2131],"CVA=0.5":[2135,2291],"unless":[2139],"specified":[2140,2452,3683],"otherwise.":[2141],"coefficient,":[2144],"rate,":[2149,2792,3492],"d,":[2150,2171],"scale,":[2156],"\u03bb=D/d.":[2157],"chosen":[2167,2197],"depend":[2174],"ratio.":[2177],"Positional":[2178,3208],"quantities,":[2179],"diameter,":[2192,2368,2519],"turn":[2195],"multiple":[2202],"length.":[2208],"fourth":[2217],"length,":[2222],"\u03bc\u03b4/\u03bc\u03bb=1/4,":[2223],"2015).":[2239],"Impact":[2240,2304,3063,3154,3419,3603],"previously":[2248,3560],"showed":[2249],"there":[2256,2898,3129],"negligible":[2259,3049],"long":[2266,2766,2859],"CVA<1":[2268],"find":[2275,3325,4268,4337],"holds":[2278],"similarly":[2279],"3A),":[2284],"justifying":[2285],"remainder":[2294],"analysis.":[2297],"3":[2299],"precision.":[2310,2325,3418,3865,3916],"Physiological":[2312],"no":[2320,2464,3517],"significant":[2321],"plotted":[2331],"\u03bc\u03b4":[2339,3620],"(symbols),":[2348],"degrees":[2352,3223,3631],"non-linearity":[2354,2749,2805,2864,3225,3633,3854],"(colours).":[2355,2524,3226,3634],"increases":[2360,2498,2535,2645,2694,2730,2866,2941],"square":[2363,2599],"root":[2364,2600],"irrespective":[2369,2912],"Dotted":[2372],"lines":[2373],"\u03c3x=\u03b1\u2062\u03bc\u03b4":[2375],"\u03b1=2.6,5.2":[2377],"reference,":[2379],"lengths":[2381],"Lp=100\u2062\u03bc\u03b4.":[2386],"marginally":[2393,3805],"Inset":[2402],"plot":[2403],"shows":[2404],"\u03c3x/\u03bc\u03b4":[2405],"distance":[2408,2557,2663,2724],"non-linearity.":[2420],"no-flux":[2423,2686],"x=Lp,":[2426],"shallowness":[2428],"lets":[2434],"strongly":[2439],"far":[2440,3200,3645],"Colours":[2444],"correspond":[2445],"exponents":[2449],"n,":[2450,2914],"panel":[2454],"D.":[2455],"(D)":[2456],"Variability":[2457],"alone":[2462],"effect":[2465,2830,2910,3518,3760,4054,4161],"(blue).":[2476],"stronger":[2478,2804,3852],"non-linearity,":[2480,3705],"(inset).":[2490],"rapidly":[2499,2693],"Difference":[2504],"n=1":[2513,2826],"(F)":[2525,3240],"Effect":[2526],"finite":[2528],"size.":[2531],"distant":[2539,2677,2736],"zero-flux":[2540,2895],"(shades":[2547],"blue,":[2549],"n=2).":[2550],"Patterning":[2551],"remains":[2552,2719,2754,3593,4459],"precise":[2553,3884,4174],"across":[2554],"(black,":[2564],"n=1).":[2565],"panels,":[2568,3724],"point":[2571,3275,3727],"represents":[2572,3276,3728],"103":[2576,3280,3732],"simulations.":[2578,3282],"Error":[2579,3283],"bars":[2580,3284,3736],"errors.":[2583,3035,3287,3739],"Much":[2584],"scales":[2596],"3B).":[2611],"Small":[2612],"diameters,":[2614,3833],"known":[2619],"employ":[2622],"gradient-based":[2623],"important":[2631],"less":[2647,2817,3764],"than":[2648,2773,2818,2851,2902,3028,3778,3885],"75":[2665],"away":[2668,2776,2840,3867],"3C).":[2673],"Close":[2674],"condition":[2687,2897,3066,3099,3158,4358],"imposed,":[2689],"while":[2698,4050],"remaining":[2699],"relatively":[2700],"low":[2701,3692,3842],"varied":[2713,2787],"(CVp=0.3,":[2714],"CVd,D=0),":[2715],"increases,":[2728],"again":[2731,3790],"sharply":[2732],"end":[2737,3201],"3D).":[2744],"But":[2745],"strong":[2748,3703,3964],"(n=4),":[2750],"sub-cellular":[2757],"range":[2758,2918,3027,3709],"considered,":[2764],"\u03bb":[2775],"distal":[2779,2872,2891,2965,3075,4085],"end.":[2780],"Independent":[2781],"drops":[2796],"vicinity":[2799,2962,3933],"(insets":[2809],"3C":[2812],"D).":[2814,3263],"20%":[2819],"n=4,":[2828],"likely":[2832],"too":[2833,4484],"physiologically":[2837,3053],"relevant.":[2838,3054],"Further":[2839,3264,3866,3967],"yields":[2846,3803,3978],"3D\u2013E).":[2855],"No":[2856],"matter":[2857],"how":[2858],"is,":[2863,3761],"always":[2865],"approached":[2876],"3F).":[2878],"What":[2879],"causes":[2881],"increased":[2883,3033],"errors":[2885,2956,3141],"near":[2889,4057],"boundary?":[2893],"implies":[2899,4228],"infinite":[2904,2936],"domains:":[2905],"C\u2032\u2062(x)\u21920":[2906],"x\u2192Lp.":[2908],"flattens":[2923],"(and":[2924],"deviates":[2926],"pure":[2929],"forms":[2934],"domains,":[2937],"Equations":[2938],"3;":[2939],"4)":[2940],"By":[2944],"virtue":[2945],"5,":[2948],"greater":[2954,4139],"summary,":[2972,3898],"computer":[2974],"suggest":[2980],"insufficient":[2984],"robustness":[2988],"considering":[2993],"alone.":[2999],"Moreover,":[3000,4335],"exit":[3005],"flatten":[3022,3839,4118],"gain":[3037,4062],"barely":[3052],"Overall,":[3055],"patterning.":[3062,3850,3981],"Given":[3070],"boundary,":[3077,4109]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2023-04-30T00:00:00"}
