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A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called
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sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems.
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Generalized autoregressive conditional heteroskedasticity (GARCH) model
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are examples of diffusion processes. It is used heavily in
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Autoregressive conditional heteroskedasticity (ARCH) model
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Independent and identically distributed random variables
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Autoregressive integrated moving average (ARIMA) model
191:. The position of the particle is then random; its
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1646:Stochastic chains with memory of variable length
16:Solution to a stochastic differential equation
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58:introducing citations to additional sources
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1774:Autoregressive–moving-average (ARMA) model
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48:Relevant discussion may be found on the
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2080:Doob's martingale convergence theorems
1832:Constant elasticity of variance (CEV)
1822:Chan–Karolyi–Longstaff–Sanders (CKLS)
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299:
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1156:Generative adversarial network (GAN)
25:
13:
2319:Skorokhod's representation theorem
2100:Law of large numbers (weak/strong)
14:
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2289:Martingale representation theorem
2510:
2334:Stochastic differential equation
2224:Doob's optional stopping theorem
2219:Doob–Meyer decomposition theorem
1194:
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1173:
41:relies largely or entirely on a
30:
2204:Convergence of random variables
2090:Fisher–Tippett–Gnedenko theorem
133:are a class of continuous-time
1802:Binomial options pricing model
1106:Recurrent neural network (RNN)
1096:Differentiable neural computer
268:
1:
2269:Kolmogorov continuity theorem
2105:Law of the iterated logarithm
1151:Variational autoencoder (VAE)
1111:Long short-term memory (LSTM)
378:Computational learning theory
261:
201:convection–diffusion equation
2526:. You can help Knowledge by
2274:Kolmogorov extension theorem
1953:Generalized queueing network
1461:Interacting particle systems
1131:Convolutional neural network
193:probability density function
154:Ornstein–Uhlenbeck processes
19:For the marketing term, see
7:
1406:Continuous-time random walk
1126:Multilayer perceptron (MLP)
234:
225:Kolmogorov forward equation
10:
2594:
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2414:Extreme value theory (EVT)
2214:Doob decomposition theorem
1506:Ornstein–Uhlenbeck process
1277:Chinese restaurant process
1202:Artificial neural networks
1116:Gated recurrent unit (GRU)
342:Differentiable programming
197:function of space and time
18:
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2294:Optional stopping theorem
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2095:Large deviation principle
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1847:Heath–Jarrow–Morton (HJM)
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1784:Moving-average (MA) model
1769:Autoregressive (AR) model
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1594:Hidden Markov model (HMM)
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1528:Schramm–Loewner evolution
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358:Automatic differentiation
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256:Sample-continuous process
150:reflected Brownian motion
2209:Doléans-Dade exponential
2039:Progressively measurable
1837:Cox–Ingersoll–Ross (CIR)
363:Neuromorphic engineering
326:Differentiable computing
276:"9. Diffusion processes"
21:Diffusion of innovations
2429:Mathematical statistics
2419:Large deviations theory
2249:Infinitesimal generator
2110:Maximal ergodic theorem
2029:Piecewise-deterministic
1631:Random dynamical system
1496:Markov additive process
1136:Residual neural network
552:Artificial Intelligence
221:continuous sample paths
207:Mathematical definition
2522:-related article is a
2264:Karhunen–Loève theorem
2199:Cameron–Martin formula
2163:Burkholder–Davis–Gundy
1558:Variance gamma process
229:Fokker–Planck equation
2394:Actuarial mathematics
2356:Uniform integrability
2351:Stratonovich integral
2279:Lévy–Prokhorov metric
2183:Marcinkiewicz–Zygmund
2070:Central limit theorem
1672:Gaussian random field
1501:McKean–Vlasov process
1421:Dyson Brownian motion
1282:Galton–Watson process
1091:Neural Turing machine
679:Human image synthesis
2469:Time series analysis
2424:Mathematical finance
2309:Reflection principle
1636:Regenerative process
1436:Fleming–Viot process
1251:Stochastic processes
1182:Computer programming
1161:Graph neural network
736:Text-to-video models
714:Text-to-image models
562:Large language model
547:Scientific computing
353:Statistical manifold
348:Information geometry
162:statistical analysis
54:improve this article
2464:Stochastic analysis
2304:Quadratic variation
2299:Prokhorov's theorem
2234:Feynman–Kac formula
1704:Markov random field
1352:Birth–death process
528:In-context learning
368:Pattern recognition
158:statistical physics
131:diffusion processes
69:"Diffusion process"
2434:Probability theory
2314:Skorokhod integral
2284:Malliavin calculus
1867:Korn-Kreer-Lenssen
1751:Time series models
1714:Pitman–Yor process
1121:Echo state network
1009:JĂĽrgen Schmidhuber
704:Facial recognition
699:Speech recognition
609:Software libraries
199:is governed by a
166:information theory
123:probability theory
2578:Probability stubs
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2534:
2500:
2499:
2454:Signal processing
2173:Doob's upcrossing
2168:Doob's martingale
2132:Engelbert–Schmidt
2075:Donsker's theorem
2009:Feller-continuous
1877:Rendleman–Bartter
1667:Dirichlet process
1584:Branching process
1553:Telegraph process
1446:Geometric process
1426:Empirical process
1416:Diffusion process
1272:Branching process
1267:Bernoulli process
1217:
1216:
979:Stephen Grossberg
952:
951:
213:diffusion process
119:
118:
104:
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2573:Markov processes
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2507:
2474:Machine learning
2361:Usual hypotheses
2244:Girsanov theorem
2229:Dynkin's formula
1994:Continuous paths
1902:Actuarial models
1842:Garman–Kohlhagen
1812:Black–Karasinski
1807:Black–Derman–Toy
1794:Financial models
1660:Fields and other
1589:Gaussian process
1538:Sigma-martingale
1342:Additive process
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1207:Machine learning
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932:Action selection
922:Self-driving car
729:Stable Diffusion
694:Speech synthesis
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523:Machine learning
399:Gradient descent
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2439:Queueing theory
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2324:Skorokhod space
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2178:Kunita–Watanabe
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2115:Sanov's theorem
2085:Ergodic theorem
2058:
2054:Time-reversible
1972:
1935:Queueing models
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1925:Sparre–Anderson
1915:Cramér–Lundberg
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1882:SABR volatility
1788:
1745:
1697:Boolean network
1655:
1641:Renewal process
1572:
1521:Non-homogeneous
1511:Poisson process
1401:Contact process
1364:Brownian motion
1334:Continuous time
1328:
1322:Maximal entropy
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1213:
1165:
1079:
1045:Google DeepMind
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989:Geoffrey Hinton
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885:
811:Project Debater
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655:Implementations
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453:Backpropagation
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373:Tensor calculus
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189:Brownian motion
174:neural networks
146:Brownian motion
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2487:List of topics
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2444:Renewal theory
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2399:Control theory
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2329:Snell envelope
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2128:Borel–Cantelli
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2063:Limit theorems
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1599:Markov process
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1568:Wiener sausage
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1563:Wiener process
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1543:Stable process
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1533:Semimartingale
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1476:Jump diffusion
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1451:Hawkes process
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1431:Feller process
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1396:Cauchy process
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1347:Bessel process
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1019:Ilya Sutskever
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984:Demis Hassabis
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974:Ian Goodfellow
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448:Loss functions
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383:Inductive bias
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251:Jump diffusion
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223:for which the
217:Markov process
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135:Markov process
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52:. Please help
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2197:
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2171:
2169:
2166:
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2161:
2160:
2158:
2156:
2152:
2145:
2141:
2137:
2136:Hewitt–Savage
2133:
2129:
2125:
2121:
2120:Zero–one laws
2118:
2116:
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2015:
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1818:
1817:Black–Scholes
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1722:
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1720:
1719:Point process
1717:
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1698:
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1677:Gibbs measure
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1469:
1467:
1466:ItĂ´ diffusion
1464:
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1459:
1457:
1454:
1452:
1449:
1447:
1444:
1442:
1441:Gamma process
1439:
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1312:Self-avoiding
1310:
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1300:
1298:
1297:Moran process
1295:
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1259:Discrete time
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1084:Architectures
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1066:
1063:
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1038:
1036:
1033:
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1030:
1028:Organizations
1026:
1020:
1017:
1015:
1012:
1010:
1007:
1005:
1002:
1000:
997:
995:
992:
990:
987:
985:
982:
980:
977:
975:
972:
970:
967:
965:
964:Yoshua Bengio
962:
961:
959:
955:
945:
944:Robot control
942:
938:
935:
934:
933:
930:
928:
925:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
894:
892:
888:
882:
879:
877:
874:
872:
869:
867:
864:
862:
861:Chinchilla AI
859:
857:
854:
852:
849:
847:
844:
842:
839:
837:
834:
832:
829:
827:
824:
822:
819:
817:
814:
812:
809:
807:
804:
800:
797:
796:
795:
792:
790:
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782:
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777:
775:
772:
770:
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760:
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742:
739:
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727:
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664:
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629:
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619:
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601:
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593:
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588:
586:
583:
581:
578:
577:
575:
571:
563:
560:
559:
558:
555:
553:
550:
548:
545:
541:
540:Deep learning
538:
537:
536:
533:
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526:
525:
524:
521:
520:
518:
514:
508:
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503:
500:
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492:
491:
488:
486:
483:
479:
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474:
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466:
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464:
461:
459:
456:
454:
451:
449:
446:
444:
441:
439:
436:
434:
431:
429:
428:Hallucination
426:
422:
419:
418:
417:
414:
412:
409:
405:
402:
401:
400:
397:
396:
394:
390:
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344:
343:
339:
338:
336:
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330:
321:
316:
314:
309:
307:
302:
301:
298:
277:
271:
267:
257:
254:
252:
249:
247:
246:ItĂ´ diffusion
244:
242:
239:
238:
232:
230:
226:
222:
218:
214:
204:
202:
198:
194:
190:
185:
183:
179:
175:
171:
167:
163:
159:
155:
151:
147:
143:
140:
139:almost surely
136:
132:
128:
124:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
51:
45:
44:
43:single source
39:This article
37:
33:
28:
27:
22:
2528:expanding it
2517:
2502:
2404:Econometrics
2366:Wiener space
2254:ItĂ´ integral
2155:Inequalities
2044:Self-similar
2014:Gauss–Markov
2004:Exchangeable
1984:CĂ dlĂ g paths
1920:Risk process
1872:LIBOR market
1741:Random graph
1736:Random field
1548:Superprocess
1486:LĂ©vy process
1481:Jump process
1456:Hunt process
1415:
1292:Markov chain
1050:Hugging Face
1014:David Silver
662:Audio–visual
516:Applications
501:
495:Augmentation
340:
282:. Retrieved
270:
212:
210:
186:
170:data science
130:
120:
107:
97:
90:
83:
76:
64:
40:
2520:probability
2449:Ruin theory
2387:Disciplines
2259:ItĂ´'s lemma
2034:Predictable
1709:Percolation
1692:Potts model
1687:Ising model
1651:White noise
1609:Differences
1471:ItĂ´ process
1411:Cox process
1307:Loop-erased
1302:Random walk
1198:Categories
1146:Autoencoder
1101:Transformer
969:Alex Graves
917:OpenAI Five
821:IBM Watsonx
443:Convolution
421:Overfitting
284:October 10,
2567:Categories
2459:Statistics
2239:Filtration
2140:Kolmogorov
2124:Blumenthal
2049:Stationary
1989:Continuous
1977:Properties
1862:Hull–White
1604:Martingale
1491:Local time
1379:Fractional
1357:pure birth
1187:Technology
1040:EleutherAI
999:Fei-Fei Li
994:Yann LeCun
907:Q-learning
890:Decisional
816:IBM Watson
724:Midjourney
616:TensorFlow
463:Activation
416:Regression
411:Clustering
262:References
142:continuous
127:statistics
110:March 2024
80:newspapers
2371:Classical
1384:Geometric
1374:Excursion
1070:MIT CSAIL
1035:Anthropic
1004:Andrew Ng
902:AlphaZero
746:VideoPoet
709:AlphaFold
646:MindSpore
600:SpiNNaker
595:Memristor
502:Diffusion
478:Rectifier
458:Batchnorm
438:Attention
433:Adversary
241:Diffusion
182:marketing
50:talk page
2492:Category
2376:Abstract
1910:BĂĽhlmann
1516:Compound
1178:Portals
937:Auto-GPT
769:Word2vec
573:Hardware
490:Datasets
392:Concepts
235:See also
1999:Ergodic
1887:VašĂÄŤek
1729:Poisson
1389:Meander
1060:Meta AI
897:AlphaGo
881:PanGu-ÎŁ
851:ChatGPT
826:Granite
774:Seq2seq
753:Whisper
674:WaveNet
669:AlexNet
641:Flux.jl
621:PyTorch
473:Sigmoid
468:Softmax
333:General
227:is the
178:finance
94:scholar
2339:Tanaka
2024:Mixing
2019:Markov
1892:Wilkie
1857:Ho–Lee
1852:Heston
1624:Super-
1369:Bridge
1317:Biased
1075:Huawei
1055:OpenAI
957:People
927:MuZero
789:Gemini
784:Claude
719:DALL-E
631:Theano
96:
89:
82:
75:
67:
2518:This
2192:Tools
1968:M/M/c
1963:M/M/1
1958:M/G/1
1948:Fluid
1614:Local
1141:Mamba
912:SARSA
876:LLaMA
871:BLOOM
856:GPT-J
846:GPT-4
841:GPT-3
836:GPT-2
831:GPT-1
794:LaMDA
626:Keras
279:(pdf)
219:with
215:is a
195:as a
137:with
101:JSTOR
87:books
2524:stub
2144:LĂ©vy
1943:Bulk
1827:Chen
1619:Sub-
1577:Both
1065:Mila
866:PaLM
799:Bard
779:BERT
762:Text
741:Sora
286:2011
180:and
152:and
125:and
73:news
1724:Cox
806:NMT
689:OCR
684:HWR
636:JAX
590:VPU
585:TPU
580:IPU
404:SGD
121:In
56:by
2569::
2142:,
2138:,
2134:,
2130:,
2126:,
231:.
211:A
203:.
184:.
176:,
172:,
168:,
164:,
160:,
148:,
129:,
2555:e
2548:t
2541:v
2530:.
2146:)
2122:(
1243:e
1236:t
1229:v
319:e
312:t
305:v
288:.
112:)
108:(
98:·
91:·
84:·
77:·
60:.
46:.
23:.
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