3896:. They can be used to solve various computer vision problems which can be posed as energy minimization problems or problems where different regions have to be distinguished using a set of discriminating features, within a Markov random field framework, to predict the category of the region. Markov random fields were a generalization over the Ising model and have, since then, been used widely in combinatorial optimizations and networks.
100:, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies ); on the other hand, it can't represent certain dependencies that a Bayesian network can (such as induced dependencies ). The underlying graph of a Markov random field may be finite or infinite.
31:
3868:. MRFs are used in image processing to generate textures as they can be used to generate flexible and stochastic image models. In image modelling, the task is to find a suitable intensity distribution of a given image, where suitability depends on the kind of task and MRFs are flexible enough to be used for image and texture synthesis,
739:
The Global Markov property is stronger than the Local Markov property, which in turn is stronger than the
Pairwise one. However, the above three Markov properties are equivalent for positive distributions (those that assign only nonzero probabilities to the associated variables).
2950:
3274:
1785:
Some MRF's do not factorize: a simple example can be constructed on a cycle of 4 nodes with some infinite energies, i.e. configurations of zero probabilities, even if one, more appropriately, allows the infinite energies to act on the complete graph on
463:
2288:
2151:
1993:
3097:
3279:
Unfortunately, though the likelihood of a logistic Markov network is convex, evaluating the likelihood or gradient of the likelihood of a model requires inference in the model, which is generally computationally infeasible (see
3427:
1541:
1016:
3516:
362:
1130:
856:
575:
669:
2519:
34:
An example of a Markov random field. Each edge represents dependency. In this example: A depends on B and D. B depends on A and D. D depends on A, B, and E. E depends on D and C. C depends on E.
2797:
1141:
As the Markov property of an arbitrary probability distribution can be difficult to establish, a commonly used class of Markov random fields are those that can be factorized according to the
3658:
3595:
3111:
2622:
3700:
1616:
2416:
2774:
to be applied to the solution of the problem: one can attach a driving force to one or more of the random variables, and explore the reaction of the network in response to this
1745:
1198:
499:
379:
231:
2733:
2315:
2174:
3799:
3726:, or most likely assignment, inference; examples of these include associative networks. Another interesting sub-class is the one of decomposable models (when the graph is
1702:
1663:
1051:
911:
2449:
777:
3337:
2655:
2552:
2348:
2004:
179:
1312:
1233:
885:
2698:
1869:
1780:
1423:
4612:
1877:
2987:
3841:
3826:
3772:
3722:), have polynomial-time inference algorithms; discovering such subclasses is an active research topic. There are also subclasses of MRFs that permit efficient
1804:
1636:
1584:
1564:
1446:
1392:
1372:
1352:
1332:
1277:
1257:
931:
733:
713:
693:
599:
519:
271:
251:
4342:
3353:
5147:
1454:
936:
4971:
3438:
290:
4339:
Proceedings of the
Twentieth Annual Conference on Neural Information Processing Systems, Vancouver, British Columbia, Canada, December 4-7, 2006
1056:
5574:
4567:
2707:
is often called the Gibbs measure. This expression of a Markov field as a logistic model is only possible if all clique factors are non-zero,
4524:
Zhang & Zakhor, Richard & Avideh (2014). "Automatic
Identification of Window Regions on Indoor Point Clouds Using LiDAR and Cameras".
782:
5104:
5084:
4273:
4334:
5488:
4017:
5405:
524:
5089:
5415:
5099:
4275:
Proceedings of the Twenty-First
International Conference on Machine Learning (ICML 2004), Banff, Alberta, Canada, July 4-8, 2004
5457:
5354:
5644:
5634:
5480:
5172:
5157:
4420:
4248:
4030:
2317:
denotes the set of all possible assignments of values to all the network's random variables. Usually, the feature functions
615:
5544:
5508:
3916:
3853:
17:
5812:
5549:
4279:
2945:{\displaystyle Z=\sum _{x\in {\mathcal {X}}}\exp \left(\sum _{k}w_{k}^{\top }f_{k}(x_{\{k\}})+\sum _{v}J_{v}x_{v}\right)}
2462:
3269:{\displaystyle C={\frac {1}{Z}}\left.{\frac {\partial ^{2}Z}{\partial J_{u}\,\partial J_{v}}}\right|_{J_{u}=0,J_{v}=0}.}
5461:
4659:
4560:
4305:
4104:
5614:
4129:
4079:
2560:
5659:
5465:
5449:
5364:
5192:
5162:
4584:
3298:
2165:
5564:
5529:
5498:
5493:
4929:
4846:
3921:
1814:
112:
3600:
3537:
5503:
5132:
5127:
4934:
4831:
1844:
Any positive Markov random field can be written as exponential family in canonical form with feature functions
104:
123:; indeed, the Markov random field was introduced as the general setting for the Ising model. In the domain of
5817:
5594:
5430:
5329:
5314:
4853:
4726:
4642:
4553:
3961:
1752:
606:
Global Markov property: Any two subsets of variables are conditionally independent given a separating subset:
5589:
5469:
1589:
5599:
1236:
458:{\displaystyle X_{v}\perp \!\!\!\perp X_{V\smallsetminus \operatorname {N} }\mid X_{\operatorname {N} (v)}}
5604:
5240:
2360:
370:
Local Markov property: A variable is conditionally independent of all other variables given its neighbors:
5202:
4786:
4731:
4647:
3931:
3731:
578:
5534:
1711:
1151:
184:
5539:
5524:
5167:
5137:
4704:
4602:
3906:
3828:
to the nonnegative real numbers. This form of the Markov network may be more appropriate for producing
2459:-th clique and 0 otherwise. This model is equivalent to the clique factorization model given above, if
472:
2283:{\displaystyle Z=\sum _{x\in {\mathcal {X}}}\exp \left(\sum _{k}w_{k}^{\top }f_{k}(x_{\{k\}})\right).}
5838:
5619:
5420:
5334:
5319:
5250:
4826:
4709:
4607:
743:
The relation between the three Markov properties is particularly clear in the following formulation:
86:
3710:
problem, and thus computationally intractable in the general case. Approximation techniques such as
2714:
2296:
5843:
5453:
5339:
4841:
4816:
4761:
4534:
4288:
3750:
3743:
3711:
3663:
3531:
278:
3777:
1680:
1641:
1024:
119:
for an appropriate (locally defined) energy function. The prototypical Markov random field is the
5754:
5744:
5559:
5435:
5217:
5142:
4956:
4821:
4677:
4632:
124:
4438:"Enhancing gene regulatory network inference through data integration with markov random fields"
2146:{\displaystyle w_{k}^{\top }f_{k}(x_{\{k\}})=\sum _{i=1}^{N_{k}}w_{k,i}\cdot f_{k,i}(x_{\{k\}})}
890:
5696:
5624:
5049:
5039:
4883:
4529:
4283:
3956:
3889:
2740:
2421:
97:
750:
5719:
5701:
5681:
5676:
5395:
5227:
5207:
5054:
4997:
4836:
4746:
3893:
3865:
3861:
3802:
3718:
are often more feasible in practice. Some particular subclasses of MRFs, such as trees (see
3304:
2759:
2735:
are assigned a probability of 0. This allows techniques from matrix algebra to be applied,
2627:
2524:
2320:
1988:{\displaystyle P(X=x)={\frac {1}{Z}}\exp \left(\sum _{k}w_{k}^{\top }f_{k}(x_{\{k\}})\right)}
1705:
1142:
146:
3092:{\displaystyle E={\frac {1}{Z}}\left.{\frac {\partial Z}{\partial J_{v}}}\right|_{J_{v}=0}.}
1282:
1203:
864:
5794:
5749:
5739:
5425:
5400:
5369:
5349:
5187:
5109:
5094:
4961:
4449:
4366:
4184:
4154:
4044:
4040:
3991:
3951:
3829:
3723:
3102:
2676:
1847:
1758:
1401:
3754:, in which each random variable may also be conditioned upon a set of global observations
8:
5789:
5629:
5554:
5359:
5119:
4919:
4505:. Proceedings of the 28th ACM SIGIR Conference. Salvador, Brazil: ACM. pp. 472–479.
3941:
2775:
4453:
4158:
3995:
96:
in its representation of dependencies; the differences being that
Bayesian networks are
5759:
5724:
5639:
5609:
5440:
5379:
5374:
5197:
5034:
4699:
4637:
4576:
4478:
4437:
4311:
4188:
3877:
3873:
3811:
3757:
3715:
2771:
2351:
1789:
1621:
1569:
1549:
1431:
1377:
1357:
1337:
1317:
1262:
1242:
916:
718:
698:
678:
584:
504:
256:
236:
5779:
4992:
4909:
4878:
4771:
4751:
4741:
4597:
4592:
4483:
4465:
4416:
4301:
4244:
4192:
4125:
4100:
4075:
4026:
3881:
3869:
3719:
3344:
2965:
5584:
5235:
4315:
5799:
5686:
5569:
5445:
5182:
4939:
4914:
4863:
4714:
4667:
4506:
4473:
4457:
4293:
4219:
4170:
4162:
3999:
3926:
3885:
3857:
3833:
3832:, which do not model the distribution over the observations. CRFs were proposed by
3707:
3527:
3422:{\displaystyle X=(X_{v})_{v\in V}\sim {\mathcal {N}}({\boldsymbol {\mu }},\Sigma )}
3340:
2748:
1825:
1748:
128:
93:
74:
4791:
5764:
5664:
5649:
5410:
5344:
5022:
4966:
4949:
4694:
4180:
4069:
4036:
3982:
Sherrington, David; Kirkpatrick, Scott (1975), "Solvable Model of a Spin-Glass",
3911:
3837:
3703:
2770:
understanding can thereby be gained. In addition, the partition function allows
1638:. The definition is equivalent if only maximal cliques are used. The functions
132:
70:
66:
61:
5579:
4811:
4003:
85:
random field if it satisfies Markov properties. The concept originates from the
5769:
5734:
5654:
5260:
5007:
4924:
4893:
4888:
4868:
4858:
4801:
4776:
4756:
4721:
4689:
4672:
3734:, it is possible to discover a consistent structure for hundreds of variables.
4796:
4224:
4207:
4175:
1536:{\displaystyle P(X=x)=\prod _{C\in \operatorname {cl} (G)}\varphi _{C}(x_{C})}
1011:{\displaystyle X_{i}\perp \!\!\!\perp X_{J}|X_{V\smallsetminus (\{i\}\cup J)}}
30:
5832:
5671:
5212:
5044:
5002:
4944:
4766:
4682:
4622:
4469:
4362:
4330:
4269:
4265:
4208:"A note on Gibbs and Markov Random Fields with constraints and their moments"
4145:
Moussouris, John (1974). "Gibbs and Markov random systems with constraints".
3727:
3511:{\displaystyle (\Sigma ^{-1})_{uv}=0\quad {\text{iff}}\quad \{u,v\}\notin E.}
1821:
116:
82:
4510:
4297:
357:{\displaystyle X_{u}\perp \!\!\!\perp X_{v}\mid X_{V\smallsetminus \{u,v\}}}
127:, a Markov random field is used to model various low- to mid-level tasks in
5729:
5691:
5245:
5177:
5066:
5061:
4873:
4806:
4781:
4617:
4487:
3946:
3852:
Markov random fields find application in a variety of fields, ranging from
1833:
78:
1809:
MRF's factorize if at least one of the following conditions is fulfilled:
1125:{\displaystyle X_{I}\perp \!\!\!\perp X_{J}|X_{V\smallsetminus (I\cup J)}}
107:
of the random variables is strictly positive, it is also referred to as a
5774:
5309:
5293:
5288:
5283:
5273:
5076:
5017:
5012:
4976:
4736:
4627:
3936:
2744:
2157:
120:
43:
4335:"Using Combinatorial Optimization within Max-Product Belief Propagation"
851:{\displaystyle X_{i}\perp \!\!\!\perp X_{j}|X_{V\smallsetminus \{i,j\}}}
5784:
5324:
5268:
5152:
5105:
Generalized autoregressive conditional heteroskedasticity (GARCH) model
4545:
4166:
3660:
in the Markov random field by summing over all possible assignments to
4461:
5278:
4346:
2747:, with the matrix representation of a graph arising from the graph's
3981:
1832:
When such a factorization does exist, it is possible to construct a
4385:
4337:, in Schölkopf, Bernhard; Platt, John C.; Hoffman, Thomas (eds.),
4374:. International Conference on Data Mining. Dallas, TX, USA: IEEE.
2763:
2554:
corresponds to the logarithm of the corresponding clique factor,
39:
4386:"Two classic paper prizes for papers that appeared at ICML 2013"
4278:, ACM International Conference Proceeding Series, vol. 69,
2521:
is the cardinality of the clique, and the weight of a feature
570:{\displaystyle \operatorname {N} =v\cup \operatorname {N} (v)}
2766:, directly generalize to the case of Markov networks, and an
1673:. Note, however, conflicting terminology is in use: the word
277:
Pairwise Markov property: Any two non-adjacent variables are
1428:
If this joint density can be factorized over the cliques of
3162:
3025:
5085:
Autoregressive conditional heteroskedasticity (ARCH) model
4613:
Independent and identically distributed random variables
4263:
1871:
such that the full-joint distribution can be written as
1314:
is the probability of finding that the random variables
4328:
5090:
Autoregressive integrated moving average (ARIMA) model
4410:
4360:
4241:
Gaussian Markov random fields: theory and applications
664:{\displaystyle X_{A}\perp \!\!\!\perp X_{B}\mid X_{S}}
475:
3814:
3780:
3760:
3666:
3603:
3540:
3441:
3356:
3307:
3114:
3105:
are computed likewise; the two-point correlation is:
2990:
2800:
2717:
2679:
2630:
2563:
2527:
2465:
2424:
2363:
2323:
2299:
2177:
2007:
1880:
1850:
1792:
1761:
1714:
1683:
1644:
1624:
1592:
1572:
1552:
1457:
1434:
1404:
1380:
1360:
1340:
1320:
1285:
1265:
1245:
1206:
1154:
1059:
1027:
939:
919:
893:
867:
785:
753:
721:
701:
681:
618:
587:
527:
507:
382:
293:
259:
239:
187:
149:
4368:
Scaling log-linear analysis to high-dimensional data
3301:
forms a Markov random field with respect to a graph
273: if they satisfy the local Markov properties:
4268:(2004), "Learning associative Markov networks", in
2514:{\displaystyle N_{k}=|\operatorname {dom} (C_{k})|}
1394:should be understood to be taken with respect to a
4523:
4411:Kindermann & Snell, Ross & Laurie (1980).
3820:
3793:
3766:
3748:One notable variant of a Markov random field is a
3694:
3652:
3589:
3510:
3421:
3331:
3268:
3091:
2944:
2727:
2692:
2649:
2616:
2546:
2513:
2443:
2410:
2342:
2309:
2282:
2145:
1987:
1863:
1798:
1774:
1739:
1696:
1657:
1630:
1610:
1578:
1558:
1535:
1440:
1417:
1386:
1366:
1346:
1326:
1306:
1271:
1251:
1227:
1192:
1124:
1045:
1010:
925:
905:
879:
850:
771:
727:
707:
687:
663:
593:
569:
513:
493:
457:
356:
265:
253: form a Markov random field with respect to
245:
225:
173:
4503:A Markov random field model for term dependencies
4343:Advances in Neural Information Processing Systems
2778:. Thus, for example, one may add a driving term
1075:
1074:
1073:
955:
954:
953:
801:
800:
799:
634:
633:
632:
398:
397:
396:
309:
308:
307:
5830:
4972:Stochastic chains with memory of variable length
3339:if the missing edges correspond to zeros on the
2791:of the graph, to the partition function to get:
4415:. Rhode Island: American Mathematical Society.
4205:
4015:
4119:
4071:Markov Random Field Modeling in Image Analysis
3801:is a mapping from all assignments to both the
2617:{\displaystyle w_{k,i}=\log \varphi (c_{k,i})}
4561:
4378:
4329:Duchi, John C.; Tarlow, Daniel; Elidan, Gal;
4500:
4436:Banf, Michael; Rhee, Seung Y. (2017-02-01).
4212:Mathematics and Mechanics of Complex Systems
3737:
3647:
3615:
3584:
3552:
3496:
3484:
2896:
2890:
2436:
2430:
2394:
2388:
2264:
2258:
2135:
2129:
2047:
2041:
1972:
1966:
1566:forms a Markov random field with respect to
994:
988:
843:
831:
349:
337:
4413:Markov Random Fields and their Applications
4206:Gandolfi, Alberto; Lenarda, Pietro (2016).
4019:Markov Random Fields and Their Applications
4016:Kindermann, Ross; Snell, J. Laurie (1980).
5100:Autoregressive–moving-average (ARMA) model
4568:
4554:
4144:
3653:{\displaystyle W'=\{w_{1},\ldots ,w_{j}\}}
3590:{\displaystyle V'=\{v_{1},\ldots ,v_{i}\}}
4533:
4477:
4354:
4287:
4223:
4174:
4094:
3204:
2955:Formally differentiating with respect to
2754:The importance of the partition function
4575:
4501:Metzler, Donald; Croft, W.Bruce (2005).
4435:
4264:Taskar, Benjamin; Chatalbashev, Vassil;
92:A Markov network or MRF is similar to a
29:
4238:
4099:. Oxford: Clarendon Press. p. 33.
3406:
1136:
14:
5831:
5406:Doob's martingale convergence theorems
4120:Koller, Daphne; Friedman, Nir (2009).
3847:
2673:-th value in the domain of the clique
1611:{\displaystyle \operatorname {cl} (G)}
5158:Constant elasticity of variance (CEV)
5148:Chan–Karolyi–Longstaff–Sanders (CKLS)
4549:
3876:, 3D image inference from 2D images,
3597:given values to another set of nodes
1839:
1677:is often applied to the logarithm of
4239:Rue, HĂĄvard; Held, Leonhard (2005).
3917:Dependency network (graphical model)
2411:{\displaystyle f_{k,i}(x_{\{k\}})=1}
1239:of a particular field configuration
4280:Association for Computing Machinery
1747:has a direct interpretation as the
24:
5645:Skorokhod's representation theorem
5426:Law of large numbers (weak/strong)
4067:
3446:
3413:
3397:
3205:
3191:
3168:
3047:
3030:
2867:
2829:
2720:
2661:-th possible configuration of the
2455:-th possible configuration of the
2302:
2235:
2197:
2018:
1943:
1740:{\displaystyle \log(\varphi _{C})}
1193:{\displaystyle X=(X_{v})_{v\in V}}
552:
528:
494:{\textstyle \operatorname {N} (v)}
476:
438:
413:
226:{\displaystyle X=(X_{v})_{v\in V}}
115:, it can then be represented by a
25:
5855:
5615:Martingale representation theorem
4025:. American Mathematical Society.
5660:Stochastic differential equation
5550:Doob's optional stopping theorem
5545:Doob–Meyer decomposition theorem
3730:): having a closed-form for the
3706:. However, exact inference is a
3299:multivariate normal distribution
1813:the density is positive (by the
1148:Given a set of random variables
675:where every path from a node in
5530:Convergence of random variables
5416:Fisher–Tippett–Gnedenko theorem
4517:
4494:
4429:
4404:
4322:
3774:. In this model, each function
3483:
3477:
2354:of the clique's configuration,
2350:are defined such that they are
2160:over field configurations, and
5128:Binomial options pricing model
4257:
4232:
4199:
4147:Journal of Statistical Physics
4138:
4124:. MIT Press. p. 114-122.
4122:Probabilistic Graphical Models
4113:
4088:
4061:
4009:
3975:
3459:
3442:
3416:
3402:
3377:
3363:
3326:
3314:
3281:
3186:
3180:
3144:
3118:
3042:
3036:
3007:
2994:
2901:
2882:
2810:
2804:
2728:{\displaystyle {\mathcal {X}}}
2611:
2592:
2507:
2503:
2490:
2480:
2399:
2380:
2310:{\displaystyle {\mathcal {X}}}
2269:
2250:
2140:
2121:
2052:
2033:
1977:
1958:
1896:
1884:
1734:
1721:
1605:
1599:
1530:
1517:
1502:
1496:
1473:
1461:
1301:
1289:
1222:
1210:
1175:
1161:
1117:
1105:
1090:
1053:not intersecting or adjacent,
1003:
985:
970:
913:not containing or adjacent to
816:
564:
558:
540:
534:
488:
482:
450:
444:
425:
419:
208:
194:
168:
156:
13:
1:
5595:Kolmogorov continuity theorem
5431:Law of the iterated logarithm
3968:
3962:Stochastic cellular automaton
3695:{\displaystyle u\notin V',W'}
1665:are sometimes referred to as
1374:is a set, the probability of
1334:take on the particular value
138:
87:Sherrington–Kirkpatrick model
5600:Kolmogorov extension theorem
5279:Generalized queueing network
4787:Interacting particle systems
3794:{\displaystyle \varphi _{k}}
3521:
1697:{\displaystyle \varphi _{C}}
1658:{\displaystyle \varphi _{C}}
1046:{\displaystyle I,J\subset V}
181:, a set of random variables
111:, because, according to the
7:
4732:Continuous-time random walk
4361:Petitjean, F.; Webb, G.I.;
4095:Lauritzen, Steffen (1996).
4004:10.1103/PhysRevLett.35.1792
3932:Interacting particle system
3922:Hammersley–Clifford theorem
3899:
3292:
3287:
2977:associated with the vertex
2758:is that many concepts from
2711:if none of the elements of
1815:Hammersley–Clifford theorem
501:is the set of neighbors of
113:Hammersley–Clifford theorem
10:
5860:
5740:Extreme value theory (EVT)
5540:Doob decomposition theorem
4832:Ornstein–Uhlenbeck process
4603:Chinese restaurant process
3907:Constraint composite graph
3830:discriminative classifiers
3741:
2743:of a matrix is log of the
906:{\displaystyle J\subset V}
281:given all other variables:
143:Given an undirected graph
5808:
5712:
5620:Optional stopping theorem
5517:
5479:
5421:Large deviation principle
5388:
5302:
5259:
5226:
5173:Heath–Jarrow–Morton (HJM)
5118:
5110:Moving-average (MA) model
5095:Autoregressive (AR) model
5075:
4985:
4920:Hidden Markov model (HMM)
4902:
4854:Schramm–Loewner evolution
4658:
4583:
4225:10.2140/memocs.2016.4.407
3738:Conditional random fields
2444:{\displaystyle x_{\{k\}}}
1618:is the set of cliques of
279:conditionally independent
105:joint probability density
5535:Doléans-Dade exponential
5365:Progressively measurable
5163:Cox–Ingersoll–Ross (CIR)
3751:conditional random field
3744:Conditional random field
3712:Markov chain Monte Carlo
3532:conditional distribution
3530:, one may calculate the
772:{\displaystyle i,j\in V}
5755:Mathematical statistics
5745:Large deviations theory
5575:Infinitesimal generator
5436:Maximal ergodic theorem
5355:Piecewise-deterministic
4957:Random dynamical system
4822:Markov additive process
4511:10.1145/1076034.1076115
4298:10.1145/1015330.1015444
3984:Physical Review Letters
3332:{\displaystyle G=(V,E)}
2968:of the random variable
2650:{\displaystyle c_{k,i}}
2547:{\displaystyle f_{k,i}}
2343:{\displaystyle f_{k,i}}
1704:. This is because, in
779:not equal or adjacent,
174:{\displaystyle G=(V,E)}
125:artificial intelligence
27:Set of random variables
5590:Karhunen–Loève theorem
5525:Cameron–Martin formula
5489:Burkholder–Davis–Gundy
4884:Variance gamma process
3957:Maximum entropy method
3822:
3795:
3768:
3696:
3654:
3591:
3512:
3423:
3333:
3270:
3093:
2946:
2729:
2694:
2651:
2618:
2548:
2515:
2445:
2412:
2344:
2311:
2284:
2147:
2085:
1989:
1865:
1800:
1776:
1741:
1698:
1659:
1632:
1612:
1580:
1560:
1537:
1442:
1419:
1388:
1368:
1348:
1328:
1308:
1307:{\displaystyle P(X=x)}
1273:
1253:
1229:
1228:{\displaystyle P(X=x)}
1194:
1126:
1047:
1012:
927:
907:
881:
880:{\displaystyle i\in V}
852:
773:
729:
709:
689:
665:
595:
571:
515:
495:
459:
358:
267:
247:
227:
175:
35:
5720:Actuarial mathematics
5682:Uniform integrability
5677:Stratonovich integral
5605:Lévy–Prokhorov metric
5509:Marcinkiewicz–Zygmund
5396:Central limit theorem
4998:Gaussian random field
4827:McKean–Vlasov process
4747:Dyson Brownian motion
4608:Galton–Watson process
3894:information retrieval
3866:information retrieval
3862:computational biology
3842:Fernando C.N. Pereira
3823:
3808:and the observations
3796:
3769:
3697:
3655:
3592:
3513:
3424:
3334:
3271:
3103:Correlation functions
3094:
2947:
2760:statistical mechanics
2730:
2695:
2693:{\displaystyle C_{k}}
2652:
2619:
2549:
2516:
2446:
2413:
2345:
2312:
2285:
2148:
2058:
1990:
1866:
1864:{\displaystyle f_{k}}
1824:(by equivalence to a
1801:
1777:
1775:{\displaystyle x_{C}}
1742:
1706:statistical mechanics
1699:
1660:
1633:
1613:
1581:
1561:
1538:
1443:
1420:
1418:{\displaystyle X_{v}}
1389:
1369:
1349:
1329:
1309:
1274:
1254:
1230:
1195:
1127:
1048:
1013:
928:
908:
882:
853:
774:
730:
710:
690:
666:
596:
572:
516:
496:
460:
359:
268:
248:
228:
176:
33:
5795:Time series analysis
5750:Mathematical finance
5635:Reflection principle
4962:Regenerative process
4762:Fleming–Viot process
4577:Stochastic processes
4526:VIP Lab Publications
3952:Markov logic network
3856:to computer vision,
3812:
3778:
3758:
3664:
3601:
3538:
3439:
3354:
3305:
3112:
2988:
2798:
2715:
2677:
2628:
2561:
2525:
2463:
2422:
2361:
2321:
2297:
2175:
2005:
1878:
1848:
1790:
1759:
1712:
1681:
1642:
1622:
1590:
1570:
1550:
1455:
1432:
1402:
1378:
1358:
1338:
1318:
1283:
1263:
1243:
1204:
1152:
1137:Clique factorization
1057:
1025:
937:
917:
891:
865:
783:
751:
719:
699:
679:
616:
585:
579:closed neighbourhood
525:
505:
473:
380:
291:
257:
237:
185:
147:
98:directed and acyclic
77:. In other words, a
18:Markov random fields
5790:Stochastic analysis
5630:Quadratic variation
5625:Prokhorov's theorem
5560:Feynman–Kac formula
5030:Markov random field
4678:Birth–death process
4454:2017NatSR...741174B
4159:1974JSP....10...11M
3996:1975PhRvL..35.1792S
3942:Log-linear analysis
3848:Varied applications
2871:
2772:variational methods
2451:corresponds to the
2239:
2022:
1998:where the notation
1947:
48:Markov random field
5760:Probability theory
5640:Skorokhod integral
5610:Malliavin calculus
5193:Korn-Kreer-Lenssen
5077:Time series models
5040:Pitman–Yor process
4442:Scientific Reports
4349:, pp. 369–376
4176:10338.dmlcz/135184
4167:10.1007/BF01011714
4068:Li, S. Z. (2009).
3878:image registration
3874:image segmentation
3818:
3791:
3764:
3716:belief propagation
3692:
3650:
3587:
3534:of a set of nodes
3508:
3419:
3329:
3266:
3089:
2942:
2916:
2857:
2856:
2835:
2787:, for each vertex
2725:
2690:
2647:
2614:
2544:
2511:
2441:
2408:
2340:
2307:
2280:
2225:
2224:
2203:
2166:partition function
2143:
2008:
1985:
1933:
1932:
1861:
1840:Exponential family
1796:
1772:
1737:
1694:
1655:
1628:
1608:
1576:
1556:
1533:
1506:
1438:
1415:
1396:joint distribution
1384:
1364:
1344:
1324:
1304:
1269:
1249:
1225:
1190:
1122:
1043:
1008:
923:
903:
877:
848:
769:
747:Pairwise: For any
725:
705:
685:
661:
591:
567:
511:
491:
455:
354:
263:
243:
223:
171:
109:Gibbs random field
36:
5826:
5825:
5780:Signal processing
5499:Doob's upcrossing
5494:Doob's martingale
5458:Engelbert–Schmidt
5401:Donsker's theorem
5335:Feller-continuous
5203:Rendleman–Bartter
4993:Dirichlet process
4910:Branching process
4879:Telegraph process
4772:Geometric process
4752:Empirical process
4742:Diffusion process
4598:Branching process
4593:Bernoulli process
4462:10.1038/srep41174
4422:978-0-8218-5001-5
4270:Brodley, Carla E.
4250:978-1-58488-432-3
4032:978-0-8218-5001-5
3990:(35): 1792–1796,
3882:texture synthesis
3872:and restoration,
3870:image compression
3854:computer graphics
3821:{\displaystyle o}
3767:{\displaystyle o}
3702:; this is called
3481:
3345:covariance matrix
3219:
3158:
3061:
3021:
2966:expectation value
2907:
2847:
2816:
2215:
2184:
1923:
1910:
1836:for the network.
1799:{\displaystyle V}
1671:clique potentials
1667:factor potentials
1631:{\displaystyle G}
1579:{\displaystyle G}
1559:{\displaystyle X}
1479:
1441:{\displaystyle G}
1387:{\displaystyle x}
1367:{\displaystyle X}
1347:{\displaystyle x}
1327:{\displaystyle X}
1272:{\displaystyle X}
1252:{\displaystyle x}
926:{\displaystyle i}
728:{\displaystyle S}
708:{\displaystyle B}
688:{\displaystyle A}
594:{\displaystyle v}
514:{\displaystyle v}
266:{\displaystyle G}
246:{\displaystyle V}
38:In the domain of
16:(Redirected from
5851:
5839:Graphical models
5800:Machine learning
5687:Usual hypotheses
5570:Girsanov theorem
5555:Dynkin's formula
5320:Continuous paths
5228:Actuarial models
5168:Garman–Kohlhagen
5138:Black–Karasinski
5133:Black–Derman–Toy
5120:Financial models
4986:Fields and other
4915:Gaussian process
4864:Sigma-martingale
4668:Additive process
4570:
4563:
4556:
4547:
4546:
4540:
4539:
4537:
4521:
4515:
4514:
4498:
4492:
4491:
4481:
4433:
4427:
4426:
4408:
4402:
4401:
4399:
4397:
4382:
4376:
4375:
4373:
4358:
4352:
4350:
4345:, vol. 19,
4326:
4320:
4318:
4291:
4261:
4255:
4254:
4236:
4230:
4229:
4227:
4218:(3–4): 407–422.
4203:
4197:
4196:
4178:
4142:
4136:
4135:
4117:
4111:
4110:
4097:Graphical models
4092:
4086:
4085:
4065:
4059:
4058:
4056:
4055:
4049:
4043:. Archived from
4024:
4013:
4007:
4006:
3979:
3927:Hopfield network
3886:super-resolution
3858:machine learning
3834:John D. Lafferty
3827:
3825:
3824:
3819:
3800:
3798:
3797:
3792:
3790:
3789:
3773:
3771:
3770:
3765:
3701:
3699:
3698:
3693:
3691:
3680:
3659:
3657:
3656:
3651:
3646:
3645:
3627:
3626:
3611:
3596:
3594:
3593:
3588:
3583:
3582:
3564:
3563:
3548:
3528:Bayesian network
3517:
3515:
3514:
3509:
3482:
3479:
3470:
3469:
3457:
3456:
3428:
3426:
3425:
3420:
3409:
3401:
3400:
3391:
3390:
3375:
3374:
3341:precision matrix
3338:
3336:
3335:
3330:
3275:
3273:
3272:
3267:
3262:
3261:
3254:
3253:
3235:
3234:
3224:
3220:
3218:
3217:
3216:
3203:
3202:
3189:
3176:
3175:
3165:
3159:
3151:
3143:
3142:
3130:
3129:
3098:
3096:
3095:
3090:
3085:
3084:
3077:
3076:
3066:
3062:
3060:
3059:
3058:
3045:
3028:
3022:
3014:
3006:
3005:
2951:
2949:
2948:
2943:
2941:
2937:
2936:
2935:
2926:
2925:
2915:
2900:
2899:
2881:
2880:
2870:
2865:
2855:
2834:
2833:
2832:
2749:incidence matrix
2734:
2732:
2731:
2726:
2724:
2723:
2703:The probability
2699:
2697:
2696:
2691:
2689:
2688:
2656:
2654:
2653:
2648:
2646:
2645:
2623:
2621:
2620:
2615:
2610:
2609:
2579:
2578:
2553:
2551:
2550:
2545:
2543:
2542:
2520:
2518:
2517:
2512:
2510:
2502:
2501:
2483:
2475:
2474:
2450:
2448:
2447:
2442:
2440:
2439:
2417:
2415:
2414:
2409:
2398:
2397:
2379:
2378:
2349:
2347:
2346:
2341:
2339:
2338:
2316:
2314:
2313:
2308:
2306:
2305:
2289:
2287:
2286:
2281:
2276:
2272:
2268:
2267:
2249:
2248:
2238:
2233:
2223:
2202:
2201:
2200:
2152:
2150:
2149:
2144:
2139:
2138:
2120:
2119:
2101:
2100:
2084:
2083:
2082:
2072:
2051:
2050:
2032:
2031:
2021:
2016:
1994:
1992:
1991:
1986:
1984:
1980:
1976:
1975:
1957:
1956:
1946:
1941:
1931:
1911:
1903:
1870:
1868:
1867:
1862:
1860:
1859:
1826:Bayesian network
1805:
1803:
1802:
1797:
1781:
1779:
1778:
1773:
1771:
1770:
1749:potential energy
1746:
1744:
1743:
1738:
1733:
1732:
1703:
1701:
1700:
1695:
1693:
1692:
1664:
1662:
1661:
1656:
1654:
1653:
1637:
1635:
1634:
1629:
1617:
1615:
1614:
1609:
1585:
1583:
1582:
1577:
1565:
1563:
1562:
1557:
1542:
1540:
1539:
1534:
1529:
1528:
1516:
1515:
1505:
1447:
1445:
1444:
1439:
1424:
1422:
1421:
1416:
1414:
1413:
1393:
1391:
1390:
1385:
1373:
1371:
1370:
1365:
1353:
1351:
1350:
1345:
1333:
1331:
1330:
1325:
1313:
1311:
1310:
1305:
1278:
1276:
1275:
1270:
1258:
1256:
1255:
1250:
1234:
1232:
1231:
1226:
1199:
1197:
1196:
1191:
1189:
1188:
1173:
1172:
1131:
1129:
1128:
1123:
1121:
1120:
1093:
1088:
1087:
1069:
1068:
1052:
1050:
1049:
1044:
1021:Global: For any
1017:
1015:
1014:
1009:
1007:
1006:
973:
968:
967:
949:
948:
932:
930:
929:
924:
912:
910:
909:
904:
886:
884:
883:
878:
857:
855:
854:
849:
847:
846:
819:
814:
813:
795:
794:
778:
776:
775:
770:
734:
732:
731:
726:
714:
712:
711:
706:
694:
692:
691:
686:
670:
668:
667:
662:
660:
659:
647:
646:
628:
627:
600:
598:
597:
592:
576:
574:
573:
568:
520:
518:
517:
512:
500:
498:
497:
492:
464:
462:
461:
456:
454:
453:
429:
428:
392:
391:
363:
361:
360:
355:
353:
352:
322:
321:
303:
302:
272:
270:
269:
264:
252:
250:
249:
244:
232:
230:
229:
224:
222:
221:
206:
205:
180:
178:
177:
172:
129:image processing
94:Bayesian network
81:is said to be a
75:undirected graph
73:described by an
67:random variables
21:
5859:
5858:
5854:
5853:
5852:
5850:
5849:
5848:
5844:Markov networks
5829:
5828:
5827:
5822:
5804:
5765:Queueing theory
5708:
5650:Skorokhod space
5513:
5504:Kunita–Watanabe
5475:
5441:Sanov's theorem
5411:Ergodic theorem
5384:
5380:Time-reversible
5298:
5261:Queueing models
5255:
5251:Sparre–Anderson
5241:Cramér–Lundberg
5222:
5208:SABR volatility
5114:
5071:
5023:Boolean network
4981:
4967:Renewal process
4898:
4847:Non-homogeneous
4837:Poisson process
4727:Contact process
4690:Brownian motion
4660:Continuous time
4654:
4648:Maximal entropy
4579:
4574:
4544:
4543:
4522:
4518:
4499:
4495:
4434:
4430:
4423:
4409:
4405:
4395:
4393:
4384:
4383:
4379:
4371:
4363:Nicholson, A.E.
4359:
4355:
4327:
4323:
4308:
4282:, p. 102,
4262:
4258:
4251:
4237:
4233:
4204:
4200:
4143:
4139:
4132:
4118:
4114:
4107:
4093:
4089:
4082:
4066:
4062:
4053:
4051:
4047:
4033:
4022:
4014:
4010:
3980:
3976:
3971:
3966:
3912:Graphical model
3902:
3890:stereo matching
3850:
3838:Andrew McCallum
3813:
3810:
3809:
3785:
3781:
3779:
3776:
3775:
3759:
3756:
3755:
3746:
3740:
3704:exact inference
3684:
3673:
3665:
3662:
3661:
3641:
3637:
3622:
3618:
3604:
3602:
3599:
3598:
3578:
3574:
3559:
3555:
3541:
3539:
3536:
3535:
3524:
3478:
3462:
3458:
3449:
3445:
3440:
3437:
3436:
3405:
3396:
3395:
3380:
3376:
3370:
3366:
3355:
3352:
3351:
3306:
3303:
3302:
3295:
3290:
3249:
3245:
3230:
3226:
3225:
3212:
3208:
3198:
3194:
3190:
3171:
3167:
3166:
3164:
3161:
3160:
3150:
3138:
3134:
3125:
3121:
3113:
3110:
3109:
3072:
3068:
3067:
3054:
3050:
3046:
3029:
3027:
3024:
3023:
3013:
3001:
2997:
2989:
2986:
2985:
2976:
2963:
2931:
2927:
2921:
2917:
2911:
2889:
2885:
2876:
2872:
2866:
2861:
2851:
2846:
2842:
2828:
2827:
2820:
2799:
2796:
2795:
2786:
2719:
2718:
2716:
2713:
2712:
2684:
2680:
2678:
2675:
2674:
2635:
2631:
2629:
2626:
2625:
2599:
2595:
2568:
2564:
2562:
2559:
2558:
2532:
2528:
2526:
2523:
2522:
2506:
2497:
2493:
2479:
2470:
2466:
2464:
2461:
2460:
2429:
2425:
2423:
2420:
2419:
2387:
2383:
2368:
2364:
2362:
2359:
2358:
2328:
2324:
2322:
2319:
2318:
2301:
2300:
2298:
2295:
2294:
2257:
2253:
2244:
2240:
2234:
2229:
2219:
2214:
2210:
2196:
2195:
2188:
2176:
2173:
2172:
2128:
2124:
2109:
2105:
2090:
2086:
2078:
2074:
2073:
2062:
2040:
2036:
2027:
2023:
2017:
2012:
2006:
2003:
2002:
1965:
1961:
1952:
1948:
1942:
1937:
1927:
1922:
1918:
1902:
1879:
1876:
1875:
1855:
1851:
1849:
1846:
1845:
1842:
1791:
1788:
1787:
1766:
1762:
1760:
1757:
1756:
1728:
1724:
1713:
1710:
1709:
1688:
1684:
1682:
1679:
1678:
1649:
1645:
1643:
1640:
1639:
1623:
1620:
1619:
1591:
1588:
1587:
1571:
1568:
1567:
1551:
1548:
1547:
1524:
1520:
1511:
1507:
1483:
1456:
1453:
1452:
1433:
1430:
1429:
1409:
1405:
1403:
1400:
1399:
1379:
1376:
1375:
1359:
1356:
1355:
1339:
1336:
1335:
1319:
1316:
1315:
1284:
1281:
1280:
1264:
1261:
1260:
1244:
1241:
1240:
1205:
1202:
1201:
1178:
1174:
1168:
1164:
1153:
1150:
1149:
1139:
1098:
1094:
1089:
1083:
1079:
1064:
1060:
1058:
1055:
1054:
1026:
1023:
1022:
978:
974:
969:
963:
959:
944:
940:
938:
935:
934:
918:
915:
914:
892:
889:
888:
866:
863:
862:
861:Local: For any
824:
820:
815:
809:
805:
790:
786:
784:
781:
780:
752:
749:
748:
720:
717:
716:
715:passes through
700:
697:
696:
680:
677:
676:
655:
651:
642:
638:
623:
619:
617:
614:
613:
586:
583:
582:
526:
523:
522:
506:
503:
502:
474:
471:
470:
437:
433:
406:
402:
387:
383:
381:
378:
377:
330:
326:
317:
313:
298:
294:
292:
289:
288:
258:
255:
254:
238:
235:
234:
211:
207:
201:
197:
186:
183:
182:
148:
145:
144:
141:
133:computer vision
71:Markov property
62:graphical model
28:
23:
22:
15:
12:
11:
5:
5857:
5847:
5846:
5841:
5824:
5823:
5821:
5820:
5815:
5813:List of topics
5809:
5806:
5805:
5803:
5802:
5797:
5792:
5787:
5782:
5777:
5772:
5770:Renewal theory
5767:
5762:
5757:
5752:
5747:
5742:
5737:
5735:Ergodic theory
5732:
5727:
5725:Control theory
5722:
5716:
5714:
5710:
5709:
5707:
5706:
5705:
5704:
5699:
5689:
5684:
5679:
5674:
5669:
5668:
5667:
5657:
5655:Snell envelope
5652:
5647:
5642:
5637:
5632:
5627:
5622:
5617:
5612:
5607:
5602:
5597:
5592:
5587:
5582:
5577:
5572:
5567:
5562:
5557:
5552:
5547:
5542:
5537:
5532:
5527:
5521:
5519:
5515:
5514:
5512:
5511:
5506:
5501:
5496:
5491:
5485:
5483:
5477:
5476:
5474:
5473:
5454:Borel–Cantelli
5443:
5438:
5433:
5428:
5423:
5418:
5413:
5408:
5403:
5398:
5392:
5390:
5389:Limit theorems
5386:
5385:
5383:
5382:
5377:
5372:
5367:
5362:
5357:
5352:
5347:
5342:
5337:
5332:
5327:
5322:
5317:
5312:
5306:
5304:
5300:
5299:
5297:
5296:
5291:
5286:
5281:
5276:
5271:
5265:
5263:
5257:
5256:
5254:
5253:
5248:
5243:
5238:
5232:
5230:
5224:
5223:
5221:
5220:
5215:
5210:
5205:
5200:
5195:
5190:
5185:
5180:
5175:
5170:
5165:
5160:
5155:
5150:
5145:
5140:
5135:
5130:
5124:
5122:
5116:
5115:
5113:
5112:
5107:
5102:
5097:
5092:
5087:
5081:
5079:
5073:
5072:
5070:
5069:
5064:
5059:
5058:
5057:
5052:
5042:
5037:
5032:
5027:
5026:
5025:
5020:
5010:
5008:Hopfield model
5005:
5000:
4995:
4989:
4987:
4983:
4982:
4980:
4979:
4974:
4969:
4964:
4959:
4954:
4953:
4952:
4947:
4942:
4937:
4927:
4925:Markov process
4922:
4917:
4912:
4906:
4904:
4900:
4899:
4897:
4896:
4894:Wiener sausage
4891:
4889:Wiener process
4886:
4881:
4876:
4871:
4869:Stable process
4866:
4861:
4859:Semimartingale
4856:
4851:
4850:
4849:
4844:
4834:
4829:
4824:
4819:
4814:
4809:
4804:
4802:Jump diffusion
4799:
4794:
4789:
4784:
4779:
4777:Hawkes process
4774:
4769:
4764:
4759:
4757:Feller process
4754:
4749:
4744:
4739:
4734:
4729:
4724:
4722:Cauchy process
4719:
4718:
4717:
4712:
4707:
4702:
4697:
4687:
4686:
4685:
4675:
4673:Bessel process
4670:
4664:
4662:
4656:
4655:
4653:
4652:
4651:
4650:
4645:
4640:
4635:
4625:
4620:
4615:
4610:
4605:
4600:
4595:
4589:
4587:
4581:
4580:
4573:
4572:
4565:
4558:
4550:
4542:
4541:
4535:10.1.1.649.303
4516:
4493:
4428:
4421:
4403:
4377:
4353:
4331:Koller, Daphne
4321:
4307:978-1581138283
4306:
4289:10.1.1.157.329
4266:Koller, Daphne
4256:
4249:
4231:
4198:
4137:
4130:
4112:
4106:978-0198522195
4105:
4087:
4080:
4060:
4031:
4008:
3973:
3972:
3970:
3967:
3965:
3964:
3959:
3954:
3949:
3944:
3939:
3934:
3929:
3924:
3919:
3914:
3909:
3903:
3901:
3898:
3849:
3846:
3817:
3788:
3784:
3763:
3742:Main article:
3739:
3736:
3690:
3687:
3683:
3679:
3676:
3672:
3669:
3649:
3644:
3640:
3636:
3633:
3630:
3625:
3621:
3617:
3614:
3610:
3607:
3586:
3581:
3577:
3573:
3570:
3567:
3562:
3558:
3554:
3551:
3547:
3544:
3523:
3520:
3519:
3518:
3507:
3504:
3501:
3498:
3495:
3492:
3489:
3486:
3476:
3473:
3468:
3465:
3461:
3455:
3452:
3448:
3444:
3430:
3429:
3418:
3415:
3412:
3408:
3404:
3399:
3394:
3389:
3386:
3383:
3379:
3373:
3369:
3365:
3362:
3359:
3328:
3325:
3322:
3319:
3316:
3313:
3310:
3294:
3291:
3289:
3286:
3277:
3276:
3265:
3260:
3257:
3252:
3248:
3244:
3241:
3238:
3233:
3229:
3223:
3215:
3211:
3207:
3201:
3197:
3193:
3188:
3185:
3182:
3179:
3174:
3170:
3163:
3157:
3154:
3149:
3146:
3141:
3137:
3133:
3128:
3124:
3120:
3117:
3100:
3099:
3088:
3083:
3080:
3075:
3071:
3065:
3057:
3053:
3049:
3044:
3041:
3038:
3035:
3032:
3026:
3020:
3017:
3012:
3009:
3004:
3000:
2996:
2993:
2972:
2959:
2953:
2952:
2940:
2934:
2930:
2924:
2920:
2914:
2910:
2906:
2903:
2898:
2895:
2892:
2888:
2884:
2879:
2875:
2869:
2864:
2860:
2854:
2850:
2845:
2841:
2838:
2831:
2826:
2823:
2819:
2815:
2812:
2809:
2806:
2803:
2782:
2722:
2687:
2683:
2644:
2641:
2638:
2634:
2613:
2608:
2605:
2602:
2598:
2594:
2591:
2588:
2585:
2582:
2577:
2574:
2571:
2567:
2541:
2538:
2535:
2531:
2509:
2505:
2500:
2496:
2492:
2489:
2486:
2482:
2478:
2473:
2469:
2438:
2435:
2432:
2428:
2407:
2404:
2401:
2396:
2393:
2390:
2386:
2382:
2377:
2374:
2371:
2367:
2337:
2334:
2331:
2327:
2304:
2291:
2290:
2279:
2275:
2271:
2266:
2263:
2260:
2256:
2252:
2247:
2243:
2237:
2232:
2228:
2222:
2218:
2213:
2209:
2206:
2199:
2194:
2191:
2187:
2183:
2180:
2154:
2153:
2142:
2137:
2134:
2131:
2127:
2123:
2118:
2115:
2112:
2108:
2104:
2099:
2096:
2093:
2089:
2081:
2077:
2071:
2068:
2065:
2061:
2057:
2054:
2049:
2046:
2043:
2039:
2035:
2030:
2026:
2020:
2015:
2011:
1996:
1995:
1983:
1979:
1974:
1971:
1968:
1964:
1960:
1955:
1951:
1945:
1940:
1936:
1930:
1926:
1921:
1917:
1914:
1909:
1906:
1901:
1898:
1895:
1892:
1889:
1886:
1883:
1858:
1854:
1841:
1838:
1830:
1829:
1818:
1795:
1769:
1765:
1736:
1731:
1727:
1723:
1720:
1717:
1691:
1687:
1652:
1648:
1627:
1607:
1604:
1601:
1598:
1595:
1575:
1555:
1544:
1543:
1532:
1527:
1523:
1519:
1514:
1510:
1504:
1501:
1498:
1495:
1492:
1489:
1486:
1482:
1478:
1475:
1472:
1469:
1466:
1463:
1460:
1437:
1412:
1408:
1383:
1363:
1343:
1323:
1303:
1300:
1297:
1294:
1291:
1288:
1268:
1248:
1224:
1221:
1218:
1215:
1212:
1209:
1187:
1184:
1181:
1177:
1171:
1167:
1163:
1160:
1157:
1145:of the graph.
1138:
1135:
1134:
1133:
1119:
1116:
1113:
1110:
1107:
1104:
1101:
1097:
1092:
1086:
1082:
1078:
1072:
1067:
1063:
1042:
1039:
1036:
1033:
1030:
1019:
1005:
1002:
999:
996:
993:
990:
987:
984:
981:
977:
972:
966:
962:
958:
952:
947:
943:
922:
902:
899:
896:
876:
873:
870:
859:
845:
842:
839:
836:
833:
830:
827:
823:
818:
812:
808:
804:
798:
793:
789:
768:
765:
762:
759:
756:
737:
736:
724:
704:
684:
673:
672:
671:
658:
654:
650:
645:
641:
637:
631:
626:
622:
608:
607:
603:
602:
590:
566:
563:
560:
557:
554:
551:
548:
545:
542:
539:
536:
533:
530:
510:
490:
487:
484:
481:
478:
467:
466:
465:
452:
449:
446:
443:
440:
436:
432:
427:
424:
421:
418:
415:
412:
409:
405:
401:
395:
390:
386:
372:
371:
367:
366:
365:
364:
351:
348:
345:
342:
339:
336:
333:
329:
325:
320:
316:
312:
306:
301:
297:
283:
282:
262:
242:
220:
217:
214:
210:
204:
200:
196:
193:
190:
170:
167:
164:
161:
158:
155:
152:
140:
137:
56:Markov network
26:
9:
6:
4:
3:
2:
5856:
5845:
5842:
5840:
5837:
5836:
5834:
5819:
5816:
5814:
5811:
5810:
5807:
5801:
5798:
5796:
5793:
5791:
5788:
5786:
5783:
5781:
5778:
5776:
5773:
5771:
5768:
5766:
5763:
5761:
5758:
5756:
5753:
5751:
5748:
5746:
5743:
5741:
5738:
5736:
5733:
5731:
5728:
5726:
5723:
5721:
5718:
5717:
5715:
5711:
5703:
5700:
5698:
5695:
5694:
5693:
5690:
5688:
5685:
5683:
5680:
5678:
5675:
5673:
5672:Stopping time
5670:
5666:
5663:
5662:
5661:
5658:
5656:
5653:
5651:
5648:
5646:
5643:
5641:
5638:
5636:
5633:
5631:
5628:
5626:
5623:
5621:
5618:
5616:
5613:
5611:
5608:
5606:
5603:
5601:
5598:
5596:
5593:
5591:
5588:
5586:
5583:
5581:
5578:
5576:
5573:
5571:
5568:
5566:
5563:
5561:
5558:
5556:
5553:
5551:
5548:
5546:
5543:
5541:
5538:
5536:
5533:
5531:
5528:
5526:
5523:
5522:
5520:
5516:
5510:
5507:
5505:
5502:
5500:
5497:
5495:
5492:
5490:
5487:
5486:
5484:
5482:
5478:
5471:
5467:
5463:
5462:Hewitt–Savage
5459:
5455:
5451:
5447:
5446:Zero–one laws
5444:
5442:
5439:
5437:
5434:
5432:
5429:
5427:
5424:
5422:
5419:
5417:
5414:
5412:
5409:
5407:
5404:
5402:
5399:
5397:
5394:
5393:
5391:
5387:
5381:
5378:
5376:
5373:
5371:
5368:
5366:
5363:
5361:
5358:
5356:
5353:
5351:
5348:
5346:
5343:
5341:
5338:
5336:
5333:
5331:
5328:
5326:
5323:
5321:
5318:
5316:
5313:
5311:
5308:
5307:
5305:
5301:
5295:
5292:
5290:
5287:
5285:
5282:
5280:
5277:
5275:
5272:
5270:
5267:
5266:
5264:
5262:
5258:
5252:
5249:
5247:
5244:
5242:
5239:
5237:
5234:
5233:
5231:
5229:
5225:
5219:
5216:
5214:
5211:
5209:
5206:
5204:
5201:
5199:
5196:
5194:
5191:
5189:
5186:
5184:
5181:
5179:
5176:
5174:
5171:
5169:
5166:
5164:
5161:
5159:
5156:
5154:
5151:
5149:
5146:
5144:
5143:Black–Scholes
5141:
5139:
5136:
5134:
5131:
5129:
5126:
5125:
5123:
5121:
5117:
5111:
5108:
5106:
5103:
5101:
5098:
5096:
5093:
5091:
5088:
5086:
5083:
5082:
5080:
5078:
5074:
5068:
5065:
5063:
5060:
5056:
5053:
5051:
5048:
5047:
5046:
5045:Point process
5043:
5041:
5038:
5036:
5033:
5031:
5028:
5024:
5021:
5019:
5016:
5015:
5014:
5011:
5009:
5006:
5004:
5003:Gibbs measure
5001:
4999:
4996:
4994:
4991:
4990:
4988:
4984:
4978:
4975:
4973:
4970:
4968:
4965:
4963:
4960:
4958:
4955:
4951:
4948:
4946:
4943:
4941:
4938:
4936:
4933:
4932:
4931:
4928:
4926:
4923:
4921:
4918:
4916:
4913:
4911:
4908:
4907:
4905:
4901:
4895:
4892:
4890:
4887:
4885:
4882:
4880:
4877:
4875:
4872:
4870:
4867:
4865:
4862:
4860:
4857:
4855:
4852:
4848:
4845:
4843:
4840:
4839:
4838:
4835:
4833:
4830:
4828:
4825:
4823:
4820:
4818:
4815:
4813:
4810:
4808:
4805:
4803:
4800:
4798:
4795:
4793:
4792:ItĂ´ diffusion
4790:
4788:
4785:
4783:
4780:
4778:
4775:
4773:
4770:
4768:
4767:Gamma process
4765:
4763:
4760:
4758:
4755:
4753:
4750:
4748:
4745:
4743:
4740:
4738:
4735:
4733:
4730:
4728:
4725:
4723:
4720:
4716:
4713:
4711:
4708:
4706:
4703:
4701:
4698:
4696:
4693:
4692:
4691:
4688:
4684:
4681:
4680:
4679:
4676:
4674:
4671:
4669:
4666:
4665:
4663:
4661:
4657:
4649:
4646:
4644:
4641:
4639:
4638:Self-avoiding
4636:
4634:
4631:
4630:
4629:
4626:
4624:
4623:Moran process
4621:
4619:
4616:
4614:
4611:
4609:
4606:
4604:
4601:
4599:
4596:
4594:
4591:
4590:
4588:
4586:
4585:Discrete time
4582:
4578:
4571:
4566:
4564:
4559:
4557:
4552:
4551:
4548:
4536:
4531:
4527:
4520:
4512:
4508:
4504:
4497:
4489:
4485:
4480:
4475:
4471:
4467:
4463:
4459:
4455:
4451:
4447:
4443:
4439:
4432:
4424:
4418:
4414:
4407:
4391:
4387:
4381:
4370:
4369:
4364:
4357:
4348:
4344:
4340:
4336:
4332:
4325:
4317:
4313:
4309:
4303:
4299:
4295:
4290:
4285:
4281:
4277:
4276:
4271:
4267:
4260:
4252:
4246:
4243:. CRC Press.
4242:
4235:
4226:
4221:
4217:
4213:
4209:
4202:
4194:
4190:
4186:
4182:
4177:
4172:
4168:
4164:
4160:
4156:
4152:
4148:
4141:
4133:
4131:9780262013192
4127:
4123:
4116:
4108:
4102:
4098:
4091:
4083:
4081:9781848002791
4077:
4073:
4072:
4064:
4050:on 2017-08-10
4046:
4042:
4038:
4034:
4028:
4021:
4020:
4012:
4005:
4001:
3997:
3993:
3989:
3985:
3978:
3974:
3963:
3960:
3958:
3955:
3953:
3950:
3948:
3945:
3943:
3940:
3938:
3935:
3933:
3930:
3928:
3925:
3923:
3920:
3918:
3915:
3913:
3910:
3908:
3905:
3904:
3897:
3895:
3891:
3887:
3883:
3879:
3875:
3871:
3867:
3863:
3859:
3855:
3845:
3843:
3839:
3835:
3831:
3815:
3807:
3804:
3786:
3782:
3761:
3753:
3752:
3745:
3735:
3733:
3729:
3725:
3721:
3720:Chow–Liu tree
3717:
3713:
3709:
3705:
3688:
3685:
3681:
3677:
3674:
3670:
3667:
3642:
3638:
3634:
3631:
3628:
3623:
3619:
3612:
3608:
3605:
3579:
3575:
3571:
3568:
3565:
3560:
3556:
3549:
3545:
3542:
3533:
3529:
3505:
3502:
3499:
3493:
3490:
3487:
3474:
3471:
3466:
3463:
3453:
3450:
3435:
3434:
3433:
3410:
3392:
3387:
3384:
3381:
3371:
3367:
3360:
3357:
3350:
3349:
3348:
3346:
3343:(the inverse
3342:
3323:
3320:
3317:
3311:
3308:
3300:
3285:
3283:
3263:
3258:
3255:
3250:
3246:
3242:
3239:
3236:
3231:
3227:
3221:
3213:
3209:
3199:
3195:
3183:
3177:
3172:
3155:
3152:
3147:
3139:
3135:
3131:
3126:
3122:
3115:
3108:
3107:
3106:
3104:
3086:
3081:
3078:
3073:
3069:
3063:
3055:
3051:
3039:
3033:
3018:
3015:
3010:
3002:
2998:
2991:
2984:
2983:
2982:
2980:
2975:
2971:
2967:
2962:
2958:
2938:
2932:
2928:
2922:
2918:
2912:
2908:
2904:
2893:
2886:
2877:
2873:
2862:
2858:
2852:
2848:
2843:
2839:
2836:
2824:
2821:
2817:
2813:
2807:
2801:
2794:
2793:
2792:
2790:
2785:
2781:
2777:
2773:
2769:
2765:
2761:
2757:
2752:
2750:
2746:
2742:
2738:
2710:
2706:
2701:
2685:
2681:
2672:
2668:
2664:
2660:
2642:
2639:
2636:
2632:
2606:
2603:
2600:
2596:
2589:
2586:
2583:
2580:
2575:
2572:
2569:
2565:
2557:
2539:
2536:
2533:
2529:
2498:
2494:
2487:
2484:
2476:
2471:
2467:
2458:
2454:
2433:
2426:
2405:
2402:
2391:
2384:
2375:
2372:
2369:
2365:
2357:
2353:
2335:
2332:
2329:
2325:
2277:
2273:
2261:
2254:
2245:
2241:
2230:
2226:
2220:
2216:
2211:
2207:
2204:
2192:
2189:
2185:
2181:
2178:
2171:
2170:
2169:
2167:
2163:
2159:
2132:
2125:
2116:
2113:
2110:
2106:
2102:
2097:
2094:
2091:
2087:
2079:
2075:
2069:
2066:
2063:
2059:
2055:
2044:
2037:
2028:
2024:
2013:
2009:
2001:
2000:
1999:
1981:
1969:
1962:
1953:
1949:
1938:
1934:
1928:
1924:
1919:
1915:
1912:
1907:
1904:
1899:
1893:
1890:
1887:
1881:
1874:
1873:
1872:
1856:
1852:
1837:
1835:
1827:
1823:
1820:the graph is
1819:
1816:
1812:
1811:
1810:
1807:
1793:
1783:
1767:
1763:
1754:
1753:configuration
1750:
1729:
1725:
1718:
1715:
1707:
1689:
1685:
1676:
1672:
1668:
1650:
1646:
1625:
1602:
1596:
1593:
1573:
1553:
1525:
1521:
1512:
1508:
1499:
1493:
1490:
1487:
1484:
1480:
1476:
1470:
1467:
1464:
1458:
1451:
1450:
1449:
1435:
1426:
1410:
1406:
1397:
1381:
1361:
1341:
1321:
1298:
1295:
1292:
1286:
1266:
1246:
1238:
1219:
1216:
1213:
1207:
1185:
1182:
1179:
1169:
1165:
1158:
1155:
1146:
1144:
1114:
1111:
1108:
1102:
1099:
1095:
1084:
1080:
1076:
1070:
1065:
1061:
1040:
1037:
1034:
1031:
1028:
1020:
1000:
997:
991:
982:
979:
975:
964:
960:
956:
950:
945:
941:
920:
900:
897:
894:
874:
871:
868:
860:
840:
837:
834:
828:
825:
821:
810:
806:
802:
796:
791:
787:
766:
763:
760:
757:
754:
746:
745:
744:
741:
722:
702:
695:to a node in
682:
674:
656:
652:
648:
643:
639:
635:
629:
624:
620:
612:
611:
610:
609:
605:
604:
588:
580:
561:
555:
549:
546:
543:
537:
531:
508:
485:
479:
468:
447:
441:
434:
430:
422:
416:
410:
407:
403:
399:
393:
388:
384:
376:
375:
374:
373:
369:
368:
346:
343:
340:
334:
331:
327:
323:
318:
314:
310:
304:
299:
295:
287:
286:
285:
284:
280:
276:
275:
274:
260:
240:
218:
215:
212:
202:
198:
191:
188:
165:
162:
159:
153:
150:
136:
134:
130:
126:
122:
118:
117:Gibbs measure
114:
110:
106:
101:
99:
95:
90:
88:
84:
80:
76:
72:
68:
64:
63:
57:
53:
49:
45:
41:
32:
19:
5730:Econometrics
5692:Wiener space
5580:ItĂ´ integral
5481:Inequalities
5370:Self-similar
5340:Gauss–Markov
5330:Exchangeable
5310:CĂ dlĂ g paths
5246:Risk process
5198:LIBOR market
5067:Random graph
5062:Random field
5029:
4874:Superprocess
4812:LĂ©vy process
4807:Jump process
4782:Hunt process
4618:Markov chain
4525:
4519:
4502:
4496:
4448:(1): 41174.
4445:
4441:
4431:
4412:
4406:
4394:. Retrieved
4389:
4380:
4367:
4356:
4338:
4324:
4274:
4259:
4240:
4234:
4215:
4211:
4201:
4153:(1): 11–33.
4150:
4146:
4140:
4121:
4115:
4096:
4090:
4074:. Springer.
4070:
4063:
4052:. Retrieved
4045:the original
4018:
4011:
3987:
3983:
3977:
3947:Markov chain
3851:
3805:
3749:
3747:
3525:
3431:
3296:
3278:
3101:
2978:
2973:
2969:
2960:
2956:
2954:
2788:
2783:
2779:
2776:perturbation
2767:
2755:
2753:
2736:
2708:
2704:
2702:
2670:
2666:
2665:-th clique,
2662:
2658:
2555:
2456:
2452:
2355:
2292:
2161:
2156:is simply a
2155:
1997:
1843:
1834:factor graph
1831:
1808:
1784:
1674:
1670:
1666:
1545:
1427:
1395:
1147:
1140:
742:
738:
142:
108:
102:
91:
79:random field
65:is a set of
59:
55:
51:
47:
37:
5775:Ruin theory
5713:Disciplines
5585:ItĂ´'s lemma
5360:Predictable
5035:Percolation
5018:Potts model
5013:Ising model
4977:White noise
4935:Differences
4797:ItĂ´ process
4737:Cox process
4633:Loop-erased
4628:Random walk
4396:15 December
3937:Ising model
3708:#P-complete
3282:'Inference'
2745:determinant
2158:dot product
1354:. Because
1237:probability
233:indexed by
121:Ising model
60:undirected
44:probability
5833:Categories
5785:Statistics
5565:Filtration
5466:Kolmogorov
5450:Blumenthal
5375:Stationary
5315:Continuous
5303:Properties
5188:Hull–White
4930:Martingale
4817:Local time
4705:Fractional
4683:pure birth
4054:2012-04-09
3969:References
3714:and loopy
3432:such that
2964:gives the
2762:, such as
2352:indicators
1279:—that is,
139:Definition
5697:Classical
4710:Geometric
4700:Excursion
4530:CiteSeerX
4470:2045-2322
4347:MIT Press
4284:CiteSeerX
4193:121299906
3844:in 2001.
3783:φ
3671:∉
3632:…
3569:…
3522:Inference
3500:∉
3451:−
3447:Σ
3414:Σ
3407:μ
3393:∼
3385:∈
3206:∂
3192:∂
3169:∂
3048:∂
3031:∂
2909:∑
2868:⊤
2849:∑
2840:
2825:∈
2818:∑
2768:intuitive
2739:that the
2590:φ
2587:
2488:
2236:⊤
2217:∑
2208:
2193:∈
2186:∑
2103:⋅
2060:∑
2019:⊤
1944:⊤
1925:∑
1916:
1726:φ
1719:
1686:φ
1675:potential
1647:φ
1597:
1586:. Here,
1509:φ
1494:
1488:∈
1481:∏
1183:∈
1112:∪
1103:∖
1077:⊥
1071:⊥
1038:⊂
998:∪
983:∖
957:⊥
951:⊥
898:⊂
872:∈
829:∖
803:⊥
797:⊥
764:∈
649:∣
636:⊥
630:⊥
556:
550:∪
532:
480:
442:
431:∣
417:
411:∖
400:⊥
394:⊥
335:∖
324:∣
311:⊥
305:⊥
216:∈
103:When the
69:having a
5818:Category
5702:Abstract
5236:BĂĽhlmann
4842:Compound
4488:28145456
4365:(2013).
4333:(2006),
4316:11312524
3900:See also
3689:′
3678:′
3609:′
3546:′
3526:As in a
3293:Gaussian
3288:Examples
3284:below).
2624:, where
1259:in
5325:Ergodic
5213:VašĂÄŤek
5055:Poisson
4715:Meander
4479:5286517
4450:Bibcode
4272:(ed.),
4185:0432132
4155:Bibcode
4041:0620955
3992:Bibcode
3728:chordal
2764:entropy
2657:is the
2164:is the
1822:chordal
1398:of the
1235:be the
1143:cliques
577:is the
40:physics
5665:Tanaka
5350:Mixing
5345:Markov
5218:Wilkie
5183:Ho–Lee
5178:Heston
4950:Super-
4695:Bridge
4643:Biased
4532:
4486:
4476:
4468:
4419:
4392:. 2013
4314:
4304:
4286:
4247:
4191:
4183:
4128:
4103:
4078:
4039:
4029:
3864:, and
3803:clique
2293:Here,
1755:
1200:, let
521:, and
469:where
83:Markov
5518:Tools
5294:M/M/c
5289:M/M/1
5284:M/G/1
5274:Fluid
4940:Local
4372:(PDF)
4312:S2CID
4189:S2CID
4048:(PDF)
4023:(PDF)
2741:trace
1751:of a
1546:then
5470:LĂ©vy
5269:Bulk
5153:Chen
4945:Sub-
4903:Both
4484:PMID
4466:ISSN
4417:ISBN
4398:2014
4390:ICML
4302:ISBN
4245:ISBN
4126:ISBN
4101:ISBN
4076:ISBN
4027:ISBN
3892:and
3840:and
2737:e.g.
2709:i.e.
2669:the
2667:i.e.
2556:i.e.
2356:i.e.
887:and
131:and
46:, a
42:and
5050:Cox
4507:doi
4474:PMC
4458:doi
4294:doi
4220:doi
4171:hdl
4163:doi
4000:doi
3860:or
3732:MLE
3724:MAP
3480:iff
3347:):
2837:exp
2584:log
2485:dom
2418:if
2205:exp
1913:exp
1716:log
1669:or
1448:as
581:of
58:or
54:),
52:MRF
5835::
5468:,
5464:,
5460:,
5456:,
5452:,
4528:.
4482:.
4472:.
4464:.
4456:.
4444:.
4440:.
4388:.
4341:,
4310:,
4300:,
4292:,
4214:.
4210:.
4187:.
4181:MR
4179:.
4169:.
4161:.
4151:10
4149:.
4037:MR
4035:.
3998:,
3988:35
3986:,
3888:,
3884:,
3880:,
3836:,
3297:A
2981::
2751:.
2700:.
2168::
1806:.
1782:.
1708:,
1594:cl
1491:cl
1425:.
933:,
135:.
89:.
5472:)
5448:(
4569:e
4562:t
4555:v
4538:.
4513:.
4509::
4490:.
4460::
4452::
4446:7
4425:.
4400:.
4351:.
4319:.
4296::
4253:.
4228:.
4222::
4216:4
4195:.
4173::
4165::
4157::
4134:.
4109:.
4084:.
4057:.
4002::
3994::
3816:o
3806:k
3787:k
3762:o
3686:W
3682:,
3675:V
3668:u
3648:}
3643:j
3639:w
3635:,
3629:,
3624:1
3620:w
3616:{
3613:=
3606:W
3585:}
3580:i
3576:v
3572:,
3566:,
3561:1
3557:v
3553:{
3550:=
3543:V
3506:.
3503:E
3497:}
3494:v
3491:,
3488:u
3485:{
3475:0
3472:=
3467:v
3464:u
3460:)
3454:1
3443:(
3417:)
3411:,
3403:(
3398:N
3388:V
3382:v
3378:)
3372:v
3368:X
3364:(
3361:=
3358:X
3327:)
3324:E
3321:,
3318:V
3315:(
3312:=
3309:G
3264:.
3259:0
3256:=
3251:v
3247:J
3243:,
3240:0
3237:=
3232:u
3228:J
3222:|
3214:v
3210:J
3200:u
3196:J
3187:]
3184:J
3181:[
3178:Z
3173:2
3156:Z
3153:1
3148:=
3145:]
3140:v
3136:X
3132:,
3127:u
3123:X
3119:[
3116:C
3087:.
3082:0
3079:=
3074:v
3070:J
3064:|
3056:v
3052:J
3043:]
3040:J
3037:[
3034:Z
3019:Z
3016:1
3011:=
3008:]
3003:v
2999:X
2995:[
2992:E
2979:v
2974:v
2970:X
2961:v
2957:J
2939:)
2933:v
2929:x
2923:v
2919:J
2913:v
2905:+
2902:)
2897:}
2894:k
2891:{
2887:x
2883:(
2878:k
2874:f
2863:k
2859:w
2853:k
2844:(
2830:X
2822:x
2814:=
2811:]
2808:J
2805:[
2802:Z
2789:v
2784:v
2780:J
2756:Z
2721:X
2705:P
2686:k
2682:C
2671:i
2663:k
2659:i
2643:i
2640:,
2637:k
2633:c
2612:)
2607:i
2604:,
2601:k
2597:c
2593:(
2581:=
2576:i
2573:,
2570:k
2566:w
2540:i
2537:,
2534:k
2530:f
2508:|
2504:)
2499:k
2495:C
2491:(
2481:|
2477:=
2472:k
2468:N
2457:k
2453:i
2437:}
2434:k
2431:{
2427:x
2406:1
2403:=
2400:)
2395:}
2392:k
2389:{
2385:x
2381:(
2376:i
2373:,
2370:k
2366:f
2336:i
2333:,
2330:k
2326:f
2303:X
2278:.
2274:)
2270:)
2265:}
2262:k
2259:{
2255:x
2251:(
2246:k
2242:f
2231:k
2227:w
2221:k
2212:(
2198:X
2190:x
2182:=
2179:Z
2162:Z
2141:)
2136:}
2133:k
2130:{
2126:x
2122:(
2117:i
2114:,
2111:k
2107:f
2098:i
2095:,
2092:k
2088:w
2080:k
2076:N
2070:1
2067:=
2064:i
2056:=
2053:)
2048:}
2045:k
2042:{
2038:x
2034:(
2029:k
2025:f
2014:k
2010:w
1982:)
1978:)
1973:}
1970:k
1967:{
1963:x
1959:(
1954:k
1950:f
1939:k
1935:w
1929:k
1920:(
1908:Z
1905:1
1900:=
1897:)
1894:x
1891:=
1888:X
1885:(
1882:P
1857:k
1853:f
1828:)
1817:)
1794:V
1768:C
1764:x
1735:)
1730:C
1722:(
1690:C
1651:C
1626:G
1606:)
1603:G
1600:(
1574:G
1554:X
1531:)
1526:C
1522:x
1518:(
1513:C
1503:)
1500:G
1497:(
1485:C
1477:=
1474:)
1471:x
1468:=
1465:X
1462:(
1459:P
1436:G
1411:v
1407:X
1382:x
1362:X
1342:x
1322:X
1302:)
1299:x
1296:=
1293:X
1290:(
1287:P
1267:X
1247:x
1223:)
1220:x
1217:=
1214:X
1211:(
1208:P
1186:V
1180:v
1176:)
1170:v
1166:X
1162:(
1159:=
1156:X
1132:.
1118:)
1115:J
1109:I
1106:(
1100:V
1096:X
1091:|
1085:J
1081:X
1066:I
1062:X
1041:V
1035:J
1032:,
1029:I
1018:.
1004:)
1001:J
995:}
992:i
989:{
986:(
980:V
976:X
971:|
965:J
961:X
946:i
942:X
921:i
901:V
895:J
875:V
869:i
858:.
844:}
841:j
838:,
835:i
832:{
826:V
822:X
817:|
811:j
807:X
792:i
788:X
767:V
761:j
758:,
755:i
735:.
723:S
703:B
683:A
657:S
653:X
644:B
640:X
625:A
621:X
601:.
589:v
565:)
562:v
559:(
553:N
547:v
544:=
541:]
538:v
535:[
529:N
509:v
489:)
486:v
483:(
477:N
451:)
448:v
445:(
439:N
435:X
426:]
423:v
420:[
414:N
408:V
404:X
389:v
385:X
350:}
347:v
344:,
341:u
338:{
332:V
328:X
319:v
315:X
300:u
296:X
261:G
241:V
219:V
213:v
209:)
203:v
199:X
195:(
192:=
189:X
169:)
166:E
163:,
160:V
157:(
154:=
151:G
50:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
