Description Details Author(s) See Also Examples
This package performs parametric and non-parametric estimation and simulation for multi-state discrete-time semi-Markov processes. For the parametric estimation, several discrete distributions are considered for the sojourn times: Uniform, Geometric, Poisson, Discrete Weibull and Negative Binomial. The non-parametric estimation concerns the sojourn time distributions, where no assumptions are done on the shape of distributions. Moreover, the estimation can be done on the basis of one or several sample paths, with or without censoring at the beginning or/and at the end of the sample paths. Estimation and simulation of discrete-time k-th order Markov chains are also considered.
This R package provides the following functions: estimSM, simulSM, LoglikelihoodSM, AIC_SM, BIC_SM, InitialLawSM, estimMk, simulMk, LoglikelihoodMK, AIC_Mk, BIC_Mk and InitialLawMk.
Vlad Stefan Barbu, barbu@univ-rouen.fr
Caroline Berard, caroline.berard@univ-rouen.fr
Dominique Cellier, dominique.cellier@laposte.net
Mathilde Sautreuil, mathilde.sautreuil@etu.univ-rouen.fr
Nicolas Vergne, nicolas.vergne@univ-rouen.fr
simulMk
estimMk
simulSM
estimSM
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 | ##--------------------------------------##
# An example for the simulMk function #
# see more examples >help(simulMk) #
##--------------------------------------##
### Example 1 ###
# Second order model with the finite state space {a,c,g,t}
E <- c("a","c","g","t")
S = length(E)
init.distribution <- c(1/6,1/6,5/12,3/12)
k<-2
p <- matrix(0.25, nrow = S^k, ncol = S)
# We simulate 3 sequences of size 1000, 10000 and 2000 respectively
simulMk(E = E, nbSeq = 3, lengthSeq = c(1000, 10000, 2000), Ptrans = p,
init = init.distribution, k = k)
##--------------------------------------##
# An example for the estimMk function #
# see more examples >help(estimMk) #
##--------------------------------------##
### Example 1 ###
# Second order model with the finite state space {a,c,g,t}
E <- c("a","c","g","t")
S = length(E)
init.distribution <- c(1/6,1/6,5/12,3/12)
k<-2
p <- matrix(0.25, nrow = S^k, ncol = S)
## simulation of 3 sequences with the simulMk function
seq3 = simulMk(E = E, nbSeq = 3, lengthSeq = c(1000, 10000, 2000), Ptrans = p,
init = init.distribution, k = 2)
## estimation of simulated sequences
res3 = estimMk(seq = seq3, E = E, k = 2)
##--------------------------------------##
# An example for the simulSM function #
# see more examples >help(simulSM) #
##--------------------------------------##
alphabet = c("a","c","g","t")
S = length(alphabet)
## creation of the initial distribution
vect.init = c(1/4,1/4,1/4,1/4)
# creation of the transition matrix
Pij = matrix(c(0,0.2,0.3,0.5,0.4,0,0.2,0.4,0.1,0.2,0,0.7,0.8,0.1,0.1,0),
nrow = S, ncol = S, byrow = TRUE)
################################
## Parametric simulation of a trajectory (of length equal to 50)
## where the sojourn times do not depend on the present state and on the next state
################################
## Simulation of a sequence of length 50
seq50 = simulSM(E = alphabet, NbSeq = 1, lengthSeq = 50, TypeSojournTime = "f",
init = vect.init, Ptrans = Pij, distr = "pois", param = 2)
##--------------------------------------##
# An example for the simulSM function #
# see more examples >help(simulSM) #
##--------------------------------------##
alphabet = c("a","c","g","t")
S = length(alphabet)
# creation of the transition matrix
Pij = matrix(c(0,0.2,0.3,0.5,0.4,0,0.2,0.4,0.1,0.2,0,0.7,0.8,0.1,0.1,0),
nrow = S, ncol = S, byrow = TRUE)
Pij
# [,1] [,2] [,3] [,4]
#[1,] 0.0 0.2 0.3 0.5
#[2,] 0.4 0.0 0.2 0.4
#[3,] 0.1 0.2 0.0 0.7
#[4,] 0.8 0.1 0.1 0.0
################################
## Parametric estimation of a trajectory (of length equal to 5000)
## where the sojourn times do not depend on the present state and on the next state
################################
## Simulation of a sequence of length 5000
seq5000 = simulSM(E = alphabet, NbSeq = 1, lengthSeq = 5000, TypeSojournTime = "f",
init = c(1/4,1/4,1/4,1/4), Ptrans = Pij, distr = "pois", param = 2)
## Estimation of the simulated sequence
estSeq5000 = estimSM(seq = seq5000, E = alphabet, TypeSojournTime = "f",
distr = "pois", cens.end = 0, cens.beg = 0)
|
Loading required package: seqinr
Loading required package: DiscreteWeibull
Loading required package: Rsolnp
[[1]]
[1] "c" "t" "t" "g" "g" "c" "g" "c" "t" "g" "a" "g" "t" "c" "a" "c" "t" "c"
[19] "a" "t" "t" "a" "g" "g" "a" "t" "t" "c" "a" "a" "g" "c" "c" "a" "a" "g"
[37] "a" "a" "g" "c" "a" "c" "g" "t" "a" "t" "c" "t" "c" "a" "t" "c" "g" "g"
[55] "g" "a" "c" "a" "c" "c" "t" "c" "t" "a" "t" "g" "a" "a" "g" "t" "a" "a"
[73] "g" "a" "a" "c" "t" "c" "t" "c" "c" "c" "c" "t" "g" "c" "t" "c" "c" "a"
[91] "t" "g" "a" "t" "a" "a" "t" "a" "a" "t" "t" "c" "a" "t" "t" "c" "c" "a"
[109] "c" "a" "c" "g" "g" "a" "g" "c" "c" "c" "a" "c" "t" "c" "g" "t" "a" "c"
[127] "t" "t" "a" "t" "t" "g" "t" "g" "c" "t" "c" "a" "c" "g" "g" "g" "t" "t"
[145] "a" "a" "c" "a" "a" "g" "t" "a" "g" "g" "g" "t" "t" "a" "g" "a" "g" "a"
[163] "g" "c" "a" "g" "a" "g" "t" "a" "a" "c" "a" "g" "t" "a" "a" "c" "t" "t"
[181] "g" "c" "a" "c" "c" "c" "t" "t" "g" "a" "a" "g" "g" "t" "t" "g" "g" "c"
[199] "a" "t" "g" "g" "a" "g" "c" "c" "a" "t" "a" "t" "g" "a" "t" "a" "t" "a"
[217] "c" "c" "c" "t" "g" "g" "c" "a" "a" "t" "t" "c" "c" "a" "c" "a" "c" "t"
[235] "a" "g" "t" "a" "g" "c" "t" "c" "a" "a" "g" "g" "a" "a" "c" "g" "t" "c"
[253] "a" "g" "g" "g" "t" "g" "t" "g" "a" "g" "c" "c" "t" "g" "a" "a" "a" "c"
[271] "t" "t" "a" "g" "c" "t" "g" "a" "g" "c" "g" "a" "g" "a" "g" "a" "c" "g"
[289] "a" "t" "g" "t" "a" "c" "a" "a" "g" "t" "g" "g" "g" "a" "a" "t" "c" "g"
[307] "a" "a" "t" "g" "g" "c" "a" "c" "t" "c" "g" "a" "c" "t" "g" "c" "a" "a"
[325] "c" "a" "a" "a" "c" "a" "c" "a" "c" "g" "a" "g" "t" "c" "c" "g" "g" "c"
[343] "c" "a" "g" "c" "g" "a" "c" "g" "g" "g" "a" "g" "c" "g" "t" "t" "t" "t"
[361] "t" "g" "c" "c" "g" "t" "t" "a" "g" "a" "g" "c" "c" "a" "c" "g" "t" "a"
[379] "c" "t" "c" "g" "a" "t" "c" "t" "c" "c" "g" "c" "a" "t" "a" "g" "t" "g"
[397] "a" "c" "g" "g" "g" "c" "a" "a" "t" "t" "a" "g" "c" "g" "t" "a" "t" "a"
[415] "a" "t" "c" "c" "c" "t" "a" "g" "a" "g" "t" "g" "a" "c" "a" "c" "t" "a"
[433] "g" "t" "a" "t" "c" "g" "t" "c" "t" "c" "c" "c" "c" "a" "g" "c" "c" "t"
[451] "g" "a" "c" "g" "a" "a" "a" "c" "c" "c" "c" "t" "g" "t" "c" "g" "a" "a"
[469] "c" "t" "c" "c" "t" "c" "t" "g" "g" "c" "a" "c" "a" "t" "c" "c" "c" "t"
[487] "g" "a" "c" "c" "g" "a" "a" "g" "c" "a" "t" "a" "g" "c" "c" "a" "c" "g"
[505] "t" "c" "c" "c" "g" "a" "a" "t" "a" "t" "c" "g" "c" "t" "c" "t" "c" "g"
[523] "a" "t" "a" "t" "c" "t" "t" "t" "t" "g" "a" "t" "g" "c" "c" "c" "t" "a"
[541] "c" "t" "t" "c" "a" "t" "a" "t" "c" "a" "a" "c" "g" "t" "t" "g" "g" "c"
[559] "t" "c" "a" "t" "g" "c" "c" "a" "a" "a" "c" "g" "c" "t" "t" "g" "g" "t"
[577] "c" "t" "g" "g" "g" "c" "t" "t" "c" "a" "c" "t" "c" "g" "g" "c" "c" "c"
[595] "c" "g" "c" "g" "c" "c" "t" "g" "a" "g" "g" "g" "g" "c" "g" "c" "t" "t"
[613] "a" "c" "c" "g" "c" "c" "c" "c" "t" "g" "t" "a" "t" "c" "c" "g" "a" "c"
[631] "g" "g" "c" "t" "g" "t" "t" "a" "t" "t" "g" "a" "t" "c" "g" "g" "g" "c"
[649] "t" "t" "g" "a" "c" "c" "c" "t" "a" "g" "c" "c" "a" "c" "g" "a" "a" "a"
[667] "g" "a" "t" "g" "a" "a" "t" "g" "c" "t" "g" "g" "t" "t" "a" "t" "a" "c"
[685] "c" "a" "t" "a" "g" "c" "t" "t" "t" "a" "c" "t" "g" "g" "c" "g" "c" "t"
[703] "a" "c" "a" "g" "g" "a" "c" "a" "c" "t" "g" "t" "t" "c" "t" "t" "t" "a"
[721] "a" "g" "g" "c" "t" "g" "t" "a" "a" "c" "t" "a" "a" "t" "t" "g" "a" "t"
[739] "t" "c" "a" "t" "a" "a" "a" "t" "a" "c" "a" "g" "a" "a" "a" "g" "t" "c"
[757] "c" "a" "a" "g" "t" "g" "g" "a" "g" "a" "c" "t" "a" "c" "g" "g" "a" "g"
[775] "g" "a" "g" "c" "g" "t" "g" "g" "g" "a" "a" "t" "c" "a" "g" "a" "a" "a"
[793] "g" "t" "t" "g" "a" "a" "c" "a" "t" "g" "c" "a" "g" "t" "a" "t" "g" "g"
[811] "a" "g" "a" "g" "c" "a" "a" "t" "a" "a" "t" "g" "c" "g" "a" "a" "c" "c"
[829] "g" "g" "c" "c" "a" "c" "t" "c" "a" "a" "g" "c" "a" "t" "c" "t" "a" "g"
[847] "a" "a" "t" "a" "t" "t" "a" "c" "g" "g" "a" "g" "g" "a" "g" "g" "a" "t"
[865] "a" "a" "g" "c" "a" "a" "g" "a" "t" "t" "c" "g" "g" "c" "c" "a" "a" "t"
[883] "t" "c" "c" "a" "t" "t" "a" "g" "g" "a" "t" "g" "g" "t" "c" "a" "c" "a"
[901] "t" "a" "c" "t" "c" "g" "t" "t" "g" "t" "t" "c" "c" "t" "g" "t" "c" "a"
[919] "t" "a" "c" "a" "g" "t" "g" "t" "a" "a" "c" "a" "t" "c" "a" "c" "a" "t"
[937] "c" "t" "t" "t" "a" "g" "c" "a" "g" "a" "g" "t" "g" "g" "a" "t" "a" "a"
[955] "c" "c" "a" "a" "t" "t" "g" "c" "g" "t" "t" "g" "g" "c" "a" "a" "c" "a"
[973] "g" "t" "a" "g" "c" "a" "c" "t" "a" "g" "t" "a" "g" "c" "t" "g" "t" "g"
[991] "t" "a" "c" "a" "c" "g" "g" "g" "t" "c"
[[2]]
[1] "g" "t" "c" "t" "c" "g" "c" "g" "c" "g" "a" "g" "g" "g" "t" "a" "c" "a"
[19] "c" "a" "a" "t" "g" "a" "t" "a" "g" "g" "c" "c" "t" "g" "t" "g" "a" "a"
[37] "t" "a" "g" "c" "t" "g" "t" "g" "g" "g" "a" "t" "c" "c" "t" "a" "t" "c"
[55] "g" "c" "g" "g" "g" "g" "g" "g" "c" "c" "c" "c" "a" "g" "t" "t" "g" "a"
[73] "c" "t" "t" "a" "a" "g" "c" "c" "c" "g" "t" "c" "a" "a" "c" "a" "t" "c"
[91] "t" "g" "t" "c" "a" "a" "c" "c" "t" "c" "g" "t" "t" "a" "a" "a" "a" "a"
[109] "c" "c" "t" "t" "g" "g" "c" "c" "a" "a" "a" "a" "a" "c" "g" "t" "t" "g"
[127] "t" "a" "t" "a" "g" "a" "t" "g" "a" "a" "g" "a" "c" "t" "t" "t" "a" "c"
[145] "c" "t" "c" "g" "a" "t" "c" "g" "g" "t" "t" "t" "a" "c" "a" "a" "a" "c"
[163] "t" "c" "a" "c" "a" "a" "g" "t" "a" "c" "c" "g" "a" "a" "a" "c" "g" "g"
[181] "c" "t" "g" "g" "g" "c" "c" "a" "c" "a" "c" "c" "g" "a" "a" "a" "a" "g"
[199] "a" "g" "c" "g" "g" "c" "g" "t" "g" "t" "a" "g" "t" "t" "a" "a" "c" "t"
[217] "c" "t" "t" "a" "a" "g" "a" "t" "c" "g" "t" "c" "a" "g" "g" "c" "g" "a"
[235] "c" "c" "g" "g" "c" "t" "g" "g" "g" "c" "g" "a" "a" "c" "a" "a" "g" "a"
[253] "g" "a" "g" "g" "a" "t" "t" "t" "a" "a" "c" "g" "a" "c" "c" "c" "g" "t"
[271] "g" "g" "g" "c" "t" "a" "t" "t" "g" "c" "c" "a" "g" "g" "a" "t" "a" "c"
[289] "t" "a" "c" "c" "a" "t" "a" "c" "t" "a" "a" "c" "c" "a" "a" "c" "t" "t"
[307] "c" "c" "c" "g" "g" "c" "g" "g" "g" "a" "c" "g" "t" "a" "t" "g" "a" "g"
[325] "a" "a" "a" "g" "t" "g" "t" "a" "g" "t" "t" "a" "a" "t" "a" "t" "t" "a"
[343] "c" "g" "a" "c" "g" "c" "g" "g" "a" "g" "g" "c" "c" "c" "c" "g" "t" "g"
[361] "t" "t" "c" "a" "t" "t" "c" "a" "t" "t" "a" "c" "a" "t" "c" "g" "c" "t"
[379] "c" "g" "g" "g" "c" "g" "g" "a" "a" "t" "t" "g" "a" "g" "g" "a" "g" "a"
[397] "c" "g" "c" "a" "t" "c" "g" "t" "t" "g" "c" "a" "t" "t" "c" "g" "c" "a"
[415] "g" "a" "c" "g" "g" "g" "a" "a" "a" "a" "g" "a" "t" "a" "c" "g" "g" "c"
[433] "g" "c" "t" "g" "t" "c" "a" "g" "g" "t" "g" "g" "a" "a" "c" "g" "a" "t"
[451] "t" "g" "a" "t" "a" "c" "g" "c" "c" "g" "g" "a" "c" "t" "a" "a" "g" "c"
[469] "t" "a" "a" "g" "g" "t" "a" "a" "c" "a" "g" "t" "g" "c" "c" "t" "a" "t"
[487] "c" "c" "a" "g" "c" "g" "c" "g" "c" "c" "t" "a" "c" "c" "g" "g" "a" "t"
[505] "g" "a" "c" "g" "a" "a" "g" "c" "a" "a" "g" "t" "c" "t" "c" "a" "c" "t"
[523] "c" "t" "c" "c" "a" "c" "g" "t" "t" "a" "c" "g" "g" "t" "t" "g" "t" "g"
[541] "g" "c" "c" "t" "c" "g" "c" "g" "a" "a" "t" "c" "g" "a" "c" "a" "g" "t"
[559] "g" "t" "t" "t" "a" "c" "c" "a" "g" "g" "c" "a" "g" "g" "c" "g" "c" "t"
[577] "a" "a" "c" "g" "c" "g" "c" "t" "c" "t" "c" "c" "t" "g" "t" "a" "c" "g"
[595] "c" "a" "g" "t" "c" "a" "c" "g" "c" "g" "t" "c" "a" "c" "c" "a" "c" "t"
[613] "c" "c" "a" "a" "c" "t" "c" "c" "g" "c" "a" "a" "c" "g" "c" "a" "t" "g"
[631] "a" "t" "c" "c" "g" "a" "c" "g" "c" "g" "t" "a" "g" "g" "g" "t" "t" "c"
[649] "c" "a" "t" "c" "g" "t" "a" "a" "t" "a" "t" "a" "c" "g" "a" "c" "a" "c"
[667] "t" "a" "c" "t" "c" "a" "a" "g" "a" "g" "a" "g" "c" "t" "g" "c" "t" "t"
[685] "g" "t" "g" "g" "a" "c" "c" "c" "t" "g" "t" "t" "a" "t" "c" "a" "t" "c"
[703] "t" "g" "t" "t" "c" "t" "g" "g" "g" "t" "t" "t" "a" "c" "g" "t" "t" "t"
[721] "g" "a" "t" "t" "g" "a" "a" "g" "c" "g" "c" "c" "a" "t" "a" "g" "a" "c"
[739] "t" "g" "c" "a" "t" "c" "c" "c" "g" "g" "g" "a" "c" "c" "a" "g" "g" "a"
[757] "c" "c" "a" "a" "c" "c" "t" "c" "c" "a" "g" "c" "t" "c" "g" "t" "c" "c"
[775] "c" "c" "t" "c" "t" "c" "a" "a" "g" "c" "g" "g" "t" "a" "t" "g" "a" "c"
[793] "g" "t" "g" "a" "a" "t" "g" "c" "t" "a" "g" "g" "c" "t" "t" "t" "t" "t"
[811] "g" "t" "a" "a" "g" "c" "g" "g" "g" "t" "g" "t" "g" "g" "g" "a" "a" "c"
[829] "t" "c" "a" "c" "c" "a" "c" "a" "a" "t" "a" "g" "a" "t" "g" "c" "t" "t"
[847] "g" "g" "t" "t" "t" "g" "g" "c" "g" "t" "g" "g" "g" "c" "t" "t" "a" "c"
[865] "t" "c" "c" "a" "a" "a" "c" "g" "c" "c" "a" "g" "c" "a" "c" "a" "t" "t"
[883] "a" "g" "t" "t" "a" "c" "g" "c" "a" "a" "c" "g" "a" "c" "c" "a" "t" "c"
[901] "c" "g" "c" "g" "t" "t" "c" "c" "c" "g" "c" "g" "c" "a" "a" "g" "t" "g"
[919] "g" "t" "t" "a" "g" "t" "g" "c" "c" "g" "g" "t" "g" "g" "g" "t" "a" "t"
[937] "a" "g" "t" "t" "a" "t" "a" "g" "g" "a" "a" "a" "a" "c" "t" "g" "t" "a"
[955] "t" "t" "t" "t" "c" "g" "a" "a" "a" "g" "a" "c" "c" "t" "g" "c" "t" "a"
[973] "c" "a" "c" "t" "g" "c" "a" "t" "g" "a" "t" "t" "c" "g" "g" "t" "a" "c"
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[1063] "t" "t" "a" "g" "g" "c" "g" "a" "a" "g" "g" "t" "g" "c" "t" "c" "c" "c"
[1081] "c" "g" "c" "c" "c" "g" "c" "t" "g" "c" "a" "a" "a" "c" "g" "a" "c" "c"
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[1117] "g" "g" "g" "g" "t" "g" "a" "c" "t" "t" "t" "t" "c" "t" "t" "t" "g" "g"
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[1225] "t" "c" "c" "g" "g" "c" "t" "t" "g" "t" "t" "t" "a" "c" "t" "c" "c" "a"
[1243] "a" "g" "a" "a" "g" "a" "c" "g" "t" "g" "g" "g" "g" "a" "c" "t" "t" "g"
[1261] "c" "c" "a" "g" "c" "t" "c" "g" "c" "c" "t" "g" "a" "a" "a" "g" "a" "t"
[1279] "g" "c" "t" "a" "g" "a" "c" "t" "a" "c" "c" "g" "t" "a" "c" "t" "c" "a"
[1297] "a" "g" "c" "t" "c" "a" "c" "c" "a" "g" "g" "c" "c" "c" "t" "g" "g" "a"
[1315] "t" "a" "c" "g" "c" "a" "g" "t" "c" "t" "g" "g" "g" "g" "c" "a" "a" "c"
[1333] "t" "c" "t" "a" "a" "g" "g" "a" "t" "t" "c" "a" "c" "a" "t" "c" "c" "a"
[1351] "t" "a" "g" "t" "t" "c" "c" "g" "c" "t" "g" "a" "a" "g" "g" "g" "a" "c"
[1369] "a" "c" "a" "g" "c" "c" "a" "t" "t" "c" "g" "c" "g" "g" "c" "a" "c" "a"
[1387] "g" "g" "c" "g" "c" "a" "c" "g" "g" "a" "c" "a" "t" "a" "t" "g" "g" "a"
[1405] "c" "t" "g" "c" "t" "c" "c" "t" "a" "g" "t" "t" "g" "g" "a" "a" "g" "c"
[1423] "a" "c" "c" "t" "a" "c" "a" "t" "t" "t" "a" "t" "a" "a" "g" "t" "a" "t"
[1441] "c" "c" "g" "a" "t" "c" "a" "a" "c" "t" "g" "c" "t" "a" "t" "g" "t" "c"
[1459] "t" "g" "c" "a" "a" "t" "c" "t" "c" "a" "c" "g" "t" "g" "c" "c" "c" "g"
[1477] "t" "t" "a" "g" "a" "g" "t" "t" "t" "c" "t" "c" "a" "t" "a" "a" "c" "t"
[1495] "c" "g" "c" "g" "t" "c" "g" "t" "g" "g" "a" "g" "c" "g" "t" "a" "a" "t"
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[1531] "c" "t" "t" "t" "a" "a" "g" "g" "a" "g" "g" "a" "g" "c" "t" "g" "g" "g"
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[1567] "t" "t" "t" "g" "t" "t" "a" "a" "t" "t" "g" "g" "c" "c" "t" "c" "c" "g"
[1585] "c" "c" "g" "g" "g" "t" "t" "a" "g" "g" "a" "c" "c" "a" "t" "c" "c" "c"
[1603] "t" "a" "g" "c" "c" "g" "t" "g" "a" "c" "t" "g" "a" "a" "c" "a" "a" "t"
[1621] "g" "t" "t" "c" "c" "c" "g" "g" "c" "c" "g" "g" "a" "c" "a" "t" "g" "c"
[1639] "c" "a" "a" "t" "c" "c" "t" "c" "g" "c" "g" "g" "g" "t" "a" "c" "a" "c"
[1657] "c" "g" "c" "c" "a" "t" "a" "g" "t" "g" "g" "c" "a" "c" "a" "g" "c" "a"
[1675] "t" "t" "c" "a" "a" "t" "t" "t" "t" "c" "g" "c" "c" "a" "a" "t" "a" "a"
[1693] "a" "a" "t" "c" "g" "t" "g" "t" "a" "c" "g" "t" "t" "g" "g" "g" "a" "g"
[1711] "a" "c" "c" "t" "g" "g" "g" "t" "a" "a" "g" "a" "t" "c" "g" "c" "a" "c"
[1729] "g" "g" "g" "t" "a" "g" "c" "c" "g" "c" "g" "t" "c" "c" "c" "c" "g" "t"
[1747] "g" "c" "c" "a" "t" "t" "t" "a" "c" "t" "t" "t" "g" "g" "c" "c" "a" "a"
[1765] "t" "t" "g" "a" "a" "a" "g" "g" "g" "c" "t" "g" "t" "g" "a" "c" "c" "a"
[1783] "g" "g" "t" "c" "a" "t" "a" "a" "c" "g" "g" "a" "t" "g" "t" "a" "a" "c"
[1801] "a" "t" "c" "c" "g" "t" "a" "t" "c" "c" "t" "t" "t" "g" "a" "t" "t" "t"
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[1837] "a" "a" "a" "t" "g" "a" "c" "g" "a" "t" "t" "g" "c" "a" "c" "a" "c" "a"
[1855] "a" "t" "g" "t" "t" "c" "g" "c" "a" "a" "c" "c" "g" "g" "g" "a" "c" "g"
[1873] "g" "c" "t" "t" "g" "g" "g" "c" "c" "c" "a" "g" "t" "c" "a" "a" "c" "c"
[1891] "t" "t" "c" "a" "g" "g" "g" "c" "a" "g" "g" "c" "a" "a" "t" "c" "t" "t"
[1909] "g" "c" "g" "g" "c" "t" "g" "g" "c" "c" "t" "g" "c" "c" "t" "t" "t" "c"
[1927] "g" "c" "g" "g" "t" "t" "g" "c" "g" "g" "g" "t" "t" "t" "c" "g" "g" "c"
[1945] "t" "a" "t" "g" "g" "t" "c" "c" "g" "t" "g" "g" "c" "g" "g" "a" "c" "c"
[1963] "c" "t" "t" "a" "t" "g" "g" "t" "g" "g" "t" "a" "a" "g" "t" "t" "a" "a"
[1981] "c" "t" "c" "c" "c" "t" "c" "c" "a" "t" "g" "g" "g" "c" "g" "a" "a" "t"
[1999] "g" "a" "t" "t" "a" "t" "g" "t" "g" "g" "t" "g" "g" "t" "t" "c" "t" "t"
[2017] "c" "c" "a" "c" "t" "t" "t" "t" "c" "t" "c" "a" "c" "a" "a" "g" "g" "c"
[2035] "c" "t" "a" "t" "t" "g" "t" "c" "c" "t" "a" "t" "g" "g" "c" "t" "t" "g"
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[2071] "a" "t" "g" "a" "t" "a" "c" "g" "a" "a" "g" "t" "a" "a" "t" "g" "g" "t"
[2089] "t" "t" "c" "t" "c" "a" "a" "g" "a" "c" "t" "c" "a" "c" "a" "a" "a" "t"
[2107] "g" "c" "g" "a" "t" "c" "t" "a" "c" "t" "c" "t" "t" "a" "a" "t" "a" "a"
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[2143] "t" "a" "t" "a" "c" "c" "g" "g" "a" "a" "t" "g" "t" "g" "t" "c" "g" "t"
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[649] "t" "t" "a" "t" "c" "c" "a" "g" "c" "g" "a" "c" "g" "g" "t" "c" "c" "t"
[667] "c" "a" "a" "g" "t" "a" "g" "t" "g" "g" "t" "a" "g" "g" "t" "c" "a" "c"
[685] "a" "t" "g" "t" "a" "a" "g" "t" "c" "a" "a" "g" "a" "g" "a" "t" "a" "t"
[703] "g" "g" "c" "g" "a" "g" "g" "a" "c" "g" "t" "c" "g" "g" "a" "g" "a" "t"
[721] "c" "c" "c" "t" "g" "g" "t" "c" "t" "a" "g" "t" "g" "t" "t" "c" "a" "a"
[739] "c" "a" "a" "t" "c" "t" "t" "t" "t" "g" "t" "g" "g" "a" "c" "c" "a" "g"
[757] "g" "g" "a" "c" "a" "t" "t" "g" "t" "c" "g" "c" "a" "a" "a" "c" "t" "a"
[775] "c" "a" "t" "g" "a" "a" "g" "t" "a" "t" "g" "a" "c" "a" "g" "g" "c" "c"
[793] "t" "a" "g" "t" "t" "g" "c" "c" "t" "t" "g" "t" "g" "t" "c" "c" "g" "t"
[811] "a" "g" "t" "a" "c" "c" "c" "t" "t" "t" "t" "a" "a" "a" "g" "g" "t" "a"
[829] "a" "t" "g" "c" "t" "t" "t" "g" "g" "a" "g" "c" "g" "c" "c" "t" "c" "t"
[847] "c" "c" "c" "t" "g" "t" "c" "c" "a" "a" "t" "t" "t" "t" "a" "c" "t" "a"
[865] "g" "t" "c" "t" "t" "t" "c" "g" "g" "c" "g" "a" "t" "c" "g" "a" "t" "g"
[883] "t" "c" "a" "g" "t" "a" "c" "c" "t" "t" "a" "a" "c" "t" "c" "g" "t" "g"
[901] "t" "g" "c" "t" "c" "g" "c" "c" "t" "t" "t" "t" "c" "g" "a" "t" "t" "a"
[919] "t" "a" "a" "c" "c" "c" "t" "a" "g" "c" "g" "t" "g" "t" "t" "g" "t" "t"
[937] "c" "c" "g" "g" "t" "a" "c" "a" "g" "c" "t" "g" "a" "c" "a" "c" "c" "a"
[955] "c" "g" "g" "c" "a" "c" "c" "t" "c" "a" "c" "t" "c" "a" "g" "t" "g" "c"
[973] "c" "g" "c" "t" "c" "a" "c" "g" "c" "g" "a" "a" "c" "g" "a" "a" "a" "t"
[991] "a" "t" "t" "t" "a" "g" "t" "t" "c" "t" "g" "t" "t" "g" "c" "g" "g" "g"
[1009] "a" "g" "t" "c" "g" "t" "g" "c" "g" "c" "a" "t" "c" "c" "g" "g" "t" "t"
[1027] "c" "a" "g" "t" "a" "t" "g" "t" "c" "g" "g" "t" "g" "a" "a" "c" "a" "g"
[1045] "t" "c" "t" "c" "g" "a" "c" "t" "t" "c" "g" "t" "t" "g" "g" "t" "a" "t"
[1063] "t" "a" "c" "g" "a" "a" "t" "g" "a" "g" "a" "t" "t" "g" "c" "c" "t" "c"
[1081] "a" "t" "c" "g" "a" "t" "c" "c" "c" "t" "t" "c" "c" "g" "c" "t" "g" "a"
[1099] "t" "c" "a" "a" "g" "g" "g" "a" "a" "c" "t" "c" "t" "a" "t" "a" "c" "a"
[1117] "a" "g" "a" "g" "a" "t" "g" "a" "t" "a" "g" "g" "a" "t" "t" "g" "t" "a"
[1135] "g" "g" "c" "g" "a" "g" "a" "a" "c" "c" "g" "a" "g" "c" "a" "a" "c" "t"
[1153] "t" "t" "c" "g" "g" "t" "c" "t" "c" "g" "c" "c" "g" "g" "a" "g" "c" "c"
[1171] "t" "a" "a" "c" "c" "a" "t" "t" "a" "t" "t" "t" "g" "c" "a" "a" "a" "c"
[1189] "g" "t" "a" "c" "t" "g" "c" "a" "t" "a" "a" "g" "c" "a" "g" "t" "a" "g"
[1207] "a" "t" "t" "c" "g" "a" "a" "t" "g" "g" "c" "a" "a" "c" "t" "g" "c" "c"
[1225] "a" "g" "a" "t" "c" "t" "t" "t" "t" "t" "a" "c" "t" "a" "a" "c" "c" "g"
[1243] "a" "a" "a" "g" "g" "c" "g" "a" "c" "t" "c" "c" "a" "c" "t" "c" "t" "t"
[1261] "a" "t" "a" "t" "g" "a" "a" "a" "g" "g" "c" "c" "t" "t" "g" "a" "t" "t"
[1279] "g" "t" "c" "a" "c" "c" "c" "a" "c" "t" "a" "a" "g" "c" "g" "c" "g" "c"
[1297] "a" "g" "a" "g" "a" "c" "t" "g" "t" "t" "c" "a" "g" "c" "a" "t" "a" "t"
[1315] "a" "t" "g" "c" "t" "g" "c" "g" "g" "c" "g" "c" "t" "g" "a" "t" "g" "a"
[1333] "t" "a" "a" "g" "g" "g" "g" "a" "c" "a" "c" "t" "g" "a" "c" "c" "a" "g"
[1351] "a" "g" "a" "c" "g" "c" "g" "c" "c" "c" "a" "c" "a" "t" "c" "a" "g" "g"
[1369] "c" "c" "a" "a" "c" "c" "t" "a" "c" "a" "g" "a" "t" "c" "g" "t" "t" "a"
[1387] "a" "a" "c" "g" "a" "a" "c" "c" "c" "a" "t" "a" "g" "c" "a" "c" "g" "a"
[1405] "c" "a" "c" "c" "a" "c" "t" "c" "t" "g" "c" "c" "t" "t" "c" "t" "t" "a"
[1423] "t" "a" "t" "t" "c" "g" "c" "t" "t" "t" "c" "g" "c" "c" "t" "c" "a" "c"
[1441] "t" "t" "t" "t" "g" "c" "a" "g" "a" "t" "g" "g" "g" "t" "g" "g" "t" "a"
[1459] "a" "g" "a" "a" "g" "a" "t" "t" "a" "c" "a" "a" "g" "a" "c" "a" "t" "c"
[1477] "g" "t" "g" "a" "g" "t" "c" "a" "g" "a" "c" "t" "t" "g" "t" "t" "a" "t"
[1495] "a" "g" "c" "t" "g" "t" "t" "c" "g" "a" "g" "g" "t" "g" "a" "t" "g" "t"
[1513] "t" "g" "t" "t" "g" "c" "a" "c" "t" "g" "g" "a" "a" "a" "c" "c" "a" "a"
[1531] "a" "t" "t" "t" "t" "c" "a" "c" "t" "a" "t" "c" "c" "c" "c" "g" "g" "c"
[1549] "g" "a" "g" "a" "c" "t" "g" "a" "g" "t" "t" "g" "a" "g" "g" "g" "g" "a"
[1567] "t" "t" "c" "g" "t" "g" "t" "c" "t" "t" "a" "t" "a" "t" "t" "a" "a" "g"
[1585] "c" "a" "g" "t" "a" "g" "c" "c" "t" "t" "c" "a" "t" "g" "g" "g" "c" "a"
[1603] "a" "g" "c" "t" "g" "a" "g" "t" "a" "a" "c" "a" "t" "t" "a" "t" "c" "c"
[1621] "a" "a" "a" "g" "c" "a" "c" "t" "g" "c" "g" "a" "g" "a" "g" "t" "g" "c"
[1639] "g" "g" "t" "c" "a" "t" "t" "t" "a" "g" "t" "t" "c" "t" "g" "t" "t" "c"
[1657] "c" "g" "t" "a" "g" "a" "g" "g" "g" "t" "c" "a" "g" "t" "g" "c" "g" "c"
[1675] "t" "g" "g" "g" "t" "c" "t" "t" "a" "g" "c" "t" "t" "a" "a" "t" "g" "t"
[1693] "a" "g" "g" "a" "g" "a" "a" "c" "c" "t" "t" "a" "g" "t" "a" "t" "c" "g"
[1711] "t" "g" "g" "t" "t" "t" "g" "c" "t" "c" "a" "t" "t" "g" "g" "a" "t" "g"
[1729] "c" "g" "g" "t" "g" "t" "g" "c" "t" "a" "g" "g" "t" "a" "t" "g" "g" "g"
[1747] "c" "t" "c" "c" "g" "c" "t" "a" "t" "g" "t" "t" "c" "g" "t" "c" "c" "t"
[1765] "c" "g" "t" "a" "t" "a" "a" "c" "t" "a" "t" "c" "c" "a" "g" "c" "a" "c"
[1783] "g" "t" "g" "a" "a" "t" "c" "a" "a" "g" "g" "a" "g" "g" "t" "t" "t" "t"
[1801] "t" "g" "t" "c" "c" "c" "g" "c" "a" "a" "t" "t" "t" "a" "a" "a" "g" "t"
[1819] "c" "a" "c" "t" "g" "a" "g" "t" "a" "c" "c" "a" "g" "t" "t" "t" "c" "t"
[1837] "a" "c" "c" "g" "a" "a" "a" "t" "c" "t" "c" "t" "g" "c" "a" "a" "g" "c"
[1855] "c" "a" "a" "g" "g" "a" "g" "a" "a" "a" "a" "a" "g" "g" "a" "a" "g" "g"
[1873] "a" "a" "c" "a" "c" "c" "a" "a" "g" "g" "t" "t" "g" "c" "c" "t" "c" "g"
[1891] "a" "c" "c" "g" "t" "c" "g" "c" "g" "c" "a" "c" "t" "t" "t" "c" "a" "g"
[1909] "t" "a" "t" "g" "c" "g" "a" "a" "a" "g" "c" "t" "t" "c" "a" "t" "g" "t"
[1927] "c" "a" "a" "a" "c" "c" "t" "a" "a" "c" "c" "t" "t" "t" "c" "a" "a" "c"
[1945] "a" "a" "c" "c" "g" "g" "t" "t" "c" "a" "t" "a" "g" "g" "a" "g" "c" "a"
[1963] "c" "c" "t" "c" "t" "t" "g" "c" "g" "c" "a" "t" "c" "a" "t" "c" "a" "a"
[1981] "c" "c" "t" "g" "c" "a" "c" "g" "a" "t" "t" "t" "a" "a" "g" "t" "c" "t"
[1999] "g" "t" "t" "t" "a" "t" "g" "t" "g" "g" "t" "g" "g" "t" "t" "c" "t" "t"
[2017] "c" "c" "a" "c" "t" "t" "t" "t" "c" "t" "c" "a" "c" "a" "a" "g" "g" "c"
[2035] "c" "t" "a" "t" "t" "g" "t" "c" "c" "t" "a" "t" "g" "g" "c" "t" "t" "g"
[2053] "c" "a" "a" "a" "a" "c" "a" "a" "c" "c" "c" "t" "c" "t" "a" "t" "g" "g"
[2071] "a" "t" "g" "a" "t" "a" "c" "g" "a" "a" "g" "t" "a" "a" "t" "g" "g" "t"
[2089] "t" "t" "c" "t" "c" "a" "a" "g" "a" "c" "t" "c" "a" "c" "a" "a" "a" "t"
[2107] "g" "c" "g" "a" "t" "c" "t" "a" "c" "t" "c" "t" "t" "a" "a" "t" "a" "a"
[2125] "a" "a" "a" "t" "g" "g" "t" "t" "g" "c" "t" "a" "g" "t" "g" "t" "a" "t"
[2143] "t" "a" "t" "a" "c" "c" "g" "g" "a" "a" "t" "g" "t" "g" "t" "c" "g" "t"
[2161] "a" "g" "c" "a" "t" "c" "c" "a" "g" "c" "a" "g" "c" "c" "g" "a" "c" "t"
[2179] "a" "a" "t" "g" "g" "a" "c" "g" "c" "g" "c" "t" "t" "a" "t" "a" "a" "a"
[2197] "a" "a" "c" "t" "c" "a" "g" "a" "a" "t" "t" "g" "a" "g" "c" "t" "a" "a"
[2215] "g" "a" "g" "a" "t" "c" "t" "g" "g" "t" "a" "t" "c" "a" "g" "c" "g" "t"
[2233] "c" "t" "g" "t" "t" "c" "t" "t" "g" "a" "g" "t" "t" "g" "t" "g" "a" "g"
[2251] "c" "g" "t" "g" "c" "g" "c" "t" "a" "t" "a" "t" "c" "g" "t" "t" "g" "a"
[2269] "a" "c" "t" "g" "t" "g" "a" "c" "g" "t" "t" "g" "a" "a" "a" "t" "t" "a"
[2287] "c" "g" "t" "c" "t" "a" "c" "t" "t" "a" "g" "c" "g" "g" "g" "c" "g" "g"
[2305] "t" "g" "a" "c" "g" "c" "g" "g" "c" "c" "a" "a" "a" "g" "c" "t" "g" "c"
[2323] "a" "a" "t" "c" "t" "g" "a" "g" "c" "t" "c" "c" "c" "c" "t" "c" "a" "c"
[2341] "c" "g" "a" "g" "t" "t" "g" "a" "t" "c" "c" "a" "c" "c" "t" "t" "c" "a"
[2359] "t" "t" "t" "c" "c" "c" "t" "t" "t" "t" "c" "c" "a" "c" "a" "c" "t" "a"
[2377] "t" "t" "c" "t" "t" "t" "a" "t" "a" "t" "t" "a" "c" "a" "g" "a" "a" "c"
[2395] "g" "g" "t" "a" "c" "c" "c" "g" "g" "c" "a" "t" "a" "t" "c" "t" "a" "g"
[2413] "c" "g" "c" "c" "a" "g" "t" "a" "a" "g" "g" "c" "a" "g" "c" "c" "c" "c"
[2431] "t" "g" "a" "c" "t" "c" "t" "a" "a" "t" "a" "t" "t" "g" "t" "a" "c" "t"
[2449] "a" "c" "g" "g" "g" "c" "c" "a" "a" "g" "t" "c" "g" "a" "c" "g" "a" "a"
[2467] "g" "g" "t" "t" "t" "g" "g" "c" "t" "a" "t" "c" "c" "a" "c" "t" "t" "g"
[2485] "g" "c" "t" "t" "a" "g" "g" "t" "t" "a" "a" "a" "a" "g" "c" "g" "c" "c"
[2503] "a" "a" "c" "t" "a" "c" "a" "t" "c" "g" "a" "t" "c" "t" "c" "g" "g" "a"
[2521] "t" "a" "g" "a" "c" "t" "a" "t" "t" "g" "a" "a" "a" "a" "c" "c" "a" "c"
[2539] "c" "g" "t" "a" "g" "a" "t" "c" "t" "c" "c" "c" "c" "t" "g" "c" "c" "t"
[2557] "c" "t" "t" "g" "a" "a" "a" "c" "g" "g" "a" "g" "g" "t" "t" "a" "g" "g"
[2575] "t" "a" "c" "g" "a" "g" "t" "c" "g" "t" "g" "a" "a" "t" "g" "a" "g" "t"
[2593] "t" "c" "a" "g" "a" "c" "a" "c" "g" "c" "g" "a" "g" "g" "g" "t" "g" "t"
[2611] "t" "t" "g" "g" "g" "a" "g" "c" "t" "a" "c" "t" "g" "t" "c" "a" "g" "g"
[2629] "c" "t" "a" "g" "g" "t" "c" "g" "g" "t" "a" "a" "c" "t" "g" "c" "g" "g"
[2647] "c" "t" "g" "g" "g" "t" "g" "g" "a" "a" "g" "c" "c" "t" "g" "c" "a" "a"
[2665] "g" "c" "c" "a" "g" "g" "t" "t" "g" "a" "a" "t" "c" "c" "a" "g" "a" "c"
[2683] "g" "c" "a" "a" "a" "c" "t" "c" "g" "g" "t" "g" "g" "g" "c" "t" "t" "t"
[2701] "t" "c" "c" "g" "c" "c" "t" "g" "a" "c" "c" "c" "a" "t" "c" "t" "g" "a"
[2719] "c" "c" "a" "c" "a" "t" "c" "t" "c" "c" "c" "g" "t" "a" "a" "t" "t" "g"
[2737] "a" "g" "a" "a" "c" "g" "g" "c" "g" "t" "t" "a" "g" "t" "t" "a" "g" "g"
[2755] "a" "c" "t" "a" "a" "a" "c" "a" "g" "a" "a" "t" "t" "c" "a" "t" "g" "g"
[2773] "a" "a" "a" "g" "c" "t" "c" "a" "c" "c" "t" "g" "a" "t" "a" "c" "g" "g"
[2791] "g" "a" "t" "c" "a" "t" "c" "a" "g" "t" "g" "t" "g" "g" "t" "t" "a" "a"
[2809] "t" "t" "a" "g" "a" "a" "c" "a" "g" "g" "a" "g" "a" "a" "c" "a" "c" "a"
[2827] "g" "g" "g" "a" "t" "c" "a" "t" "c" "g" "a" "a" "c" "c" "c" "g" "c" "t"
[2845] "c" "a" "g" "a" "c" "g" "g" "g" "t" "g" "g" "a" "c" "t" "a" "t" "c" "t"
[2863] "t" "c" "a" "t" "g" "t" "a" "a" "a" "g" "g" "t" "g" "g" "g" "g" "g" "g"
[2881] "t" "c" "a" "g" "a" "t" "t" "a" "g" "c" "c" "c" "t" "c" "t" "t" "a" "t"
[2899] "a" "a" "c" "a" "g" "g" "t" "t" "g" "c" "g" "a" "a" "g" "c" "g" "a" "g"
[2917] "c" "t" "t" "a" "g" "a" "c" "t" "g" "a" "g" "a" "t" "a" "t" "c" "c" "c"
[2935] "g" "a" "t" "g" "c" "g" "c" "a" "t" "t" "g" "g" "c" "c" "c" "g" "t" "c"
[2953] "g" "c" "a" "a" "g" "a" "g" "t" "a" "g" "c" "c" "t" "a" "c" "t" "g" "g"
[2971] "g" "t" "c" "t" "c" "t" "c" "g" "t" "t" "t" "a" "c" "a" "c" "g" "g" "a"
[2989] "t" "c" "t" "t" "c" "a" "t" "t" "g" "a" "g" "t" "t" "a" "a" "t" "t" "t"
[3007] "g" "a" "t" "c" "t" "c" "t" "a" "c" "g" "a" "t" "g" "g" "a" "a" "c" "t"
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