From d4e89f24163aff9c04d2aa295bf74552c4bab21f Mon Sep 17 00:00:00 2001 From: Nicholas Clark Date: Tue, 16 Jan 2024 21:04:15 +1000 Subject: [PATCH] add seminar embed; update site --- NAMESPACE | 2 + R/families.R | 4 +- R/mvgam.R | 2 +- README.Rmd | 2 +- README.md | 44 +++--- docs/index.html | 10 ++ .../figures/README-unnamed-chunk-13-1.png | Bin 19035 -> 18509 bytes .../figures/README-unnamed-chunk-14-1.png | Bin 26964 -> 26572 bytes .../figures/README-unnamed-chunk-15-1.png | Bin 8032 -> 8067 bytes .../figures/README-unnamed-chunk-16-1.png | Bin 9890 -> 9906 bytes .../figures/README-unnamed-chunk-17-1.png | Bin 6994 -> 7048 bytes .../figures/README-unnamed-chunk-18-1.png | Bin 9323 -> 9275 bytes .../figures/README-unnamed-chunk-19-1.png | Bin 16408 -> 16466 bytes .../figures/README-unnamed-chunk-20-1.png | Bin 11389 -> 11301 bytes .../figures/README-unnamed-chunk-21-1.png | Bin 13715 -> 13470 bytes .../figures/README-unnamed-chunk-22-1.png | Bin 25162 -> 25169 bytes .../figures/README-unnamed-chunk-23-1.png | Bin 14506 -> 14716 bytes .../figures/README-unnamed-chunk-24-1.png | Bin 36973 -> 36522 bytes .../figures/README-unnamed-chunk-8-1.png | Bin 18799 -> 19035 bytes docs/reference/get_mvgam_priors.html | 16 +-- docs/reference/mvgam.html | 2 +- docs/reference/mvgam_families.html | 132 +++++++++++++++++- docs/reference/update.mvgam.html | 2 +- index.Rmd | 6 + index.md | 8 ++ man/figures/README-unnamed-chunk-13-1.png | Bin 19035 -> 18509 bytes man/figures/README-unnamed-chunk-14-1.png | Bin 26964 -> 26572 bytes man/figures/README-unnamed-chunk-15-1.png | Bin 8032 -> 8067 bytes man/figures/README-unnamed-chunk-16-1.png | Bin 9890 -> 9906 bytes man/figures/README-unnamed-chunk-17-1.png | Bin 6994 -> 7048 bytes man/figures/README-unnamed-chunk-18-1.png | Bin 9323 -> 9275 bytes man/figures/README-unnamed-chunk-19-1.png | Bin 16408 -> 16466 bytes man/figures/README-unnamed-chunk-20-1.png | Bin 11389 -> 11301 bytes man/figures/README-unnamed-chunk-21-1.png | Bin 13715 -> 13470 bytes man/figures/README-unnamed-chunk-22-1.png | Bin 25162 -> 25169 bytes man/figures/README-unnamed-chunk-23-1.png | Bin 14506 -> 14716 bytes man/figures/README-unnamed-chunk-24-1.png | Bin 36973 -> 36522 bytes man/figures/README-unnamed-chunk-8-1.png | Bin 18799 -> 19035 bytes man/get_mvgam_priors.Rd | 2 +- man/mvgam.Rd | 2 +- man/mvgam_families.Rd | 4 +- man/update.mvgam.Rd | 2 +- src/mvgam.dll | Bin 1084416 -> 1084416 bytes 43 files changed, 197 insertions(+), 43 deletions(-) diff --git a/NAMESPACE b/NAMESPACE index 8c08ea78..0959ab48 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -220,11 +220,13 @@ importFrom(stats,predict) importFrom(stats,printCoefmat) importFrom(stats,qbinom) importFrom(stats,qcauchy) +importFrom(stats,qlogis) importFrom(stats,qnorm) importFrom(stats,qqline) importFrom(stats,qqnorm) importFrom(stats,quantile) importFrom(stats,rbeta) +importFrom(stats,rbinom) importFrom(stats,reformulate) importFrom(stats,rgamma) importFrom(stats,rlnorm) diff --git a/R/families.R b/R/families.R index 7711267d..84f7424c 100644 --- a/R/families.R +++ b/R/families.R @@ -26,7 +26,7 @@ #' \item \code{nmix} for count data with imperfect detection modeled via a #' State-Space N-Mixture model. The latent states are Poisson (with log link), capturing the 'true' latent #' abundance, while the observation process is Binomial to account for imperfect detection. The -#' observation formula in these models is used to set up a linear predictor for the detection +#' observation \code{formula} in these models is used to set up a linear predictor for the detection #' probability (with logit link). See the example below for a more detailed worked explanation #' of the `nmix()` family #' } @@ -174,7 +174,7 @@ student_t = function(link = 'identity'){ #' det_plot <- plot(conditional_effects(mod, #' type = 'detection', #' effects = 'rainfall'), -#' plot = FALSE +#' plot = FALSE) #' det_plot[[1]] + #' ylab('Pr(detection)') #' diff --git a/R/mvgam.R b/R/mvgam.R index b6c9f0b3..baaafd2a 100644 --- a/R/mvgam.R +++ b/R/mvgam.R @@ -35,7 +35,7 @@ #'@param trend_knots As for `knots` above, this is an optional \code{list} of knot values for smooth #'functions within the `trend_formula` #'@param data A \code{dataframe} or \code{list} containing the model response variable and covariates -#'required by the GAM \code{formula}. Should include columns: +#'required by the GAM \code{formula} and optional \code{trend_formula}. Should include columns: #'`series` (a \code{factor} index of the series IDs;the number of levels should be identical #'to the number of unique series labels (i.e. `n_series = length(levels(data$series))`)) #'`time` (\code{numeric} or \code{integer} index of the time point for each observation). diff --git a/README.Rmd b/README.Rmd index df593d54..0ad75ffc 100644 --- a/README.Rmd +++ b/README.Rmd @@ -33,7 +33,7 @@ A series of [vignettes cover data formatting, forecasting and several extended c ## Installation Install from `GitHub` using: -`devtools::install_github("nicholasjclark/mvgam")`. Note that to condition models with MCMC sampling, either `JAGS` (along with packages `rjags` and `runjags`) or `Stan` must be installed (along with either `rstan` and/or `cmdstanr`). Please refer to installation links for `JAGS` [here](https://sourceforge.net/projects/mcmc-jags/files/){target="_blank"}, for `Stan` with `rstan` [here](https://mc-stan.org/users/interfaces/rstan){target="_blank"}, or for `Stan` with `cmdstandr` [here](https://mc-stan.org/cmdstanr/){target="_blank"}. You will need a fairly recent version of `Stan` to ensure all syntax is recognized. If you see warnings such as `variable "array" does not exist`, this is usually a sign that you need to update `Stan`. We highly recommend you use `Cmdstan` through the `cmdstanr` interface. This is because `Cmdstan` is easier to install, is more up to date with new features, and uses less memory than `Rstan`. See [this documentation from the `Cmdstan` team for more information](http://mc-stan.org/cmdstanr/articles/cmdstanr.html#comparison-with-rstan){target="_blank"}. +`devtools::install_github("nicholasjclark/mvgam")`. Note that to condition models on observed data, either `JAGS` (along with packages `rjags` and `runjags`) or `Stan` must be installed (along with either `rstan` and/or `cmdstanr`). Please refer to installation links for `JAGS` [here](https://sourceforge.net/projects/mcmc-jags/files/){target="_blank"}, for `Stan` with `rstan` [here](https://mc-stan.org/users/interfaces/rstan){target="_blank"}, or for `Stan` with `cmdstandr` [here](https://mc-stan.org/cmdstanr/){target="_blank"}. You will need a fairly recent version of `Stan` to ensure all syntax is recognized. If you see warnings such as `variable "array" does not exist`, this is usually a sign that you need to update `Stan`. We highly recommend you use `Cmdstan` through the `cmdstanr` interface. This is because `Cmdstan` is easier to install, is more up to date with new features, and uses less memory than `Rstan`. See [this documentation from the `Cmdstan` team for more information](http://mc-stan.org/cmdstanr/articles/cmdstanr.html#comparison-with-rstan){target="_blank"}. ## Citing mvgam and related software When using any software please make sure to appropriately acknowledge the hard work that developers and maintainers put into making these packages available. Citations are currently the best way to formally acknowledge this work, so we highly encourage you to cite any packages that you rely on for your research. diff --git a/README.md b/README.md index 19c7be45..b035b155 100644 --- a/README.md +++ b/README.md @@ -38,7 +38,7 @@ been compiled: Install from `GitHub` using: `devtools::install_github("nicholasjclark/mvgam")`. Note that to -condition models with MCMC sampling, either `JAGS` (along with packages +condition models on observed data, either `JAGS` (along with packages `rjags` and `runjags`) or `Stan` must be installed (along with either `rstan` and/or `cmdstanr`). Please refer to installation links for `JAGS` #> #> GAM coefficient (beta) estimates: -#> 2.5% 50% 97.5% Rhat n_eff -#> (Intercept) 6.10 6.600 7.000 1.00 355 -#> s(season).1 -0.59 0.046 0.710 1.00 1022 -#> s(season).2 -0.26 0.770 1.800 1.00 443 -#> s(season).3 -0.12 1.100 2.400 1.00 399 -#> s(season).4 -0.51 0.410 1.300 1.00 890 -#> s(season).5 -1.20 -0.130 0.950 1.01 503 -#> s(season).6 -1.00 -0.011 1.100 1.01 699 -#> s(season).7 -0.71 0.340 1.400 1.00 711 -#> s(season).8 -0.92 0.180 1.800 1.00 371 -#> s(season).9 -1.10 -0.290 0.710 1.00 476 -#> s(season).10 -1.30 -0.660 0.027 1.00 595 +#> 2.5% 50% 97.5% Rhat n_eff +#> (Intercept) 6.200 6.6000 7.000 1 1020 +#> s(season).1 -0.590 0.0500 0.700 1 1094 +#> s(season).2 -0.240 0.8100 1.800 1 417 +#> s(season).3 -0.057 1.2000 2.500 1 365 +#> s(season).4 -0.510 0.4200 1.400 1 951 +#> s(season).5 -1.200 -0.1400 1.000 1 538 +#> s(season).6 -1.100 0.0074 1.100 1 632 +#> s(season).7 -0.790 0.3800 1.400 1 847 +#> s(season).8 -1.000 0.2900 1.800 1 413 +#> s(season).9 -1.100 -0.2700 0.670 1 574 +#> s(season).10 -1.400 -0.6900 -0.025 1 641 #> #> Approximate significance of GAM observation smooths: -#> edf Chi.sq p-value -#> s(season) 5.08 17751 0.25 +#> edf Chi.sq p-value +#> s(season) 5 17851 0.28 #> #> Latent trend AR parameter estimates: #> 2.5% 50% 97.5% Rhat n_eff -#> ar1[1] 0.74 1.10 1.400 1 635 -#> ar2[1] -0.84 -0.40 0.062 1 1514 -#> ar3[1] -0.47 -0.13 0.290 1 540 -#> sigma[1] 0.40 0.50 0.640 1 1154 +#> ar1[1] 0.74 1.10 1.400 1 695 +#> ar2[1] -0.82 -0.41 0.045 1 1630 +#> ar3[1] -0.47 -0.12 0.280 1 453 +#> sigma[1] 0.40 0.50 0.630 1 1101 #> #> Stan MCMC diagnostics: #> n_eff / iter looks reasonable for all parameters @@ -348,7 +348,7 @@ summary(lynx_mvgam) #> 0 of 2000 iterations saturated the maximum tree depth of 12 (0%) #> E-FMI indicated no pathological behavior #> -#> Samples were drawn using NUTS(diag_e) at Mon Jan 15 8:57:57 AM 2024. +#> Samples were drawn using NUTS(diag_e) at Tue Jan 16 8:42:08 PM 2024. #> For each parameter, n_eff is a crude measure of effective sample size, #> and Rhat is the potential scale reduction factor on split MCMC chains #> (at convergence, Rhat = 1) @@ -470,7 +470,7 @@ plot(lynx_mvgam, type = 'forecast', newdata = lynx_test) #> Out of sample CRPS: - #> [1] 2892.767 + #> [1] 2856.97 And the estimated latent trend component, again using the more flexible `plot_mvgam_...()` option to show first derivatives of the estimated @@ -626,7 +626,7 @@ summary(mod, include_betas = FALSE) #> 0 of 2000 iterations saturated the maximum tree depth of 12 (0%) #> E-FMI indicated no pathological behavior #> -#> Samples were drawn using NUTS(diag_e) at Mon Jan 15 8:59:01 AM 2024. +#> Samples were drawn using NUTS(diag_e) at Tue Jan 16 8:44:20 PM 2024. #> For each parameter, n_eff is a crude measure of effective sample size, #> and Rhat is the potential scale reduction factor on split MCMC chains #> (at convergence, Rhat = 1) diff --git a/docs/index.html b/docs/index.html index f1389398..093662da 100644 --- a/docs/index.html +++ b/docs/index.html @@ -95,6 +95,16 @@

Installation. Note that to actually condition models with MCMC sampling, either the JAGS software must be installed (along with the R packages rjags and runjags) or the Stan software must be installed (along with either rstan and/or cmdstanr). Only rstan is listed as a dependency of mvgam to ensure that installation is less difficult. If users wish to fit the models using mvgam, please refer to installation links for JAGS here, for Stan with rstan here, or for Stan with cmdstandr here. You will need a fairly recent version of Stan to ensure all the model syntax is recognized. If you see warnings such as variable "array" does not exist, this is usually a sign that you need to update your version of Stan. We highly recommend you use Cmdstan through the cmdstanr interface as the backend. This is because Cmdstan is easier to install, is more up to date with new features, and uses less memory than Rstan. See this documentation from the Cmdstan team for more information.

+

Introductory seminar +

+
+
+ +
+
+
+

Cheatsheet

mvgam usage cheatsheet

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a/docs/reference/get_mvgam_priors.html b/docs/reference/get_mvgam_priors.html index f8addcc1..4b8da527 100644 --- a/docs/reference/get_mvgam_priors.html +++ b/docs/reference/get_mvgam_priors.html @@ -104,7 +104,7 @@

ArgumentsExamples#> 6 trend sd sigma ~ student_t(3, 0, 2.5); #> 7 inverse of NB dispsersion phi_inv ~ student_t(3, 0, 0.1); #> example_change new_lowerbound new_upperbound -#> 1 lambda ~ exponential(0.55); NA NA -#> 2 mu_raw ~ normal(-0.99, 0.59); NA NA -#> 3 sigma_raw ~ exponential(0.22); NA NA -#> 4 ar1 ~ normal(-0.34, 0.83); NA NA -#> 5 ar2 ~ normal(-0.34, 0.95); NA NA -#> 6 sigma ~ exponential(0.21); NA NA -#> 7 phi_inv ~ normal(0.51, 0.33); NA NA +#> 1 lambda ~ exponential(0.25); NA NA +#> 2 mu_raw ~ normal(0.96, 0.76); NA NA +#> 3 sigma_raw ~ exponential(0.17); NA NA +#> 4 ar1 ~ normal(0.58, 0.24); NA NA +#> 5 ar2 ~ normal(0.26, 0.69); NA NA +#> 6 sigma ~ exponential(0.26); NA NA +#> 7 phi_inv ~ normal(0.39, 0.35); NA NA # Make a few changes; first, change the population mean for the series-level # random intercepts diff --git a/docs/reference/mvgam.html b/docs/reference/mvgam.html index 1a510ca6..fa8b0a98 100644 --- a/docs/reference/mvgam.html +++ b/docs/reference/mvgam.html @@ -155,7 +155,7 @@

ArgumentsDetails

nmix for count data with imperfect detection modeled via a State-Space N-Mixture model. The latent states are Poisson (with log link), capturing the 'true' latent abundance, while the observation process is Binomial to account for imperfect detection. The -observation formula in these models is used to set up a linear predictor for the detection +observation formula in these models is used to set up a linear predictor for the detection probability (with logit link). See the example below for a more detailed worked explanation of the nmix() family

Only poisson(), nb(), and tweedie() are available if @@ -102,7 +102,135 @@

Author<

Examples

- +
if (FALSE) {
+# An N-mixture example using family nmix()
+# Simulate data from a Poisson-Binomial N-Mixture model
+# True abundance is predicted by a single nonlinear function of temperature
+# as well as a nonlinear long-term trend (as a Gaussian Process function)
+set.seed(123)
+gamdat <- gamSim(n = 80); N <- NROW(gamdat)
+abund_linpred <- gamdat$y; temperature <- gamdat$x2
+trend <- mvgam:::sim_gp(rnorm(3, 0, 0.1), alpha_gp = 3,
+                        rho_gp = 16, h = N)
+true_abund <- floor(10 + abund_linpred + trend)
+
+# Detection probability increases linearly with decreasing rainfall
+rainfall <- rnorm(N)
+detect_linpred <- 0.4 + -0.55 * rainfall
+detect_prob <- plogis(detect_linpred)
+
+# Simulate observed counts
+obs_abund <- rbinom(N, size = true_abund, prob = detect_prob)
+
+# Plot true and observed time series
+plot(true_abund,
+     type = 'l',
+     ylab = 'Abundance',
+     xlab = 'Time',
+     ylim = c(0, max(true_abund)),
+     bty = 'l',
+     lwd = 2)
+lines(obs_abund, col = 'darkred', lwd = 2)
+title(main = 'True = black; observed = red')
+
+# Gather data into a dataframe suitable for mvgam modelling;
+# This will require a 'cap' variable specifying the maximum K to marginalise
+# over when estimating latent abundance (it does NOT have to be a fixed value)
+model_dat <- data.frame(obs_abund,
+                        temperature,
+                        rainfall,
+                        cap = max(obs_abund) + 20,
+                        time = 1:N,
+                        series = as.factor('series1'))
+
+# Training and testing folds
+data_train <- model_dat %>% dplyr::filter(time <= 74)
+data_test <- model_dat %>% dplyr::filter(time > 74)
+
+# Fit a model with informative priors on the two intercept parameters
+# and on the length scale of the GP temporal trend parameter
+# Note that the 'trend_formula' applies to the latent count process
+# (a Poisson process with log-link), while the 'formula' applies to the
+# detection probability (logit link)
+mod <- mvgam(formula = obs_abund ~ rainfall,
+             trend_formula = ~ s(temperature, k = 5) +
+               gp(time, k = 10, c = 5/4, scale = FALSE),
+             family = nmix(),
+             data = data_train,
+             newdata = data_test,
+             priors = c(prior(std_normal(), class = '(Intercept)'),
+                        prior(normal(2, 2), class = '(Intercept)_trend'),
+                        prior(normal(15, 5), class = 'rho_gp_trend(time)')))
+
+# Model summary and diagnostics
+summary(mod)
+plot(mod, type = 'residuals')
+
+# Intercept parameters
+mcmc_plot(mod,
+          variable = "Intercept",
+          regex = TRUE,
+          type = 'hist')
+
+# Hindcasts and forecasts of latent abundance (with truth overlain)
+fc <- forecast(mod, type = 'latent_N')
+plot(fc); points(true_abund, pch = 16, cex = 0.8)
+
+# Latent abundance predictions are restricted based on 'cap'
+max(model_dat$cap); range(fc$forecasts[[1]])
+
+# Hindcasts and forecasts of detection probability (with truth overlain)
+fc <- forecast(mod, type = 'detection')
+plot(fc); points(detect_prob, pch = 16, cex = 0.8)
+
+# Hindcasts and forecasts of observations
+# (after accounting for detection error)
+fc <- forecast(mod, type = 'response')
+plot(fc)
+
+# Hindcasts and forecasts of response expectations
+# (with truth overlain)
+fc <- forecast(object = mod, type = 'expected')
+plot(fc); points(detect_prob * true_abund, pch = 16, cex = 0.8)
+
+# Plot conditional effects
+library(ggplot2)
+
+# Effects on true abundance can be visualised using type = 'link'
+abund_plots <- plot(conditional_effects(mod,
+                                        type = 'link',
+                                        effects = c('temperature', 'time')),
+                    plot = FALSE)
+
+# Effect of temperature on abundance
+abund_plots[[1]] +
+  ylab('Latent abundance')
+
+# Long-term trend in abundance
+abund_plots[[2]] +
+  ylab('Latent abundance')
+
+# Effect of rainfall on detection probability
+det_plot <- plot(conditional_effects(mod,
+                                     type = 'detection',
+                                     effects = 'rainfall'),
+                 plot = FALSE)
+det_plot[[1]] +
+  ylab('Pr(detection)')
+
+# More targeted plots can use marginaleffects capabilities;
+# Here visualise how response predictions might change
+# if we considered different possible 'cap' limits on latent
+# abundance and different rainfall measurements
+plot_predictions(mod, condition = list('temperature',
+                                       cap = c(15, 20, 40),
+                                       rainfall = c(-1, 1)),
+                type = 'response',
+                conf_level = 0.5) +
+ ylab('Observed abundance') +
+ theme_classic()
+}
+

diff --git a/docs/reference/update.mvgam.html b/docs/reference/update.mvgam.html index 5578c125..8048b58a 100644 --- a/docs/reference/update.mvgam.html +++ b/docs/reference/update.mvgam.html @@ -104,7 +104,7 @@

Arguments +
+ +
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b/man/get_mvgam_priors.Rd index 249f8962..26ccdd58 100644 --- a/man/get_mvgam_priors.Rd +++ b/man/get_mvgam_priors.Rd @@ -39,7 +39,7 @@ In \code{nmix()} family models, the \code{trend_formula} is used to set up a lin latent abundance} \item{data}{A \code{dataframe} or \code{list} containing the model response variable and covariates -required by the GAM \code{formula}. Should include columns: +required by the GAM \code{formula} and optional \code{trend_formula}. Should include columns: \code{series} (a \code{factor} index of the series IDs;the number of levels should be identical to the number of unique series labels (i.e. \code{n_series = length(levels(data$series))})) \code{time} (\code{numeric} or \code{integer} index of the time point for each observation). diff --git a/man/mvgam.Rd b/man/mvgam.Rd index 147fad36..3f1fe01e 100644 --- a/man/mvgam.Rd +++ b/man/mvgam.Rd @@ -71,7 +71,7 @@ unless they share a covariate} functions within the \code{trend_formula}} \item{data}{A \code{dataframe} or \code{list} containing the model response variable and covariates -required by the GAM \code{formula}. Should include columns: +required by the GAM \code{formula} and optional \code{trend_formula}. Should include columns: \code{series} (a \code{factor} index of the series IDs;the number of levels should be identical to the number of unique series labels (i.e. \code{n_series = length(levels(data$series))})) \code{time} (\code{numeric} or \code{integer} index of the time point for each observation). diff --git a/man/mvgam_families.Rd b/man/mvgam_families.Rd index fd2845c1..c29bc186 100644 --- a/man/mvgam_families.Rd +++ b/man/mvgam_families.Rd @@ -42,7 +42,7 @@ Finally, \code{mvgam} supports the three extended families described here: \item \code{nmix} for count data with imperfect detection modeled via a State-Space N-Mixture model. The latent states are Poisson (with log link), capturing the 'true' latent abundance, while the observation process is Binomial to account for imperfect detection. The -observation formula in these models is used to set up a linear predictor for the detection +observation \code{formula} in these models is used to set up a linear predictor for the detection probability (with logit link). See the example below for a more detailed worked explanation of the \code{nmix()} family } @@ -166,7 +166,7 @@ abund_plots[[2]] + det_plot <- plot(conditional_effects(mod, type = 'detection', effects = 'rainfall'), - plot = FALSE + plot = FALSE) det_plot[[1]] + ylab('Pr(detection)') diff --git a/man/update.mvgam.Rd b/man/update.mvgam.Rd index 67417c59..dfc7c7e6 100644 --- a/man/update.mvgam.Rd +++ b/man/update.mvgam.Rd @@ -39,7 +39,7 @@ In \code{nmix()} family models, the \code{trend_formula} is used to set up a lin latent abundance} \item{data}{A \code{dataframe} or \code{list} containing the model response variable and covariates -required by the GAM \code{formula}. Should include columns: +required by the GAM \code{formula} and optional \code{trend_formula}. Should include columns: \code{series} (a \code{factor} index of the series IDs;the number of levels should be identical to the number of unique series labels (i.e. \code{n_series = length(levels(data$series))})) \code{time} (\code{numeric} or \code{integer} index of the time point for each observation). diff --git a/src/mvgam.dll b/src/mvgam.dll index 2ead35c08c89f5647660db45e70f1bcf360d9c47..bf3f7381b0c54327601054a8c44ad676056f5a26 100644 GIT binary patch delta 81 zcmWm5yA4240EW?Uy`OgtB_rJ409un!{E0+EX95FA#4z6^I&u0l9d0_@wwQ4|_q8|I kWoLvZd|^Z&LJ^5rBq9}=$VDMaQHlD-HtpY^xU=u@0r90IM*si- delta 81 zcmZpe;nXn0X+j5c`=likyM38|2njacZoSRedYh^BHgoH3me$*>t+&})Z?m`F=4idm l*?OC+^)`3wZJyTKysfwST5t1jy)B?=2-3ct-ALePBmni5B$NOE