diff --git a/book/algorithms/TemperedSMC.md b/book/algorithms/TemperedSMC.md
index d769f09b..474862cd 100644
--- a/book/algorithms/TemperedSMC.md
+++ b/book/algorithms/TemperedSMC.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.15.2
+    jupytext_version: 1.16.2
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
@@ -158,7 +158,7 @@ We now use a NUTS kernel.
 ```{code-cell} ipython3
 %%time
 
-nuts_parameters = dict(step_size=1e-4, inverse_mass_matrix=inv_mass_matrix)
+nuts_parameters = dict(step_size=1e-4, inverse_mass_matrix=inv_mass_matrix, max_num_doublings=6)
 
 nuts = blackjax.nuts(full_logdensity, **nuts_parameters)
 nuts_state = nuts.init(jnp.ones((1,)))
@@ -219,7 +219,7 @@ tempered = blackjax.adaptive_tempered_smc(
     loglikelihood,
     blackjax.hmc.build_kernel(),
     blackjax.hmc.init,
-    extend_params(n_samples, hmc_parameters),
+    extend_params(hmc_parameters),
     resampling.systematic,
     0.5,
     num_mcmc_steps=1,
@@ -367,7 +367,7 @@ tempered = blackjax.adaptive_tempered_smc(
     loglikelihood,
     blackjax.hmc.build_kernel(),
     blackjax.hmc.init,
-    extend_params(n_samples, hmc_parameters),
+    extend_params(hmc_parameters),
     resampling.systematic,
     0.75,
     num_mcmc_steps=1,
diff --git a/book/algorithms/TemperedSMCWithOptimizedInnerKernel.md b/book/algorithms/TemperedSMCWithOptimizedInnerKernel.md
index 769af90b..b6750d77 100644
--- a/book/algorithms/TemperedSMCWithOptimizedInnerKernel.md
+++ b/book/algorithms/TemperedSMCWithOptimizedInnerKernel.md
@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.15.2
+    jupytext_version: 1.16.2
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
@@ -158,7 +158,7 @@ Although the proposal distribution is always normal, the mean and diagonal of th
 the particles outcome of the $i-th$ step, in order to mutate them in the step $i+1$
 
 ```{code-cell} ipython3
-from blackjax.smc.inner_kernel_tuning import inner_kernel_tuning
+from blackjax import inner_kernel_tuning
 from blackjax.smc.tuning.from_particles import (
     particles_covariance_matrix,
     particles_stds,
@@ -212,10 +212,9 @@ def tuned_irmh_experiment(dimensions, target_ess, num_mcmc_steps):
         mcmc_init_fn=irmh.init,
         resampling_fn=resampling.systematic,
         smc_algorithm=adaptive_tempered_smc,
-        mcmc_parameter_update_fn=lambda state, info: extend_params(n_particles, 
-                                                                                {"means":particles_means(state.particles),
-                                                                                 "stds":particles_stds(state.particles)}),
-        initial_parameter_value=extend_params(n_particles, {"means":jnp.zeros(dimensions), "stds":jnp.ones(dimensions) * 2}),
+        mcmc_parameter_update_fn=lambda state, info: extend_params({"means":particles_means(state.particles),
+                                                                    "stds":particles_stds(state.particles)}),
+        initial_parameter_value=extend_params({"means":jnp.zeros(dimensions), "stds":jnp.ones(dimensions) * 2}),
         target_ess=target_ess,
         num_mcmc_steps=num_mcmc_steps,
     )
@@ -248,7 +247,7 @@ def irmh_full_cov_experiment(dimensions, target_ess, num_mcmc_steps):
 
     def mcmc_parameter_update_fn(state, info):
         covariance = jnp.atleast_2d(particles_covariance_matrix(state.particles))
-        return extend_params(n_particles, {"means":particles_means(state.particles), "cov":covariance})
+        return extend_params({"means":particles_means(state.particles), "cov":covariance})
 
     kernel_tuned_proposal = inner_kernel_tuning(
         logprior_fn=prior_log_prob,
@@ -258,7 +257,7 @@ def irmh_full_cov_experiment(dimensions, target_ess, num_mcmc_steps):
         resampling_fn=resampling.systematic,
         smc_algorithm=adaptive_tempered_smc,
         mcmc_parameter_update_fn=mcmc_parameter_update_fn,
-        initial_parameter_value=extend_params(n_particles, {"means":jnp.zeros(dimensions), "cov":jnp.eye(dimensions) * 2}),
+        initial_parameter_value=extend_params({"means":jnp.zeros(dimensions), "cov":jnp.eye(dimensions) * 2}),
         target_ess=target_ess,
         num_mcmc_steps=num_mcmc_steps,
     )