diff --git a/scripts/plots_a_dependence.qmd b/scripts/plots_a_dependence.qmd
index 89e02c6..6cbbba5 100644
--- a/scripts/plots_a_dependence.qmd
+++ b/scripts/plots_a_dependence.qmd
@@ -256,7 +256,7 @@ title(main="Vectors for a rescaled to norm one.")
 #| cache: true
 #| echo: false
 #| collapse: true
-ns <- seq(100, 1000, 100)
+ns <- seq(250, 10000, 250)
 as <- c(1.0, 2, 5, 10, 20)
 alphas <-  seq(0.1, 0.5, 0.1)
 
@@ -271,7 +271,7 @@ for (a in as) {
     for (j in 1:length(alphas)) {
       n <- ns[i]
       K <- floor(n^alphas[j])
-      if (!K > 0) next # skip if K is equal to zero
+      if (!K > 1) next # skip if K is equal to zero lr one
       # use the default seed 1L
       Q <- compute_matrix(seed=1L,
                      a= a,
@@ -293,14 +293,16 @@ for (a in as) {
 
 ```{r hyperparameter n / k^alpha = const plotting}
 results |>
+  filter(param_alpha > 0.21 & param_alpha <= 0.32) |>
   mutate(param_alpha = as.factor(param_alpha),
          param_a = as.factor(param_a)) |>
   group_by(param_a, param_alpha) |>
-  filter(dim_k == max(dim_k)) |>
+#  filter(dim_k == max(dim_k)) |>
   ggplot(aes(dim_n, ssv, col=param_a, shape=param_alpha)) +
-  geom_point(size=1.5) +
-  geom_line() +
-  #scale_y_log10() +
+  geom_point(size=3.5) +
+  geom_line(size=1.5) +
+  geom_function(fun = function(x) {( sqrt(x)) / (floor(x^0.3))}, col="black" )+
+ # scale_y_log10() +
   theme_bw() +
   labs(x=latex2exp::TeX("$n$"),
        y=latex2exp::TeX("Smallest singular value of $Q$"),