Commit ccde022e authored by Michael Wimmer's avatar Michael Wimmer
Browse files

fix list

parent fbae490e
Pipeline #57575 passed with stages
in 1 minute and 47 seconds
......@@ -137,10 +137,8 @@ To overcome this imbalance in weights, [Grassberger](https://doi.org/10.1103/Phy
In particular, after adding a subunit to a polymer such that the current length is $L'$, the following two steps are performed for every polymer $k$:
1. *Pruning*: If the weight $w_k^{(L')} < W_-^{(L')}$, one of the following two actions is performed. Which of the two is performed is chosen randomly with equal probability (i.e. (a) with probability $1/2$ and (b) with probability $1/2$)
a. the polymer $k$ is discarded.
That means the current polymer length $L'$ is discarded and not used to grow further. However, the previous lengths of the polymer $k$ are still used for the averages for length $<L'$.
b. The weight $w_k^{(L')}$ is doubled: $w_k^{(L'), \text{new}} = 2 w_k^{(L')}$.
This new weight is used to compute the average for length $L'$ and used to compute the weight of the polymer when grown further: e.g. if in the next step there are $m_{k, L'+1}$ possibilities to place the subunit, $w_k^{(L'+1)} = m_{k, L'+1}\, w_k^{(L'), \text{new}}$, etc.
1. the polymer $k$ is discarded. <br>That means the current polymer length $L'$ is discarded and not used to grow further. However, the previous lengths of the polymer $k$ are still used for the averages for length $<L'$.
2. The weight $w_k^{(L')}$ is doubled: $w_k^{(L'), \text{new}} = 2 w_k^{(L')}$. <br>This new weight is used to compute the average for length $L'$ and used to compute the weight of the polymer when grown further: e.g. if in the next step there are $m_{k, L'+1}$ possibilities to place the subunit, $w_k^{(L'+1)} = m_{k, L'+1}\, w_k^{(L'), \text{new}}$, etc.
2. *Enrichment*: If the weight $w_k^{(L')} > W_+^{(L')}$, the polymer is copied, i.e. a second copy of this polymer is added for length $L'$. The original and the copy are assigned half of the original weight, these new weights and used for all computations of averages of length $L'$ and larger.
### Why does PERM work?
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment