Ideal Chain and Vector normalisation

In summary, the conversation discusses finding the normalization constant for a 3D probability distribution, P(N, R). The suggested approach is to break down the distribution into separate components and find the normalization constant for each, then cube it to find the overall normalization constant for P(N, R). It is suggested to look for Gaussian integrals in a textbook for assistance. The first step is not to arrange the distribution as A(e^-3R^2)(e0.5Na^2).
  • #1
Mic :)
48
0

Homework Statement


The questions are in the file.
Hint:
Part (a) asks you to find the normalization constant for P(N, R). Note that this is a 3D distribution: P(N, R)dRxdRydRz gives you the probability of finding R in a certain "differential volume" of size dRxdRydRz located at the vector position R. I would write P(N, R)=P(N, Rx)P(N, Ry)P(N, Rz) and normalize P(N, Rx), P(N, Ry) and P(N, Rz) independently. These have the same functional form (e.g. Gaussian), so you only have to find the normalization constant for one (say P(N, Rx)) and then cube the normalization constant to find the normalization constant for P(N, R). Note that Rx, Ry and Rz are vector components and run from -infinity to +infinity.I am particular unsure as to how to go about the first steps of A; ie finding the normalisation constant.

Picture5.png


Thank you very much!
Any help would be massively appreciated.
 
Last edited:
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  • #2
It's already said what is to be done: Integrate the probality distribution over all possible values of the random variables and then choose [itex]A[/itex] such that this integral gives 1.
 
  • #3
vanhees71 said:
It's already said what is to be done: Integrate the probality distribution over all possible values of the random variables and then choose [itex]A[/itex] such that this integral gives 1.

Hi! Could you please show me how?
Thanks.
I don't seem to be running on all cylinders right now, and need a bit a push.
 
  • #4
Look for Gaussian integrals in your textbook!
 
  • #5
Would the first step be to arrange it as A(e^-3R^2)(e0.5Na^2) ?
 
  • #6
No.
 

1. What is ideal chain and vector normalization?

Ideal chain and vector normalization is a statistical method used to transform data in a way that allows for better comparisons between samples. It is commonly used in fields such as genetics and bioinformatics to reduce the influence of variability in data, making it easier to identify patterns and trends.

2. How does ideal chain and vector normalization work?

This method works by dividing each data point by the total sum of the data, resulting in a value between 0 and 1. This normalized data is then multiplied by a factor to ensure that the sum of all data points is equal to 1. This process is repeated for each sample, allowing for more accurate comparisons between them.

3. What is the difference between ideal chain and vector normalization?

Ideal chain and vector normalization both aim to reduce the influence of variability in data, but they differ in the way they achieve this. Ideal chain normalization divides each data point by the total sum of the data, while vector normalization divides each data point by the vector length of the data. The end result is similar, but they may be more suitable for different types of data.

4. When should I use ideal chain and vector normalization?

Ideal chain and vector normalization are typically used when comparing data from different samples or experiments. This can be especially useful in fields such as genetics, where there may be a lot of variability in the data. It can help to identify patterns and trends that may otherwise be hidden by this variability.

5. Are there any limitations to ideal chain and vector normalization?

While ideal chain and vector normalization can be useful in reducing the influence of variability in data, it is not a perfect solution. It may not be suitable for all types of data and may not always provide the best results. Additionally, it is important to carefully select the appropriate normalization method for your specific data and research question.

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