Understanding the Invariance of Hamming Distance: A Shift Proof

  • Thread starter florenti
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In summary, The Hamming Distance is a measure of the number of positions at which two DNA sequences are different from each other. It is calculated by counting the number of nucleotide differences between two DNA sequences of equal length. In genetics, it is used to measure genetic diversity and identify mutations or errors in DNA sequences. Additionally, the concept of the Hamming Distance can be applied to non-genetic fields such as computer science. It differs from other distance measures as it only considers the number of differences and is specifically used for binary data.
  • #1
florenti
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Please help me ...

to show that the Hamming disatance d(x,y) is invariant to a shift of both x and y i.e

d(x+z, y+z)=d(x,y)

Thanks a lot

flo
 
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  • #2
florenti said:
Please help me ...

to show that the Hamming disatance d(x,y) is invariant to a shift of both x and y i.e

d(x+z, y+z)=d(x,y)

Thanks a lot

flo

Another poster, Lenti, asked this same question a couple of days ago.
 

1. What is the Hamming Distance?

The Hamming Distance is a measure of the number of positions at which two DNA sequences are different from each other.

2. How is the Hamming Distance calculated?

The Hamming Distance is calculated by counting the number of nucleotide differences between two DNA sequences of equal length.

3. What is the significance of the Hamming Distance in genetics?

The Hamming Distance is used to measure the genetic diversity between two individuals or populations. It can also be used to identify mutations or errors in DNA sequences.

4. Can the Hamming Distance be used for non-genetic applications?

Yes, the concept of the Hamming Distance can be applied to other fields such as computer science, where it is used to measure the similarity between two binary strings.

5. How is the Hamming Distance different from other distance measures?

The Hamming Distance only takes into account the number of differences between two sequences, whereas other distance measures may also consider the type or magnitude of the differences. Additionally, the Hamming Distance is specifically used for binary data, while other distance measures can be applied to continuous data as well.

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