What is the term for a set of loci that are the same?

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In summary, the loci of both parametric lines are identical, meaning they describe the same set of points. The equations can be written in different forms, but they all represent the same line with the same direction and slope.
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I'm thinking the term is congruent.

For example, let's say there are 2 parametric lines:

s0( t ) = < 2 , 1 > t + < 0 , - 3 >

s1( t ) = < -18 , -9 > t + < -6 , -6 >

The loci for both are the same line, just that one proceeds in the opposite as the other (and at a high rate) per change in parameter, and such that

s1( - t ) = s0( 9 t + 3 )

Surely, there must be a term for this.
 
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  • #2
'The loci are identical' is the way I would express it.
 
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swampwiz said:
For example, let's say there are 2 parametric lines
s0( t ) = < 2 , 1 > t + < 0 , - 3 >

s1( t ) = < -18 , -9 > t + < -6 , -6 >
I would say that the equations are equivalent, as both parametric equations describe the same set of points.

For your parametric line, there are an infinite number of parametric representations. For example, the direction along your line is given by the vector <2, 1>. Any scalar multiple of this vector will also have the same direction. In your second equation the direction vector is <-18, -9>, which is -9 * <2, 1>.
Also, the equation could be written using any point on the line.

In slope intercept form, the equation of the line is y = (1/2) x - 3, which could also be written as 2y - x + 6 = 0, and in many other ways as well.
 

1. What is the definition of a gene cluster?

A gene cluster is a set of loci, or specific locations on a chromosome, that are physically close together and often contain genes that are functionally related or co-regulated.

2. What is the term for a group of genes that are inherited together?

A gene cluster is the term used to describe a group of genes that are inherited together, as they are located in close proximity on a chromosome.

3. Is a gene cluster the same as a gene family?

No, a gene cluster and a gene family are different concepts. A gene cluster refers to a set of physically neighboring genes, while a gene family refers to a group of genes that share a common evolutionary origin and often have similar functions.

4. Are all genes within a gene cluster expressed at the same time?

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Gene clusters can play a role in the development of genetic diseases by containing multiple genes that contribute to a specific disease or by being located near other important genetic regions. Studying gene clusters can help identify potential disease-causing genes and better understand the genetic basis of diseases.

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