3. You grow a million cells, half of which are liver cells and half of which are

Question

3. You grow a million cells, half of which are liver cells and half of which are vascular cells, on the surface of a Petri dish at 370C. Initially, the liver and vascular cells fully occupy the left and right sides of the dish, respectively. A) If the cells are allowed to mix randomly, what is the AS for this mixing process? B) The only way for the initial arrangement of cells to persist is if its energy is lower than that f the mixed states. Assuming the mixed states all have the same energy, how much lower should the energy of the initial arrangement be to ensure that its probability is at least 99.9999%

Explanation / Answer

A] Minimum entropy will be S = 0 and this will be when pi = 1

this condition implies that all the pixels are of intensity i

so, for a single colour greyscale (8-bit) image, the image will have minimum entropy.

B]

Maximum entropy will be when p = 1/256

this implies that the image contains every possible colour among the 256 colours in the 8-bit image.

for this, S = ln(256) = 5.545.

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