Are Knots Common

The breakthrough came around 1970 mostly due to the work of M.D. Frank-Kamenetskii and his young co-workers A.V. Lukashin (1945-2004) and A.V. Vologodskii in the Molecular Genetics Institute in Moscow. These researchers realized that a piece of very abstract mathematics, called 

And what is t here Nothing It has no physical relevance whatsoever. Alexander A(t) is just an abstract algebraic object... This is the type of mathematics to which most physicists are usually deaf. But science teaches us time after time that prejudice of any sort is a bad advisor, that a scientist, to deserve the name, should keep his or her eyes open... In our story, the researchers in Prank Kamenetskii group realized that their computer could work out Alexander polynomial for several values of t for every loop generated and, for instance, if the result was A(—1) = 3, then the loop is most likely the trefoil. (Most likely and not for sure because some other rather complex knots also have the same Alexander polynomial as the trefoil also, Alexander polynomial does not distinguish left from right this was not a significant problem, so let s skip it here.) 

unknots are exponentially rare in long loops, almost all long loops are knotted. 

This was about knots in coils. As excluded volume reduces knotting, the negative excluded volume — the poor solvent effect or globular conformation — dramatically increases the knot probability, which is not inconsistent with our mundane experience with ropes and the like. 

The result (11.1) was proven as a mathematical theorem for several different models of loops (on cubic lattice, freely jointed, etc) — one of the 

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