Not sure why you have to read 3/4 of the article to get to a _link_ to a pdf which _only_ has the _abstract_ of the actual paper:
N. Benjamin Murphy and Kenneth M. Golden* (golden@math.utah.edu), University of
Utah, Department of Mathematics, 155 S 1400 E, Rm. 233, Salt Lake City, UT 84112-0090.
Random Matrices, Spectral Measures, and Composite Media.
"We consider composite media with a broad range of scales, whose
effective properties are important in materials science, biophysics, and
climate modeling. Examples include random resistor networks, polycrystalline media, porous bone, the brine microstructure of sea ice, ocean eddies, melt ponds on the surface of Arctic sea ice, and the polar ice packs themselves. The analytic continuation method provides Stieltjes integral representations for the bulk transport coefficients of such systems, involving spectral measures of self-adjoint random operators which depend only on the composite geometry. On finite bond lattices or discretizations of continuum systems, these random operators are represented by random matrices and the spectral measures are given explicitly in terms of their eigenvalues and eigenvectors. In this lecture we will discuss various implications and applications of these integral representations. We will also discuss computations of the spectral measures of the operators, as well as statistical measures of their eigenvalues. For example, the effective behavior of composite materials often exhibits large changes associated with transitions in the connectedness or percolation properties of a particular phase. We demonstrate that an onset of connectedness gives rise to striking transitional behavior in the short and long range correlations in the eigenvalues of the associated random matrix. This, in turn, gives rise to transitional behavior in the spectral measures, leading to observed critical behavior in the effective transport properties of the media."
In this lecture we will discuss computations of the spectral measures of this operator which yield effective transport properties, as well as statistical measures of its eigenvalues.
No, it is a hypothesis I formulated here after reading the article. I did a quick check on google scholar but I didn't hit any result. The more interesting question is, if true, what can you do with this information. Maybe it can be a way to evaluate a complete program or specific heap allocator, as in "how fast does this program reach universality". Maybe this is something very obvious and has been done before, dunno, heap algos are not my area of expertise.
If you are citing some crank with another theory of everything, than that dude had better prove it solves the thousands of problems traditional approaches already predict with 5 sigma precision. =3
> The pattern was first discovered in nature in the 1950s in the energy spectrum of the uranium nucleus, a behemoth with hundreds of moving parts that quivers and stretches in infinitely many ways, producing an endless sequence of energy levels. In 1972, the number theorist Hugh Montgomery observed it in the zeros of the Riemann zeta function(opens a new tab), a mathematical object closely related to the distribution of prime numbers. In 2000, Krbálek and Šeba reported it in the Cuernavaca bus system(opens a new tab). And in recent years it has shown up in spectral measurements of composite materials, such as sea ice and human bones, and in signal dynamics of the Erdös–Rényi model(opens a new tab), a simplified version of the Internet named for Paul Erdös and Alfréd Rényi.
Are they also cranks? Seems it at least warrants investigation.
It's not that a random shuffling of songs doesn't sound random enough, it's that certain reasonable requirements besides randomness don't hold. For example, you'd not want hear the same track twice in a row, even though this is bound to happen in a strictly random shuffling.
Random shuffling of songs usually refers to a randomized ordering of a given set of songs, so the same song can’t occur twice in a row if the set only contains unique items. People don’t usually mean an independent random selection from the set each time.
If the list of songs is random shuffled, you can only hear the same song twice if there is a duplicate or if you've cycled through the whole list. That's why you shuffle lists instead of randomly selecting list elements.
N. Benjamin Murphy and Kenneth M. Golden* (golden@math.utah.edu), University of Utah, Department of Mathematics, 155 S 1400 E, Rm. 233, Salt Lake City, UT 84112-0090. Random Matrices, Spectral Measures, and Composite Media.
"We consider composite media with a broad range of scales, whose effective properties are important in materials science, biophysics, and climate modeling. Examples include random resistor networks, polycrystalline media, porous bone, the brine microstructure of sea ice, ocean eddies, melt ponds on the surface of Arctic sea ice, and the polar ice packs themselves. The analytic continuation method provides Stieltjes integral representations for the bulk transport coefficients of such systems, involving spectral measures of self-adjoint random operators which depend only on the composite geometry. On finite bond lattices or discretizations of continuum systems, these random operators are represented by random matrices and the spectral measures are given explicitly in terms of their eigenvalues and eigenvectors. In this lecture we will discuss various implications and applications of these integral representations. We will also discuss computations of the spectral measures of the operators, as well as statistical measures of their eigenvalues. For example, the effective behavior of composite materials often exhibits large changes associated with transitions in the connectedness or percolation properties of a particular phase. We demonstrate that an onset of connectedness gives rise to striking transitional behavior in the short and long range correlations in the eigenvalues of the associated random matrix. This, in turn, gives rise to transitional behavior in the spectral measures, leading to observed critical behavior in the effective transport properties of the media."
In this lecture we will discuss computations of the spectral measures of this operator which yield effective transport properties, as well as statistical measures of its eigenvalues.
So a lecture and not a paper, sadly.
"How Physicists Approximate (Almost) Anything" (Physics Explained)
https://www.youtube.com/watch?v=SGUMC19IISY
If you are citing some crank with another theory of everything, than that dude had better prove it solves the thousands of problems traditional approaches already predict with 5 sigma precision. =3
Are they also cranks? Seems it at least warrants investigation.
That is a better question. =3
[1]: https://en.wikipedia.org/wiki/List_of_emoticons
=3
look at it like a sideways face of a cartoon cat, with 3 being the mouth shape
so their actual sentence ends at the period
I still don’t understand why the emoticon is there or its purpose but whatever.
Cheers =3
That is not helping.
I wonder if the semi-random "universality" pattern they talk about in this article aligns more closely with what people want from song shuffling.
DNA as a perfect quantum computer based on the quantum physics principles.