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Other Writing ...
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If you would like to contact me, you can at lesh@leshatton.org
or through the contact points on each page which automatically insert a reference.
About the Fundamental Law of Inequality: UPDATED Aug 2023
My co-author Greg Warr and I finally published our book on this subject:
"Exposing Nature's Bias: the Hidden Clockwork behind Society, Life and the Universe."
It is the culmination of more than 10 years of research and unifies the emergent properties of
many systems. it explains why greed dominates financial systems, why
Zipf's law of word frequencies is present in all books, why the genome has been so stable for
over 3.6 billion years, why some proteins are so long, why software structure is pre-determined
independently of its developers or the technology they use and in indeed why
power-laws dominate all discrete systems in the universe.
Here's more of the story so far ...
Jul 2023
Protein copying in the domains of life
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Proteins are exactly copied around the domains of life and viruses according to a
very precise power-law. This behaviour is predicted by the FLI and you wouldn't find it
unless the maths told you where to look. The graphs are plotted using the splendid European
Molecular Biology Lab data from 2007-2021 in snapshots. We have been trying to
publish this for a couple of years but biological journals always find an excuse to reject
it even though it can be independently tested. This copying is partly caused by HGT (Horizontal Gene Transmission)
and partly by VGT (Vertical Gene Transmission). You might like to check it out for yourself.
It turns out that viruses play an essential part in this mechanism making it harder to
claim that viruses are not alive. From the point of view of Information Theory, there is
no sensible distinction.
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May 2022
Universal Inverse Symmetry in all genomes
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Watch how the universal symmetry of DNA gradually degrades as genomes decline
in size from the extraordinary axolotl, down to the viruses such as Covid-19
which are a million times smaller. Every group of N adjacent nucleotides is
repeated but in inverse symmetry, behaviour enforced by the FLI.
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The same progression but this time showing the power-law in N-tuple behaviour
(adjacent groups of N nucleotides) enforced by the FLI. All genomes look like
this showing how DNA has an underlying stability over its 3.6 billion years in
spite of evolutionary pressures.
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October 2019
A general proof of Zipf's law
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The first general proof of Zipf's law for all discrete systems.
Download
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Strong evidence of an information-theoretical conservation principle linking all discrete systems
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A complete general theory of why disparate discrete systems such as the proteome
and collections of computer software share identical properties such as their
length distributions. There's a lot more to come.
Download
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CoHSI V; Identical multiple scale-independent systems within genomes and computer software
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The genome and hexadecimal software dumps have exactly the same information properties.
Download
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CoHSI IV; Unifying Horizontal and Vertical Gene Transfer - is Mechanism Irrelevant ?
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Shows that CoHSI correctly predicts the rate at which proteins are copied across all
domains of life, demonstrating that viruses are fundamental to this process.
Download
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CoHSI III: Long proteins and implications for protein evolution
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Shows that the longest protein depends only on the size of the protein
aggregation and demonstrates that this leaves a recognisable footprint
in the phylogenetic tree including evidence of a previously undocumented mass extinction.
Download
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CoHSI II; The average length of proteins, evolutionary pressure and eukaryotic fine structure
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Why protein average length is highly conserved and unusual fine structure
identified in the Eukaryota.
Download
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CoHSI I; Detailed properties of the Canonical Distribution for Discrete Systems such as the Proteome
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A comprehensive exploration of the properties of the CoHSI equation.
Download
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September 2017
Conservation of Hartley-Shannon Information (CoHSI) in discrete systems
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The length distribution of discrete systems such as the complete Proteome,
collections of Software in any language and digital Music all obey
the following equation
Here N is the number of ways M components each with size ti beads made up
from ai different colours can be arranged.
For components large compared with their alphabet, this asymptotes to
a power-law
It has nothing to do with natural selection, human volition or any other action
other than the natural behaviour of large random systems. It is an
emergent property and in important ways,
software and protein structural properties are therefore identical.
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Download
Heiland Lecture, CSM, Golden CO, 07-Mar-2018
NIST Lecture, Boulder CO, 06-Mar-2018
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May 2015
Conservation of Information in Proteins
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In proteins, CoHSI predicts the remarkable constancy of average
protein length and also why very long proteins exist.
PLOS ONE download
Like all my recent work, complete computational reproducibility packages
are provided which are capable of reproducing each diagram, table and statistical
result using entirely open source. As an example, for this paper it can
be found at
Reproducibility package
and a tutorial in how to build reproductibility packages is given here.
How to build reproducibility packages
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April 2014 - Software's Hidden Clockwork
Lengths of software components measured in tokens
Unique alphabets of software components measured in tokens
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Just like proteins, all software systems have
a hidden clockwork which forces them into the same component size
and alphabet size distributions
whatever they do, whoever wrote them and whatever technology or
language was used. Just watch as both the lengths and alphabets of
100 million lines of C, C++, Java, Fortran,
Ada and Tcl-Tk asymptote to the CoHSI distribution in 1/2 million line chunks.
IEEE TSE preprint
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