We analyzed completely and systematically each of the 24 chromosomes of each of the following 3 reference genomes:

Neanderthal genome

-Neanderthal genome (2014) ref (21) http://www.nature.com/nature/journal/v505/n7481/full/nature12886.html

Sapiens Build34 (2003) human reference genome ref (22)-Sapiens Build34 (2003) genome http://www.nature.com/nature/journal/v431/n7011/full/nature03001.html

Sapiens HG38 (2013) human reference genome ref (23)

- Sapiens HG38 (2013) genome https://www.ncbi.nlm.nih.gov/grc/human

chimp

http://www.ensembl.org/Pan_troglodytes/Info/Index

gorilla

http://www.ensembl.org/Gorilla_gorilla/Info/Index

orangutan

http://www.ensembl.org/Pongo_abelii/Info/Index

macaque

http://www.ensembl.org/Macaca_mulatta/Info/Index

Let's distinguish now the 3 types of HGO:

1/ Theoretical HGO (tHGO)

(3-PHI)÷2 = 0.6909830056

where PHI is the Golden Ratio PHI = 1.618033989

2/ Reference woman HGO (rwHGO)

0.6913477936

error (tHGO – rwHGO) =

0.6909830056 - 0.6913477936

¯0.0003647879784

and

Reference man HGO (rmHGO)

0.6922864236

error (tHGO – rmHGO) =

¯0.001303417973

0.6909830056 - 0.6922864236

3/ HGO is computed cumulting C+G and T+A nuclotides populations from each DNA strand.

Example here : HGOwoman =

( (C+G population from strand1) + (C+G population from strand2) )

/ ( (T+A population from strand1) + (T+A population from strand2) )

Then :

HGO woman =

( (sum C+G single strand 1 to 22 chromosomes) + (sum C+G chrX)

+ (sum C+G single strand 1 to 22 chromosomes) + (sum C+G chrX) )

/ [ (sum T+A single strand 1 to 22 chromosomes) + (sum T+A chrX)

+ (sum T+A single strand 1 to 22 chromosomes) + (sum T+A chrX) ]

HGO man =

( (sum C+G single strand 1 to 22 chromosomes) + (sum C+G chrX)

+ (sum C+G single strand 1 to 22 chromosomes) + (sum C+G chrY) )

/ ( (sum T+A single strand 1 to 22 chromosomes) + (sum T+A chrX)

+ (sum T+A single strand 1 to 22 chromosomes) + (sum T+A chrY) )

Recall the single stranded C+G, T+A and individual chromosome HGO values:Table 1

We deduce for the genome Sapiens HG38:

HGO woman =

( (sum C+G single strand 1 to 22 chromosomes) + (sum C+G chrX)

+ (sum C+G single strand 1 to 22 chromosomes) + (sum C+G chrX) )

/ ( (sum T+A single strand 1 to 22 chromosomes) + (sum T+A chrX)

+ (sum T+A single strand 1 to 22 chromosomes) + (sum T+A chrX) )

HGO woman = [ (1128757468 + 61221521) + (1128757468 + 61221521) )

/ (( 1627573573 + 93671508 ) + ( 1627573573 + 93671508 ) )

= 2379957978 / 3442490162 =0.6913477936

HGO man =

( (sum C+G single strand 1 to 22 chromosomes) + (sum C+G chrX)

+ (sum C+G single strand 1 to 22 chromosomes) + (sum C+G chrY) )

/ ( (sum T+A single strand 1 to 22 chromosomes) + (sum T+A chrX)

+ (sum T+A single strand 1 to 22 chromosomes) + (sum T+A chrY) )

HGO man =([ (1128757468 + 61221521) + (1128757468 + 10572683 ) )

/ (( 1627573573 + 93671508 ) + ( 1627573573 + 15842360 ) )

2329309140 / 3364661014 = 0.6922864236

We introduce here a method of global analysis of the roughness or fractal texture of the DNA sequences at the chromosome scale. To do this, we generalize the method of numerical analysis of the "Master Code of Biology" 1419. Thus, we restructure the sequence into different generic sequences based on "meta codons" no longer triplets of 3 nucleotides but values ranging from 17 to 377 nucleotides, ie 360 simulations. This method of analysis will then reveal, in most cases, discrete waves or interferences, most often dissonances. However, sometimes there will emerge kinds of resonances where all scales of analysis appear to be in symbiosis.

The discrete interferences fields resulting from the analysis of an entire chromosome are therefore a three-dimensional space:

 Dim y (vertical) restructuring in meta codons of lengths 17 to 377 nucleotides

 Dim x (horizontal) derivatives mobile1 such that 1/2 1/3 1/4 ... 1 / n

 Dim z cumulated populations from the "Master code" operators (14, 19).

The + 1 / -1 derivatives will be of type increase, ie +1 if derivative increasing and will be of type decrease, ie -1 if derived decreasing.

  In this context we will explore these 3d spaces in 2 forms:

  -Horizontal, meta codons dimension: curves for a dimension of meta codons given example, 22 in the example "resonances" below (see Figure 2).

  -Vertical, spectral differentiation: discrete series d2-d1 is +1 if increase and -1 if decrease (see Figure 3).

  We represent in the top the +1 and in low the -1, (see all the other examples below). Table 2

Horizontal scan example: 22 761233 774174 779102 783714 786854 …/...

(see Figure 2)

Vertical scan example: 1 if d2>d1 and -1 if d2<d1 then : -1 1 -1 1 -1 1 1 -1 1 -1 1 1 …/…

(see Figure 3).

These two independent methods lead in all the cases analyzed to the same period value: here, for example, the period "horizontal scan" is a resonance of 22bp (Figure 2) and the period "vertical scan" is a period Of repeatability of 22bp also (Figure 3).(Figure 4)

A third complementary method is presented here: knowing the period determined and confirmed by the two previous methods, we segment the complete sequence of the chromosome by consecutive segments according to this period, for example here for the chromosome21, we will "cut" the entire sequence of the chromosome in successive sections of 22 bases, the length of the period discovered. Then we record for each segment the C + G populations on the one hand and T + A on the other hand.

We then represent the cumulative distribution curve of these different CG and TA populations throughout the chromosome sequence. Table 3

Neanderthal genome: Table 4

Sapiens BUILD34 genome: Table 5

Sapiens HG38 genome: Table 6 and Table 7.

In Figure 6 below, it is found that the 3 HGOs calculated for the respective 3 Neanderthal, then Sapiens genomes (Build34 release of 2003 and HG38 release of 2013) are very close to the optimal ideal value of HGO = 0.6909830056 ( 99.67% for the least optimal genome).

It is also observed that female genomes (XX) are more optimal than male genomes (XY).

On the other hand, the genomes of Neanderthal and Sapiens (Build34 of 2003) have very close optimization levels. We believe this results from the fact that the precisions of their respective DNA sequencing are similar.

On the other hand, the HG38 genomes of 2013 show the most optimal levels, this is most certainly due to the deeper quality of their DNA sequencing.

The following 2 figure 7 and figure 8 illustrate the hierarchical spectrum of the individual HGOs of each of the 24 chromosomes for each of the three genomes analyzed. It should be noted that the upstream / downstream tipping point lies between chromosomes 14 and 21, which is closely related to the likely mechanisms explaining trisomy21 (whose disorders involve precisely these two chromosomes).

Finally, it is noted (Figure 9) that it is the downstream region that contributes most to the optimality superiority of sapiens HG38 compared to sapiens build34. However, a more detailed analysis of the upstream and downstream regions shows that the notable optimization when passing from Sapiens Builds34 2003 to HG38 2013 obeys globally (with the exception of chromosomes 13, X, Y, and 1, is 20 out of 24 chromosomes OK) - to the LOH strategy law that we present here: reduction of optimality for upstream chromosomes and improvement of optimality for downstream regions.

It is therefore remarkable that this is the same and only law which seems to control simultaneously two domains as different as: the global strategy of LOH deletions of tumors on the one hand and on the other hand the difference of evolution of the same genome following 2 increasing levels of precision DNA sequencing (Build34 2003 and HG38 2013)!

Detailed Values for HGO Chromosomes Spectral Hierarchy for the 3 Human Genomes  :

Neanderthalgénome: Table 8

Sapiens BUILD34 genome : Table 9

Sapiens HG38 genome : Table 10.

We will now analyze and compare each of the chromosomes 4 of the 3 human genomes of SAPIENS Build34 (2003),

SAPIENS HG38 (2013) and NEANDERTHAL.

Here is the study of the most advanced of these 3 genomes SAPIENS HG38 (2013). It is the most evolved in the senseof greater precision of the sequencing of its DNA. We will observe two remarkable phenomena:

On the one hand, the main resonance of 34 bases will be confirmed independently by the two methods described above.

On the other hand upstream and downstream of 34 will appear secondary harmonic resonances of Lucas (18 29 47 76 123 ...) and Fibonacci (21 55 89 144 ...).

Each of the 3 Figures below corresponds to each of the 3 types of analysis that we will use throughout this article:

Analysis of resonances and dissonances (or horizontal analysis).

The bar code analysis of periods (or vertical analysis).

The "Gauss" type analysis reveals the distribution of the proportions TA and CG by regular segments throughout the sequence.

In the following figures, we remark high selectivity to Fibonacci/Lucas numbers providing long waves : examples 18 21 29 34.Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20.

Is this rule universal for other Fibonacci/Lucas numbers ? We recall here Fibonacci numbers sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393,196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282

Harmonic resonances are observed for the Fibonacci and Lucas periods upstream and downstream of 34. However, the Fibonacci periods (21 55) seem more selective than the Lucas period (29 47) insofar as their harmonic waves are longer and less numerous. Figure 21.

Now we analyze and compare according to the same methods the older genome of SAPIENS Build34 (2003) and the prehistoric genome of Neanderthal.

In this comparative figure we note the main 34 resonances but also the 29 Lucas number harmonic secondary resonance. Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27, Figure 28, Figure 29.

Then we compare now Sapiens Build34 and Neanderthal Chomosomes4 for these Fibonacci/Lucas harmonic periods.

It will be noted that there is a 21-base DEPHASING between the sapiens barcodes (HG38 and Build34) on the one hand and the Neanderthal barcode above. It suffices to compare the positions of the first resonant bar34 in each of the 3 barcode patterns: Position 5 for Sapiens HG38 and Build34, Position 26 for Neanderthal. We deduce this phase shift of 26-5 = 21. Note that 21 is - also - a number of Fibonacci.

About possible relations between these two resonances of 34 and 123:

In the figure below we try to analyze possible links between these two resonances. We note first that 123/34 = 3.617647059 = 1 + Phi * 2 = 2 + Phi = 3 + (1 / Phi). At the same time in the figure below we have divided the first period 123 of the Neandertal barcode. As shown by the bars "-4" of the barcode graph, we have delimited this first resonance 123 in 3 sub sections: 34 55 34. This structure is symmetrical vis-à-vis the middle of the pattern 55, the 2 patterns 34 being reversed head spades on both sides.Figure 30,Figure 31, Figure 32, Figure 33, Figure 34, Figure 35, Figure 36, Figure 37, Figure 38, Figure 39, Figure 40, Figure 41, Figure 42, Figure 43, Figure 44, Figure 45.

As in the case of Sapiens HG38, harmonic resonances are observed for the Fibonacci and Lucas periods upstream and downstream of 34. However, the periods of Fibonacci (55 89) and the Lucas period (47 76) situated between the two main resonances (34 and 123) of Neanderthal have their harmonic waves longer and fewer than in the corresponding cases in Sapiens Build34 which, it contains only the major resonance 34. The 2 figures below summarize and compare these 2 main resonances 34 123 of Neanderthal and 34 of Sapiens Build34.

We can here summarize the similarities and differences characterizing on the one hand the 2 chromosomes4 of Sapiens HG38 and Build34 and, on the other hand, the chromosome4 of Neanderthal. Five remarkable points emerge quickly:

a) The resonance of 34 bases is common to these 3 chromosomes.

b) The resonances 34 of the 2 Sapiens and Neanderthals differ in their forms (see figure 46) (Figure 47).

c) Point (b) can be explained by the remarkable fact that a 21-PHASE DEPHASING differentiates chromosome4 from Neanderthal of the 2 chromosomes4 of Sapiens.

d) A second major difference differentiating Neanderthal Sapiens is the emergence in Neanderthal of a second major resonance of 123 bases. We will observe that 123 is a Lucas number.

e) We finally notice that this resonance of 123 is subdivided into a triple symmetric substructure of periods 34 between 55 and 34.

f) For each of these 3 genomes the chromosomes4 have harmonic resonances which are attenuated as we move away from the major resonance 34. Neanderthal having 2 major resonances 34 and 123, the harmonic resonances between these 2 attractors (55 76 89) will attenuate less than their counterparts of Sapiens Build34. Curiously, this remark can be generalized to ALL harmonic resonances with the exception of the resonance 47 for which the chromosomes4 of Sapiens HG38 and Build34 are more optimal than that of Neanderthal (see figure below). A possible explanation could result from a superiority of the Sapiens resonance 34 on the Neanderthal resonance 34, a superiority that would propagate on the 2 neighboring harmonic resonances 47 of Sapiens and Neanderthal. Figure 48, Figure 49.

What happens to chromosomes4 of monkeys next to humans? Table 11

As with Sapiens and Neanderthal, the chromosome4 of these primates are here also the most "optimal" of the 34 chromosomes. In the chimpanzee, the urangutan and the gorilla, they are also characterized by a Fibonacci resonance. But this is no longer the case with the macaque. Figure 50, Figure 51, Figure 52, Figure 53, Figure 54, Figure 55, Figure 56, Figure 57.

We thus note that the chimpanzee and ourangutan have the same resonance as in 21, and their barcodes of periods are analogous. The gorilla, it has a very long resonance of 55. When the macaque, it seems more foreign with a resonance of 43, which is neither a Lucas number nor a Fibonacci number.