Figure 1.
DNA Google matrix of Homo sapiens (HS) constructed for words of 5-letters (top) and 6-letters (bottom) length.
Matrix elements are shown in the basis of PageRank index
(and
). Here,
and
axes show
and
within the range
(left) and
(right). The element
at
is placed at top left corner. Color marks the amplitude of matrix elements changing from blue for minimum zero value to red at maximum value.
Figure 2.
Integrated fraction of Google matrix elements with
as a function of
.
Left panel : Various species with 6-letters word length: bull BT (magenta), dog CF (red), elephant LA (green), Homo sapiens HS (blue) and zebrafish DR(black). Right panel : Data for HS sequence with words of length (brown),
(blue),
(red). For comparison black dashed and dotted curves show the same distribution for the WWW networks of Universities of Cambridge and Oxford in 2006 respectively.
Figure 3.
Integrated fraction of sum of ingoing matrix elements with
.
Left and right panels show the same cases as in Fig. 2 in same colors. The dashed and dotted curves are shifted in -axis by one unit left to fit the figure scale.
Figure 4.
Spectrum of eigenvalues in the complex plane for DNA Google matrix of Homo sapiens (HS) shown for words of
letters (from top to bottom).
Figure 5.
Spectrum of eigenvalues in the complex plane for DNA Google matrix of of bull BT, dog CF, elephant LA, zebrafish DR shown for words of
letters (from top to bottom).
Figure 6.
Dependence of PageRank probability on PageRank index
.
Left panel : Data for different species for word length of 6-letters: bull BT (magenta), dog CF (red), elephant LA (green), Homo sapiens HS (blue) and zebrafish DR (black). Right panel : Data for HS (full curve) and LA (dashed curve) for word length (brown),
(blue/green),
(red).
Figure 7.
PageRank proximity plane diagrams for different species in comparison with Homo sapiens:
-axis shows PageRank index
of a word
and
-axis shows PageRank index of the same word
with
of bull,
of dog,
of elephant and
of zebrafish; here the word length is
.
The colors of symbols marks the purine content in a word (fractions of letters
or
in any order); the color varies from red at maximal content, via brown, yellow, green, light blue, to blue at minimal zero content.
Figure 8.
Same as in Fig. 7 but now the color marks the fraction of of letters or
in any order in a word
with red at maximal content and blue at zero content.
Figure 9.
Zoom of the PageRank proximity diagram of Fig. 8 for the range
with the same color for
or
content.
Table 1.
Top ten PageRank entries at DNA word length for species: bull BT, dog CF, elephant LA, Homo sapiens HS and zebrafish DR.
Figure 10.
PageRank proximity diagram of Homo sapiens
versus Homo sapiens
at
(see text for details).
Top panels show the content of (left) and
(right) in the same way as in Fig. 8 and Fig. 7 respectively. Bottom panels show zoom of top panels.
Table 2.
Ten words with minimal PageRank probability given at for species: bull BT, dog CF, elephant LA, Homo sapiens HS and zebrafish DR.
Figure 11.
Dependence of eigenstates amplitude on PageRank index
in
-axis and eigenvalue index
in
-axis for largest ten eigenvalues
counted by
from
at
to
at
.
The range is shown with PageRank vector for a given species at the bottom line of each panel. For each species in each panel the color is proportional to
changing from blue at zero to red at maximal amplitude value which is close to unity in each panel. The panels show the species: bull BT (top left), dog CF (top right), elephant LA (bottom left), Homo sapiens HS (bottom right).
Table 3.
Words corresponding to the maximum value of eigenvector modulus
for species bull BT, dog CF, elephant LA, Homo sapiens HS and zebrafish DR, which are shown in dark red in Fig. 11.