Dense Fractal Networks , Trends , Noises and Switches in Homeostasis Regulation of Shannon Entropy for Chromosomes ’ Activity in Living Cells for Medical Diagnostics

We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometry with nanometer spatial resolution. Experimental data present fluorescence of many ten thousands of cells, from different parts of body in each population, in various blood samples. Data is presented in histograms as frequency distributions of flashes in the dependence on their intensity. Normalized frequency distribution of information in these histograms is used as probabilistic measure for definition of Shannon entropy. Data analysis shows that for this measure of Shannon entropy common sum of entropy, i.e. total entropy E, for any histogram is invariant and has identical trends of changes all values of at reduction of rank r of histogram. This invariance reflects informational homeostasis of chromosomes activity inside cells in multi-scale networks of entropy, for varied ranks r. Shannon entropy in multi-scale DNA networks has much more dense packing of correlations than in “small world” networks. As the rule, networks of entropy differ by the mix of normal D < 2 and abnormal D > 2 fractal dimensions for varied ranks r, the new types of fractal patterns and hinges for various topology (fractal dimension) at different states of health. We show that all distributions of information entropy are divided on three classes, which associated in diagnostics with a good health or dominants of autoimmune or inflammatory diseases. This classification based on switching of stability at transcritical bifurcation in homeostasis regulation. We defined many ways for homeostasis regulation, coincidences and switching patterns in branching sequences, the averages of Hölder for deviations of entropy from homeostasis at different states of health, with various saturation levels the noises of entropy at activity of all chromosomes in support regulation of homeostasis.   ln E r r 


Introduction
We oriented on medical diagnostics of health status based on oxidative activity of DNA in cells for everyday clinical practice, for given person at given time.Oxidative activity of DNA is visualized in fluorescence.We analyze experimental data on DNA fluorescence in neutrophils of peripheral blood at biochemical reaction of oxidative burst [1].This is a high sensitive method for diagnosing many different and complex diseases, early diagnostics of illnesses, hidden diseases.Short list of clinical observations is given in [1][2][3][4].Preparation and experimental procedures, including small additions of ethidium bromide for small volumes of blood ~2 ml, excitation and measurements of fluorescence are described in [1][2][3][4][5][6].DNA fluorescence is described by histograms in flow cytometry method with spatial resolution of measurements at a few nanometers in the flow direction [5,6].Statistics of fluorescence is presented in histograms for frequency of flashes P(I) as the functions of fluorescence intensity I for large populations of many ten thousands of cells, living in different parts of human body.Chaotic Brownian motion and rotation of fluorescing cells, flowing through the laser beam in flow cytometry, ensured good statistics for illustration of real 3D chromosomal activity inside living cells.Accuracy and reproducibility of experimental results in histograms of fluorescence approximately equal to 2% that corresponds to the normal, usual levels of inevitable and fatal errors and fluctuations of physical and biological nature [1][2][3][4][5][6].Three original histograms, as the illustrations of typical examples, are shown in Figure 1.
The heterogeneous fluorescence of all chromosomes in the cells reflects simultaneously the genetic special, individual features and immune response to the pathogenic actions due to oxidative activity of DNA.Detailed accurate statistical analysis of these histograms currently is absent.Large-scale correlations for distributions of fluorescence flashes of DNA inside living cells differ from those that we would like to see by abnormal fractal dimensions and non-trivial noise level at substantially non-Gaussian statistics [3][4][5][6].These natural peculiarities of immunofluorescence are often accompanied by statistical instabilities of local intensity distributions [3][4][5][6], i.e. fast exponential growth of central moments of fluorescence intensity.We need to develop a sequence of new nonlinear statistical methods for data analysis of immunofluorescence.Standard smoothing eliminates destroys and removes various peculiarities of fractal networks and correlations in the activity of DNA, changes real statistics, blurs and distorts many aspects of reality.
According to tradition, now and in the latter time, dominating sciences about DNA based on various approaches in biochemistry, structural biology, materials science and combinatorics for lonely DNA.In this case, informational activities of DNA in real life inside living cell, for full set of 3D chromosomes, their overall communications and information flows, switches in topology and informational networks in the presence of real changeability and noises in information transfer are lost, go off, pushed back far into the background, as the basic unsolved problems.What it means for information transfer of DNA activity inside living cells, for diagnostics and comparative analysis of health and diseases?
In Part 2 of this article we defined informational homeostasis of Shannon entropy as the empirical result.In Part 3 we analyze a density of packing, new types and classes of fractal networks of DNA entropy.In Part 4 we analyze deviations of entropy from homeostasis and various switches for central moments and averages of Holder at variations regulation of homeostasis for different states of health.We observe saturation for averages of Holder if the number of averages coincides with full chromosome number; all chromosomes are involved in support of regulation of informational homeostasis.The levels of saturations have various switching at changing the state of health.In Part 5 we show that this switching connected with stability change in homeostasis regulation.We show that all distributions of information entropy are divided on three classes, which associated in diagnostics with a good health or dominants of autoimmune or inflammatory diseases.This classification based on switching of stability at transcritical bifurcation in the nonlinear dynamical system of homeostasis regulation.

Information on Oxidative Activity of DNA inside Cells. Shannon Entropy. Informational Homeostasis
Oxidizing activity of DNA in the cells activates various (all possible) correlations with different combinations of non-coding and coding DNA fragments, both within one and the same chromosome, and between different chromosomes.Actual, 3D topology of chromosomal correlations in the nuclei of cells has quite notable changes over time, during only one month, for cells living inside given human, in the process of human life or at diseases development, during medical treatment, etc. [1][2][3][4][5][6].Characteristics, changes and deviations various fractal correlations in networks of fluorescing DNA inside cells can be used for medical diagnostics [6].How these results may to use for definition varied structures of informational activity of DNA?We all, all our chromosomes and all our cells are the open systems.How to estimate quality, quantity and changeability of DNA communications and DNA information transfer in life of given person?What about information ln J P   and information entropy for DNA activity inside cells?What need for comparison various data on informational activity of DNA inside cells for one and the same human at various times and for different people?Here we have no clear criteria.How to determine the existence and level of information noise, switches, changeability and stability of information transfer inside living cells for any being?What it means for medical diagnostics from the point of view different types of oxidative metabolism of 3D DNA inside cells, for inner and inter chromosomal correlations at different states of health?The answers on these questions now are absent, that associated with deep and unsolved problems in fundamental mathematics, information theory, etc.
To diagnostics features oxidizing activity of DNA in the blood cells for one and the same person at different times or in blood cells of different people need to compare various distributions of fluorescence, which are very diverse and changeable, as for three examples in Figure 1.A huge role here is played by the irregularity, infrequency and brokenness of histograms, which define basic information on DNA activity [5][6][7].Any artificial smoothing results destroy this information.For comparison various distributions of fluorescence we must understand the origin and function of these distributions under what conditions and parameters they need to be compared.For example, at Gaussian distribution of random variables is important to know only the mean and variance.If the statistics is very complex, such parameters and their combinations can be very, very, many.Here observed non-trivial noises of fluorescence and the exponential divergence central moments for fluctuations of intensity at increasing the number of central moments [3][4][5].This is a clear sign of turbulence [3].In this case, when comparing different distributions and moments for fluctuations of intensity the number of corresponding moments also exponentially quickly grows with increasing the order of diverging statistical moments.The similar procedures of comparisons haven't the sense in nature and in science, excluding examples and illustrations the growth for rate of statistical instabilities in the interpretation of complexity.Reproducible results and clear analysis real activity various DNA inside cells produce the need of clear, stable levels and criteria for comparison different distributions of DNA fluorescence.
Let us introduce frequency distribution of Shannon entropy , based on the frequency distributions of information This invariant was observed during fluorescence of DNA in human neutrophils in different samples of blood [5,7], as in Figure 2(c).We observe only one unified value of total Shannon entropy , like the empirical invariant, as the identical sum in each given distribution of entropy, in given sample of blood, for all cells and any donor.This invariant has one and the same value of total Shannon entropy at fluorescence for given rank r of histograms, i.e. given scale of clusters in networks of DNA entropy.This invariant a very strong roughness and diffe defines the informational homeostasis of oxidative activity of 3D DNA for full set of chromosomes inside living cells, at any biodiversity of cells for Shannon-Weaver index [5].This invariant gives the overall zero level for countdown of information activity of DNA in cells for any person, at any state of health and for any genome of different people.
In Figure 2 Let us consider the normalized m distribution of inforation as the probabilistic measure for frequency distributions Data analysis of all experiments has shown the conse (4) depends on given rank r of histo d) and Equation ( 7)).Rank r is defined by the maximal number of measuring channels max gram (see Figure 2    E J I , as is for all functions, associated with the conservation laws, as the main dominant variable to describe the states and dynamics of informational activity of DNA inside cells. How will be changing the information J(I) due to reduction of rank r or the range r at definition of Shannon entropy?Here, as everywhere, are used different terms a rank r and range r for the same value of r.Range of histogram r interconnected with the selection of multistage clusters in networks with structure of bronchial tree; here range r coincides with the number of columns in a histogram or with the number of channels for measurements of fluorescence intensity at given maximal value of dimensionless intensity, i.e.
Frequency distribution of entropy Open Access AM

Manifold of Dense Fractal Networks of Shannon Entropy for Informa
Let us consider some fractal peculiarities of immu orescence distribution.Different analogies networks such as bronchial tree, structure of oncology tumor, arterials tree, etc with networks and distributions of immunofluorescence are described in [3].Many histograms of different origin are the similar to the histograms for fluorescence of neutrophils in Figure 1  Hurst exponent H [8] is determined by means of regression equation where R/S is rescaled range (R = S), R is mal deviation of P(I) from local mean le ure 3 presented three distributions of fractal dimensions D for frequency di tro range or maxivel, S is standard deviation of P(I).Illustration of definition Hurst index was presented in [5,6].Hurst index H for frequency of flashes P(I) corresponds to fractal (Hausdorff) dimension In  .Absolute majority of the authors ignore any anomaly fractal dimensions.Nonetheless, negative Hurst index H < 0 does not contradict of main definitions wer-law correlations for fractal distributions [9], subject to rejection from the hypothesis of self-affinity.In the case of H < 0 an anomalous fractal dimension D > 2 can serve as a measure of fragmentation for correlations in complex networks [10].
Abnormal fractal dimensions D > 2 give not only fragmentation of correlations but also ensure more dense packing of fractal netw l clusters d ~ N 1/D , for certain number of nodes N, decreases at increasing the value of D. We do not know characteristics of fragmentation of information entropy of DNA and we do not have the recipes and methods of its descriptions.Therefore, we guide by clear signs of new peculiarities and strong expressions of contradictions with the traditional images of modern standards, diagrams and descriptions of DNA activity inside cell.For example, we consider different unusual deviations of typical features from very popular networks of "small worlds" [11], that are often used to describe global DNA activity inside cells [12,13].
According to Random networks with a given degree distribution may be the networks of "small worlds" [14], as in one from most popular family of complex networks [11][12][13]."Small world" behavior is typically characterized by logarithmic scaling for path length tends d ~ lnN [14] We observe more fast than linear and various growth of correlations at increasing rank r in Figure 4(a).Rich diversity of various hinges in Figures 4(b)-(d oude posibility for an unambiguous and simple identification any networks of entropy as networks of "small worlds".Therefore, hypothesis about "small worlds" structure for information entropy of DNA, as a common universal principe, here is no good.Complex hinges in Figures 4(b)-(d of "small worlds".Therefore netorks of "exponentially small worlds" are more suitable nd rather no ig ra w for description of information entropy of DNA.
Other type of correlations may be presented in networks of "double logarithm scale" in Figure 6.
According to Figures 5 and 6, branching a table differences in networks corresponding to various states of health are observed for small rank r = 4 and b nk r > 32.Rather good coincidence and local universality of entropy networks for different states of health are observed at rank r = 8, 16, 32 in Figure 5 for "exponentially small worlds" and in Figure 6 for "double logarithm scale".Stratification and individual deviations from common correlations at other values of rank r depend on the states of health; variations of health status correspond to variations in informational networks of DNA activity.In Figures 5(b

Noise of Entropy in Homeostasis Support. Patterns a
We have no of ideal, absolute, correct homeostasis, noere and never.We , M e r m in Figure 7(a).Analysis show that distributions of various other averages of Hölder, for other values of rank r are rather close to each other.This means the similar noise levels of information entropy near homeo cology and in a good health for given donors at other values of rank r.In the latter case we observe very notable differences in fractal structures of networks of information entropy in Figures 3-6 and difference in their stability (see bellow Figure 8).Therefore, we cannot assume that similarity in the averages of Hölder linked with the coinciding characteristics of collective correlations inside and between chromosomes in networks of a certain scale r for different states of health.This means only some similarity in the levels of noises for ensuring information transfer and chromosomal correlations near homeostasis, as for one and the same noise level in various Brownian motions.
Mean level of experimental errors in original cytometric histograms for r = 256 is about 2% [6][7][8].We observe much more noticeable and very clear difference between initial and transformed experimental distribution  7 for a good health, oncology and for asthma here linked with ch g stability due to transcritical bifurcation in distributions of information entropy in Figure 8 tatuses of health.

Statistical Stability and Transcritical Bifurcation
Let us consider statistical stabil angin for different s ity varied distributions of pren of en Figure 8. Large-scale distributions (13) has stationary solutions that correspond to fixed information entropy following to some approaches sented in [3].Reduction of rank r leads to distributio tropy presented in of information entropy for rank r = 4 in Figure 8 have different statistical properties and different stability types for various states of health.These properties are connected with transcritical bifurcation in homeostasis regulation.Transcritical bifurcation has a normal form [15] 2 where A is a control parameter.
The Fokker-Planck equation that corres to Equation ( 15) is ponds Equation ( 16) determines the de stationary probability nsity . The probability density distribution . The statistical determina tractor is used as the more probable state, tri .attract appro 0  A tion of the atwhen the disbution function has a maximum as convex parabola in Figure 8 A similar determination of or is actually equivalent to the ach proposed in [16].If 0 A  there is a repelled fixed point and minimum of

Conclusions
We study various large-scale dist Shannon blood samples.We total Shannon entropy   , ln E J r r  the empirical invariant, as the identical sum in each given distribution of information entropy, in all samples of blood and any donor, as in Figures 2(c) and 10(b) in real time.This invariant defines the informational homeostasis of oxidative activity for full set of chromosomes inside living neutrophils, in all clusters of all multi-scale networks for information activity of DNA inside cells.This invariant gives Shannon entropy as general characteristics for definition of information activity of 3D DNA in cells for any person, at any state of health, for any genome as the overall zero level for analysis and comparison chromosomal activity and DNA networks in cells for different people (Figures 5-8) and for one and the same human in different times (Figures 12 and 13).
Invariance of total entropy   , ln E J r r  defines special role of distribution of Shannon entropy, as it is for all functions associated with the conservation laws (pulse, energy, charge etc.), as the main dominant variable to descr namics of info tivity of DNA in cells.Nevertheless, informational invariant of   , ln E J r r  is difficult to compare with the conservation laws of mass, energy, etc.; we have no different values of total entropy in different cells.Invariance of entropy reflects the unchangeable measure or quantitative units of information entropy at certain scale r of correlations at DNA activity inside all and any cells.
Informational homeostasis reflects a number of fundamental phenomena in information and physics of real life of 3D DNA inside cells.Shannon entropy of 3D DNA in cells has much more dense packing of correlations than in well known networks of 'small worlds, than in all and any technical and computer systems.As the rule, networks of entropy are characterized by various mix of normal D < 2 and abnormal D > 2 fractal dimensions (Figures 3 and 11 , which characterizes oise level of entropy for one chromosome, for averages of Hölder.This level of saturation characterizes background noise and information transfer of DNA activity inside cells in support regulation of homeostasis, comparisons and us abnormalities for noises and fluctuations of information entropy of DNA in various blood sample in diagnostics.For instance, noise level of entropy near homeostasis may be rather high and to reach ~20% for strong inflammations, as it observed for bronchial asthma in Figure 7(b).
We defined manifold of chromosomal networks of entropy in Figures 4-6 and 12 and (or) many ways for homeostasis regulation.We show that regulation of homeostasis belongs to one from three classes of stability for all statistical distributions of information average n detections vario entropy; negative ne

Figure 1 .
Figure 1.Dependence of normalized frequency distribution of flashes P(I) on their intensity I (a); for clearest, only central part of histogram (b).The area under the final histograms of P(I) normalized to unit; rhombus points correspond to bronchial asthma.Total number of flashes is N 0 = 76 623; quadrate points correspond to the healthy donor.Common number of flashes is N 0 = 40 109; triangle points correspond to the oncology disease.Common number of flashes is N 0 = 40 752.
shown in Figure2(b).We present comparison of distributions of immunofluorescence based on the universal, empirical invariant of information entropy   , E J r  at given rank r.Rank r is defined by the maximal number of measuring channels max ln r I r  .Detailed definition of empirical invariant of information entropy , in Equations (4)-(7).This empirical invariant shown in Figure2(c), as only one¸ overall numerical value of total Shannon entropy r, for DNA fluorescence inside any neutrophils, living in any people with different states of health.

Figure 2 . 1 ;
Figure 2. (a) Logarithmic dependence LnP(I) for frequency of flashes P(I) on their intensity I(r = 256); The area under the initial histograms of P(I) normalized to unit; Original histograms for P(I) shown in Figure 1; (b) Normalized distributions of information entropy     E J I

1
is the mean probability value; max min symbol  denotes the statistical average for number flashes o orescence in all of r = 256 channels of intensity measurement.The mean value of f flu P is equal to 1/256 for r = 256 channels of intensity m surement.Three examples of frequency distributions of l P for different donors with varied states of health are sho n in Figure ( rank r = 256 all experimental data, for all do give one and the same value of nors cytometry experimental errors ~2% at 256 measuring channels[1,2].Decreasing maximal number of channels or rank r leads to decreasing the value of invariant   , entropy in Figures2(a) and (b) are show 2(c) at different rank r.Other examples of informational homeostasis for different patients with various diseases had shown in [5].Invariance of total entropy  E J n in Figure  defines special ro , r tropy le of distribution of Shannon en   experiments the number of channels is r ariations of range r, i.e. rank of histogram r, or variations the scale r, when max r I = 256.V , provide the changes in irregularity and brokenfrequency distribution of fluorescence for histograms of various rank r.Various examples decreasing of histograms rank r presented in[3,5,7].Integer r defines the total range r for distribution of entropy as maximal number of columns in reduced histogram.Each reduction of r leads to the redistribution of probability density ness of cells.Total en entical for given r tropy   , E J r pends only on rank n Figure 2(c).de r, as it is shown i Dependence of   , E J r on rank r in Figure logarithmic r  in all cells of blood different old and young patients with of health and all the time.It means existence of informational homeostasis of DNA during all the life time of cells from birth to death.
[3].Range of histogram r interconnected with the selection of multistage clusters in networks with structure of bronchial tree.Variations of range r, i.e. rank of histogram r, or variations the scale r provide the changes in irregularity and brokenness of frequency distribution of fluorescence for histograms of various rank r.The quantitative measure of irregularity and brokenness for frequency distribution of flashes for any rank r, in all histograms may serve a Hurst index H.может служить.
Fig stributions of Shannon enpy in Figure 2(b).As the rule, networks of entropy are characterized by a mix of normal D < 2 and abnormal D > 2 fractal dimensions, as in Figure3.Abnormal fractals D > 2 are typical for entropy' networks in a good health and for oncology at different values of rank r and perfectly absent at bronchial asthma, where D < 2 for all rank r.Networks of

Figure 3 .
Figure 3. Dependence of fractal dimension D(r) on logarithm of range r in networks of Shannon entropy with different scales for three different states of health con ected

Figure 3
there is no unambiguous and simple connection of network topology or fractal dimension D with the certain valu .Consider an undirected network, and let us define d as the mean geodesic (i.e., shortest) distance between pairs odes in a network of flashes of fl E of vertex or n uorescence.The certain number N of synchronized nodes-flashes in networks of DNA fluorescence inside cells are characterized by the intensity I ~ N, where N defines a common number of correlated nodes in network, if every node in fluorescence network has the approximately identical fragment of oxidative activity of DNA with approximately identical quantity of fluorescing dye.More detailed determination of correlated nodes N in the clusters of fluorescence networks of DNA inside cells now is unknown.The correlation length d depends on the network topology.
. On the other hand the expression of d ~ N 1/D defines a linear size of D-dimensional lattice or the size of a fractal cluster d ~ N 1/D .Therefore estimation of fractal dimension D of fluorescence in the networks of "small worlds" is   ~ln ln ln D N N N .Standard definition of fractal dimension D [8,10] ln N in "small worlds" network.We use various experimental data in h define Hurst index H and fractal dimension D (worlds" due to reduction of range r = I ~ N leads to expression ln ~ln ln r D r .In these variables data in Figure 3 are transformed to Figure 4(a).Using of variables for networks of "small worlds" gives varied distributions of fractal Shannon entropy which have a view of the correlations presented in Figure 4.

Figure 4 .
Figure 4. Large-scale distributions of fractal dimension D( for variables corresponded to networks of 'small worlds'; (a) r)

Figure 5 .Figure 6 .
Figure 5. Dependences of fractal dimension D(r) on double logarithm of range r in the variables for 'exponentiall small worlds'

Figure 8 .
Figure 7. (a) Logarithmic distributions of central statistical moments     , M e r m homeostasis for bronchial as sented in F stasis at on s in Fig- ures 1 and 2 for different states of health and much more essential difference for averages of Hölder   , e m r for deviations of entropy in Figure 7(b).This means that in all cells exists and maintained a very effective stabilization of homeostasis in various networks of entropy for various states of health.The origin and mech f this universal stabilization now are unknown.Various regulation of homeostasis must be very quick and must have the general physical origins, as for the dipole and multiple resonances for excitations in large clusters.Switching between networks of entropy in Figures 4- 6, corresponds to different states of health, with different deviations of   l e r from homeostasis of entropy.Hidden switching between branches for averages of

Figure 8 .Figure 8 6 .
The attractor fixed point corresponds the upper parabola in Figure 8 if   lower parabola in Figure 8 corresponds to unstable D  luores ry diseases; in our case this is br   0 A  critical point, charac ealth.Fixed point of neutral stability with the ideal value of 0 A terizes a good h  was not observed.Instead, a large family of lines with very small positive and negative curvatures for va mations If o rious autoimmune and oncology diseases without inflam is observed, as the line passing through triangular points in Figure 8. ne considers the curvature or curvature radius of parabolic approximations of entropy as the bifurcation parameter A, then various types of statistical distributions of   , 4 E I r  can be classified in the frame of tr Propo tasis corre anscritical bifurcation.sed criteria correspond to informational homeostasis of entropy.The bifurcation corresponds to stability change in homeostasis regulation for various health statuses.Thus, three types of informational homeos spond to Open Access AM positive, negative and neutral stability for distributions of information entropy at oxidative activity of DNA inside cell.The bifurcation reflects the collective statistics effects of various cellular processes and switching of transitions from health to illness and from illness to health.Changeability and Switching of Entropy's Noise for a Healthy Donor in Real Time Let us compare, in real time, during one year, Shannon entropy for DNA activity inside cells of healthy donor.Three histograms are shown in Figure 9.One may to compare histograms in Figures 1 and 9. stributions of entropy are shown in Figure 10. may to compare histograms in Figures 2 and 10.Fractal peculiarities of entropy are shown in Figure 11 Dense packing of entropy is shown in Figu Some features of stability and noises of information entropy at low rank r = 4 are shown in Figure 13.One may to compare histograms in Figures 1 and 9, 2 d 10, 4 and 11, 6 and 12, 7 and 13(b), 8 and 13(a).We serve changes in distributions of entropy and fr ructures, noise level etc. in real time for one and the same healthy man and in the comparisons with vari stributions for different unhealthy people.Many of fractal peculiarities of entropy change in time and depend on health status.Constancy belongs to homeostasis or to invariance of total Shannon entropy in Figures 2(c) and 10(b) for any states of health of any human.Constancy also belongs to statistical instability (positive curvature of all approximations) for entropy distributions of unchangeable healthy man in Figures 8 and 13(b) during one year.This is example of a very good immunity, as and perfect closeness to the ideal of networks in Figure 12.

Figure 9 .
Figure 9. Dependence of normalized frequency distribution of flashes P(I) on their intensity I (a) and for clearest only central part of histogram (b), for one and the same invariably healthy, donor in different times.Triangle green po ts correspond to 832, analysis in the total flashes number N 0 = 30 time is 19 July (first year); rhombus yellow points correspond to the total flashes number N 0 = 38 758, analysis time is 11 July (next year); square red points correspond to the total flashes number N 0 = 40 109, analysis time is 03 June, before 11 July, histogram range r = 256, as in Figure 1.

9 .Figure 11 . 9 Figure 12 .
Figure 10.(a) Normalized distributions of information entropy     E J I at rank r entrop in the dependence on fluorescence intensity = 256; (b) Dependence of total Shannon information y   , ln E J r r  on logarithm of range r; initial histograms at range r = 256; initial histogram shown in Figure 9. (a).

Figure 13 .
Figure 13.(a) Dependence of normalized distributions of Shannon entropy E(I, r = 4) on intensity I at rank r = 4.The continuous lines correspond to the parabolic approximations; initial histograms shown in Figures 9 and 11(a); (b Distributions f Figure 13.(a) Dependence of normalized distributions of Shannon entropy E(I, r = 4) on intensity I at rank r = 4.The continuous lines correspond to the parabolic approximations; initial histograms shown in Figures 9 and 11(a); (b Distributions f ) or averages of Hölder   , e m r with dif- (a)) and new types of fractal patterns and fractal hinges for various fractal topology at different states of health (Figures 4-6 and 12).Results generalized in the double logarithmic scales, in the triple and quadruple logarithmic scales, etc., as a reflection of complexity, what permits, also, detect a fragmentation, as it is shown in Figures 4-6 and 12. Deviations or noises of information entropy define regulation of informational homeostasis, information transfer and information flow inside cells for different states of health.The coincidences and switching patterns in branching se r of these noises are shown in Figures 7 and 13(b).We observe various saturations for averages of Hölder   , e m r in the levels of chromosomal correlations of entropy at different states of health in Fig- ures 7(b) and 13(b), at increasing number of correlations m.All c mes are interconnected and involved in the support regulation of homeostasis; saturation of hromoso exists if [4] N. E. Galich, "Cytometric Distributions and Wavelet Spectra of Immunofluores nostics," World Congress on Medical Physics correlations number of m for average of Hölder   cence Noise in Medical Diagand Bioostics," Journal of WASET, Vol.70, 2010, dative Activity of DNA in Cells for Popunos-, e m r equals to m = 46, when all 46 chromosomes involved in homeostasis regulation.The levels of saturations are very important characteristics of inner and inter chromosomal correlations, as asymptotic values the stan-medical Engineering, Munich, 7-12 September 2009, pp.1936-1939, [5] N. E. Galich, "Shannon-Weaver Biodiversity of Neutrophils in Fractal Networks of Immunofluorescence for Medical