If the dynamics of a process is chaotic then uncertainty on the initial conditions typically grow exponentially, but if we have deterministic chaos the uncertainty can be reduced by measuring the initial state with high precision.

If external noise (randomness) is present the uncertainty cannot be reduced below a certain value by measuring the initial state.

For real world problems chaos and external noise are often present at the same time. Entropy is useful for measuring the uncertainty for both deterministic systems and systems with external randomness.

If the measurement precision is kept at a fixed level one cannot distinguish between deterministic chaos and external noise. 

Dear Peter

Which is the cost effective for the system (especially biologic systems)chaotic or random behaviour

Amended on 3 January 2017

It is an interesting question for me.   Infection of virus and bacteria occurs spontaneously during early child life, when lower immunity has occurred due to nutrition deficiency, lack of sleep, and encounter to endemic/epidemic/pandemic.   Subsequently, the latency or the co-integration of viruses occurs randomly.   The integration of +ssRNA virus (such as HCV) is aided by helper-retrovirus (such as HIV; with reverse transcriptase (RT) and integrase (IN)).   Integration of HCV's protease genes is essential for the future chaotic induction of the cancer.    

Repeated stimulus (stress) during adult period with lack of proper nutrition and insomnia (lack of proper sleep) does not wake up the integrated virus, however it causes depression and following suicide, ageing, senile dementia, and Alzheimer's dementia.   The integrated virus may sense the nutritional condition of the host cell.

On the other hand, repeated stimulus (stress) during adult period with excess of nutrition induces chaotic re-gene-expression of previously co-integrated viruses, which is the cause of cancer and amyotrophic lateral sclerosis (ALS); i.e., cancer and ALS occur among the rich people.   The time of this chaotic re-activation or re-expression of integrated virus is not predictable similar to the metal fatigue phenomenon and the Rikitake’s Earth's Dynamo system (Tsuneji Rikitake, "Stability of the Earth's Dynamo", Bulletin of the Earthquake Research Institute, Vol. 34, No. 4, January 30, 1957, pp. 283-289,  http://hdl.handle.net/2261/11863.)

In our rat-DEN-fucoidan experiment, the time of chaotic re-expression of integrated virus occurred during DEN-stimulation period of 3 months plus 3 weeks has not been estimated, however the occurred time of chaotic re-expression is similar among 3 control rats; i.e., three control rats' livers have similar size of tumor of 1.5 cm diameter.   Therefore, fucoidan (Mozuku) may have deleted or cured the liver tumors during last 3 weeks of fucoidan treatment in the three fucoidan treated sample rats.

5 January 2017

I would like to show detailed explanation about the repeated stimuli (stresses) during adult period with excess of nutrition induces chaotic re-gene-expression of previously co-integrated viruses, which is the cause of cancer.

Normal fetal liver Hc cell has human-invading virus of Envelope glycoprotein gp160 (HIV-2; without RT and IN) at 2.9, Genome polyprotein (ECHOvirus 9; Enteric Cytopathic Human Orphan; with protease) at 14.5, and Genome polyprotein (HCV; with protease) at 2.2 μg/mg of cell protein, respectively, but has no HIV-1.   Therefore, random co-integration of HCV and HIV-1 has not yet  been achieved in fetal Hc cells.   Genome polyprotein (Dengue virus 92; DENV-92; with protease; +ssRNA) is present at 6.5, Minor capsid protein L2 (Human papillomavirus type 56; HPV-56; dsDNA) at 9, and Outer capsid protein VP5 (Broadhaven virus; BRDV; dsRNA) at 6.9 μg/mg of cell protein are also present, respectively, but these virauses seem not to be linked to the future liver cancer.

Hepatoma HepG2 cell (without fucoidan treatment) has Gag-Pol polyprotein  (HIV-1; with reverse transcriptase (RT) and integrase (IN)) at  5.6 μg/mg of cell protein and Genome polyprotein (HCV; with protease) at 7.8 μg/mg of cell protein, and  this chaotic re-gene-expression caused the liver cancer.   Other viral genes such as Envelope glycoprotein gp160 (HIV-1) at 16.2, Protein Rev (HIV-1) at 1.1, Genome polyprotein (HGV; GV virus-C) at 15.4, Protein Nef (HIV-2) at 0.61, and other animal viral genes of Envelope glycoprotein gp95 (Rous sarcoma virus; RSV) at 0.5 μg/mg of cell protein, respectively, seem to be also induced via chaotic re-gene-expression, however these genes are not linked to human liver cancer.  

Hepatoma HepG2 cell (with fucoidan treatment; cured or healed cells by fucoidan through no relation to the notorious hypothesis of "apoptosis") has Protein Nef (HIV-1) at 0.8 μg/mg of cell protein and Genome polyprotein (HCV; without protease) at 1.9 μg/mg of cell protein, which surely indicates that the cancer of HepG2 is healed thoroughly during 3 days of fucoidan therapy (please see file; HepG2 fucoidan).   Therefore, the effect of fucoidan appeares within very short times.

Tissues;

Pseudo-liver-cancer tissue has Gag-Pol polyprotein (HIV-1; with peptidase A2,RT,IN) at 3.9 μg/mg of tissue protein and Genome polyprotein (HCV; without protease) at 4.4 μg/mg of tissue protein, and is not the cancer.   Other viral proteins such as Envelope glycoprotein gp160 (HIV-2) at 8.2, AKT kinase transforming protein (AKT8 Murine leukemia virus; MLVAT) at 1.0, Pol polyprotein (BLV; Bovine leukemia virus) at 4.3, RNA-directed RNA polymerase (Murine hepatitis virus; MCoV) at 3.2, and ORF1a (Avian infectious bronchitis virus;  IBV; ACoV) at 46.0 μg/mg of tissue protein, respectively, but these re-gene-expressions are not related to cancer.

Tissue of LC (with leprosy) has Genome polyprotein (HCV) at 21.9 μg/mg of tissue protein, but has no HIV-1.   Therefore, this is not HCC tissue.   Other viral proteins such as v-Mil (v-Raf) serine/threonine-protein kinase (Avian rous-associated virus; RAV) at 2.0 μg/mg of tissue protein and Nucleocapsid protein (Feline infectious peritonitis virus) at 3.4 μg/mg of tissue protein, but these proteins are not linked to cancer. 

Tissue of HCC (with PBC) has Gag-Pol polyprotein (HIV-1; with RT and IN) at 8.6 μg/mg of tissue protein and Genome polyprotein (HCV; with protease) at 35.4 μg/mg of tissue protein, and this tissue is cancer tissue.   Other viral proteins such as Virion infectivity factor (HIV-1) at 1.5, Gag-Pol polyprotein (HIV-2) at 3.4, Gag-Pol polyprotein (SIV) at 8.6, Gag polyprotein (Visna lentivirus; Maedi-Visna virus) at 8.9, Genome polyprotein (Hog cholera virus; Classical swine fever virus; CSFV) at 43.6 μg/mg of tissue protein, respectively, but these are not linked to cancer.

LC tissue of No.6 patient has Genome polyprotein (HCV; without protease) at 7.9 μg/mg of tissue protein, but has no HIV-1.   Thus, this tissue is not cancer.   Other viral proteins such as VPX protein  (HIV-2) at 1.3, Pol polyprotein (SIV) at 7.5, Gag polyprotein (Rous sarcoma virus; RSV) at 18.7, Genome polyprotein (Loupin ill virus) at 6.4, Genome polyprotein (Moscuit cell fusing agent; CFA flavivirus) at 48.9, RNA-directed RNA polymerase (Murine coronavirus; MCoV) at 29.1, Virion infectivity factor (feline immunodeficiency virus; FIV) at 0.42 μg/mg of tissue protein, respectively, but these are not linked to cancer.

HCC tissue of No.6 patient  has Gag polyprotein (SIV) at 10.9, Pol polyprotein (SIV) at 4.1, TAT protein (SIV) at 0.81, Genome polyprotein (HCV; with protease) at 0.61 μg/mg of tissue protein, respectively, and HCC has been occurred.   But, this patient has been survived, and SIV is not lethal factor due to cancer.   Other viral genes such as ORF1a  (Avian infectious bronchitis virus; IBV) at 10.9, Genome polyprotein (Hog cholera virus; Classical swine fever virus;CSFV) at 0.74, Structural polyprotein (Venezuelan equine  encephalitis virus; VEEV) at    0.77, Structural polyprotein (O'nyong Nyong virus; ONNV) at 18.8, X2A protein (Porcine transmissible gastroenteric coronavirus; PTGEV) at 0.09 μg/mg of tissue protein, respectively, but these are not linked to cancer.