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The paper presents a new Information Processing paradigm based on the dynamics encountered in life from organisms as different as Amoebas and the Mammalian brain. Our thesis contemplates that life supports information processing via metabolic dynamics in self organized enzymatic networks which have the capacity to represent functional catalytic patterns that can be instantiated by speci�fic input stimuli. Furthermore, the information patterns can be transferred from the functional dynamics of the metabolic networks to the biochemical enzymatic activity information encoded by DNA. The metabolic dynamics are governed by fractional dynamics that evolve in topological fractal spaces with multiscale time parameters generating complex attractors. The complete dynamic information process is driven by the shorterm process of metabolic dynamics and the longterm process of DNA expression via epigenetic mechanisms.
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How Nature process Information
Ignacio Ozcariz
RQuantech - Geneva (Switzterland)
Criptosasun - Madrid (Spain)
(Dated: September 10, 2020)
The paper presents a new Information Processing paradigm based on the dynamics encountered
in life from organisms as different as Amoebas and the Mammalian brain.
Our thesis contemplates that life supports information processing via metabolic dynamics in self-
organized enzymatic networks which have the capacity to represent functional catalytic patterns
that can be instantiated by specific input stimuli. Furthermore, the information patterns can be
transferred from the functional dynamics of the metabolic networks to the biochemical enzymatic
activity information encoded by DNA.
The metabolic dynamics are governed by fractional dynamics that evolve in topological fractal
spaces with multiscale time parameters generating complex attractors.
The complete dynamic information process is driven by the shorterm process of metabolic dy-
namics and the longterm process of DNA expression via epigenetic mechanisms.
“Once the development was ended, the founts of growth
and regeneration of the axons and dendrites dried up
irrevocably. In the adult centres, the nerve paths are
something fixed, ended, and immutable. Everything may
die, nothing may be regenerated. It is for the science
of the future to change, if possible, this harsh decree.”
Santiago Ram´on y Cajal
I. Introduction. 2
II. Origin and evolution of the nervous system. 2
A. Introduction 2
B. Amoeba’s information processing system 2
1. Amoeba’s Immune System 2
2. Amoeba’s development of the immune
system 2
3. From immune system to nervous system 3
C. Nervous system evolution 3
D. Mammalians Nervous system 4
III. The tetrapartite synapses 5
A. Introduction 5
B. Extracellular Matrix 5
C. Glial Networks 6
D. Neural Networks 6
E. The holo-network 8
IV. Fractional Dynamics 8
A. A history dependent and non-local dynamics 8
New Information Processing framework
Also at Universidad Politecnica Madrid. Doctorate Student;
1. Multiplicative calculus (Geometric and
Bi-geometric) 9
2. Fractional Calculus 10
B. Network fractional dynamics 12
1. Algebraic considerations 12
2. Dynamical model 12
C. Shorterm vs. longterm information
processing 15
V. Practical Device implementation 15
A. Light and sound correlated as an input
stimuli to the network 15
B. Potential effects in Epilepsy and other
neurological diseases 16
C. Potential effects on COVID-19 patients 17
A. Summary 17
B. Disclaimer 17
Acknowledgments 17
A. Biological papers 17
B. Mathematical Papers 18
References 18
The aim of the paper is to represent the organism as
a Holo-Network formed by the integrated assemblage of
neural, glial, extracellular molecular networks and the
immune system that until now has always been consid-
ered in isolated compartments.
The extracellular matrix (ECM) is produced and dy-
namically modulated by several cell types that include
neurons and glial cells. The ECM plays a role in the
communication and control of the dynamics of neuroglial,
intra-neural, and intra-glial networks. Also the immune
system is playing a central role in the molecular dance
established by these networks and the full interplay be-
tween all of them achieves the objective of the homeosta-
sis state of the organism with its environment.
A. Introduction
To understand how the most complex nervous systems
works we must first understand the species evolution of
these overly complex functions.
The nervous system is contingent on the development
of the different eukaryotes families. We will develop in
the present paper the thesis that the specialization, first
of the immune system of the primordial eukaryotes in its
information processing needs, and second the integration
of some of the networks supporting these communication
functions within the organisms, drove the development
of the vertebrate nervous system.
An efficient and integrated, in dynamic terms,
perception-action system linking information receptors
(external and internal) to actuators, was the vital func-
tion on which evolution acted to enhance the capabilities
of the nervous system. Also, the dynamics acted over
the epigenetics machinery for the cell and exerted evo-
lutionary pressures to achieve the best fitted organism
according to the characteristics of the environment.
To have achieve a complete Mammalian nervous sys-
tem (central and autonomous) required almost two bil-
lion years of evolution. During three-quarters of this
time, roughly 540 million years ago, animal life erupted,
diversifying into a kaleidoscope of forms in what is now
known as the Cambrian explosion, information process-
ing was then based on metabolic dynamics supported by
the communication channels in the internal structural
matrix of the individual cells. We will see these Amoeba
systems in the subsection B of this section.
Subsection (II C) of this section represents the part of
the evolution devoted to the mechanisms that multicel-
lular arrangements makes to maintain signal processing
coherent between the sets of cells. Also, we will look over
the nervous system of the mollusc as a first step to see
the evolution of the nervous system.
Subsection (II D) will present the full complexity of
the Mammalians nervous system. To study these next
steps in the evolutionary history of the animal kingdom,
we shall consider the fertile ground of embryology. In
these grounds we can see how the nervous systems emerge
from a cluster of cells, the morula. We will quickly run
through the fundamental discoveries of homeotic genes,
thanks to experiments on the fruit fly, Drosophila, during
the 1980s in which homeotic genes were discovered. They
are responsible to arrange the development of the embryo
and impose its final shape. We will finally get to the
current complexity of the different families of specialized
nervous cells (Neural and Glial) and the Extracellular
matrix in which these cells are structured that sits in the
core of the Mammalians nervous system.
B. Amoeba’s information processing system
1. Amoeba’s Immune System
Amoeba is one of the most abundant organisms in
ecosystems such as pond water. Under a microscope,
it is possible to see them wandering around on the slide,
but it is also remarkable to see them feeding on micro-
organisms, like a culture of macrophages. Although It is
still up for debate that the amoeba could be the earliest
form of macrophage, and by an unknown evolutionary
pathway, give raise to the modern macro phage. One
of the clear lessons from the study of the Amoeba’s be-
haviour is the complexity of the tasks that it accom-
plishes. From the feeding of Paramecium to the discrim-
ination of food from other Amoebas it is amazing the
complex dances that the simple organism develops.
One of the theories regarding the onset of innate im-
munity in eukaryotes is that it started in microorganism
such as an amoeba to accomplish the function of discrim-
ination between food and other Amoebas. The rationale
supporting this theory is that amoebas that do not make
this distinction would vanish incredibly earlier from the
ecosystem. Therefore, some kind of communication sys-
tem in the surface of the amoebas gets information from
the outside that will makes the molecules be able to dis-
tinguish between food, that is safe to be eaten, and an-
other amoeba, or even another part of the same amoeba.
The characteristics of this communication mechanism is
not yet known, but one of its basic functions is to dis-
criminate between what is self and what is not, being
extremely specific as it is the core function of the im-
mune system.
2. Amoeba’s development of the immune system
The movement of amoebas is seemingly at random,
but the more evolutionary macrophages, act with an aim
if they are exposed to a chemo-attractant. In that case
all of themwould head in the same direction. Therefore,
under the influence of these environment signals amoe-
bas behave like macrophages. A potential interplay with
the first multicellular organisms would have happened
and amoebas may have had a parasitic action. Inverte-
brates and vertebrates present phagocytic cells that have
much in common with amoebas and fill the role of the
”police” in the blood vessels and tissues, searching for
aliens. One theory is that these phagocytic cells, the
ancestors of macrophages, come from a population that
retained an ancestral, unicellular morphology, as they are
today reflected in the amoebas. One important thing to
bear in mind, is that complex means of host defence were
present in the genome by the time eukaryotes developed
into plants and animals.
This defence system, shared by plants and animals,
is the Toll receptor signalling pathway and is based on
NFκB (nuclear factor kappa-light-chain-enhancer of acti-
vated B cells) activation of gene function. This pathway
has been demonstrated in vertebrates, invertebrates and,
but not conclusively, in plants.
Experiments carried out with mice demonstrated the
following: Mice strains that cannot respond to bacte-
rial lipopolysaccharide (LPS) due to a defective Toll
gene cannot mount an adaptive immune response against
gram-negative bacteria, which carry LPS on their surface.
This is a proof that the loss of innate immunity had a
discernible effect on the adaptive immune response.
More experiments have demonstrated the above role
of genes involved in immunity to diseases in flies and
that these genes have homologues that also operate in
humans. Toll genes in flies and TLR genes in humans.
Homologues of these genes have also been found in other
rather different organisms like sharks, nematodes, and
In summary the innate immune system provides early
defence against pathogen attack, and communicates to
the adaptive immune system that a pathogen invasion
is happening. As we have seen a very ancient signalling
pathway, the Toll pathway, is acting to support this dual
function. This pathway is hundreds of million years older
than the adaptive immune system and is present in prac-
tically all the superior organisms today. The other com-
ponent of the innate immunity, the phagocytic cells, may
have their ancestors in amoeba-like eukaryotes. One of
the key points of the above discussion is that immune
system bears a signalling (information processing) mech-
anism at its deepest roots.
3. From immune system to nervous system
One of the new paradigms that have arisen in the field
of physiology is the interplay between the immune system
and the nervous system. [1] The idea that neurotrans-
mitters could serve as immunomodulators emerged with
the discovery in complex organisms, that their release
and diffusion from nervous tissue could lead to signalling
through lymphocyte cell-surface receptors and the mod-
ulation of the immune function. [2]
The main idea is that the immune system and the
nervous system, that handle thousands of neuro-immune
transmitters can sense and respond to multiple environ-
mental conditions and aggressions. Cross talk between
these two systems has been reported in all the organisms
and all states, and the neuro-immune interactions can
operate as important immunoregulatory hubs.
In the previous section we have introduced the role of
the immune system in amoebas that now we will see, can
also support nervous system-like functions. In a pub-
lished paper [3] it was presented the shocking behaviour
of the true slime mold Physarum. When these amoebas
were exposed to unfavourable conditions as three con-
secutive pulses at constant intervals, they reduced their
locomotive speed in response to each episode. When
the plasmodia was subsequently subjected to favourable
conditions, they spontaneously reduced their locomotive
speed at the time when the next unfavourable episode
would have occurred. This implies the anticipation of
impending environmental change.
Moreover, it has been also demonstrated that,
Physarum Polycephalum, displays other abilities that
could be initially tagged as intelligent. It can solve mazes
[4] and geometrical puzzles [5], control robots [6], and in
a recent paper there is presented evidence of conditioned
behaviour in the organism. [7]
In our current nature’s information processing
paradigm this behaviour would only apply to organisms
that have a nervous system. So, information processing
by unicellular eukaryotes could be thought as a precursor
of nervous-dependent functions in multicellular organ-
isms. All the functions seen in the previous paragraph, no
matter the way in which they are performed, have some
information processing abilities that until know have re-
mained unexplained.
We introduce here the hypothesis that these capabil-
ities arose from the previous signalling pathways devel-
oped by the early immune system that was adapted to
new information processing functionalities like the ones
C. Nervous system evolution
To develop in more detail the thesis introduced at the
end of the previous section we must now have a look
at the evolution of the nervous system from the simple
multicellular organisms to Mammalians. The idea is to
tackle the complexity of mammalian models, which are
comprised of highly interconnected multiple networks,
studying first simpler organisms.
One of the most promising discoveries regarding early
development of electrical conductance in multicellular ar-
rangements was made by Dr. Lars Peter Nielsen [8] at
the start of this century in 2009.
Dr.Nielsen introduced the concept of cable-bacteria
that more recently has been complemented with
nanowire-bacteria. These bacteria are arranged in a
manner that they create a cylinder of conducting wires
that encases a chain of cells. The wires allow the mi-
crobes to transfer electrons involved in redox reactions
that take place at spatially separated loci (centimetres
in cable-bacteria and micrometres in nano-bacteria).For
the cable-bacteria, the electrons are gained by oxidizing
hydrogen sulphide and are then transferred to oxygen-
rich sediment, where the electrons are linked to wa-
ter molecules. In the nanowire-bacteria the electrons
are shuttled between the oxidation side of organic com-
pounds along the so-called protein nanowires to the
electron-accepting side. There is still a lot of debate
about how the bacterial nanowires conduct electrons. Dr.
Derek Lovely [9] introduced the idea that chains of pro-
teins called pilins, which consist of ring-shaped amino
acids, are the key mechanism that support the electron
transport creating the electric current.
Once we have seen that Nature developed the mecha-
nisms to generate electric currents, we can make the hy-
pothesis that similar processes were utilized by eukary-
otes to be used in specialized cells to fulfil the signal
transfer in multicellular arrangements.
The specialized cells that we commonly associate to
the functions performed by the nervous systems are the
neurons. We will present further on in this paper that
neurons are only a part of the complex arrangement that
is necessary to carry on all the functionality of the ner-
vous system.
In any case and starting by the current paradigm, Dr.
Michael Bate [10] introduced the concept that “neurons
are born and differentiate in ways that are not condi-
tioned by their future functions as elements of neural
circuits” He also stated that “To understand how func-
tions ... can emerge from these beginnings, it is worth
remembering that fundamental attributes of the nervous
system such as the circuitry underlying locomotion or
escape behaviour are probably also present as a rather
stereotyped and evolutionary conserved set of cells and
connections. It is at least possible to envisage that there
is a fundamental framework of circuitry just as there is
a scaffolding of initial pathways”.
The nervous system would then be composed of a mix
of, evolutionary proven, signal pathways mechanisms,
many of which were already developed in early life or-
The classical works to understand the basics of the ner-
vous system has been performed in the squid giant axon.
In this “simple” system main studies have been devoted
to the models supporting functionality of the neuronal
network of the squid. One of the approaches that we can
take to get a deeper glimpse into the nervous system of
these organisms regarding the biomolecules implied in the
signalling paths is to get the response against anaesthet-
ics agents that as we know now are a powerful influencers
in the functionalities of the system.
One of these early works was performed by (Shrivastav
et al., 1976) [11] They exposed a giant squid axon to the
volatile anaesthetic halothane and recorded membrane
depolarization at low anaesthetic concentrations. They
observed a similar depolarizing effect with the volatile
anaesthetic trichloroethylene, which also increased the
threshold potential for action potential firing and reduced
the amplitude of resulting action potentials. The key
point of his experience was that the mechanism was act-
ing at the level of the synapse and generated the anaes-
thetic effect on the neuron functionality.
More experiences were carried later by Dr. Ryden
Armstrong [12]. Even if they recognized that “there re-
mains significant uncertainty as to how and where these
compounds act at the molecular and cellular levels.“, re-
garding the anaesthetics actions over nervous systems of
mollusc the results of their experiences were that “work
showed that volatile general anaesthetic compounds di-
rectly interact with ion channel proteins, a potassium
channel that hyperpolarized neurons, preventing neuro-
transmitter release. Subsequent work then showed that
general anaesthetics also directly target and suppress ion
movement through the excitatory acetylcholine receptor.
Thus, show that some general anaesthetics target both
presynaptic and postsynaptic sites on neurons. These
studies also highlight the potential target sites of anaes-
thetic actions that include classical and peptidergic neu-
rotransmitter synapses. Finally, the data from various
studies on Lymnaea demonstrate that chronic exposure
of cultured neurons to anaesthetic compounds might ren-
der neuronal growth and synaptic connectivity dysfunc-
From these experiences we can get the point that
synapses, and signal transmission in broad terms, more
than cells are the key actors of the film that nature per-
forms in the information processing representation.
D. Mammalians Nervous system
Back in 1983 Dr.Walter Gehring [13] studying
drosophila, fruit fly, discovered the existence of homeobox
genes responsible for a homeotic transformation where
legs grow from the head instead of the expected anten-
nae. It was the demonstration that the development of
multicellular organisms is based on a program of differ-
ential expression of genetic information.
One of the subsets of homeobox genes are the Hox
genes. They are the genes that determine the identity
of embryonic regions along the body axis. The precursor
cells of the nervous system cells arise within an epithelial
field of cells made competent through the expression of
one or more control genes of the bHLH type (proneural
genes) mediated by the Notch-Delta interaction.
In vertebrates, the embryogenic process known as neu-
rulation are the stages that go from the neural plate to
neural tube and to the neural crest. All the cell types
during this neurulation process arise from pluripotent
embryonic stem cells (ESCs). The adult neural stem
cells (NSCs) persist in two main areas: the ventricular-
subventricular zone, where NSCs give rise to olfactory
neurons, and the hippocampus, where new neurons in-
volved in cognitive processes are generated. In both re-
gions, the stem cells that give rise to neurons are special-
ized populations of astrocytes that maintain close inter-
actions with the brain vasculature and can be activated
by behavioural and pharmacological stimuli. [14]
The important point in the previous paragraph is that
the pluripotent adult cells of the nervous system derives
from an astrocyte population.
If now we come back to the immune origins of the ner-
vous system presented in (II B 3) we will see the current
interrelations between the two systems in the vertebrate
In a paper [2] Dr. Franco presented “Initially, the idea
that neurotransmitters could serve as immunomodulators
emerged with the discovery that their release and diffu-
sion from nervous tissue could lead to signalling through
lymphocyte cell-surface receptors and the modulation of
immune function. It is now evident that neurotransmit-
ters can also be released from leukocytes and act as au-
tocrine or paracrine modulators”. Dr. Franco finished his
paper signalling that “Current and future developments
in understanding the cross-talk between the immune and
nervous systems will probably identify new avenues for
treating immune-mediated diseases using agonists or an-
tagonists of neurotransmitter receptors.”
Last year Dra. Cristina Godinho-Silva, Dra. Filipa
Cardoso, and Dr. Henrique Veiga-Fernandes in their pa-
per [1] introduce the concept “Neuro–Immune Cell Units:
A New Paradigm in Physiology”. Their thesis is “The in-
terplay between the immune and nervous systems has
been acknowledged in the past, but only more recent
studies have started to unravel the cellular and molec-
ular players of such interactions. Mounting evidence in-
dicates that environmental signals are sensed by discrete
neuro–immune cell units (NICUs), which represent de-
fined anatomical locations in which immune and neu-
ronal cells co-localize and functionally interact to steer
tissue physiology and protection. These units have now
been described in multiple tissues throughout the body,
including lymphoid organs, adipose tissue, and mucosal
barriers. As such, NICUs are emerging as important or-
chestrators of multiple physiological processes, including
haematopoiesis, organogenesis, inflammation, tissue re-
pair, and thermogenesis.”
This year it has been reported in [15] the regulation be-
tween Neuro-Immune Circuits mainly related to gut tis-
sues and Organ Homeostasis. Main result of the report
is “Preclinical studies targeting neuro-immune interac-
tions upon stimulation of the vagus nerve, application
of acetylcholine agonist, and b2 adrenoreceptor agonists
have emerged the potential successful treatment in in-
flammatory diseases. Of note, the site-specific control of
immune functions by the nervous system via neurotrans-
mitters/neuropeptides suggest that the nervous system
can exert a rapid and local control of immune cells”.
We finalize this introduction to the Mammalian ner-
vous system emphasizing two points;
1. the origin of the multiple cell types of the system
from a unique type of “germ” that in the adult
phase are the Astrocytes.
2. the full relation at the signal processing level be-
tween the immune system and the nervous systems
A. Introduction
We could have headed this section also by the title
“The nervous system: the known unknown”, but we have
preferred to focus on the theme that in the next section
will be developed as the core of the paper. The dynamics
that underscore not the individual networks that inter-
twined in the nervous system nor the full hyper-network
which nodes are the complex synapses.
We consider that synapses are the places in which
presynaptic neurons, postsynaptic neurons, astrocytes
and all the molecules in the extracellular matrix make
their mutual interrelations. All the actors are influenced
by the results of the processing in the synapse. So, the
former paradigm that the nervous system was based on
the responses of the postsynaptic neurons to the signals
generated by the presynaptic neurons, has now changed
to a global dynamic process in which Neurons, Glial cells
and Extracellular matrix composites, evolution.
We will present in the next sections several references
for the subsystems implied that would aid to support the
change of paradigm
B. Extracellular Matrix
From the onset of the century the role of the Extracel-
lular Matrix (ECM) on the nervous system has started
to be recognized. It was not until 1971 that was accepted
the existence of the ECM initially based on the predomi-
nance of hyaluronan and chondroitin sulphate proteogly-
cans (CSPG). Taking in account that ECM suppose 20%
of the volume of the adult brain it is shocking that its
role was so diminished.
In 2008 Drs. Zimmermann in their paper [16] estab-
lished that ECM is rich in hyaluronan, CSPG (aggrecan,
versican, neurocan, brevican, phosphacan), link proteins
and tenascins (Tn-R, Tn-C) and its role is to regulate
the cellular migration and axonal growth. Thus, ECM
participates actively in the development and maturation
of the nervous system. ECM swift assembly and remod-
elling was associated with axonal guidance functions in
the periphery and with the structural stabilization of
myelinated fibre tracts and synaptic contacts in the mat-
urating central nervous system.
More recently has been reported the organization of
the CSPG into either diffuse or condensed ECM. Diffuse
ECM is distributed throughout the brain and fills peri-
synaptic spaces, whereas condensed ECM selectively sur-
rounds parvalbumin-expressing inhibitory neurons (PV
cells) in mesh-like structures called perineuronal nets
In [17]) is reported that “ECM not only forms physical
barriers that modulate neural plasticity and axon regen-
eration, but also forms molecular brakes that actively
controls maturation of PV cells and synapse plasticity in
which sulphation patterns of CS chains play a key role.
Structural remodelling of the brain ECM modulates neu-
ral function during development and pathogenesis.”
The main conclusion is ECM components and the
molecules they interact with, will provide new insight
into the molecular networks that regulate neural plastic-
C. Glial Networks
One of the strangest things in neurophysiology studies
has been for most of the time of the past century the
secondary role attributed to the Glial system. Starting
with the pejorative name gave to most of 50% of the to-
tal number of cells of the nervous system, glia, from the
Latin and Greek for glue, and continuing for the asso-
ciate role as merely “support” cells of the big kings, the
It was at the end of XIX century that the Spanish
Nobel price Ramon y Cajal brought to light the potential
role of these cells in two seminal articles, “Something
about the physiological significance of neuroglia” (1897)
and “A contribution to the understanding of neuroglia in
the human brain” (1913). [18].
The posterior oblivion of these cells in the opinion of
the author was due to the electrical characteristics of the
neuronal system in comparison with the biochemical op-
eration of the glial system. The measure of the activity of
neurons in the century of electricity was more straightfor-
ward than the comprehension of the biomolecules implied
in the functionality of glia cells.
Uniquely at the end of the century and with a big
impulse from the Spanish Institute Ramon y Cajal and
Dr. Alfonso Araque, Dra. Gertudris Perea and Dra.
Marta Navarrete the role of glia has started to become
One of the extraordinary ideas of Cajal in his paper
of 1913 was that “The gray matter neuroglia would con-
stitute a vast endocrine gland intertwined with neurons
and nerve plexus, intended perhaps to produce hormones
associated with the brain activity”. Current research has
demonstrated that the so-called gliotransmitters as par-
allel to the neuronal neurotransmitters regulate widely
neuron functionality.
The role of the Astrocytes releasing gliotransmitters
and controlling transmission and plasticity at the synap-
tic level led to a new concept in synaptic physiology, the
Tripartite Synapse, in which astrocytes are integral ele-
ments of the synapses and actively exchange information
with the neuronal elements (Araque et al.; [19] Halassa
et al.,[20] ;Perea et al. [21]).
More recently, March 2020) a Science paper written by
thirty authors [22] goes further in the relation between
neurons and glia establishing a powerful link between
these two systems at the level of the bodies of the cells via
a purinergic junction. Even if they initially stated that
“Microglia perform dynamic surveillance of their micro-
environment using motile microglial processes that con-
stantly interact with neurons. However, the molecular
mechanisms of bidirectional microglia–neuron communi-
cation are unclear” the results of their research are “
All of these results unequivocally indicate that microglia
continuously monitor neuronal status through somatic
junctions, rapidly responding to neuronal changes and
initiating neuroprotective actions”.
Other aspect of the glia functionality that we want to
take in consideration is that the most reported imaging
techniques of the brain are based on the activity of the
glial cells. Two of these techniques to monitor brain ac-
tivity, functional Magnetic Resonance Imaging (fMRI)
and Diffusion-Tensor Imaging (DTI) are not based on
the electrical activity of neurons, nor the oxygen content
supplied by blood capillaries (fMRI), or by anisotropic
water diffusion (DTI). Oxygen consumption measured in
a fMRI voxel is the result of the metabolism of differ-
ent cell types in which, glial cells (astrocytes, microglia,
endothelial, neutrophils, pericytes, NG2 glia, 0ligoden-
drocytes) are the main source with neurons and vascular
as secondary. In the case of DTI is even more focused
the role of the glia because DTI signal are based on the
myelin-axon unit and support-providing myelin sheaths
are the role of the oligodendrocytes.
So, the neuron centred brain is still today the main
paradigm in the signal processing function but as we
have seen glia cells have functions that clearly make this
paradigm complicated to support.
The functionality of the so called “tri-partite” synapse
in which Astrocytes regulate extracellular ion and trans-
mitter homeostasis [23] as well as the role of the neuron-
glia junctions is out of question and by the modulation of
neuro and glia transmitters [24], and peptide hormones,
fully influences the dynamics of neurons. Also, the role
of the oligodendrocytes metabolically supports neuronal
axons, as the base of neural circuits is clearly a powerful
influence in the dynamics of these circuits.
D. Neural Networks
Hundreds of thousands of papers have been devoted to
the functionalities of Neural Networks from a full range
of perspectives going from computational approaches to
cell biochemistry.
Taking into account that the purpose of the paper is
dealing with the dynamics of the different systems im-
plied in the information processing tasks we will focus
briefly in two aspects of the neural networks; i) the dy-
namics of the system isolated ii) the potential influence
of external factors of the dynamic system.
The historical model for the dynamics of the neuron
isolated has been the Hodgkin–Huxley and its multiple
derivations. One more developed model was introduced
by Eugene M. Izhikevich in 2003 [25]. The model con-
templated the analyses of the dynamics using bifurcation
methodologies and with only four parameters he was able
to reproduce the spiking and bursting behaviour of some
types of isolated neurons. In figures 1 and 2 we present a
Matlab c
simulation of the model using a network of one
thousand randomly coupled spiking neurons. As we can
see, we obtain some common features in the spike model
of the neuron of the neuron 927. Figure (2).
FIG. 1. 1000 Network Firing
FIG. 2. Neuron 927 Spiking Pattern
Regarding models of complete neural circuits, one that
contemplates high order dynamics is the Freeman model
(KIV model). The model was derived from the olfactory
system and presents a dynamic with chaotic evolution.
To achieve this chaotic result the model is based on dif-
ferential equations of second order.
The full model is presented in [26] and the summary of
the model states, “We postulate that the meaning of the
information exists in the interrelations of the enormous
number of neurons carrying each a fragment of informa-
tion, which constitutes the knowledge brains create from
information. This knowledge must be stored and later
mobilized in the serial processes for categorizing sensory
information and then deciding on courses of action in re-
sponse to the input. Mobilized knowledge has the form of
bursts of oscillatory electroencephalographic (EEG) and
electrocorticographic (ECoG) potentials carrying spatial
patterns of amplitude modulation (AM), which emerge
from chaotic oscillations of background activity through
episodic bifurcations (state transitions) by which the cor-
tex jumps from chaotic disorder into phase-locked limit
cycle activity and back again.”
From this model we will see in the next section, that
the interrelation with the rest of the network systems im-
plied, will get a more elaborated information processing
Going to the influence of external factors in the net-
work dynamics and with the aim to only present one of
them, we focus on the effects of alcohol on the nervous
The complete actions of ethanol in the nervous sys-
tem cannot be covered in this very brief mention and
of course the effects of ethanol includes actions on glia,
and extracellular matrix, but we will focus only on the
actions of ethanol with the molecular signalling path-
ways involved. “Among the central actions stimulated
by alcohol, its inhibitory gabaminergic effect, in con-
junction with the inhibition of certain excitatory glu-
tamatergic receptors, endocannabinoids, cerebellar cal-
cium channels and hippocampal proteins which are es-
sential for memory formation, results in sedation, loss
of inhibitions, relaxation, loss of cognitive functions, at-
tention deficit, impaired sleep-wake regulation (blackout
effect), and the final state of psycho-motor depression.
On the other hand, the excitatory action of alcohol on
mu receptors of the opioid system and subsequent acti-
vation of the limbic system by dopamine and of 5-HT1B
receptors by serotonin result in the effect of well-being
and mood elevation. In addition, the down regulation
of dopamine and GABA receptors explains the increase
in alcohol consumption and subsequent development of
chemical dependency”[27].
The key point that we want to emphasize here is that
the effect of a single molecule could alter the entire dy-
namics of the complete neural network.
FIG. 3. Organism as a Holo-Network
E. The holo-network
In the previous subsections we have made an approach
to the different networks that must be taken into account
to fully grab the inner functionalities of the nervous sys-
Here we will make a summary of the interrelations of
these networks and the ones implicated in the immune
system with the aim to delineate a common ground for
the dynamics of an entire organism. Of course, the dy-
namics must take also into account the environment in
which this organism evolves.
The objective is to demonstrate that Homeostasis of
the complete system Organism plus Environment is the
driver for the dynamic.
Starting with the tri-partite synapse contemplated in
the glia section we can now enlarge this concept to the
tetra party synapse as had been presented in (Dityatev
and Rusakov [28] ; Verkhratsky and Nedergaard [29];
Smith et al. [30] Dzyubenko et al.[31]). These papers
support the concept of the fully integration and inter-
relation of the Extracellular matrix components and the
other two networks taken into account that both, neurons
and astrocytes, synthesized components that become key
agents at the ECM level and have a critical role in the
functionality of synapses in the nervous system.
So, the actors at the synaptic level are.
(i) the presynaptic terminal
(ii) the postsynaptic element
(iii) the peri-synaptic processes of the astrocytes
(iv) the processes of neighbouring microglial cells that
periodically contact the synaptic structure
(v) the extracellular matrix (ECM), which is present
in the synaptic cleft and also extends extrasynaptically.
With this complex structure in mind we can make the
hypothesis that tetra-partite synapses are the nodes of a
kind of hyper-network (Marc) that will be the substrate
for the dynamics of the nervous system. Remembering
now the considerations done in subsection(II D) regard-
ing the relations between the nervous system and the
immune system we can fully expand the hyper-network
presented to a Holo-Network that will also include these
We are using the prefix “holo”, with the meaning of
whole, entire, capturing the idea that the organism has
an underlying global network that processes all the in-
formation coming from external and internal sources in
order to incorporate them into an integrated framework.
The clear aim of this information process is to main-
tain the life of the organism and we will take life defi-
nition as the homeostatic state of the ensemble organ-
A. A history dependent and non-local dynamics
Newtonian calculus is based on the “Method of Flux-
ions”, a book of Sir Isaac Newton completed in 1671 but
published posthumously in 1736. This late publishing
was the cause of a bitter dispute with his contemporary
Gottfried Leibniz regarding the priority of the calculus
In fact, Leibniz had a deeper understanding of the con-
cept, as we will see later, due to his potential broad scope
that he envisaged.
In the second half of the 17th century, several mathe-
maticians were occupied in the infinitesimal analysis in-
troduced earlier by Barrow and the genius of Newton and
Leibniz was to systematize the concept of derivative.
Newton defined the derivative Das the local behaviour
of a function around one-point x0taking into account one
infinitesimal δx, that would be as little as needed.
Df (x0) = f(x0+dx)
dx (1)
One of the key points in this definition is the locality
of the derivative taking into account that Dis related to
the point x0.
Also, it is important to note that this definition has
in its root a kind of average around the point x0, so
if the function has a huge variation in this point, like
exponential functions, the approach could be misleading.
1. Multiplicative calculus (Geometric and Bi-geometric)
Robert Katz and Michael Grossman introduced in
[32] one idea that even Galileo had discussed briefly;
to use ratios of the function instead of differences for
the derivative definition. From this base multiplicative
calculus also known as “star” calculus was born.
a. Definition of the * derivative.
The * derivative of the function fis given by:
f?(x) = lim
Doing some calculations (see: [32]) we can obtain the
relation between the classic (prime) and * derivatives:
f?(x) = exp(f0(x)
f(x))= exp(ln f)(0)(x)(3)
considering that (ln f)(x) = ln(f(x)). If f(x) is a posi-
tive function and f(n)exists,
f?(n)(x) = exp(ln f)(n)(x)(4)
In this expression is included the case for n= 0 and so,
f(x) = exp(ln f)(x)(5)
b. Geometric interpretation of the * derivative.
If we remember the geometric interpretation of the
classic derivative it is the slope of the line that is tan-
gent to the curve at a particular point.
y0(x) = lim
This last relation is the change rate of the function for a
change rate of the variable. Remembering the definition
of the * derivative in (2) and considering ∆x=x2
x1the variation of the independent variable and ∆?y=
y(x1the star variation of the dependent variable.
From y?(x) = limx0(∆?y)1
xwe get finally
y(x)xThen we can establish
Summarizing we have:
Classical derivative
y(x+ ∆x)y(x) + y0(x)∆x(9)
Star derivative
y(x+ ∆x)y(x) exp y0(x)
c. Linear approximation versus exponential.
approximation. A function y(x) that is differentiable at
a point x=x0has a linear approximation Lnear this
point defined as follows
L{y(x)}=y(x0) + y0(x)×(xx0) (11)
Another approximation to a function could be using ex-
ponential functions as in , y(x) = a×bx.These functions
have constant star derivative and y(x+1) = y?(x)×y(x).
The following two properties are true for all positive dif-
ferential functions [33]
1. If we scale a function with a constant factor, the
function and the scale one has the same star deriva-
tive that is the constant factor. This is the idea
behind the multiplicative rate of change. So, if
Sy(x) = c×y(x), then Sy?(x) = y?(x) = c.
2. Any positive differentiable function at a point x0
has an exponential approximation Enear x0de-
fined by;
We can show the differences between the two approxima-
tions with next example:
y(x) = 1
x2y0(x) = 2
x3y?(x) = exp2
y(1) = 1 y0(1) = 2y?(1) = exp2
Linear approximation at x= 1 is
L{y(x)}=y(1) + y0(1) ×(x1) = 3 2×x(13)
Exponential approximation at x= 1 is
E{y(x)}=y(1) ×y?(1)(x1) = exp2×(1x)(14)
We can see the results of the approximations in the Fig-
ure (4) below
FIG. 4. Linear vs. Exponential approximation
So, for the kind of curves as the exponential, the expo-
nential approximation has a better match than the linear.
d. Bi-geometric Calculus.
One further variation of the definition of derivative
gives raise to the bigeometric calculus. In this case the
bigeometric derivative is defined as being:
y??(x) = lim
ln xln x0(15)
And the relation with the classic derivative is:
y??(x) = exp x×y0
If we remember from the economy manuals that elasticity
is the ratio between y
xand y
xis the relation of quantities
and prices, we have with the bigeometric derivative the
perfect tool to deal with the functions that arise in this
domain as well as others like biology in which similar
ratios, (quantities/catalysers) have a main role. (Scale
law functions).
2. Fractional Calculus
a. Definitions. Fractional Integrals and Derivatives.
In the previous section we have seen that classic deriva-
tive gives the linear approximation of smooth functions,
and multiplicative or star derivatives, allow an exponen-
tial approximation. In both cases the derivative is linked
to a point of the curve and so has a purely local charac-
Now going further on the power laws, we will introduce
the concept of Fractional Calculus that we can define as
the field with objects that are characterized by power
law non-locality, power law longterm memory or fractal
properties by using integration and differentiation of non-
integer orders.
Returning to the quarrels between Newton and Leib-
niz, it was this last one that invented the notation dny
Perhaps it was naive play with symbols that prompted
L’Hospital in 1695 to ask Leibniz, “What if n be 1/2?”
Leibniz [34] replied: “You can see by that, sir, that one
can express by an infinite series a quantity such as D1
or D1:2xy . Although infinite series and geometry are
distant relations, infinite series admits only the use of
exponents which are positive and negative integers, and
does not, as yet, know the use of fractional exponents.”
Later, in the same letter, Leibniz continues prophet-
ically: “Thus it follows that D1
2xwill be equal to
xdx :x. This is an apparent paradox from which, one
day, useful consequences will be drawn.”
Continuing with the history Euler (1730) mentioned
interpolating between integral orders of a derivative.
Laplace (1812) defined a fractional derivative by means
of an integral, and it was Lacroix (1819) the first to write
a derivative of fractional order.
For example if we use potential functions as y=xm,
Lacroix expressed it as,
(mn)!xmn=Γ(m+ 1)
Γ(mn+ 1)xmn(17)
Replacing m= 1 and n=1
2we obtain the fractional
derivative of order 0.5 of the function y=x
dx 1
In which we can see the result advanced by Leibniz.
To summarize a long history, we will use now on the
concept of fractional derivative and integral elaborated
by Liouville and reframed by Riemann:
We start with the integral presentation.
Left side:
tf(t) = 1
Right side:
bf(t) = 1
The derivative of Riemann Liouville is defined by
xf(x) = 1
dx )nZx
αreal number, ninteger, (n1) α < n (21)
M. Caputo in 1967 made a little reformulation of the
xf(x) = 1
αreal number, ninteger, (n1) α < n (22)
Properties of Fractional Derivatives.
1. Linearity Fractional differentiation is a linear
Dα(κf(x) + λg(x)) = κDαf(x) + λDαg(x) (23)
2. Scaling and Scale invariance
3. Sequential Composition
Dαf(x) = Dα1Dα2...Dαnf(x)
α=α1+α2+... +αn
b. Geometric Interpretation of fractional integration.
In this section we will get the model of Dr. Igor Pod-
lubny [35] that introduced a very visual interpretation of
the fractional integration and subsequent derivation.
If we refer to equation (19)and consider the function
gt(τ) = 1
Γ(α+ 1){tα(tτ)α}(26)
this function has a scaling property. So, if we take t1=kt
and τ1= , then
gt1(τ1) = gkt(kτ ) = kαgt(τ) (27)
Now we can write the integral in the form
tf(t) = Zt
f(τ)dgt(τ) (28)
This expression can be considered as a Stieltjes integral
and we will try to understand it from a representation in
the axes τ, g andf , for different values of t.
First we draw the curve that results of the interception
of the surfaces gt(τ) and f(τ) for (τ, g ) for 0 τtand
different values of tfrom t= 10 and intervals of ∆t=1.
Let us establish f(τ) = |tau + 0.5 sin(τ)
Figure (5), shows in blue this curve.
FIG. 5. Geometrical Representation of Fractional Integral
Now if we consider the projection of this curve over
the three planes, projection over the plane f(τ),(τ, t) is
simply f(t) and the area under the curve in this plane
will represent the integral
t(t) = Zt
So, the integer integral.
Considering now the projection over the plane
f(τ), gt(τ) , and the area under this curve in this plane
it is precisely the Stieltjes integral. The key point is
that different values of tas parameter does not change
the classical integral and of course changes the fractional
From this reflection we can point out a geometric in-
terpretation of fractional integration, as the addition of a
third dimension gt(τ) to the classical pair f(τ)), τ . This
third dimension will act as a non-lineal time scaling over
the ffunction.
We will see later more on that with the Mellin trans-
form that act as a kernel function defined for this geo-
metrical explanation.
If we now consider the function fas a velocity or rate
of change of a variable, the first integral of the velocity is
the space travelled and if we now consider the fractional
SO(t) = Zt
v(τ)dgt(τ) = 0Iα
tv(t) (30)
The ”space” travelled in this case SOis the result coming
from a kind of geometrical time.
From here we can also develop a geometrical interpre-
tation of the Rieman-Liouville derivative. Taking into
account that the velocity is the derivative of the space
v(t) = 0Dα
tSO(t) (31)
with 0Dα
t, the Rieman-Liouville derivative of order αand
0< α < 1 is defined by
tf(t) = 1
Γ(1 α)
dt Zt
Then left-sided Rieman-Liouville fractional derivative of
the distance SOis equal to the individual speed vO(rate
of change) of that object.
vO(t) = d
dt 0Iα
tv(t) = 0D1α
tv(t) (33)
B. Network fractional dynamics
1. Algebraic considerations
In this section we must acknowledge the seminal con-
tributions of I.C. Baianu to the algebraic approach to
biology in which we have based the next paragraphs as
the roots for our Holo-Network dynamics.
As we have presented in the section (III E) an organism
would have a dynamic system supported through tightly
coupled, biochemical subsystems, dependent upon spe-
cific, metabolic processes, information processing-linked,
that we named Holo-Network.
Information processing of the kind envisaged is more a
dynamic process than a digital computation as the cur-
rent approach presents. If we consider the dynamic under
an algebraic perspective we can make the comparison be-
tween the Boolean logic of digital computers and many-
valued logic and logic algebras that is the approach that
we propose here.
Robert Rosen and I. Baianu [36] presented algebraic
models for ”ultra-complex, in the sense of extreme com-
plexity, in order to avoid any possible confusion, and
clearly distinguish it from the complicated model systems
that are routinely called Complex Systems”, They intro-
duced ” the presence of a higher dimensional algebra and
mathematical structure in categories that are represent-
ing these systems and their transformations”
Capabilities of an ultra-complex system for both
metabolism, M, and repair, R, must be generated from
within the system’s own sufficiently complex organiza-
tion; this implies also that metabolism leads naturally to
repair, or Metabolism-Replacement, or (M,R), system.
It is considered to be non-reducible to its components
and algorithmically non-computable, in the sense of not
being valuable as a function by a Turing machine. From
the point of view of ultra-complex dynamics evolution is
extremely complex, chaos-like.
In the paper [37] Baianu formulated the Non-
linear dynamics of non-random genetic and cell net-
works through categorical constructions enabled by the
Lukasiewicz–Moisil Logic algebras.
This is the algebraic approach that we will also ap-
ply to the Holo-Network, In fact this approach has only
certain broad similarities to the well-known method of
McCulloch and Pitts.There are major differences aris-
ing from the fact that we consider the sub-networks of
the Holo-Net acting in a multiple, quantum manner, and
strongly coupled via signaling pathways.
The use of a Lukasiewicz–Moisil (LM) Topos expands
the potential dynamics range to any sub-Network like
Neural,Glial, EMC, or Genetic-Epigenetic processes.
Non-commutative and non-distributive varieties of
many-valued LM-logic algebras, as applied by Baianu
([38]), open a broad field for applications both to our
Holo-Networks and also to quantum systems, as we will
see later on.
2. Dynamical model
Now we will develop the dynamics of our model. Based
on the algebraic considerations introduced in the pre-
vious section and using the calculus tools presented in
the (IV A 1 and IV A 2) sections. Holo-networks in our
new framework are Categories of the Lukasiewicz–Moisil
Topos, which Functors will evolve according to the mul-
tiplicative fractional calculus.
The key point is that dynamics get the non-locality
and historical properties from fractional dynamics and
power law “additivity” via the multiplicative geometric
and bigeometric calculus.
a. Info-Mechanics [39]
The above framework could be nominated Info-
Mechanics as a new dynamic framework related to the
classical mechanics and quantum mechanics. To briefly
remember the basics for these systems: Classical Me-
1. Dynamic evolution in a spacetime that is 3D Eu-
clidean and 1D time independent.
2. Galileo relativity principia. All the nature laws are
the same for all the Inertial systems (Systems that
move straight and uniformly)
3. Newton determination principia. All the move-
ments are fully determined by the initial position
and velocity
Hamiltonian Mechanics:
1. Dynamics is described in the Phase-Space that has
the structure of a sympletic variety and the Poisson
Integral as the Invariant.
2. A new relativity principium (Einstein’s special rel-
ativity) could be introduced in the framework.
3. Hamiltonian Function. Each uniparametric group
of symplectic diffeomorphisms of the phase space
that keeps constant the Hamiltonian are associated
to a prime integral of the movement.
Info Mechanics
1. Dynamic evolution over a Lukasiewicz–Moisil
2. Nature is structured in Categories which inner mor-
phisms are based on holo-networks.
3. Functors between Categories evolution according to
multiplicative fractional calculus.
We introduce the hypothesis that the different models of
mechanics that apply to Nature are related to the spatial-
temporal scale in which we make the analysis.
With this approach Quantum Mechanics (a Hamil-
tonian quantized mechanics) and its broad application
Quantum Field Theory (QFT) are applied to Nature
in the microworld., from Plank distance to micrometre.
Info-Mechanics will appear as the necessary framework
for the mesoscale, to planet wide scale, and finally Gen-
eral Relativity (GR) as the frame for the Universe scale.
The inconsistencies between QFT and GR could now
be contemplated as a scale factor in a wide theory Info
related. Considering Mellin transform as the convolution
model for the RL Integral with kernel tswith respect
to the Haar measure dt
t(multiplicative invariant),
some nice relations have been developed by Dr. Liam
Fitzpatrick, showing that Mellin space serves the Info
role in the context of the AdS/CFT correspondence. [40].
b. Toy Model
In this section we will develop one simplest model
based on the previous statements.
The model takes in account the evolution of the Func-
tors between a simple Category on Info, a virus, and the
three subcategories, Neural Nets, Glial Nets, and Im-
mune Nets, of a Superior Organism Category (Holo-net).
For the dynamic equations we will use the Chua sys-
tem that initially contemplates an electronic circuit that
achieves chaotic dynamics (Figure 6). The system was
implemented in Matlab c
, Simulink c
. This circuit has
a memristor component that according with [41] intro-
duces the current according to the parameters shown in
the circuit,
IM(t) = W(φ(t))V1(t) (34)
where W(φ(t)) is the incremental memductance defined
W(φ(t)) = dq(φ)
FIG. 6. Chua’s circuit with Memristor
The dynamics of this circuit with a passive memristor
(flux-controlled memristor and negative conductance) are
given by the ODE (Ordinary Differential Equations) sys-
dt =1
dt =1
dt =1
dt =V1(t)
If we translate these variables to the Info space:
V1=ImmuneNet .Info
V2=GliaN et.I nf o
IL=NeuralN et.I nf o
φ=V irus.Inf o
That reflects the action of the virus (Memristor com-
ponent in the Chua system) over the three sub-networks,
Immune system, Neural system and Glial System.
If we now transform the variables in dimensionless pa-
rameters according to [42]
C2= 1 R= 1
The system (36) is transformed to
dt =α(y(t)x(t) + x(t)W(w)x(t)
dt =x(t)y(t) + z(t)
dt =βy(t)γz(t)
dt =x(t)
where piecewise-linear function W(w) is defined by
W(w) = a for |w|<1
=b for |w|>1(39)
Now, to obtain our system dynamics, we will change the
first derivative by fractional ones.
tx(t) = α(y(t)x(t) + x(t)W(w)x(t)
ty(t) = x(t)y(t) + z(t)
tz(t) = βy(t)γz(t)
tw(t) = x(t)
To solve numerically the system of fractional deriva-
tives equations we will use a method described by Petras
[43]. It is a time domain method that leads to equations
described by
x(tk)=(α(y(tk1)x(tk1) + x(tk1)
W(w(tk1)x(tk1))) hq1
y(tk)=(x(tk)y(tk1) + z(tk1)) hq2
z(tk)=(βy(tk)γz(tk1)) hq3
w(tk) = x(tk)hq4
W(w(tk1)) = a for |w(tk1)|<1
=b for |w(tk1)|>1(42)
The total time for simulation that we will use is 200
seconds and his the interval of calculation that is 0.005
seconds. So, total number of points per curve for each
calculation is forty thousand.
The coefficients c(qi)
jj= 0.1....) are binomials (1)j(qi
that we will calculate according to the expression [44]
0= 1, c(q)
j= (1 1 + q
Value of the parameters for calculation are:
α= 10, β = 13 γ0.1= 1.5a= 0.3b= 0.8
q1= 0.97 q2= 0.97 q3= 0.97 q4= 0.97
x(0) = 0.8y(0) = 0.05 z(0) = 0.007 w(0) = 0.6
The results are presented in the Figures (7, 8, 9, 10).
FIG. 7. Holo-Network Axes (x, y, z)
FIG. 8. Holo-Network Axes (w, x, y)
FIG. 9. Holo-Network Axes (w, x, z)
FIG. 10. Holo-Network Axes (w, y, z)
In the complementing materials( [45], [46], and [47])
you will find three videos that contain the graphics pre-
sented related to ”Virus.Info” variable interactions, with
a variation of the αparameter.
C. Shorterm vs. longterm information processing
In the previous sections we have focused on the math-
ematical approach to the Info space, here we will present
briefly how the short and long time scales of the space
are processed.
If we start considering organism’s biomolecular pro-
cesses, they would be the substrate that could allow to
implement one of the instantiations of the Info Functor
previously described.
Anther clear instantiation of the Info Functor is the
structure of DNA/RNA as we have used in our Toy model
with the Virus role.
As we have seen in the dynamics graphics (Virus.Info),
figures (8, 9, and 10) introduces two separate regions on
the phase space. The permanence of the system in one of
the regions is abruptly broken with a transfer to the other
region that takes place after a usual long time, compared
with the time of the transfer.
We can speculate that dynamics that happen within
the regions are short term processes based on the
biomolecular mechanisms while the transfer region corre-
sponds to DNA/RNA processes. These last plastic pro-
cesses could be genetic or epigenetic.
In our toy example Virus.Info, DNA/RNA instantia-
tion gets the system from its initial state to one of the re-
gions. From this moment metabolic processes in the three
networks (Holo-Net) lead the dynamics of the system un-
til a new DNA/RNA process happens, usually replication
of the Virus.Info, but could also be DNA/RNA processes
on the Holo-Net. From this moment a totally different
dynamic of the system takes place. It is not highly spec-
ulative to associate these dynamical changes to the dif-
ferent states that organisms suffer under virus stress.
We will not go any further in this part of the analysis
because a more detailed mathematical model beyond the
toy model presented is necessary.
Only as a matter of quantification of the different time
scales for the different Nets.Info, we see that for the
biomolecular/metabolic processes it takes times from mi-
croseconds to seconds, while plastic processes take place
during hours (circadian) or several days.
A. Light and sound correlated as an input stimuli
to the network
The device that we have developed profiting from the
concepts presented in the previous sections, is mainly a
Light and sound generators that focus the visual and ear
channels of the patient in the two signals that we can
advance are highly correlated.
The current prototype is shown in the picture of the
Figure (11 )
FIG. 11. Device Sound & Light (Prototype)
showing the light matrix and the earphones for the
For the first implementation of the device we are work-
ing in an Info related open loop, with the meaning that
the light and sound signals generated are independent of
the state in which that the holo-net system is taken.
The evaluation in this initial approach is more focused
on the demonstration of the reaction of the Holo-Net
system, more than the optimization of the actions and
potential improvements on the health (dynamics) of the
patient. As we will see in the next section, there are
health conditions, such as Epilepsy, in which an immedi-
ate change in the dynamics of the system entered after
the Epileptic seizure is more than enough to prevent ma-
jor damages.
Of course, a subsequent close-loop device will be devel-
oped after we obtain the results of the tests with the cur-
rent prototype. Unfortunately for this second device the
current status of the technique will not allow us to have
an on-line feedback from Immune-Net.Info and even will
be difficult (Imaging techniques) from Glia-Net.Info, but
we hope that a full set of interfaces with these systems
will be developed in the near future. Even the interfaces
with Neural-Net.Info are in the first stages but the news
coming from this front are very exciting (see: Neuralink
presentation [48]).
The characteristics of the sound and light waveforms
as well as the times and protocols for its implementation
are at the time being under industrial secrecy and we are
not able to fully disclose them in the present paper.
An example of a treatment with one of the devices is
shown in the picture of the figure (12.
FIG. 12. Treatment with the Device Sound & Light
B. Potential effects in Epilepsy and other
neurological diseases
As we have advanced in the previous section the initial
tests of the device are being made with patients suffering
from Epilepsy.
Epilepsy is a grave central nervous system illness that
is normally related to other complex neurological disor-
ders, resulting frequently in the development of recur-
rent seizures. These seizures can potentially result in the
death of the patient as they usually occur without previ-
ous warning.
The WHO (World Health Organization) estimates that
epilepsy affects more than 50 million people worldwide.
Taking into account that the total world population is
about 7 billion there are 7 people out of 1000 suffering
epilepsy in the world. Epilepsy has an enormous influence
on the quality of life of the patient with collateral effects
such as body lesions related to seizures and in the case of
treatment with antiepileptic drugs, depression, anxiety
and other adverse neurological disorders induced by the
An epileptic disorder can be classified as partial, gen-
eralized, or unclassified nature depending on the diverse
types of seizures suffered. The most damaging is the sta-
tus epilepticus (SE) in which the seizure is sustained for
prolonged time. SE has been defined as a prolonged gen-
eralized tonic-clonic seizure persisting for more than 5
minutes (or 10 minutes for focal seizures with or without
impairment of consciousness), or more than one seizure
within a period of 5 minutes without recovery of con-
sciousness in between.[49].
Incidence of SE, according to different estimates, varies
from 6.8 to 41 cases per 100.000. Taking into account
that 60% of the total cases are refractory to drug treat-
ment and death is common between the SE patients there
is so far a dim future for these patients.
We have focussed our tests on the use of the device
immediately after the first symptoms of the seizure are
For the current experiments of light stimuli methods
in the Holo-Net.Info system we introduce the work made
with mice by Kristie M. Garza, Lu Zhang, Ben Borron,
Levi B. Wood, and Annabelle C. Singer. [50]. The results
are summarized; “Many neurodegenerative and neuro-
logical diseases are rooted in dysfunction of the neuroim-
mune system; therefore, manipulating this system has
strong therapeutic potential. Prior work has shown that
exposing mice to flickering lights at 40 Hz drives gamma
frequency (40 Hz) neural activity and recruits microglia,
the primary immune cells of the brain, revealing a novel
method to manipulate the neuroimmune system. How-
ever, the biochemical signalling mechanisms between 40
Hz neural activity and immune recruitment remain un-
Other remarkably interesting experiment was made in
this case with zebra fish by Carmen Diaz Verdugo, Sverre
Myren-Svelstad and several collaborators. They studied
[51] Glia-neuron interactions that underlie state transi-
tions to generalized seizures. The briefly conclusion of
the work was “The transition from a preictal state to a
generalized seizure is an abrupt process accompanied by
strong alteration of the functional connectivity between
glial and neural networks”.
Even if the subjects of the experiments were mice and
zebrafish and not humans the results for our thesis are
appealing and induce a high positive potential for the
results of the device.
Other tests related to other neurodegenerative dis-
eases, like Alzheimer disease, will be carried on in the
near future even as in this case the positive effects of the
treatment could take more time to be acknowledged.
C. Potential effects on COVID-19 patients
As a supplementary material due to the current dis-
mal situation caused by the COVID-19 we have been
committed to start without any delay a battery of tests
with special waveforms of sound and light in the device
to test in COVID-19 newly confirmed patients.
One of the most characteristic symptoms of the disease
is the acknowledgement that patients cannot smell the
food nor taste that they are eating. Normally these early
symptoms are the first indicators of the virus SARS-Cov-
2 in action in the human body.
Therefore, this action links, as in our toy model, the ac-
tion, information processing of a virus with the networks
of the nervous system. Several papers of the thousands
edited during the last months regarding SARS-Cov-2,
take into account the potential short term and long term
problems caused by the disease in the nervous system but
for the moment only general treatments aimed at known
therapy paths are being tested.
One of the points that we want to raise in this no-
ticeably short justification for the ongoing tests of the
device in COVID-19 patients is the cytokine release syn-
drome (CRS)–induced ARDS and secondary hemophago-
cytic lymphohistiocytosis (sHLH). This cytokine “storm”
was observed in patients with SARS-CoV and MERS-
CoV in 2008 as well as in leukaemia patients receiving
engineered T-cell therapy. The suppression of the storm
was the base for the first treatments in March and April
this year 2020, based on therapeutics suppressing CRS,
such as tocilizumab, that entered clinical trials with some
positive effects but with a severe and grave secondary
Our current approach will try to change the dynamics
of the virus via the effects that we will induce in the ner-
vous system (neural, glial, and potentially affecting the
extracellular matrix), with the Sound and Light device
The first essays will be done in a way patients newly
diagnosed with COVID-19 will be subject, with their to-
tal and positive consent, to a session of 15-30 minutes
interaction with the device before their sleeping period.
The next morning, they will be checked again for the
virus absence or presence ideally quantitatively and qual-
A. Summary
Further work must be done with the aim to:
1. Develop more complex models of Holo-Nets and
evaluate the fitting with natural occurring cases.
2. Evaluate potential implementations of more ad-
vanced devices according with the results obtained
from complex models.
3. Study advanced artificial implementations for the
dynamic models going beyond electronic circuits.
4. Make deeper studies in the relation Quantum Me-
chanics and Info Mechanics, that could help to es-
tablish a bridge between quantum computation and
Holo-Network dynamics. At this point a potential
implementation of quantum algorithms over Holo-
Networks is the most appealing result envisaged.
B. Disclaimer
All rights reserved. All content (texts, illustrations,
photos, graphics, files, designs, arrangements etc.) not
referenced to third parties on this paper are protected by
copyright and other protective laws. The contents of this
paper are to be used only in accordance with Intellectual
rights International regulations.
Without the explicit written permission of the compa-
nies of the Author,RQuanTech (Geneva) and Criptosasun
(Madrid), it is prohibited to integrate in whole, or in part,
any of the protected contents published on this paper into
any materials or to use them by any other means.
The Author wishes to acknowledge the support of the
teams of his companies , RQuanTech and Criptosasun
for their full support with the corrections and marvelous
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... 1) Quantum Cryptography 2) Block signatures via Quantum Measurements 3) Information processing via Holo-Networks Unfortunately the present paper is not the best support to develop the above concepts with the necessary depth. We can advance that RQT is fully involved in the development of these technologies and we invite the reader to see the papers from the Author "QUANTUM SUPREMACY : in FINANCIAL MARKETS (FOREX)" [5] for quantum technology applied to markets and "From AMOEBA to BRAIN: How Nature process Information" [6] for the Holo-Network concept. ...
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