Vyacheslav L. Kalmykov

Institute of Cell Biophysics, Russian Academy of Sciences,

Abstract

It is the first (as I know) physical theory of organization and evolution of life. The theory may be of vital importance as the functional invariant (the semantic configurator) for:

the most integral understanding organization and evolution of life,
the most integral computer simulation of life (Strong Artificial Life),
the most integral engineering decisions in AI and computer science.

In the last case the theory may be considered as the conceptualization for creation the formal ontology of evolution, self organizing, complexity, life, culture and as the base for formulation of the generalized theory of any autonomous agents. It may be helpful and for creation of  new computer architectures.

The theory is the synthesis of my own generalized formulations of the key terms, rules, relations and the key theoretical intentions of the following fields: theoretical biology, systems theory, theory of information, theory of self-organization, theory of evolution, science of wholeness, science of synthesis, theory of function emergence, theory of complexity, cybernetics, autopoiesis, artificial life, artificial intelligence, theory of symmetry, theory of culture, theoretical ecology, theory of sustainable development. It is not unlikely that today it gives the last, most deep and most  integral understanding of organization and evolution of life. And it is in the very compact form.

The paper was appeared as the result of attempts of the biologist to invent and formulate the functional logic of organizing and evolving of life. This theory includes elements of axiomatic approach and is physically interpretable. It was  formulated by me as the holistic system of an ideal objects (of a creative synthetic definitions) that are still absent for a sufficiently good understanding of the living.

The new generalized definitions of the following notions are given:

1. The organic structures
2. The environment
3. Self-organization
4. The structures of order
5. The possible types of order of structures
6. The morphogenetic space
7. The behavioural space
8. Symmetry of the structure
9. Complete entropy
10. The function of information
11. Information
12. Physical specificity of the living
13. The physical side of the purposefulness
14. Level of organization
15. Ten pairs of mutually antipodal elementary operations (operations generate a mathematical groupoid) that underlie the living
16. Autonomous integral unit of behavior and evolution
17. A specific ecosystem of organic structure(s)
18. Functional intraclosure (wholeness, integrity, holon, organism, organization)
19. Integral quantitative criterion of spontaneous evolutionary changes of structures (Parameter of the comparative evolutionary progress of the structures)
20. Steps of self-organization of organic structures
21. Stages of emergence of organisms and/or of organizations
22. The fractal organization of life
23. Emergent function
24. Control
25. Reproduction
26. Creation
27. Life
28. The invariant cognitive cycle
29. Culture
30. The most general functional elements of culture
31. The most general fields of professional human activities
32. Discovery ...
33. The motive power of the combinatorial creation process
34. The highest form of emotions

Subjects and keywords.
i) theory of evolution, theory of life, theoretical biology, systems theory, wholeness, self-organization theory, Claud Shannon, organization theory, behaviour, theory of information, self-organising systems, autonomous agents;
ii) (unified, integral, generalised, holistic) (formal, abstract, algebraic, functional, operational, physical) (logic, algorithm*, theory, invariant, understanding, definition*) (evolution, information, organization, self-organization, life, living);
iii) ai, evol*, whole*, organi*, self*, complex*, bio*, emergen*, sustainab*, bihavio*, ontolog*, integr*, system*, eco*, *group*, al. 

The page tracking: 

 Introduction.

    Future generation computation will be characterized by the use of models and paradigms based on developments in biology [1]. There is an urgent need for interdisciplinary collaboration and cross-fertilization of ideas between researchers adopting biologically motivated and biologically inspired computing paradigms. Mathematicians and physicists would help in bridging the gap between biology on one side and computer science and artificial intelligence on the other. This work presents the generalized functional scheme (the ontological invariant) of the living as the theoretical outline of a spontaneous multidimensional holo-dynamics of any structures. The task is close to the questions of what life is and why it is organized so. Whilst traditional in the theoretical biology, these questions are at present especially urgent in connection with the problems of development of computers, robots and cyberspace. In the latter cases the development of computers with soft- or/and hardware, based in essence on the logic of organization and evolution of the living, is meant. Besides, for a valuable and justified presentation of knowledge about the living in computers a generalized (universal) functional description is necessary. The work presents such a generalized theoretical description of the life.

Building of the generalized ontological invariant as specification of this theory may be the most direct way to an autonomous and creative artificial intelligence and to new foundations of computation.

Theoretical ecology. In addition, this paper would be the "brick" in building of Environmental Ideology. Following the standpoint of Albert Gore [2], I believe the prospects of solving ecological problems to be, in the first line, related to the progress in overcoming the spiritual crisis consisting in the absence of an integral theoretical understanding ("The Big Picture" -[3]) of the processes underlying the dynamics of our civilization. In addition we believe [4] the main problem of environmental education to be the absence of integral ecological ideology ( generalized theoretical ecology), that is the poor language of theoretical ecology. The language of theoretical ecology means an integral system of scientific definitions of such notions as "life", "information", "living organisms" and "biosphere on the whole", as well as "evolution and criterion of its direction", "culture", "progress" etc. To our mind, the generalized theoretical ecology and the generalized theory of the living are identical. This paper may be considered as outline of the integral ecological ideology, which should help in "planting" environmental ideas into heads and hearts of ecological students. In addition the integral theoretical understanding implies the possibility of studying and projecting the balance of both local and global dynamics of our civilization in order to achieve ecological harmony. It is of fundamental inportance as and the most deep methodology for elaboration of the national information infrastructures and global information infrastructure (global information sphere).

About a fear of Progress. Now some words about a rather spread fear of progress, which mounts to its maximum in the face of the "coming" cyborgs and high-intellectual robots [5]. When it really happens, the artificial intelligence systems will be as much clever and more sinless than modern people as nowadays they are excelling Man in rapidity of arithmetic calculation. People are a maternal medium for the coming robots, which is as necessary for them as the ecologically pure biosphere for the modern Man. So, it is no use of expecting these artificial creatures to destroy their maternal medium they were born by. I do not support any reduction or limitation of progress. I think the chief condition of social and ecological sustainability to consist in continuous development, constant progress, in eternal (as far as time scales of our Universe permit) cognition of the environment and people themselves aimed at perfecting the human society. These are only scientifically understood laws of organization and evolution of the living that are able to provide an ecologically balanced development of our civilization.

Symmetry and a group theoretical approach. This theory includes elements of axiomatic approach and is physically interpretable. Combinatorial generation of the mathematical groupoid G of elementary operations in set R, which are not reducible to each other, is suggested as a fundamental notion for evolution of the living. This groupoid may be called "the universal ontological matrix" of any structure. The groupoid looks as the most general of all possible groupoids of symmetry. Combinatorial generation of the groupoid is the essence of evolution - the essence of life and the essence of cognition. Rules for the mechanisms of integral closure of the elementary operations onto each other in the course of biological self-organization are examined. The suggested functional invariant of organization and evolution of the organisms appears to be fundamental not only for biological objects themselves but also for any organizational levels of the living. It may be considered as "the universal invariant of complexity (or universal invariant of self-organization)". The invariant is one and the same for organization, behavior and evolution of biological life as well as of social and artificial life.

Why do I try to use the group theoretical approach? As I understand it, this is the only one viable way to formulate the main points of organization, behavior and evolution of the living for science and technological use. The law of organization of integral structure and the structure symmetry is one and the same. The structure symmetry is the highest automorphism group of the structure [6].

Were the operations in set R come from?
How I have formulated (have invented) the set R and groupoid G?
    - Being the biologist and trying to follow traditions general theory of systems and cybernetics, I have found one interesting analogy. All alive organisms have substantially similar functional organization - all of them have informational, energy, impellent, bearing, excretory and number of other systems. I had such feeling, that there is a certain functional invariant, which in a main part remains same for any alive organisms - both one-celled and multicellular. Moreover, the rather standalone social systems (especially so-called juridical persons) are obviously organized in according to the same common functional invariant. In all these cases a base elements and entirety of realization of a complete matrix of the generalized functional invariant in essence differs only.
It was very interesting. The similarity of the general functional organization was obvious and for various languages. It is possible to say, that in a basis of the language the communicational reflection of the same generalized - functional invariant lays. Languages differ by elements (by words) and by grammars, but functionally they are invariant and identical each other. The functional invariance of languages provide the possibility of their mutual translation. By which way it would be possible to formulate a required functional invariant? Originally I have made the list of the all possible functions, known for me as realized in alive, - since listing functions of separate organs and systems of organisms. Then to this list I have added all main verbs designating the most elementary and irreducible to each other functional mutual relations. The main types of the functional operations realized in biochemical processes were taken into account also. Further all synonyms were reduced to sole values, and all other synonymic variants were discarded. The obviously composite functions were discarded also. Only the most elementary and unique functions were left. Thus list from ten pairs of the mutually antipodal elementary functions (operations with substance, energy and information) - the set R was obtained. The combinations of these elementary functions will derivate more complex functions up to highest integrating functions - such, as control, reproduction and creation. Any alive organism realizes all elementary functions of set R and integrating function of control. The function of reproduction is realized by many organisms. The function of creation in the individual order is realized in the full volume only by man. In case of organisms of lower level of organization than man the function of creation is realized as natural selection on level of population, but not on an individual level. The positive result of solution of the set task of a statement of the functional invariant of organization was achieved by me due to the following initial sending: the invariant of the functional organization should be mathematical group (or groupoid) - from here directed search of mutually antipodal elementary operations.

Some variants of this theory were prepublished earlier [4, 7-8].

The main statements, notions and interpretations

Some axioms (4 in all):

1. The basis of the emergence of life is a set of compatible structures (set M). The set M include inorganic and organic structures of the universe. The organic structures are of the most importance for the life emergence.
The organic structures - structures which are formed by fixation of free environmental energy in their structure (e.g. organic molecules) and, as a result, they are able to do some work. Compatibility of these structures is structurally homomorphic in character, i.e. they have a fundamental unity of specific morphological arrangement. In consequence, this eases their interaction encouraging the possibility of reciprocal transformations.

2. The environment, as an initial source of inflowing and a final drainage receiver of outflowing of substance and/or energy, is necessary for existence of the living. The environment sets the parameters under which living systems realize optimal kinetic stability in their structures.

3. Organic structures of the set M possess such a vast structural variety (polymorphism), that they are capable of establishing ten pairs of simple mutually opposite functional relations between each other, including relations of organic structures with inorganic constituents and with the environment - set R (SEE Table 1). This set of functions is basically invariant for the living. Stressing the orientation and asymmetry of the notion "function", the word "operation" is used in this work as a synonym.

4. There is the physically interpretableautonomous  integral unit of  behavior and  evolution of  the organic structure(s). The application of the extreme physical principles to this autonomous  unit is possible. The unit  is  the  specific ecosystem  of organic structure(s).
The specific ecosystem can be called "the autonomous evolutionary unit".
A specific ecosystem of organic structure(s) is the part of the set M which is including:
(i) the compatible and complementary organic structures which completely or partially cover  the set R of ten pairs of mutually antipodal elementary operations and their combinations and
(ii) the specific environment of the organic structure(s) - the specific environment which is the domain of operational plenary power of the organic structure(s).
The ecosystem is the sum of the organic structure(s) and their specific environment.Organic structure senses and acts (operationally) upon its specific ecosystem (organic structure itself + the specific environment)..
 

Table 1. Set R includes ten pairs of mutually antipodal elementary operations (with substance, energy and information) on the set of compatible organic structures of set M that underlie the living
 

Direct operations	Reverse operations
1. Identification	1'. Identification
2. Right-hand mirror reflection	2'. Left-hand mirror reflection
3. Change of position in space	3'. Reversion of position in space
4. Transformation of configuration	4'. Restoration of configuration
5. Increase of number of elements	5'. Decrease of number of elements
6. Provision of inlet	6'. Provision of outlet
7. Connection	7'. Isolation
8. Switching-on, i.e. mediating initiation of a specific action of the operation object, affected by a definite way	8'. Switching-off
9. Concentrating	9'. Scattering
10.Inflowing	10'.Outflowing

The operations of set R and their combinations entirely cover all kinds of relations that are obligatory for emergence and for a stable existence of organic structures of the set M. The operations are equally be performed with substance and energy and information.

The operations of set R generate the mathematical groupoid G over all possible combinations. The proofs are:

1. In case of combinations (unlike permutation) the sequence of operations is not significant, hence the performance of properties of associativity appears.

2. All combinations of operations belong to one groupoid. This follows from the conditions of specifying this set, in combinations of which all possible changes in the structure are embedded.

3. There is the only one common unit, which is the operation of identification.

4. There is a reverse element for each element (SEE Table 1).

Self-organization is a spontaneous emergence of the structures of order in the course of spontaneous processes.
The structures of order are in principle thermodynamically unstable yet kinetically stable (in other words far from equilibrium, yet maintaining a constant state). During self-organization the spontaneous transitions from one structure of order to another are conditioned by thermodynamic instability (nonequilibrium).

The possible types of order of structures are as follows:

1. The static ones. For instance, molecules and their crystals.

2. The informationally unmediated stationary structures. They are dynamic structures existing due to an informationally unmediated return to the initial position (state, form). For example, dissipative autocatalytic structures of the Belousov - Zhabotinsky reaction type, whirlwinds, rivers (permanent stations based on the water circulation)...

3. The informationally mediated stationary structures. They are dynamic structures existing due to an informationally mediated return to the initial position (state, form). The kinds of such automorphic processes are:
reproduction, adaptive behavior, recovery (regeneration, repair).

As can be seen from the points listed, any structure of order can be characterized by its specific group of symmetry. In particular, this appears from the fact that the set of transformations, which make the structure return to its initial position (state, form), are just one of the definitions of a group of symmetry.

Let us consider two neighboring levels of the structure organization - the structure itself and its substructures of the first lower level.

In case of the microapproach the structure is supposed to be examined from inside, and behavioural characteristics of the substructures (microstructures) are relevant.

In the macroapproach the notion "space of possible (virtual) transitional states of structures of order" is used. This space is the morphogenetic space.

In the microapproach we use the notion "space of possible behavioural forms of the substructure (microstructure) of the first lower level of structure organization". The last space is the behavioural space.

There are certain criteria (the extreme physical principles) for the direction of spontaneous autonomous transformations of macrostructures, i.e. a spontaneous behavior of microstructures within an isolated macrostructure is only "permitted" when:

1. Free energy of the macrostructure (its capability of doing some work) decreases.

2. Entropy of the macrostructure increases.

3. Symmetry of the macrostructure increases.

By "macrostructure of organic structure" in this paper I  mean "a specific ecosystem of organic structure(s)".
Criteria 1 and 2 formulate the 2nd law of thermodynamics. Criterion 3 is a corollary of the general principle of symmetry of physical phenomena formulated by Pierre Curie [12] in 1894. This principle is also developed in the works by A.V. Shubnikov and V.A. Kopcik [6, 13].
Free energy of the structure is defined as the ability to do some work autonomously.
Symmetry of the structure is characterized by the highest group of transformations, which leave the structure unchanged. "Highest" means here "including all possible transformations".

As for entropy, the matter is more difficult. In this work the complete entropy of an isolated structure of order is defined as a volume of the space of possible transitional structures of order on their way to equilibrium. This definition is close to that of absolute entropy by Max Plank [14, 15], which does not require any probabilistic ideas and is applicable to physical structures with any number of degrees of freedom.

I believe that the conception about the space of possible transitional structures of order could be defined as a space of possible transitional groups of the structure symmetry. Hence it appears that complete entropy of the structure is an extensive characteristic of its potential (evolutionary achievable) symmetry, which seems to be rather paradoxical.
 

the integral quantitative criterion of spontaneous evolutionary changes of structures is an increase of the specific product of the power of the new-emerging structure on its symmetry.

In the divisor of the specific product of its power on its symmetry may be some extensive characteristic of the structure - for example the mass.

Let us consider emergence of organisms and/of of organizations on the basis of the set of organic structures. The following steps of self-organization of organic structures leading to the origin and evolution of the living can be discerned:

1. Emergence of elementary cycles of catalysis;

2. Emergence of cycles of autocatalysis consisting of elementary cycles of catalysis;

3. Emergence of hypercycles [16] consisting of cycles of autocatalysers;

4. Emergence of functional intraclosure  (wholeness, integrity, integron, holon, organism, organization) over the operations of  set R of hypercyclic, autocatalytic, catalytic and simple noncatalytic structures. Two operations of the functional intraclosures finally remain open to the environment: inflowing from sources and outflowing to drains.

1'. Beginning of the next iteration of the self-organization. Functional intraclosures (wholeness, holons, organisms), formed by this process fill up the set of self-organised organic structures of the set M. They belong to a higher level of organization. The new level of organization is basic for the recurrence of the described self-organised logic etc. The last peculiarity - the functional isomorphism of organization of the living on any levels of organization is the property of the fractal organization of life.

Table 2. The metaphoric examples of the emergence stages
 

	cycles of  catalysis	cycles of autocatalysis	hypercycles	functional intraclosure (wholeness, inegrity, holon, integron, organization)
A	macromolecules	complexes of macromolecules	subcell structures	cell
B	cells	tissues	organs	organism
C	personnel	groups	departments (sections)	institute
D	institutes	branches	ministries (boards)	state
E	the empirical descriptions	the particular theories	the partially generalized theories	the integrally generalized theory

On the levels A, B, C, D and F functional algorithm of subordination is similar.

A level of organization is a stage in evolution of structures, on which the functional intraclosure of their substructures goes with a principle unity of their specific morphological conformation (with their structural homomorphism).

Information mediating the selection of these behavioural forms appears at the points where alternative behavioural forms (combinations of dissipation flows) are equally probable or realization of hardly probable behavioural forms is necessary from the standpoint of satisfaction of extreme principles.

Realization of the selection of the given behavioural form by the structure occurs with the help of controlling substructures making selective steps in potential kinetic barriers, which keep back the dissipation of free energy of the structure and/or selectively lower such potential barriers in accordance with the available information.

The mediating function of information becomes a participator of principle in mutual co-ordination of self-organised organic structures beginning with the stage of emergence of hypercycles.

Information is the central factor determining the stability and the functional efficiency of informationally mediated stationary structures that living organisms belong to. Hence, the main link in the evolutionary process of the living is a functional perfection for obtaining, accumulating, processing and using information.

From our standpoint, the physical essence of information and the physical essence of the living are in close interrelation. The well-known theory of optimal coding by Claude Shannon, based on the statistical determination of entropy, is very often called the theory of information. Yet both statistical manipulations by quantity of bits in a file and statistical manipulations by quantity of individuals in a population did not allow us simply and distinctly to understand the physical essence of these phenomena until now.

A long search for physical specificity of the living did not permit us to relate it either to growth, or to reproduction, or to structural regeneration, or to substance exchange ... These phenomena have been found in crystals and other purely physicochemical structures. Information is the only attribute, which specifically inheres in the living.The function of information is a configuring mediating co-ordination of processes, taking place in organisms, and with each other.

The co-ordination and organization of all living processes presume the presence of purposefulness that is intrinsic for the living. To our mind, the physical side of this purposefulness consists in that the living is not a direct way of realizing extreme physical principles, as these occur in traditional physics, but an organizationally mediated one. When considering the living as a "black box", then the change in generalized physical characteristics at the entrance and exit of this black box will correspond to our extreme physical principles. At the same time, some processes, hardly probable from the standpoint of traditional physics, may deterministically occur inside this black box. Determined realization of such hardly probable processes is the consequence of living organization, which is mediated by information. Thus, information fulfills the function of mediating the co-organization of living processes. Life is, in its turn, the way of realizing extreme principles of physics through integral co-organization of behavior of living elements.

Information is a reflection of a definite trajectory of behavior of the structure in the space of its possible behavioural forms, that allows the structure an identical reproduction of the selection made by the structure earlier in its behavior.It can be also said that information is the fixed in any way interrelation of events. In the last sense information and reflection of the function is one and the same.

Information is the central link in the mechanism of the co-ordination of operations of set R within the substructures of organisms, communities of organisms and the whole biosphere.

Functionally, information manifests itself in three different forms, being part of three integrating functions: control, reproduction and creation. The three functions integrate elementary operations set R to angle whole within functional intraclosures.
 

Control is a directed change in the probability of realizing alternative trajectories of the controlled object behavior.

Reproduction is a cycle of the structure transformations under control, which results in emergence of its copy.

Creation is the combinatorial process  forming a new type information
mediating a polymorphic reproduction of the structures and of the substructures on higher (in accordance to the extremal principles) evolutionary level
 (i.e. reproduction of a new type of permutation of elements by introducing and/or removing its elements and/or by changing configurations).

Reproduction is the hypercycle of the control cycles and creation is inducing a polimorphism by hypercycle of reproduction cycles. Arising in the creation cycle information  is the base for reproduction of controlling structures on the new higher level of organization and behaviour. Creation is the emergent function.

Life is a spontaneous process of combinatorial generation of the groupoid G of functional intraclosures (organisms, organizations) by combining the operations of the set R above the set M.

Culture is the whole complex of all the highest (the evolutionary most progressive) achievements in all fields of human activities.
 

Estimates of evolutional progressivity occurs according to the evolutionary progress criterion, which has been formulated in this work. Human activities proceed within the limits of the universal mechanisms of self-organization that are typical for the living (SEE the definition of life and the above in context). In general outline these activities can be defined as the man-mediated process of combinatorial mutual enclosure of universal integrating operations: control (C), reproduction (R) and creation (Cr). In the simplest and most general form this combinatorial enclosure is represented by all possible length two permutations of the three integrating operations. The 9 pairs of the permutations have been analyzed, and the conclusion has been made that they correspond to the most general functional elements of culture or (the same) to the most general fields of professional human activities (SEE Tables 3 and 4).

The real content of individual elements of culture (professional positions) are in addition profoundly differentiated. So, each of the 9 cells in Table 3 can be divided into analogous 9 subcells. This results from the formulated combinatorial nature of life. And according to common sense, it is clear as well, that, for instance, there are some elements of art in real policy, and there are some elements of ideology in real religion (or art).

Table 3. Functional Elements of Culture (the most general fields of  professional work of the active persons - mentors and generators of ideas) as combinatorial length two combinations of integrating operations: creation, reproduction and control
 

	Creation (Cr)	Reproduction (R)	Control (C)
Cr	1 - CrCr Religion Art Metaphysics	2 - CrR Science	3 - CrC Policy
R	4 - RCr Upbringing (Game)	5 - RR Education Technology (Enlightenment)	6 - RC Teaching (Drill)
C	7 - CCr Methodology	8 - CR Organization Management	9 - CC Ideology

CrCr: creation of creation; CR: creation of reproduction; etc.

New information emerges in the course of creation, and by means of reproduction it is used as the basis of control processes.

Old information moves in the opposite direction - from control to reproduction and from reproduction to creation. This results from the definitions formulated in this work as well as from common sense. Hence, a conclusion inevitably comes to mind: in culture new information emerges in religion, art and metaphysics and moves through science to policy and, farther on, to upbringing, education, teaching, methodology and, in the end, to ideology (SEE Table 3). But it is the moving of new information through active persons (through subjects) - through the mentors and through so called generators of ideas. Old information moves in culture through in the opposite direction beginning with ideology. The moving of information through passive persons (through objects) is something different - from religion, art and metaphysics through upbringing to methodology and, farther on, to science, education, organization, policy, teaching and, in the end, to ideology (SEE Table 4). Old information moves in the reverse sequence beginning with ideology.

Table 4. Functional Elements of Culture (the most general fields of professional work of the passive persons - students and others users of ideas) as length two permutations of integrating operations: creation, reproduction and control
 

	Creation (Cr)	Reproduction (R)	Control (C)
Cr	1 - CrCr Religion Art Metaphysics	4 - CrR Science	7 - CrC Policy
R	2 - RCr Upbringing (Game)	5 - RR Technology Education (Enlightenment)	8 - RC Teaching (Drill)
C	3 - CCr Methodology	6 - CR Organization Management	9 - CC Ideology

CrCr: creation of creation; CR: creation of reproduction; etc.

The report on the united logic of organization, behavior and evolution of the living would be incomplete without an additional precision of creation mechanisms. When defining creation as a specific combinatorial process, sources of its participators should be considered as well. Creation can occur on the basis of a fixed number of known elements to be combined. In case the range of known (accessible) combined elements is not replenished, the creation process may reach a deadlock, and new creative prospects can arise thanks to discovery either of new, earlier unknown elements or to that of new sources of the exhausted known elements.

Thus, discovery is the special form of the creation process replenishing it with new participators.

Let us consider the motive power of the combinatorial creation process. When life is born, it is mainly a chaotic thermal motion in the primary "broth" of organic and inorganic molecules. In the most ordinary organisms the chaotic behavior is supplemented with sexual process, the essence of which is to provide genetic combinations. In the human society the sexual process mounts to
the highest form of emotions - love for cognition, which provide motivation of the tendency towards a search as well as a creative combination of information as knowledge that is the basis of human activities and creative development of techniques.

I thank Mr. Alexander S. Kharitonov and Mr. Chris Lucas for stimulating, helpful discussions and technical assistance. Many thanks to my unknown referees for the feedbacks which were highly useful for me.

REFERENCES

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