Complex-Dynamical and Its Applications in Life Sciences--论文代写范文精选

在生物系统结构分析的分形范例,反映了效率高的分形几何，在生活中所使用的函数实现的构思和自然本身。在更广泛的意义上,分形结构效率似乎不可避免地出现在各种各样的真实过程,从物理化学结构对经济系统进化。下面的essay代写范文进行详述。

Summary
Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution to an arbitrary interaction problem. Intrinsic creativity of this extension of usual fractality determines its exponentially high operation efficiency, which underlies many specific functions of living systems, such as autonomous adaptability, “purposeful” development, intelligence and consciousness (at higher complexity levels). We outline in more detail genetic applications of complex-dynamic fractality, demonstrate the dominating role of genome interactions, and show that further progressive development of genetic research, as well as other life-science applications, should be based on the dynamically fractal structure analysis of interaction processes involved. We finally summarise the obtained extension of mathematical concepts and approaches closely related to their biological applications.

Introduction 
The success of fractal paradigm in bio-system structure analysis, as presented in this series of conferences [1-3], reflects high efficiency of fractal geometry in life function realisation conceived and used by nature itself. In a broader sense, fractal structure efficiency appears inevitably and naturally in a wide variety of real processes, from physico-chemical structures to economic system evolution [4-8], driven by unreduced interaction processes and often referred to as systems with complex dynamics. 

Using the universally nonperturbative analysis of a generic interaction process, we have rigorously specified the connection between fractality and dynamic complexity [9,10], where the extended, complex-dynamic fractality has been derived as inevitably emerging structure of any real interaction process. In that way, the dynamic complexity as such acquires a rigorous and universally applicable definition, while the fractal structure of a real interaction is obtained as the truly complete, dynamically multivalued (probabilistic) general solution of a problem, replacing its reduced, dynamically singlevalued (regular) version. The dynamically probabilistic, permanently changing fractal of real system dynamics is a natural extension of the canonical, “geometric” fractality possessing an involved, but basically predictable (regular) and fixed structure. Complex-dynamic fractality is not a “model” any more, but the unreduced version of any real, “nonintegrable” and “nonseparable” system structure and dynamics, which is especially interesting for fractality involvement with living systems because it provides rigorously derived versions of those essential life properties — such as intrinsic adaptability, self-development and “reasonable” behaviour — that determine its specific efficiency and remain largely “mysterious” within usual, perturbative theory.

Multivalued fractal solution of eqs. (20)-(22) can be obtained in a number of versions, but with the same essential result of probabilistically adapting hierarchy of realisations. Consecutive level emergence of unreduced dynamic fractality should be distinguished from perturbative series expansion: the latter provides a qualitatively incorrect, generically “diverging” (because of dynamic single-valuedness [9]) approximation for a single level of structure, while the series of levels of dynamic fractality corresponds to really emerging structures, where each level is obtained in its unreduced, dynamically multivalued and entangled version. 

In fact, the ultimately complete, dynamically fractal version of the general solution demonstrates the genuine, physically transparent origin of a generic problem “nonintegrability” (absence of a “closed”, unitary solution) and related “nonseparability” (now being clearly due to the physical, fractally structured and chaotically changing component entanglement). The dynamically probabilistic fractal thus obtained is a natural extension of the ordinary, dynamically single-valued (basically regular) fractality, which is especially important for life-science applications because it possesses the essential living system properties absent in any unitary model, including autonomous dynamic adaptability, “purposeful” self-development, intrinsic mixture of omnipresent randomness with often implicit but strong order, and the resulting qualitatively superior dynamic efficiency. 

These properties are unified within the universal dynamic symmetry, or conservation, of complexity [9,11,12] providing the general framework for the described process of interaction development into a probabilistically fractal structure. The initial interaction configuration, as described by the starting equations (1), (2), (5), is characterised by the latent, “potential” complexity form of dynamic information, universally measured by generalised action. System structure emergence in the form of unreduced dynamical fractal, eqs. (8)-(22), is described by unceasing transformation of dynamic information into a dual complexity form, dynamic entropy, generalising the usual entropy to any real system dynamics and reflecting the fully developed structure. Symmetry of complexity means that the sum of dynamic information and entropy, or total complexity, remains unchanged for any given system or process, which gives rise to the universal HamiltonSchrödinger formalism mentioned above and extended, causally complete versions of all other (correct) laws and principles. 

Due to the intrinsic randomness of the unreduced fractality and contrary to any unitary symmetry, the universal symmetry of complexity relates irregular, configurationally “asymmetric” structures and elements, while remaining always exact (unbroken), which is especially important for description of biological, explicitly irregular, but internally ordered structures. Constituting thus the unreduced symmetry of natural structures, the symmetry of complexity extends somewhat too regular symmetry of usual fractals and approaches the fractal paradigm to the unreduced complexity of living organism structure and dynamics.

Note finally the essential extension of mathematical concepts and approaches involved with that urgently needed progress in applications, as the development of fundamental science tools represents also its own interest, especially evident on the background of persisting stagnation [9,11,18] and “loss of certainty” in fundamental knowledge (cf. [19]). (i) First of all, one should mention the nonuniqueness of any real problem solution, taking the form of its dynamic multivaluedness (section 2), and related complex-dynamic existence of any system that replace the usual “uniqueness and existence theorems” valid only for reduced, unitary models [9]. (ii) It follows that the related unitary concept of “exact” (closed) solutions and its perturbative versions are basically insufficient and fundamentally incorrect with respect to real world structures. 

The true, dynamical meaning of the notions of “(non)integrability”, “(non)separability”, “(non)computability”, “uncertainty”, “randomness”, and “probability” becomes clear: we obtain now the nonintegrable and nonseparable, but solvable dynamics of a generic many-body system (see eqs. (8)-(22)), while real world mathematics regains its certainty and unification, but contains a well-defined, dynamic indeterminacy and fractally structured diversity (i.e. it cannot be reduced to number properties and geometry, contrary to unitary hopes). (iii) The property of dynamic entanglement and its fractal extension (section 2) provides the rigorous mathematical definition of the tangible quality of a structure, applicable at any level of dynamics, which contributes to the truly exact mathematical representation of real objects, especially important for biological applications. (iv) The irreducible dynamic discreteness, or quantization, of real interaction dynamics expresses its holistic character and introduces essential modification in standard calculus applications and their formally discrete versions, including “evolution operators”, “Lyapunov exponents”, “path integrals”, etc. [9,11]. (v) The unceasing, probabilistic change of system realisations provides the dynamic origin of time, absent in any version of unitary theory: in the new mathematics and in the real world one always has a for any measurable, realistically expressed quantity or structure , while one of the basic, often implicit postulates of the canonical mathematics is “self-identity”, a ≠ a a = a (related to “computability”). 

It has a direct bioinspired implication: every real structure is “alive” and “noncomputable”, in the sense that it always probabilistically moves and changes internally. In fact, any realistically conceived represents a part of a single, unified structure of the new mathematics introduced above as dynamically multivalued (probabilistic) fractal (of the world structure) and obtained as the truly exact, unreduced solution of a real interaction problem (section 2). We can see in that way that such recently invented terms as “biofractals” and “biomathematics” can have much deeper meaning and importance than usually implied “(extensive) use of mathematics in biological object studies”.

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