Andrei P. Kirilyuk Andrei P. Kirilyuk Institute of Metal Physics, Kiev, Ukraine Institute of Metal Physics, Kiev, Ukraine http://myprofile.cos.com/mammoth http://myprofile.cos.com/mammoth UNREDUCED DYNAMIC UNREDUCED DYNAMIC COMPLEXITY COMPLEXITY Towards the Unified Science of Intelligent Communication Networks and Software
ICT COMPLEXITY AGENDA ICT COMPLEXITY AGENDA ICT COMPLEXITY AGENDA • Autonomic communication as a • Autonomic communication as a complex-dynamic interaction process complex-dynamic interaction process Unreduced , user , user- -oriented interaction oriented interaction Unreduced • Universal science of complexity • Universal science of complexity Real world dynamics, from particles to consciousness world dynamics, from particles to consciousness Real • Exact science of intelligent ICT • Exact science of intelligent ICT Neither reduced “ “models models” ”, no ambiguous , no ambiguous “ “philosophy philosophy” ” Neither reduced • Practical applications and perspectives • Practical applications and perspectives http://arXiv.org/abs/physics/0412058 http://arXiv.org/abs/physics/0412058
Complex Dynamics of Knowledge- -Based Networks Based Networks Complex Dynamics of Knowledge and the Intelligent Communication Paradigm and the Intelligent Communication Paradigm User- -oriented oriented communication = communication = unreduced unreduced interaction interaction User Unreduced interaction analysis: permanent chaotic, fractally Unreduced interaction analysis: permanent chaotic, fractally structured realisation change → → universal dynamic complexity universal dynamic complexity structured realisation change exceeds usual “ “science of complexity science of complexity” ” (fractured, no complexity definition) (fractured, no complexity definition) exceeds usual Classification of dynamic regimes (more regular or chaotic) (more regular or chaotic) Classification of dynamic regimes and transitions between them and transitions between them Intrinsic chaos is inevitable inevitable in intense communication: in intense communication: Intrinsic chaos is unreduced communication complexity unreduced communication complexity FRACTAL ⇓ ⇓ FRACTAL FRACTAL FRACTAL Exponentially high efficiency instead of network failures instead of network failures Exponentially high efficiency Universal evolution law (direction of development): (direction of development): Universal evolution law what can happen and how to control it what can happen and how to control it http://arXiv.org/abs/physics/0412058, http://cogprints.org/3988 , http://cogprints.org/3988 http://arXiv.org/abs/physics/0412058
Complex Dynamics of Knowledge- -Based Networks Based Networks Complex Dynamics of Knowledge and the Intelligent Communication Paradigm and the Intelligent Communication Paradigm Universal concept of dynamic complexity and its concept of dynamic complexity and its Universal successful applications to various systems: successful applications to various systems: http://arxiv.org/find/quant- -ph,gr ph,gr- -qc,physics/1/au:+ Kirilyuk/0/1/0/all/0/1 qc,physics/1/au:+ Kirilyuk/0/1/0/all/0/1 http://arxiv.org/find/quant Unreduced communication dynamics is as complex Unreduced communication dynamics is as complex as transmitted information content (“ “life semantics life semantics” ”) ): : as transmitted information content ( complexity correspondence principle complexity correspondence principle ⇓ ⇓ knowledge- -based networks based networks, complexity growth , complexity growth knowledge ⇓ ⇓ Principle and method of practical practical design and use design and use Principle and method of of intelligent communication networks of intelligent communication networks Natural inclusion of all man man- -related aspects related aspects Natural inclusion of all true intelligence and consciousness, physics/0409140 true intelligence and consciousness, physics/0409140 FUNDAMENTAL, RIGOROUSLY DERIVED RIGOROUSLY DERIVED MEANING MEANING AND AND PURPOSE PURPOSE FUNDAMENTAL, OF AUTONOMIC COMMUNICATION AND RELATED INITIATIVES OF AUTONOMIC COMMUNICATION AND RELATED INITIATIVES http://arXiv.org/abs/physics/0412058, http://cogprints.org/3988 , http://cogprints.org/3988 http://arXiv.org/abs/physics/0412058
Universal Science of Complexity Unreduced Interaction Cosmos ICT Dynamic Complexity Dynamic Complexity Nano Brain Bio http://arxiv.org/find/quant- http://arxiv.org/find/quant -ph,gr ph,gr- -qc,physics/1/au:+Kirilyuk/0/1/0/all/0/1 qc,physics/1/au:+Kirilyuk/0/1/0/all/0/1
Science Progress Diagram NEW MATHEMATICS OF COMPLEXITY NEW MATHEMATICS OF COMPLEXITY Unitary science: only one only one from many real system realisations from many real system realisations Unitary science: Universal Science of Complexity (USciCom): all all system realisations system realisations Universal Science of Complexity (USciCom): Unitary 1 Unitary 2 USciCom Unitary 1 Unitary 2 USciCom Unitary 1 Unitary 2 USciCom Mechanistic Dynamic Mechanistic Mechanistic Mechanistic Dynamic Mechanistic Mechanistic Dynamic discreteness: continuity: discreteness: discreteness: continuity: discreteness: discreteness: continuity: discreteness: Numbers Calculus Calculus Multivaluedness Multivaluedness Numbers Numbers Calculus Multivaluedness Classical figures Deformable shapes Dynamical fractal Classical figures Deformable shapes Dynamical fractal Classical figures Deformable shapes Dynamical fractal No interaction Trivial interaction Full interaction No interaction Trivial interaction Full interaction No interaction Trivial interaction Full interaction No chan No chang ge e Formal chang Formal chan ge e Intrinsic chang Intrinsic chan ge e Formal change Intrinsic change No change No quality No quality Full quality No quality No quality Full quality No quality No quality Full quality http://arXiv.org/abs/physics/9806002 http://arXiv.org/abs/physics/9806002
Unreduced Interaction Dynamics Unreduced Interaction Dynamics Arbitrary many- -body interaction process: body interaction process: Arbitrary many ⎧ ⎫ ⎡ ⎤ N N ∑ ∑ ⎪ ⎪ ( ) ( ) ( ) ( ) ⎢ ⎥ ( ) h q + V q q , Ψ Q = E Ψ Q Q = q q , ,..., q , ⎨ ⎬ k k kl k l N ⎢ ⎥ 1 2 ⎪ ⎪ ⎢ ⎥ k = 0 l k > ⎣ ⎦ ⎩ ⎭ or ⎧ ⎫ ⎡ ⎤ N N ∑ ∑ ⎪ ⎪ ( ) ( ) ( ) ( ) ( ) ( ) ⎢ ⎥ h ξ + h q + V ξ , q V q q , Ψ ξ , Q = E Ψ ξ , Q ξ ≡ q + , ⎨ ⎬ 0 ⎢ k k 0 k k kl k l ⎥ 0 ⎪ ⎪ ⎢ ⎥ k = 1 l k > ⎣ ⎦ ⎩ ⎭ The unreduced (nonperturbative) general solution is always probabilistic probabilistic The unreduced (nonperturbative) general solution is always (phenomenon of dynamic multivaluedness dynamic multivaluedness = = i intrinsic chaoticity ntrinsic chaoticity ): ): (phenomenon of N = ∑ ℜ ⊕ ( ) ( ) ρ ξ , Q ρ ξ , Q r r = 1 Dynamically determined probability Dynamically determined probability , ∑ N r α α = = 1 r r N ℜ r
Unreduced Interaction Dynamics Unreduced Interaction Dynamics Arbitrary interaction process in terms of (free) component eigenvalues: values: Arbitrary interaction process in terms of (free) component eigen ∑ ( ) ( ) ( ) ( ) ( ) h ξ ψ ξ + V ξ ψ ξ = η ψ ξ 0 n nn ′ n ′ n n n ′ where the total system state- -function is obtained as function is obtained as where the total system state ∑ ∑ ( ) ( ) ( ) ( ) ( ) ( ) ( ) Ψ ξ , Q = ψ q ϕ q ϕ q ... ϕ q ≡ ψ ξ Φ Q n 0 n n n n n 1 1 2 2 N N 1 2 N ( ) n ≡ n n , ,..., n n 1 2 N Usual perturbative approximations: Usual perturbative approximations: ∑ � � ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ⎡ ⎤ h ξ + V ξ + V ξ ψ ξ = η ψ ξ , V ξ < V ξ < V ξ ⎣ ⎦ ′ 0 nn n n n n 0 n nn ′ n
Unreduced general solution of the same problem: of the same problem: Unreduced general solution N ℜ ∑ ⊕ 2 2 ( ) ( ) ( ) ( ) ( ) ρ ξ , Q ≡ Ψ ξ , Q = ρ ξ , Q , ρ ξ , Q = Ψ ξ , Q r r r ∑ r = 1 ∑ ⎡ ⎤ ∫ * r ( ) 0 ( ) ′ 0 ( ′ ) ( ′ ) ( ′ ) Φ Q ψ ξ d ξ ψ ξ V ξ ψ ξ ⎢ ⎥ ′ ′ n ni ni n i 0 0 ⎢ ⎥ Ω r r ξ ( ) ( ) ( ) Ψ ξ , Q = c ⎢ Φ Q ψ ξ + ⎥ r i i 0 0 ⎢ ⎥ r 0 η − η − ε i ni ′ n 0 ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ′ n i , i ( ) r r { ψ ξ , η } where are eigen- -solutions of the solutions of the effective effective equation equation where are eigen i i 0 ( ) ( ) ( ) ( ) ( ) h ξ ψ ξ + V ξ η ψ ; ξ = ηψ ξ eff 0 0 0 0 ∑ ∫ * ( ) ( ) ( ) ( ) ( ) r 0 0 V ξ ψ ξ d ξ ψ ′ ξ ′ V ξ ψ ′ ξ ′ ′ ′ n ni ni n i 0 0 0 ( ) Ω r r ( ) ( ) r ( ) ξ V ξ η ψ ; ξ = V ξ ψ ξ + eff i i i 0 00 0 r 0 η − η − ε i ni ′ n 0 ′ n i , r Elementary length Δ = x λ = Δ η , time Δ = Δ t x , action Δ A = V Δ t v i eff 0
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