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How to artificially encode observer in universal information coding structure like DNA ? It requires naturally creating information Bits and natural encoding triplet code enables recognizing other encoded information. These Bits become standard units of different information languages in modern communications. Fundamental interactions build structure of Universe. Numerous multilevel inter-species interactions selforganize biosystems. Human interactions unify these and many others. Physical reality is only interactions identified or not yet. Each interaction is elementary yes-no action of impulse which models a natural Bit. Natural interactive process, transferring Bits, models information process. Information is universal physical substance a phenomenon of interaction which not only originates information but transfers it sequentially. Mutually interacting processes enable creating new elements like chemical chain reactions. The elements enclosing components of reaction memorize the interactive yes-no result similar to encoding. Energy quantity and quality of specific interaction determine sequence of transferring information, its encoding, and limit the code length. The introduced formalism of natural emergence information and its encoding also shows advantage over non-natural encoding. The impulse sequential natural encoding merges memory with the time of memorizing information and compensates the cost by running time intervals of encoding. Information process binds the encoding impulse reversible microprocesses in multiple impulses macroprocess of information irreversible dynamics establishing interactive integrated information dynamics. The encoding process integrates geometrical triplet coding structure rotating double helix of sequencing cells Bits, which commands cognition, intelligence including conscience. The results validate computer simulation, and experiments., Comment: 20 pages include four figures, arXiv admin note: substantial text overlap with arXiv:1603.01879, arXiv:1307.0449

Interacting random field of probabilities links Kolmogorov law 0-1 and Bayesian probabilities observing Markov diffusion process under Yes-No actions of random impulse. These objective probabilities measure virtual probing impulses processing the interactions in observable process. The impulse observation increases each posteriori correlation reducing conditional entropy measures from finite uncertainty up to certainty of real impulse. The reduced entropy conveys probabilistic causality with time course and temporal memory in collecting correlations, which interactive impulse innately cuts exposing hidden process entropy. The natural cut of this entropy reveals information hidden in the correlation connections. Inside the merging probing impulse emerges reversible microprocess with yes-no conjugated entangled entropy, curvature and logical complexity. Within the impulse time interval, entanglement starts before its space is formed and ends with beginning the space during reversible relative time interval being small part of impulse time interval. Merging impulse curves and rotates the impulse interactive actions in microprocess whose space interval measures this transitive movement.The cutting entropy sequentially converting to information memorizes the probes logic in Bit, participating in next probe conversions and encoding which memorizes information causality. The complexity and mass appears after the space emerges from the entanglement.The cognition assembles common units through the multiple attraction and resonances at forming network (IN) of triplet hierarchy, which accept only units that concentrates and recognizes each triplet IN node. The ended triplet of hierarchical INs measures level of the observer intelligence. The synthesized optimal process minimizes the observations time in Artificial designed information Observer with intellectual searching logic., Comment: 92 pages include 8 figures. arXiv admin note: text overlap with arXiv:1511.03601, substantial text overlap with arXiv:1307.0449

Up to now both information and its connection to reality have not scientifically conclusive definitions neither implicit origin. They emerge in observing multiple impulses interactive yes-no actions modeling information Bits. The observed information process connects reality, information, and creates Observer. Interaction is fundamental reality building structure of Universe from quantum physics up to brain neurons interactive actions. Merging action and reaction joins probabilistic prior and posterior actions on edge of the observed predictability and begins microprocess. Its time of entanglement starts space interval composing two qubits or Bit of reversible logic in the emerging information process. The impulse interacting action curves impulse geometry creating asymmetrical logic Bit as logical Maxwell demon. With approaching probability one, the attracting interaction captures energy memorizing asymmetrical logic in information certain Bit. Such Bit is naturally extracted at minimal quality energy equivalent ln2 working as Maxwell Demon. The memorized impulse Bit and its free information self-organizes multiple Bits in triplets sructuring macroprocess. Memorized information binds reversible microprocess with irreversible information macroprocess along multidimensional observing process. The macroprocess self-forming triplet units UP attract new UP through free Information. Multiple UP adjoin hierarchical network whose free information produces new UP at higher level node and encodes triplets in multi-levels hierarchical organization. The interactive information dynamics assemble geometrical and information structures of cognition and intelligence in double spiral rotating code. Information Path Functional integrates multiple interactive dynamics in finite bits which observe and measure reality. The time and space of reality exists only as units of information as Wheeler predicted., Comment: 228 pages include 14 figures. arXiv admin note: substantial text overlap with arXiv:1511.03601, arXiv:1212.1710, arXiv:1401.7041

What is information originating in observation? Until now it has no scientifically conclusive definition. Information is memorized entropy cutting in random observations which processing interactions. Randomness of various interactive observations is source of entropy as uncertainty. Observation under random 1-0 impulses probabilities reveals hidden correlation which connects Bayesian probabilities increasing each posterior correlation. That sequentially reduces relational entropy conveying probabilistic casualty with temporal memory of correlations which interactive impulse innately cuts. Within hidden correlation emerges reversible time space microprocess with conjugated entangled entropy which probing impulse intentionally cuts and memorizes information as certainty. Sequential interactive cuts integrates cutting information in information macroprocess with irreversible time course. Memorized information binds reversible microprocess within impulse with irreversible information macroprocess. Observer probes collect cutting information data bits of observing frequencies impulses. Each impulse cuts maximum of impulse minimal information performing dual max-min principle of converting process entropy to information through uncertain gap. Multiple naturally encoding bits moving in macroprocess join triplet macrounits which logically organize information networks encoding macrounits in structures enclosing triplet code. Network time space distributed structure self renews and cooperates information decreasing its complexity. Integrating process entropy functional and bits information in information path integral embraces variation minimax law which determines processes regularities. Solving problem mathematically describes micro macro processes, network, and invariant conditions of observer network self replication., Comment: 73 pages, 10 figures

Finding observing path creating its observer is important problem in physics and information science. In observing processes, each observation is act changing the observing process that generates interactive observation. Each interaction is discrete Yes-No impulse modeling Bit. Recurring inter-actions independent of physical nature is phenomenon of information. Multiple interactions generate random Markov chains covering multiple Bits. Impulse No action cuts maximum entropy-uncertainty, Yes action transfers cut minimum to next impulse creating maximin principle decreasing uncertainty. The cutoff entropies reveal hidden information naturally observing interactive impulse as elementary observer. Conversion impulse entropies to information integrates path functional. The maxmin variation principle formalizes interactive information equations. Merging Yes-No actions generate microprocess within bordered impulses running superposition of conjugated entropies entangling during time interval within forming space intervals. Interaction curves impulse geometry creating asymmetry which logically erases entangled entropy removing causal probabilistic entropy with symmetrical reversible logic and bringing asymmetrical information logic. Entropy-information topological gap connects asymmetrical logic with physical Markov diffusion whose energy memorizes logical Bit. Moving Bits selfform unit of information macroprocess attracting new UP through free Information. Multiple UP triples adjoin hierarchical network (IN) whose free information produces new UP at higher level node and encodes triple code logic. Each UP unique position in IN hierarchy defines location of each code logical structure. The IN node hierarchical level classifies quality of assembled Information. Ending IN node enfolds all IN levels. Multiple INs enclose Observer cognition and intelligence with consciousness., Comment: 144 pages included 13 figures. arXiv admin note: text overlap with arXiv:1207.3091

The approach defines information process from probabilistic observation, emerging microprocess,qubit, encoding bits, evolving macroprocess, and extends to Observer information self-organization, cognition, intelligence and understanding communicating information. Studying information originating in quantum process focuses not on particle physics but on natural interactive impulse modeling Bit composing information observer. Information emerges from Kolmogorov probabilities field when sequences of 1-0 probabilities link Markov probabilities modeling arising observer. These objective yes-no probabilities virtually cuts observing entropy hidden in cutting correlation decreasing Markov process entropy and increasing entropy of cutting impulse running minimax principle. Merging impulse curves and rotates yes-no conjugated entropies in microprocess. The entropies entangle within impulse time interval ending with beginning space. The opposite curvature lowers potential energy converting entropy to memorized bit. The memorized information binds reversible microprocess with irreversible information macroprocess. Multiple interacting Bits self-organize information process encoding causality, logic and complexity. Trajectory of observation process carries probabilistic and certain wave function self-building structural macrounits. Macrounits logically self-organize information networks encoding in triplet code. Multiple IN enclose observer information cognition and intelligence. Observer cognition assembles attracting common units in resonances forming IN hierarchy accepting only units recognizing IN node. Maximal number of accepted triplets measures the observer information intelligence. Intelligent observer recognizes and encodes digital images in message transmission enables understanding the message meaning. Cognitive logic self-controls encoding the intelligence in double helix code., Comment: 138 pages include 16 figures. arXiv admin note: text overlap with arXiv:1212.1710

Bayesian integral functional measure of entropy-uncertainty (EF) on trajectories of Markov multi-dimensional diffusion process is cutting off by interactive impulses (controls). Each cutoff minimax of EF superimposes and entangles conjugated fractions in microprocess, enclosing the captured entropy fractions as source of an information unit. The impulse step-up action launches the unit formation and step-down action finishes it and brings energy from the interactive jump. This finite jump transfers the entangled entropy from uncertain Yes-logic to the certain-information No-logic information unit whose measuring at end of the cut kills final entropy-uncertainty and limits unit. The Yes-No logic holds Bit Participator creating elementary information observer without physical pre-law. Cooperating two units in doublet and an opposite directional information unit in triplet forms minimal stable structure. Information path functional (IPF) integrates multiple hidden information contributions along the cutting process correlations in information units of cooperating doublets-triplets, bound by free information, and enfolds the sequence of enclosing triplet structures in the information network (IN) that sequentially decreases the entropy and maximizes information. The IN bound triplets release free information rising information forces enable attracting new information unit and ordering it. While IPF collects the information units, the IN performs logical computing using doublet-triplet code. The IN different levels unite logic of quantum micro- and macro- information processes, composing quantum and/or classical computation., Comment: 22 pages,7 figures. arXiv admin note: text overlap with arXiv:1212.1710

The aim is formal principles of origin information and information process creating information observer self-creating information in interactive observations. The interactive phenomenon creates Yes-No actions of information Bits in its information observer. Information emerges from interacting random field of Kolmogorov probabilities, which link Kolmogorov 0-1 law probabilities and Bayesian probabilities observing Markov diffusion process by probabilistic 0-1 impulses. Each No-0 action cuts maximum of impulse minimal entropy while following Yes-1 action transfers maxim between impulses performing dual principle of converting process entropy to information. Merging Yes-No actions generate microprocess within bordered impulse producing Bit with free information when the microprocess probability approaches 1. Interacting bits memorize free information which attracts multiple Bits moving macroprocess self joining triplet macrounits. Memorized information binds reversible microprocess with irreversible macroprocess. The observation converts cutting entropy to information macrounits. Macrounits logically self-organize information networks encoding the units in geometrical structures enclosing triplet code. Multiple IN binds their ending triplets enclosing observer information cognition and intelligence. The observer cognition assembles common units through multiple attraction and resonances at forming IN triplet hierarchy which accept only units that recognizes each IN node. Maximal number of accepted triplet levels in multiple IN measures the observer maximum comparative information intelligence. The observation process carries probabilistic and certain wave functions which self-organize the space hierarchical structures. These information regularities create integral logic and intelligence self-requesting needed information., Comment: 83 pages include 16 figures

This presentation's Part 3 studies the evolutionary information processes and regularities of evolution dynamics, evaluated by an entropy functional (EF) of a random field (modeled by a diffusion information process) and an informational path functional (IPF) on trajectories of the related dynamic process (Lerner 2012). The integral information measure on the process' trajectories accumulates and encodes inner connections and dependencies between the information states, and contains more information than a sum of Shannon's entropies, which measures and encodes each process's states separately. Cutting off the process' measured information under action of impulse controls (Lerner 2012a), extracts and reveals hidden information, covering the states' correlations in a multi-dimensional random process, and implements the EF-IPF minimax variation principle (VP). The approach models an information observer (Lerner 2012b)-as an extractor of such information, which is able to convert the collected information of the random process in the information dynamic process and organize it in the hierarchical information network (IN), Part2 (Lerner, 2012c). The IN's highest level of the structural hierarchy, measured by a maximal quantity and quality of the accumulated cooperative information, evaluates the observer's intelligence level, associated with its ability to recognize and build such structure of a meaningful hidden information. The considered evolution of optimal extraction, assembling, cooperation, and organization of this information in the IN, satisfying the VP, creates the phenomena of an evolving observer's intelligence. The requirements of preserving the evolutionary hierarchy impose the restrictions that limit the observer's intelligence level in the IN. The cooperative information geometry, evolving under observations, limits the size and volumes of a particular observer., Comment: 27 pages,7 figures. arXiv admin note: text overlap with arXiv:1109.3125

Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states. Information appears phenomenon of interaction cutting correlations carrying entropy. Each inter action models Kronicker impulse, delta impulse models interaction between the Kronicker impulses. Each impulse step down action cuts maximum of impulse minimal entropy and impulse step up action transits cutting minimal entropy to each step up action of merging delta function. Delta step down action kills delivering entropy producing equivalent minimax information. The merging action initiates quantum microprocess. Multiple cutting entropy is converting to information micro macroprocess. Cutting impulse entropy integrates entropy functional EF along trajectories of multidimensional diffusion process. Information which delivers ending states of each impulse integrates information path functional IPF along process trajectories. Hidden information evaluates Feller kernel whose minimal path transforms Markov transition probability to probability of Brownian diffusion. Each transitive transformation virtually observes origin of hidden information probabilities correlated states. IPF integrates observing Bits along minimal path assembling information Observer. Minimax imposes variation principle on EF and IPF whose extreme equations describe observing micro and macroprocess which describes irreversible thermodynamics. Hidden information curries free information frozen from correlated connections. Free information binds observing micro macro processes in information macrodynamics. Each dynamic three free information composes triplet structures. Three structural triplets assemble information network. Triple networks free information cooperate information Observer., Comment: 87 pages

The impulses, cutting entropy functional (EF) measure on trajectories Markov diffusion process, integrate information path functional (IPF) composing discrete information Bits extracted from observing random process. Each cut brings memory of the cutting entropy, which provides both reduction of the process entropy and discrete unit of the cutting entropy a Bit. Consequently, information is memorized entropy cutting in random observations which process interactions. The origin of information associates with anatomy creation of impulse enables both cut entropy and stipulate random process generating information under the cut. Memory of the impulse cutting time interval freezes the observing events dynamics in information processes. Diffusion process additive functional defines EF reducing it to a regular integral functional. Compared to Shannon entropy measure of random state, cutting process on separated states decreases quantity information concealed in the states correlation holding hidden process information. Infinite dimensional process cutoffs integrate finite information in IPF whose information approaches EF restricting process maximal information. Within the impulse reversible microprocess, conjugated entropy increments are entangling up to the cutoff converting entropy in irreversible information. Extracting maximum of minimal impulse information and transferring minimal entropy between impulses implement maxmin-minimax principle of optimal conversion process entropy to information. Macroprocess extremals integrate entropy of microprocess and cutoff information of impulses in the IPF information physical process. IPF measures Feller kernel information. Estimation extracting information confirms nonadditivity of EF measured process increments., Comment: 54 pages,1 figure

We study a stochastic control system, described by Ito controllable equation, and evaluate the solutions by an entropy functional (EF), defined by the equation functions of controllable drift and diffusion. Considering a control problem for this functional, we solve the EF control variation problem (VP), which leads to both a dynamic approximation of the process entropy functional by an information path functional (IPF) and information dynamic model (IDM) of the stochastic process. The IPF variation equations allow finding the optimal control functions, applied to both stochastic system and the IDM for joint solution of the identification and optimal control problems, combined with state consolidation. In this optimal dual strategy, the IPF optimum predicts each current control action not only in terms of total functional path goal, but also by setting for each following control action the renovated values of this functional controllable drift and diffusion, identified during the optimal movement, which concurrently correct this goal. The VP information invariants allow optimal encoding of the identified dynamic model operator and control. The introduced method of cutting off the process by applying an impulse control estimates the cutoff information, accumulated by the process inner connections between its states. It has shown that such a functional information measure contains more information than the sum of Shannon entropies counted for all process separated states, and provides information measure of Feller kernel. Examples illustrate the procedure of solving these problems, which has been implemented in practice. Key words: Entropy and information path functionals, variation equations, information invariants, controllable dynamics, impulse controls, cutting off the diffusion process, identification, cooperation, encoding., Comment: 39 pages including 5 figures

An interactive stochastics, evaluated by an entropy functional (EF) of a random field and informational process' path functional (IPF), allows us modeling the evolutionary information processes and revealing regularities of evolution dynamics. Conventional Shannon's information measure evaluates a sequence of the process' static events for each information state and do not reveal hidden dynamic connections between these events. The paper formulates the mathematical forms of the information regularities, based on a minimax variation principle (VP) for IPF, applied to the evolution's both random microprocesses and dynamic macroprocesses. The paper shows that the VP single form of the mathematical law leads to the following evolutionary regularities: -creation of the order from stochastics through the evolutionary macrodynamics, described by a gradient of dynamic potential, evolutionary speed and the evolutionary conditions of a fitness and diversity; -the evolutionary hierarchy with growing information values and potential adaptation; -the adaptive self-controls and a self-organization with a mechanism of copying to a genetic code. This law and the regularities determine unified functional informational mechanisms of evolution dynamics. By introducing both objective and subjective information observers, we consider the observers' information acquisition, interactive cognitive evolution dynamics, and neurodynamics, based on the EF-IPF approach. An evolution improvement consists of the subjective observer s ability to attract and encode information whose value progressively increases. The specific properties of a common information structure of evolution processes are identifiable for each particular object-organism by collecting a behavioral data from these organisms.

The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, and the information path functional (IPF), analyzing their connections to the Kolmogorov's entropy, complexity and the Lyapunov's characteristics. Considering the IPF's essentials and specifics, the paper studies the singularities of the IPF extremal equations and the created invariant relations, which both are useful for the solution of important mathematical and applied problems. Keywords: Additive functional; Entropy; Singularities, Natural Border Problem; Invariant