By Vladimir S. Lerner (Marina Del Rey, CA, USA)

The ebook topic is mathematical formalism, describing the construction of the dynamic and knowledge regularities from stochastics.

The formalism is predicated at the creation of an informational course sensible, outlined on trajectories of a managed random technique, and the answer of edition challenge for this novel functional.

The resolution presents either the data dynamic version of a random procedure and the version of optimum keep an eye on. this permits construction a two-level info version with a random approach on the microlevel and a dynamic procedure at macrolevel. contemplating a edition precept (VP) as a mathematical shape that expresses a few regularity, it truly is assumed that the vice chairman extremals, represented by way of the ideas of the above dynamic version, describe a circulation owning those regularities. Such an technique has been utilized by R. P. Feynman, who brought the sensible on trajectories of an electron’s circulate and utilized the adaptation precept for this direction useful to procure the equations of quantum mechanics. Feynman’s course practical is outlined at the dynamic trajectories and has no longer been utilized to random trajectories of a managed process.

Table of Contents:

Preface

Introduction

Part 1. the data direction functional’s origin, pp. 1-332

1.0. Introduction

1.1. The preliminary mathematical models

1.1.1. version of the microlevel process

1.1.2. version of the macrolevel process

1.1.3. The suggestions equation-control law

1.1.4. version of the programmable trajectories (as a role) at microlevel

1.1.5. version of the programmable trajectories (as a job) on the macrolevel

1.1.6. The equations in deviations

1.1.7. version of disturbances

1.1.8. The microlevel method’ functional

1.1.9. The Jensen inequality for entropy functional

1.2. Dynamic approximation of a random details practical and the trail functional

1.2.1. The extremal precept and the matter formulation

1.2.2. the matter resolution. details direction functional

1.2.3. The estimation of an accuracy of the probability’s approximation

1.3. version challenge for the knowledge course useful and its solution

1.3.1. the matter statements

1.3.2. way to the difference problem

1.3.3. A minimal for the microlevel’s functional

1.3.4. The optimum keep watch over synthesis

1.3.5. A precis of the knowledge direction practical method and IMD

1.4. The IMD info house disbursed macromodels

1.4.0. Introduction

1.4.1. the adaptation challenge for area dispensed macromodel

1.4.2. The invariant stipulations on the transformation of the gap coordinates

1.4.3. The parameters of the distance transformation and the allotted macromodels

1.4.4. The IMD macromodel’s singular issues and the singular trajectories

1.4.5. The IPF typical edition challenge, singular trajectories, and the field’s invariants.

1.5. The cooperative info macromodels and data network

1.5.1. The time-space circulation towards the macromodel's cooperation

1.5.2. The consolidation of the model’s strategies in a cooperative info community (IN)

1.5.3. The IN dynamic structure

1.5.4. Geometrical constitution of the optimum area disbursed cooperative macromodel (OPMC). The IN’s geometric structure

1.6. The IMD model’s phenomena and knowledge code

1.6.1. The model’s time direction and the assessment of the knowledge contributions into IN. The triplet’s genetic code

1.6.2. The model’s details geometry (IG), its particular, and the structure

1.6.3. The mode’s uncertainty region and its evaluation

1.6.4. construction of the IN’s geometry and genetic code of the data mobile geometry

1.6.5. The minimum admissible uncertainty and its connection to physics

1.6.6 info constitution of the double spiral (DSS) keep watch over mechanism

1.6.7. Examples of the DSS codes

1.6.8. A system’s concord, regularities, and the VP

1.7. The macrodynamic and cooperative complexities

1.7.0. Introduction

1.7.1. The concept of interactive and cooperative complexities and the knowledge measures

1.7. 2. the data indicator of a cooperative complexity

1.7.3. representation of bobbing up of the knowledge cooperative complexity at discrete issues of utilized controls

1.7.4. The MC complexity invariant degree in a cooperative dynamic process

1.7.5. The IN’s cooperative mechanism with the MC complexity’s measures

1.7.6. The equations of the spatial details cooperative dynamics. details allure and complexity

1.8. The regularities of evolutionary dynamics and the data legislations of evolution

1.8.0. Introduction

1.8.1. The equations regularities and the evolutionary law

1.8.2. A mechanism of an enhancement of the suitable mutations

1.8.3. The stipulations of the model’s self-discipline, model, and self-organization

1.8.4. The evolution of the model’s invariants and a possible the macroprocess’ cyclicity

1.8.5. requisites for the model’s self–organization. the result of laptop simulations

1.8.6. assessment of a few analysis parameters of the evolutionary dynamics. Example

1.8.7. info mechanism of assembling the node's frequencies and automated selection

1.8.8. The practical schema of the evolutionary informational mechanisms

1.9. The actual analogies relating to the data direction functional

1.9.1. the relationship among the knowledge direction sensible (PF) and the Kolmogorov’s (K)

entropy of a dynamic approach, and the kin to physics.

1.9.2. An IPF analogy with the Feynman direction practical in Quantum Mechanics

1.9.3. concerning the invariant transformation of the model's imaginary eigenvalues

1.9.4. The superimposing approaches, regulate, and asymmetry. The IMD relation to Nonequilibrium Thermodynamics (NT)

Part 2. the knowledge direction functional’s and IMD’s functions, pp. 335-471

2.1. resolution of the regulate difficulties for a posh object

2.1.1. The keep an eye on difficulties for a fancy object

2.1.2. fixing the identity problem

2.1.2.1. The identity of the focused object's models

2.1.2.2. The id of the distance disbursed object's models

2.1.3. fixing the optimum regulate problem

2.1.3.1. A joint resolution of the optimum keep an eye on and id difficulties. the fundamental results

2.1.3.2. The technique of the joint id, optimum keep an eye on, and consolidation

2.1.3.3. construction the object’s cooperative info network

2.2. the knowledge modeling of a few organic and cognitive processes

2.2.0. the target and methodology

2.2.1. An internal info constitution of the IN with the ranged and the nonranged sequences of the beginning eigenvalues. The DSS code.

2.2.2 Mathematical version of the IN with an arbitrary series of the beginning eigenvalues

2.2.3. The approach of encoding, compression, synthesis, and deciphering the IN's information

2.2.4 Summarized results

2.2.5. approximately different similar applications

2.2.6. The connections among a few actual neuronal features and mechanisms and their IMD details analogies

2.3. details modeling and regulate of a few commercial expertise strategies with advanced superimposing phenomena

2.3.1. procedure solidification and its program in casting technology

2.3.2. a few electrotechnological processes

2.4. An user-friendly details macrodynamic version of a industry monetary system

2.4.1. approximately details platforms Modeling of a latest financial system. The objectives

2.4.2. An common neighborhood creation procedure (LP)

2.4.3. a data version of a neighborhood Market

2.4.4. dealing with the LP. A financial institution and a inventory Market

2.4.5. different info Markets

2.4.6. Example

2.4.7. Summary

2.5. an overview of the pc dependent methodology

2.5.1. The hierarchy of the model’s micro-and macrovariables and their identification

2.5.2. The computer’s recovery of the IMD model

2.5.3. The constitution of the IMD software program package

Conclusion

References

Index