مشخصات کتاب

Information Path Functional and Informational Macrodynamics

ویرایش:  
نویسندگان: Vladimir S. Lerner (Marina Del Rey,  CA,  USA)  
سری:  
ISBN (شابک) : 9781614700920 
ناشر: Nova publishers 
سال نشر: 2011 
تعداد صفحات: 506 
زبان: English 
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) 
حجم فایل: 4 مگابایت 

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توضیحاتی درمورد کتاب به خارجی

The book subject is mathematical formalism, describing the creation of the dynamic and information regularities from stochastics. The formalism is based on the introduction of an informational path functional, defined on trajectories of a controlled random process, and the solution of variation problem for this novel functional. The solution provides both the information dynamic model of a random process and the model of optimal control. This allows building a two-level information model with a random process at the microlevel and a dynamic process at macrolevel. Considering a variation principle (VP) as a mathematical form that expresses some regularity, it is assumed that the VP extremals, represented by the solutions of the above dynamic model, describe a movement possessing these regularities. Such an approach has been used by R. P. Feynman, who introduced the functional on trajectories of an electron’s movement and applied the variation principle for this path functional to obtain the equations of quantum mechanics. Feynman’s path functional is defined on the dynamic trajectories and has not been applied to random trajectories of a controlled process. Table of Contents: Preface Introduction Part 1. The information path functional’s foundation, pp. 1-332 1.0. Introduction 1.1. The initial mathematical models 1.1.1. Model of the microlevel process 1.1.2. Model of the macrolevel process 1.1.3. The feedback equation-control law 1.1.4. Model of the programmable trajectories (as a task) at microlevel 1.1.5. Model of the programmable trajectories (as a task) at the macrolevel 1.1.6. The equations in deviations 1.1.7. Model of disturbances 1.1.8. The microlevel process’ functional 1.1.9. The Jensen inequality for entropy functional 1.2. Dynamic approximation of a random information functional and the path functional 1.2.1. The extremal principle and the problem formulation 1.2.2. The problem solution. Information path functional 1.2.3. The estimation of an accuracy of the probability’s approximation 1.3. Variation problem for the information path functional and its solution 1.3.1. The problem statements 1.3.2. Solution to the variation problem 1.3.3. A minimum condition for the microlevel’s functional 1.3.4. The optimal control synthesis 1.3.5. A summary of the information path functional approach and IMD 1.4. The IMD information space distributed macromodels 1.4.0. Introduction 1.4.1. The variation problem for space distributed macromodel 1.4.2. The invariant conditions at the transformation of the space coordinates 1.4.3. The parameters of the space transformation and the distributed macromodels 1.4.4. The IMD macromodel’s singular points and the singular trajectories 1.4.5. The IPF natural variation problem, singular trajectories, and the field’s invariants. 1.5. The cooperative information macromodels and information network 1.5.1. The time-space movement toward the macromodel's cooperation 1.5.2. The consolidation of the model’s processes in a cooperative information network (IN) 1.5.3. The IN dynamic structure 1.5.4. Geometrical structure of the optimal space distributed cooperative macromodel (OPMC). The IN’s geometric structure 1.6. The IMD model’s phenomena and information code 1.6.1. The model’s time course and the evaluation of the information contributions into IN. The triplet’s genetic code 1.6.2. The model’s information geometry (IG), its specific, and the structure 1.6.3. The mode’s uncertainty zone and its evaluation 1.6.4. Creation of the IN’s geometry and genetic code of the information cellular geometry 1.6.5. The minimal admissible uncertainty and its connection to physics 1.6.6 Information structure of the double spiral (DSS) control mechanism 1.6.7. Examples of the DSS codes 1.6.8. A system’s harmony, regularities, and the VP 1.7. The macrodynamic and cooperative complexities 1.7.0. Introduction 1.7.1. The notion of interactive and cooperative complexities and the information measures 1.7. 2. The information indicator of a cooperative complexity 1.7.3. Illustration of arising of the information cooperative complexity at discrete points of applied controls 1.7.4. The MC complexity invariant measure 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 information cooperative dynamics. Information attraction and complexity 1.8. The regularities of evolutionary dynamics and the information law 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 acceptable mutations 1.8.3. The conditions of the model’s self-control, adaptation, and self-organization 1.8.4. The evolution of the model’s invariants and a potential the macroprocess’ cyclicity 1.8.5. Requirements for the model’s self–organization. The results of computer simulations 1.8.6. Evaluation of some prognosis parameters of the evolutionary dynamics. Example 1.8.7. Information mechanism of assembling the node's frequencies and automatic selection 1.8.8. The functional schema of the evolutionary informational mechanisms 1.9. The physical analogies related to the information path functional 1.9.1. The connection between the information path functional (PF) and the Kolmogorov’s (K) entropy of a dynamic system, and the relations to physics. 1.9.2. An IPF analogy with the Feynman path functional in Quantum Mechanics 1.9.3. About the invariant transformation of the model's imaginary eigenvalues 1.9.4. The superimposing processes, control, and asymmetry. The IMD relation to Nonequilibrium Thermodynamics (NT) Part 2. The information path functional’s and IMD’s applications, pp. 335-471 2.1. Solution of the control problems for a complex object 2.1.1. The control problems for a complex object 2.1.2. Solving the identification problem 2.1.2.1. The identification of the concentrated object's models 2.1.2.2. The identification of the space distributed object's models 2.1.3. Solving the optimal control problem 2.1.3.1. A joint solution of the optimal control and identification problems. The basic results 2.1.3.2. The procedure of the joint identification, optimal control, and consolidation 2.1.3.3. Building the object’s cooperative information network 2.2. The information modeling of some biological and cognitive processes 2.2.0. The objective and methodology 2.2.1. An inner information structure of the IN with the ranged and the nonranged sequences of the starting eigenvalues. The DSS code. 2.2.2 Mathematical Model of the IN with an arbitrary sequence of the starting eigenvalues 2.2.3. The procedure of encoding, compression, synthesis, and decoding the IN's information 2.2.4 Summarized results 2.2.5. About other related applications 2.2.6. The connections between some physical neuronal functions and mechanisms and their IMD information analogies 2.3. Information modeling and control of some industrial technology processes with complex superimposing phenomena 2.3.1. Process solidification and its application in casting technology 2.3.2. Some electrotechnological processes 2.4. An elementary information macrodynamic model of a market economic system 2.4.1. About Information Systems Modeling of a Modern Economy. The objectives 2.4.2. An Elementary Local Production System (LP) 2.4.3. An Information Model of a Local Market 2.4.4. Managing the LP. A Bank and a Stock Market 2.4.5. Other Information Markets 2.4.6. Example 2.4.7. Summary 2.5. An outline of the computer based methodology 2.5.1. The hierarchy of the model’s micro-and macrovariables and their identification 2.5.2. The computer’s restoration of the IMD model 2.5.3. The structure of the IMD software package Conclusion References Index

فهرست مطالب

INFORMATION PATH FUNCTIONAL AND INFORMATIONAL MACRODYNAMICS\r......Page 4
CONTENTS......Page 6
ABSTRACT......Page 12
PREFACE......Page 14
ACKNOWLEDGMENTS......Page 18
INTRODUCTION......Page 20
PART 1.THE INFORMATION PATH FUNCTIONAL’S FOUNDATION\r......Page 24
INTRODUCTION......Page 26
1.1.1. Model of Microlevel Process......Page 30
1.1.3. The Feedback Equation-Control Law......Page 32
1.1.4. Model of Programmable Trajectories (as a Task) atMicrolevel......Page 33
1.1.6. The Equations in Deviations......Page 34
1.1.8. The Microlevel Process’ Functional......Page 36
1.1.9. The Jensen\'s Inequality for the Entropy Functional......Page 41
1.2.1. The Extremal Principle and the Problem Formulation......Page 46
1.2.2. The Problem Solution. Information Path Functional......Page 47
1.2.3. The Estimation of an Accuracy of the Probability’sApproximation......Page 65
1.3.1. The Problem Formulation......Page 68
1.3.2. Solution to the Variation Problem......Page 69
1.3.3. The Minimum Condition for the Microlevel Functional......Page 83
1.3.4. The Optimal Control Synthesis......Page 86
1.3.5. A Summary of the Information Path Functional Approach.The IPF invariants......Page 100
1.4.1. Introduction......Page 126
1.4.2. The Variation Problem for Space Distributed Macromodel......Page 128
1.4.3. The Invariant Conditions at the Transformationof the Space Coordinates......Page 130
1.4.4. The Parameters of the Space Transformation and theDistributed Macromodels......Page 137
1.4.5. The IPF Macromodel’s Singular Points and the SingularTrajectories......Page 143
1.4.6. The IPF Natural Variation Problem, Singular Trajectories,and The Field’s Invariants for the IPF......Page 151
1.5.1. Introduction......Page 164
1.5.2. The Time-Space Movement Toward the Macromodel\'sCooperation......Page 165
1.5.3. The Consolidation and Aggregation of the Model Processes.Forming an Information Network (IN)......Page 187
1.5.4. The IN Dynamic Structure......Page 196
1.5.5. Geometrical Structure of the Optimal Space DistributedCooperative Macromodel (OPMC).The IN Geometrical Structure......Page 205
1.6.1. The Model Time Course and the Evaluationof the Information Contributions into IN.The Triplet Genetic Code......Page 218
1.6.2. The Model Information Geometry (IG), Its Specific,and the Structure......Page 226
1.6.3. The Model Uncertainty Zone and Its Evaluation......Page 234
1.6.4. Creation of the IN geometry and a Genetic Code of theInformation Cellular Geometry......Page 235
1.6.5. The Minimal Admissible Uncertainty and Its Connectionto Physics......Page 240
1.6.6. Information Structure of the model Double Spiral’s (DSS)Control Mechanism......Page 244
1.6.7. Examples of the DSS codes......Page 247
1.6.8. A System’s Harmony, Regularities, and the VP......Page 249
1.7.1. Introduction......Page 252
1.7.2. The Notion of Interactive and Cooperative Complexitiesand Their Information Measures......Page 254
1.7.3. The Information Indicator of a Cooperative Complexity......Page 256
1.7.4. Illustration of Arising of the Information CooperativeComplexity at Discrete Points of Applied Controls......Page 262
1.7.5. The Complexity Invariant Measure in a CooperativeDynamic Process......Page 268
1.7.6. The IN Cooperative Mechanism with the Complexity Measure......Page 274
1.7.7. The Equations of the Spatial Information CooperativeDynamics. Information Attraction and Complexity......Page 282
1.7.8. Connection to Kolmogorov’s Complexity......Page 292
1.8.1. Introduction......Page 294
1.8.2. The Equations Regularities and the Evolutionary Law......Page 295
1.8.3. A Mechanism of an Enhancement of the AcceptableMutations......Page 303
1.8.4. The Conditions of the Model’s Self-control, Adaptation, andSelf-organization......Page 309
1.8.5. The Evolution of the Model Invariants and a PotentialMacroprocess’ Cyclicity......Page 314
1.8.6. Requirements for the Model Self–organization.The Results of Computer Simulations......Page 320
1.8.7. Evaluation of Some Prognostic Parametersof the Evolutionary Dynamics. Example......Page 324
1.8.8. Information Mechanism of Assembling the Node\'sFrequencies and Automatic Selection......Page 325
1.8.9. The Functional Schema of the Evolutionary InformationalMechanisms. A Summary......Page 330
1.9.1. The Connection between the Information Path Functional(IPF) and the Kolmogorov’s (K) Entropy of a DynamicSystem, and the Relations to Physics......Page 334
1.9.2. An IPF Analogy with the Feynman Path Functionalin Quantum Mechanics and Informational Form ofSchrödinger’s Equation......Page 337
1.9.3. About the Invariant Transformation of the ModelImaginary Eigenvalues and Information......Page 344
1.9.4. The Superimposing Processes, Control and Asymmetry.The IMD Relation to Nonequilibrium Thermodynamics (NT)......Page 346
1.9.5. About the Notion of a System......Page 353
PART 2. THE INFORMATION PATH FUNCTIONAL’S AND IMD’S APPLICATIONS \r......Page 356
2.1.1. The Control Problems for a Complex Object......Page 358
2.1.2.1. The Identification of the Concentrated Object\'s Models......Page 361
2.1.2.2. The Identification of the Space Distributed Object\'s Models......Page 365
2.1.3.1. A Joint Solution of the Optimal Control and Identification Problems.The Basic Results......Page 372
2.1.3.2. The Procedure of the Joint Identification, Optimal Control,and Consolidation......Page 376
2.1.3.3. Building the Object Cooperative Information Network......Page 393
2.2.1. The Objective and Methodology......Page 396
2.2.2. An Inner Information Structure of the IN with the Rangedand the Nonranged Sequences of the Starting Eigenvalues.The DSS Code......Page 397
2.2.3. Mathematical Model of the IN with an Arbitrary Sequenceof the Starting Eigenvalues......Page 401
2.2.4. The Procedure of Encoding, Compression, Synthesis, andDecoding of the IN Information......Page 411
2.2.5. Summarized Results......Page 417
2.2.6. About Other Related Applications......Page 422
2.2.7. The Connections between Some Physical Neuronal Functionsand Mechanisms and Their IMD Information Analogies......Page 425
2.3.1. Process Solidification and its Application in CastingTechnology......Page 432
2.3.2. Some Electrotechnological Processes......Page 443
A.3.1. Control System in the Casing Technology......Page 444
A.3.2. Control System in the Electrotechnology......Page 446
2.4.1. About Information Systems Modeling of a ModernEconomy. The Objectives......Page 450
2.4.2. An elementary Local Production System ( LP)......Page 453
2.4.3. An Information Model of a Local Market......Page 455
2.4.4. Managing the LP. A Bank and a Stock Market......Page 460
2.4.5. Other Information Markets......Page 464
2.4.6. Example......Page 465
2.4.7. Summary......Page 466
2.5.1. The Hierarchy of the Model’s Micro-and Macrovariablesand Their Identification......Page 468
2.5.2.The Computer’s Restoration of the IMD Model......Page 469
2.5.3. The Structure of the IMD Software Package......Page 472
CONCLUSION......Page 474
REFERENCES......Page 478
ABOUT THE AUTHOR......Page 494
INDEX......Page 496

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