Entropy Measures, Maximum Entropy Principle and Emerging Applications

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Karmeshu (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Έκδοση: 1st ed. 2003.
• Σειρά: Studies in Fuzziness and Soft Computing, 119
• Θέματα: Applied mathematics.; Engineering mathematics.; Computational complexity.; System theory.; Statistical physics.; Dynamical systems.; Vibration.; Dynamics.; Mathematical and Computational Engineering.; Complexity.; Systems Theory, Control.; Complex Systems.; Vibration, Dynamical Systems, Control.; Statistical Physics and Dynamical Systems.

 This book is dedicated to Prof. J. Kapur and his contributions to the field of entropy measures and maximum entropy applications. Eminent scholars in various fields of applied information theory have been invited to contribute to this Festschrift, collected on the occasion of his 75th birthday. The articles cover topics in the areas of physical, biological, engineering and social sciences such as information technology, soft computing, nonlinear systems or molecular biology with a thematic coherence. The volume will be useful to researchers working in these different fields enabling them to see the underlying unity and power of entropy optimization frameworks. 

 1 Uncertainty, Entropy and Maximum Entropy Principle - An Overview -- 1.1 Uncertainty -- 1.2 Measure of Uncertainty in Random Phenomena -- 1.3 Shannon's Entropy -- 1.4 Properties of Shannon's Entropy -- 1.5 Asymptotic Equipartition Property (AEP) -- 1.6 Joint and Conditional Entropies, Mutual Information -- 1.7 Kullback-Leibler (KL) Directed Divergence -- 1.8 Entropy of Continuous Distribution: Boltzmann Entropy -- 1.9 Entropy and Applications -- 1.10 Weighted Entropy -- 1.11 Fuzzy Uncertainty -- 1.12 Generalized Measures of Entropy -- 1.13 Maximum Entropy Principle -- 1.14 Entropy and MEP based applications -- 1.15 Conclusions -- References -- 2 Facets of Generalized Uncertainty-based Information -- 2.1 Introduction -- 2.2 Uncertainty Formalization -- 2.3 Uncertainty Measurement -- 2.4 Uncertainty Utilization -- 2.5 Conclusions -- References -- 3 Application of the Maximum (Information) Entropy Principle to Stochastic Processes far from Thermal Equilibrium -- 3.1 Introduction -- 3.2 The Fokker-Planck Equation Belonging to the Short-Time Propagator -- 3.3 Correlation Functions as Constraints -- 3.4 Calculation of the Lagrange Multipliers -- 3.5 Practical Feasibility -- 3.6 Concluding Remarks -- References -- 4 Maximum Entropy Principle, Information of Non-Random Functions and Complex Fractals -- 4.1 Introduction -- 4.2 MEP and Entropy of Non-Random Functions -- 4.3 Fractional Brownian Motion of Order n -- 4.4 Maximum Entropy Principle and Fractional Brownian Motion -- 4.5 Concluding Remarks -- References -- 5 Geometric Ideas in Minimum Cross-Entropy -- 5.1 Introduction -- 5.2 "Pythagoran" theorem and projection -- 5.3 Differential geometry -- 5.4 Hausdorff dimension -- References -- 6 Information-Theoretic Measures for Knowledge Discovery and Data Mining -- 6.1 Introduction -- 6.2 Analysis of Information Tables -- 6.3 A Review of Information-Theoretic Measures -- 6.4 Information-theoretic Measures of Attribute Importance -- 6.5 Conclusion -- References -- 7 A Universal Maximum Entropy Solution for Complex Queueing Systems and Networks -- 7.1 Introduction -- 7.2 The Principle of ME -- 7.3 The GE Distribution -- 7.4 ME Analysis of a Complex G/G/1/N Queue -- 7.5 ME Analysis of Complex Open Queueing Networks -- 7.6 Conclusions and Further Comments -- References -- 8 Minimum Mean Deviation from the Steady-State Condition in Queueing Theory -- 8.1 Introduction -- 8.2 Mathematical Formalism -- 8.3 Number of Arrivals -- 8.4 Interarrival Time -- 8.5 Service Time -- 8.6 Computer Program -- 8.7 Conclusion -- References -- 9 On the Utility of Different Entropy Measures in Image Thresholding -- 9.1 Introduction -- 9.2 Summarization of Image Information -- 9.3 Measures of Information -- 9.4 Thresholding with Entropy Measures -- 9.5 Implementation and Results -- 9.6 Conclusions -- References -- 10 Entropic Thresholding Algorithms and their Optimizations -- 10.1 Introduction -- 10.2 Iterative Method for Minimum Cross Entropy Thresholding -- 10.3 Iterative Maximum Entropy Method -- 10.4 Extension to Multi-level Thresholding -- 10.5 Results and Discussions -- References -- 11 Entropy and Complexity of Sequences -- 11.1 Introduction -- 11.2 Representations of Sequences and Surrogates -- 11.3 Entropy-like Measures of Sequence Structure -- 11.4 Results of Entropy Analysis -- 11.5 Grammar Complexity and Information Content -- 11.6 Results of the Grammar Analysis -- 11.7 Conclusions -- References -- 12 Some Lessons for Molecular Biology from Information Theory -- 12.1 Precision in Biology -- 12.2 The Address is the Message -- 12.3 Breaking the Rules -- 12.4 Waves in DNA Patterns -- 12.5 On Being Blind -- 12.6 Acknowledgments -- References -- 13 Computation of the MinMax Measure -- 13.1 Introduction -- 13.2 Minimum Entropy and the MinMax Measure -- 13.3 An Algorithm for the MinMax measure -- 13.4 Numerical Example: A traffic engineering problem -- 13.5 Concluding Remarks -- References -- 14 On Three Functional Equations Related to the Bose-Einstein Entropy -- 14.1 Introduction -- 14.2 Solution of equations (14.4) and (14.5) -- 14.3 Solution of the equation (14.6) -- References -- 15 The Entropy Theory as a Decision Making Tool in Environmental and Water Resources -- 15.1 Introduction -- 15.2 Entropy Theory -- 15.3 Other Representations of Entropy -- 15.4 Entropy as a Decision Making Tool in Environmental and Water Resources -- 15.5 Implications for Developing Countries -- 15.6 Concluding Remarks -- References.