Information Measures - Arndt, C.
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From the reviews: "Bioinformaticians are facing the challenge of how to handle immense amounts of raw data, [...] and render them accessible to scientists working on a wide variety of problems. [This book] can be such a tool." IEEE Engineering in Medicine and Biology

Produktbeschreibung
From the reviews: "Bioinformaticians are facing the challenge of how to handle immense amounts of raw data, [...] and render them accessible to scientists working on a wide variety of problems. [This book] can be such a tool." IEEE Engineering in Medicine and Biology
  • Produktdetails
  • Signals and Communication Technology
  • Verlag: Springer, Berlin
  • Repr. of the original 1st ed. 2001
  • Seitenzahl: 572
  • Erscheinungstermin: 5. November 2003
  • Englisch
  • Abmessung: 235mm x 155mm x 30mm
  • Gewicht: 860g
  • ISBN-13: 9783540408550
  • ISBN-10: 354040855X
  • Artikelnr.: 12301933
Autorenporträt
Christoph Arndt, University of Siegen, Germany

Inhaltsangabe
'Abstract.- Structure and Structuring.- 1 Introduction.- Science and information.- Man as control loop.- Information, complexity and typical sequences.- Concepts of information.- Information, its technical dimension and the meaning of a message.- Information as a central concept.- 2 Basic considerations.- 2.1 Formal derivation of information.- 2.1.1 Unit and reference scale.- 2.1.2 Information and the unit element.- 2.2 Application of the information measure (Shannon's information).- 2.2.1 Summary.- 2.3 The law of Weber and Fechner.- 2.4 Information of discrete random variables.- 3 Historic development of information theory.- 3.1 Development of information transmission.- 3.1.1 Samuel F. B. Morse 1837.- 3.1.2 Thomas Edison 1874.- 3.1.3 Nyquist 1924.- 3.1.4 Optimal number of characters of the alphabet used for the coding.- 3.2 Development of information functions.- 3.2.1 Hartley 1928.- 3.2.2 Dennis Gabor 1946.- 3.2.3 Shannon 1948.- 3.2.3.1 Validity of the postulates for Shannon's Information.- 3.2.3.2 Shannon's information (another possibility of a derivation).- 3.2.3.3 Properties of Shannon's information, entropy.- 3.2.3.4 Shannon's entropy or Shannon's information.- 3.2.3.5 The Kraft inequality.- Kraft's inequality:.- Proof of Kraft's inequality:.- 3.2.3.6 Limits of the optimal length of codewords.- 3.2.3.6.1 Shannon's coding theorem.- 3.2.3.6.2 A sequence of n symbols (elements).- 3.2.3.6.3 Application of the previous results.- 3.2.3.7 Information and utility (coding, porfolio analysis).- 4 The concept of entropy in physics.- The laws of thermodynamics:.- 4.1 Macroscopic entropy.- 4.1.1 Sadi Carnot 1824.- 4.1.2 Clausius's entropy 1850.- 4.1.3 Increase of entropy in a closed system.- 4.1.4 Prigogine's entropy.- 4.1.5 Entropy balance equation.- 4.1.6 Gibbs's free energy and the quality of the energy.- 4.1.7 Considerations on the macroscopic entropy.- 4.1.7.1 Irreversible transformations.- 4.1.7.2 Perpetuum mobile and transfer of heat.- 4.2 Statistical entropy.- 4.2.1 Boltzmann's entropy.- 4.2.2 Derivation of Boltzmann's entropy.- 4.2.2.1 Variation, permutation and the formula of Stirling.- 4.2.2.2 Special case: Two states.- 4.2.2.3 Example: Lottery.- 4.2.3 The Boltzmann factor.- 4.2.4 Maximum entropy in equilibrium.- 4.2.5 Statistical interpretation of entropy.- 4.2.6 Examples regarding statistical entropy.- 4.2.6.1 Energy and fluctuation.- 4.2.6.2 Quantized oscillator.- 4.2.7 Brillouin-Schrödinger negentropy.- 4.2.7.1 Brillouin: Precise definition of information.- 4.2.7.2 Negentropy as a generalization of Carnot's principle.- Maxwell's demon.- 4.2.8 Information measures of Hartley and Boltzmann.- 4.2.8.1 Examples.- 4.2.9 Shannon's entropy.- 4.3 Dynamic entropy.- 4.3.1 Eddington and the arrow of time.- 4.3.2 Kolmogorov's entropy.- 4.3.3 Rényi's entropy.- 5 Extension of Shannon's information.- 5.1 Rényi's Information 1960.- 5.1.1 Properties of Rényi's entropy.- 5.1.2 Limits in the interval 0 ? ? ?.- 5.1.3 Nonnegativity for discrete events.- 5.1.4 Additivity and a connection to Minkowski's norm.- 5.1.5 The meaning of S?(A) for ? 1.- 5.1.6 Graphical presentations of Rényi's information.- 5.2 Another generalized entropy (logical expansion).- 5.3 Gain of information via conditional probabilities.- 5.4 Other entropy or information measures.- 5.4.1 Daroczy's entropy.- 5.4.2 Quadratic entropy.- 5.4.3 R-norm entropy.- 6 Generalized entropy measures.- 6.1 The corresponding measures of divergence.- 6.2 Weighted entropies and expectation values of entropies.- 7 Information functions and gaussian distributions.- 7.1 Rényi's information of a gaussian distributed random variable.- 7.1.1 Rényi's ?-information.- 7.1.2 Rényi's G-divergence.- 7.2 Shannon's information.- 8 Shannon's information of discrete probability distributions.- 8.1 Continuous and discrete random variables.- 8.1.1 Summary.- 8.2 Shannon's information of a gaussian distribution.-
Rezensionen
"Bioinformaticians are facing the challenge of how to handle immense amounts of raw data, such as are generated from genome mapping, make sense of them, and render them accessible to scientists working on a wide variety of problems. "Information Measures: Information and its Description in Science and Engineering" can be such a tool." -- IEEE Engineering in Medicine and Biology