Numbers, Information and Complexity is a collection of about 50 articles in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, `Numbers and Combinations', `Information Theory (Channels and Networks, Combinatorial and Algebraic Coding, Cryptology, with the related fields Data Compression, Entropy Theory, Symbolic Dynamics, Probability and Statistics)', and `Complexity'. Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results. The book features surveys on…mehr
Numbers, Information and Complexity is a collection of about 50 articles in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, `Numbers and Combinations', `Information Theory (Channels and Networks, Combinatorial and Algebraic Coding, Cryptology, with the related fields Data Compression, Entropy Theory, Symbolic Dynamics, Probability and Statistics)', and `Complexity'. Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results. The book features surveys on Combinatorics about topics such as intersection theorems, which are not yet covered in textbooks, several contributions by leading experts in data compression, and relations to Natural Sciences are discussed.
1 On Prefix-free and Suffix-free Sequences of Integers.- 2 Almost Arithmetic Progressions.- 3 A Method to Estimate Partial-Period Correlations.- 4 Splitting Properties in Partially Ordered Sets and Set Systems.- 5 Old and New Results for the Weighted t-Intersection Problem via AK-Methods.- 6 Some New Results on Macaulay Posets.- 7 Minimizing the Absolute Upper Shadow.- 8 Convex Bounds for the 0,1 Co-ordinate Deletions Function.- 9 The Extreme Points of the Probabilistic Capacities Cone Problem.- 10 On Shifts of Cascades.- 11 Eröas-Ko-Rado Theorems of Higher Order.- 12 On the Prague Dimension of Kneser Graphs.- 13 The cycle method and its limits.- 14 Extremal Problems on ?-Systems.- 15 The AVC with Noiseless Feedback.- 16 Calculation of the Asymptotically Optimal Capacity of a T-User M-Frequency Noiseless Multiple-Access Channel.- 17 A Survey of Coding Methods for the Adder Channel.- 18 Communication Network with Self-Similar Traffic.- 19 Error Probabilities for Identification Coding and Least Length Single Sequence Hopping.- 20 A New Upper Bound On Codes Decodable Into Size-2 Lists.- 21 Constructions of Optimal Linear Codes.- 22 New Applications and Results of Superimposed Code Theory Arising from the Potentialities of Molecular Biology.- 23 Rudified Convolutional Encoders.- 24 On Check Digit Systems Using Anti-symmetric Mappings.- 25 Switchings and Perfect Codes.- 26 On Superimposed Codes.- 27 The MacWilliams Identity for Linear Codes over Galois Rings.- 28 Structure of a Common Knowledge Created by Correlated Observations and Transmission over Helping Channels.- 29 How to Broadcast Privacy: Secret Coding for Deterministic Broadcast Channels.- 30 Additive-Like Instantaneous Block Encipherers.- 31 Space Efficient Linear Time Computation of the Burrows andWheeler-Transformation.- 32 Sequences Incompressible by SLZ (LZW), yet Fully Compressible by ULZ.- 33 Universal Coding of Non-Prefix Context Tree Sources.- 34 How Much Can You Win When Your Adversary is Handicapped?.- 35 On Random-Access Data Compaction.- 36 Universal Lossless Coding of Sources with Large and Unbounded Alphabets.- 37 Metric Entropy Conditions for Kernels.- 38 On Subshifts and Topological Markov Chains.- 39 Large Deviations Problem for the Shape of a Random Young Diagram with Restrictions.- 40 BSC: Testing of Hypotheses with Information Constraints.- 41 The Ahlswede-Daykin Theorem.- 42 Some Aspects of Random Shapes.- 43 Decision Support Systems with Multiple Choice Structure.- 44 Quantum Computers and Quantum Automata.- 45 Routing in All-Optical Networks.- 46 Proving the Correctness of Processors with Delayed Branch Using Delayed PC.- 47 Communication Complexity of Functions on Direct Sums.- 48 Ordering in Sequence Spaces: an Overview.- 49 Communication Complexity and BDD Lower Bound Techniques.- 50 Reminiscences About Professor Ahlswede: And A Last Word By Thomas Mann.- 51 List of Invited Lectures held at the Symposium "Numbers, Information and Complexity" in Bielefeld, October 8-11, 1998.- 52 Bibliography of Publications by Rudolf Ahlswede.
1 On Prefix-free and Suffix-free Sequences of Integers.- 2 Almost Arithmetic Progressions.- 3 A Method to Estimate Partial-Period Correlations.- 4 Splitting Properties in Partially Ordered Sets and Set Systems.- 5 Old and New Results for the Weighted t-Intersection Problem via AK-Methods.- 6 Some New Results on Macaulay Posets.- 7 Minimizing the Absolute Upper Shadow.- 8 Convex Bounds for the 0,1 Co-ordinate Deletions Function.- 9 The Extreme Points of the Probabilistic Capacities Cone Problem.- 10 On Shifts of Cascades.- 11 Eröas-Ko-Rado Theorems of Higher Order.- 12 On the Prague Dimension of Kneser Graphs.- 13 The cycle method and its limits.- 14 Extremal Problems on ?-Systems.- 15 The AVC with Noiseless Feedback.- 16 Calculation of the Asymptotically Optimal Capacity of a T-User M-Frequency Noiseless Multiple-Access Channel.- 17 A Survey of Coding Methods for the Adder Channel.- 18 Communication Network with Self-Similar Traffic.- 19 Error Probabilities for Identification Coding and Least Length Single Sequence Hopping.- 20 A New Upper Bound On Codes Decodable Into Size-2 Lists.- 21 Constructions of Optimal Linear Codes.- 22 New Applications and Results of Superimposed Code Theory Arising from the Potentialities of Molecular Biology.- 23 Rudified Convolutional Encoders.- 24 On Check Digit Systems Using Anti-symmetric Mappings.- 25 Switchings and Perfect Codes.- 26 On Superimposed Codes.- 27 The MacWilliams Identity for Linear Codes over Galois Rings.- 28 Structure of a Common Knowledge Created by Correlated Observations and Transmission over Helping Channels.- 29 How to Broadcast Privacy: Secret Coding for Deterministic Broadcast Channels.- 30 Additive-Like Instantaneous Block Encipherers.- 31 Space Efficient Linear Time Computation of the Burrows andWheeler-Transformation.- 32 Sequences Incompressible by SLZ (LZW), yet Fully Compressible by ULZ.- 33 Universal Coding of Non-Prefix Context Tree Sources.- 34 How Much Can You Win When Your Adversary is Handicapped?.- 35 On Random-Access Data Compaction.- 36 Universal Lossless Coding of Sources with Large and Unbounded Alphabets.- 37 Metric Entropy Conditions for Kernels.- 38 On Subshifts and Topological Markov Chains.- 39 Large Deviations Problem for the Shape of a Random Young Diagram with Restrictions.- 40 BSC: Testing of Hypotheses with Information Constraints.- 41 The Ahlswede-Daykin Theorem.- 42 Some Aspects of Random Shapes.- 43 Decision Support Systems with Multiple Choice Structure.- 44 Quantum Computers and Quantum Automata.- 45 Routing in All-Optical Networks.- 46 Proving the Correctness of Processors with Delayed Branch Using Delayed PC.- 47 Communication Complexity of Functions on Direct Sums.- 48 Ordering in Sequence Spaces: an Overview.- 49 Communication Complexity and BDD Lower Bound Techniques.- 50 Reminiscences About Professor Ahlswede: And A Last Word By Thomas Mann.- 51 List of Invited Lectures held at the Symposium "Numbers, Information and Complexity" in Bielefeld, October 8-11, 1998.- 52 Bibliography of Publications by Rudolf Ahlswede.
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