Information, physics, and computation:
A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2009
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford graduate texts
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields. |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIII, 569 S. graph. Darst. |
| ISBN: | 9780198570837 |
Internformat
MARC
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| 100 | 1 | |a Mézard, Marc |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Information, physics, and computation |c Marc Mézard ; Andrea Montanari |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2009 | |
| 300 | |a XIII, 569 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford graduate texts | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 520 | 3 | |a A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields. | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Coding theory | |
| 650 | 4 | |a Computer science | |
| 650 | 4 | |a Statistical physics | |
| 650 | 0 | 7 | |a Informationstheorie |0 (DE-588)4026927-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Codierungstheorie |0 (DE-588)4139405-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistische Physik |0 (DE-588)4057000-9 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016491985 | ||
Datensatz im Suchindex
| _version_ | 1804137639848181760 |
|---|---|
| adam_text | Contents
PART I BACKGROUND
Introduction to information theory
3
1.1
Random variables
3
1.2
Entropy
5
1.3
Sequences of random variables and their entropy rate
8
1.4
Correlated variables and mutual information
10
1.5
Data compression
12
1.6
Data transmission
16
Notes
21
Statistical physics and probability theory
23
2.1
The Boltzmann distribution
24
2.2
Thermodynamic potentials
28
2.3
The fluctuation-dissipation relations
32
2.4
The thermodynamic limit
33
2.5
Ferromagnets and Ising models
35
2.6
The Ising spin glass
44
Notes
46
Introduction to combinatorial optimization
47
3.1
A first example: The minimum spanning tree
48
3.2
General definitions
51
3.3
More examples
51
3.4
Elements of the theory of computational complexity
54
3.5
Optimization and statistical physics
60
3.6
Optimization and coding
61
Notes
62
A probabilistic toolbox
65
4.1
Many random variables: A qualitative preview
65
4.2
Large deviations for independent variables
66
4.3
Correlated variables
72
4.4
The Gibbs free energy
77
4.5
The Monte Carlo method
80
4.6
Simulated annealing
86
4.7
Appendix: A physicist s approach to Sanov s theorem
87
Notes
89
χ
Contents
PART II INDEPENDENCE
5
The random energy model
93
5.1
Definition of the model
93
5.2
Thermodynamics of the
REM
94
5.3
The condensation phenomenon
100
5.4
A comment on quenched and annealed averages
101
5.5
The random
subcube
model
103
Notes
105
6
The random code ensemble
107
6.1
Code ensembles
107
6.2
The geometry of the random code ensemble
110
6.3
Communicating over a binary symmetric channel
112
6.4
Error-free communication with random codes
120
6.5
Geometry again: Sphere packing
123
6.6
Other random codes
126
6.7
A remark on coding theory and disordered systems
127
6.8
Appendix: Proof of Lemma
6.2 128
Notes
128
7
Number partitioning
131
7.1
A fair distribution into two groups?
131
7.2
Algorithmic issues
132
7.3
Partition of a random list: Experiments
133
7.4
The random cost model
136
7.5
Partition of a random list: Rigorous results
140
Notes
143
8
Introduction to replica theory
145
8.1
Replica solution of the random energy model
145
8.2
The fully connected p-spin glass model
155
8.3
Extreme value statistics and the
REM
163
8.4
Appendix: Stability of the RS saddle point
166
Notes 169
PART 111 MODELS ON GRAPHS
9
Factor graphs and graph ensembles I73
9.1
Factor graphs
^73
9.2
Ensembles of factor graphs: Definitions
180
9.3
Random factor graphs: Basic, properties
182
9.4
Random factor graphs: The giant component
187
9.5
The locally tree-like structure of random graphs
191
Notes 194
10
Satisfiability 197
10.1
The satisfiability problem
107
Contents xi
10.2
Algorithms
199
10.3 Random,
-řr-satisfiability
ensembles
206
10.4
Random 2-SAT
209
10.5
The phase transition in random K(> 3)-SAT
209
Notes
217
11
Low-density parity-check codes
219
11.1
Definitions
220
11.2
The geometry of the
codebook
222
11.3
LDPC codes for the binary symmetric channel
231
11.4
A simple decoder: Bit flipping
236
Notes
239
12
Spin glasses
241
12.1
Spin glasses and factor graphs
241
12.2
Spin glasses: Constraints and frustration
245
12.3
What is a glass phase?
250
12.4
An example: The phase diagram of the SK model
262
Notes
265
13
Bridges: Inference and the Monte Carlo method
267
13.1
Statistical inference
268
13.2
The Monte Carlo method: Inference via sampling
272
13.3
Free-energy barriers
281
Notes
287
PART IV SHORT-RANGE CORRELATIONS
14
Belief propagation
291
14.1
Two examples
292
14.2
Belief propagation on tree graphs
296
14.3
Optimization: Max-product and min-sum
305
14.4
Loopy BP
310
14.5
General message-passing algorithms
316
14.6
Probabilistic analysis
317
Notes
325
15
Decoding with belief propagation
327
15.1
BP decoding: The algorithm
327
15.2
Analysis: Density evolution
329
15.3
BP decoding for an erasure channel
342
15.4
The Bethe free energy and MAP decoding
347
Notes
352
16
The assignment problem
355
16.1
The assignment problem and random assignment ensembles
356
16.2
Message passing and its probabilistic analysis
357
16.3
A polynomial message-passing algorithm
366
xii Contents
471
16.4
Combinatorial results
*
16.5
An exercise: Multi-index assignment 37b
Notes 378
17
Ising models on random graphs 381
17.1
The BP equations for Ising spins
381
17.2
RS cavity analysis 384
17.3
Ferromagnetic model
386
17 4
Spin glass models
391
Notes 3
PART V LONG-RANGE CORRELATIONS
18
Linear equations with Boolean variables
403
18.1
Definitions and general remarks
404
18.2
Belief propagation
409
18.3
Core percolation and BP
412
18.4
The SAT-UNSAT threshold in random XORSAT
415
18.5
The Hard-SAT phase: Clusters of solutions
421
18.6
An alternative approach: The cavity method
422
Notes
427
19
The 1RSB cavity method
429
19.1
Beyond BP: Many states
430
19.2
The 1RSB cavity equations
434
19.3
A first application: XORSAT
444
19.4
The special value
χ
= 1 449
19.5
Survey propagation
453
19.6
The nature of 1RSB phases
459
19.7
Appendix: The SP(y) equations for XORSAT
463
Notes
465
20
Random K-satisflability
467
20.1
Belief propagation and the replica-symmetric analysis
468
20.2
Survey propagation and the 1RSB phase
474
20.3
Some ideas about the full phase diagram
485
20.4
An exercise: Colouring random graphs
488
Notes
491
21
Glassy states in coding theory
493
21.1
Local search algorithms and metastable states
493
21.2
The binary erasure channel 5OO
21.3
General binary memoryless symmetric channels
506
21.4
Metastable states and near-codewords 513
Notes 515
22
An ongoing story
22.1
Gibbs measures and long-range correlations
517
518
Contents
хні
22.2 Higher
levels of replica symmetry breaking
524
22.3
Phase structure and the behaviour of algorithms
535
Notes
538
Appendix A Symbols and notation
541
A.I Equivalence relations
541
A.2 Orders of growth
542
A.3 Combinatorics and probability
543
A.4 Summary of mathematical notation
544
A.
5
Information theory
545
A.
6
Factor graphs
545
A.
7
Cavity and message-passing methods
545
References
547
Index
565
|
| adam_txt |
Contents
PART I BACKGROUND
Introduction to information theory
3
1.1
Random variables
3
1.2
Entropy
5
1.3
Sequences of random variables and their entropy rate
8
1.4
Correlated variables and mutual information
10
1.5
Data compression
12
1.6
Data transmission
16
Notes
21
Statistical physics and probability theory
23
2.1
The Boltzmann distribution
24
2.2
Thermodynamic potentials
28
2.3
The fluctuation-dissipation relations
32
2.4
The thermodynamic limit
33
2.5
Ferromagnets and Ising models
35
2.6
The Ising spin glass
44
Notes
46
Introduction to combinatorial optimization
47
3.1
A first example: The minimum spanning tree
48
3.2
General definitions
51
3.3
More examples
51
3.4
Elements of the theory of computational complexity
54
3.5
Optimization and statistical physics
60
3.6
Optimization and coding
61
Notes
62
A probabilistic toolbox
65
4.1
Many random variables: A qualitative preview
65
4.2
Large deviations for independent variables
66
4.3
Correlated variables
72
4.4
The Gibbs free energy
77
4.5
The Monte Carlo method
80
4.6
Simulated annealing
86
4.7
Appendix: A physicist's approach to Sanov's theorem
87
Notes
89
χ
Contents
PART II INDEPENDENCE
5
The random energy model
93
5.1
Definition of the model
93
5.2
Thermodynamics of the
REM
94
5.3
The condensation phenomenon
100
5.4
A comment on quenched and annealed averages
101
5.5
The random
subcube
model
103
Notes
105
6
The random code ensemble
107
6.1
Code ensembles
107
6.2
The geometry of the random code ensemble
110
6.3
Communicating over a binary symmetric channel
112
6.4
Error-free communication with random codes
120
6.5
Geometry again: Sphere packing
123
6.6
Other random codes
126
6.7
A remark on coding theory and disordered systems
127
6.8
Appendix: Proof of Lemma
6.2 128
Notes
128
7
Number partitioning
131
7.1
A fair distribution into two groups?
131
7.2
Algorithmic issues
132
7.3
Partition of a random list: Experiments
133
7.4
The random cost model
136
7.5
Partition of a random list: Rigorous results
140
Notes
143
8
Introduction to replica theory
145
8.1
Replica solution of the random energy model
145
8.2
The fully connected p-spin glass model
155
8.3
Extreme value statistics and the
REM
163
8.4
Appendix: Stability of the RS saddle point
166
Notes 169
PART 111 MODELS ON GRAPHS
9
Factor graphs and graph ensembles I73
9.1
Factor graphs
^73
9.2
Ensembles of factor graphs: Definitions
180
9.3
Random factor graphs: Basic, properties
182
9.4
Random factor graphs: The giant component
187
9.5
The locally tree-like structure of random graphs
191
Notes 194
10
Satisfiability 197
10.1
The satisfiability problem
107
Contents xi
10.2
Algorithms
199
10.3 Random,
-řr-satisfiability
ensembles
206
10.4
Random 2-SAT
209
10.5
The phase transition in random K(> 3)-SAT
209
Notes
217
11
Low-density parity-check codes
219
11.1
Definitions
220
11.2
The geometry of the
codebook
222
11.3
LDPC codes for the binary symmetric channel
231
11.4
A simple decoder: Bit flipping
236
Notes
239
12
Spin glasses
241
12.1
Spin glasses and factor graphs
241
12.2
Spin glasses: Constraints and frustration
245
12.3
What is a glass phase?
250
12.4
An example: The phase diagram of the SK model
262
Notes
265
13
Bridges: Inference and the Monte Carlo method
267
13.1
Statistical inference
268
13.2
The Monte Carlo method: Inference via sampling
272
13.3
Free-energy barriers
281
Notes
287
PART IV SHORT-RANGE CORRELATIONS
14
Belief propagation
291
14.1
Two examples
292
14.2
Belief propagation on tree graphs
296
14.3
Optimization: Max-product and min-sum
305
14.4
Loopy BP
310
14.5
General message-passing algorithms
316
14.6
Probabilistic analysis
317
Notes
325
15
Decoding with belief propagation
327
15.1
BP decoding: The algorithm
327
15.2
Analysis: Density evolution
329
15.3
BP decoding for an erasure channel
342
15.4
The Bethe free energy and MAP decoding
347
Notes
352
16
The assignment problem
355
16.1
The assignment problem and random assignment ensembles
356
16.2
Message passing and its probabilistic analysis
357
16.3
A polynomial message-passing algorithm
366
xii Contents
471
16.4
Combinatorial results
*
16.5
An exercise: Multi-index assignment 37b
Notes 378
17
Ising models on random graphs 381
17.1
The BP equations for Ising spins
381
17.2
RS cavity analysis 384
17.3
Ferromagnetic model
386
17 4
Spin glass models
391
Notes 3"
PART V LONG-RANGE CORRELATIONS
18
Linear equations with Boolean variables
403
18.1
Definitions and general remarks
404
18.2
Belief propagation
409
18.3
Core percolation and BP
412
18.4
The SAT-UNSAT threshold in random XORSAT
415
18.5
The Hard-SAT phase: Clusters of solutions
421
18.6
An alternative approach: The cavity method
422
Notes
427
19
The 1RSB cavity method
429
19.1
Beyond BP: Many states
430
19.2
The 1RSB cavity equations
434
19.3
A first application: XORSAT
444
19.4
The special value
χ
= 1 449
19.5
Survey propagation
453
19.6
The nature of 1RSB phases
459
19.7
Appendix: The SP(y) equations for XORSAT
463
Notes
465
20
Random K-satisflability
467
20.1
Belief propagation and the replica-symmetric analysis
468
20.2
Survey propagation and the 1RSB phase
474
20.3
Some ideas about the full phase diagram
485
20.4
An exercise: Colouring random graphs
488
Notes
491
21
Glassy states in coding theory
493
21.1
Local search algorithms and metastable states
493
21.2
The binary erasure channel 5OO
21.3
General binary memoryless symmetric channels
506
21.4
Metastable states and near-codewords 513
Notes 515
22
An ongoing story
22.1
Gibbs measures and long-range correlations
517
518
Contents
хні
22.2 Higher
levels of replica symmetry breaking
524
22.3
Phase structure and the behaviour of algorithms
535
Notes
538
Appendix A Symbols and notation
541
A.I Equivalence relations
541
A.2 Orders of growth
542
A.3 Combinatorics and probability
543
A.4 Summary of mathematical notation
544
A.
5
Information theory
545
A.
6
Factor graphs
545
A.
7
Cavity and message-passing methods
545
References
547
Index
565 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Mézard, Marc Montanari, Andrea |
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| ctrlnum | (OCoLC)234430714 (DE-599)BVBBV023307643 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik Informatik Mathematik |
| discipline_str_mv | Physik Informatik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV023307643 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:49:08Z |
| indexdate | 2024-07-09T21:15:30Z |
| institution | BVB |
| isbn | 9780198570837 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016491985 |
| oclc_num | 234430714 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-29T DE-12 DE-83 DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-29T DE-12 DE-83 DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 |
| physical | XIII, 569 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford graduate texts |
| spelling | Mézard, Marc Verfasser aut Information, physics, and computation Marc Mézard ; Andrea Montanari 1. publ. Oxford [u.a.] Oxford Univ. Press 2009 XIII, 569 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts Hier auch später erschienene, unveränderte Nachdrucke A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields. Informatik Coding theory Computer science Statistical physics Informationstheorie (DE-588)4026927-9 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Statistische Physik (DE-588)4057000-9 s Codierungstheorie (DE-588)4139405-7 s Informationstheorie (DE-588)4026927-9 s DE-604 Montanari, Andrea Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016491985&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mézard, Marc Montanari, Andrea Information, physics, and computation Informatik Coding theory Computer science Statistical physics Informationstheorie (DE-588)4026927-9 gnd Codierungstheorie (DE-588)4139405-7 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4026927-9 (DE-588)4139405-7 (DE-588)4057000-9 |
| title | Information, physics, and computation |
| title_auth | Information, physics, and computation |
| title_exact_search | Information, physics, and computation |
| title_exact_search_txtP | Information, physics, and computation |
| title_full | Information, physics, and computation Marc Mézard ; Andrea Montanari |
| title_fullStr | Information, physics, and computation Marc Mézard ; Andrea Montanari |
| title_full_unstemmed | Information, physics, and computation Marc Mézard ; Andrea Montanari |
| title_short | Information, physics, and computation |
| title_sort | information physics and computation |
| topic | Informatik Coding theory Computer science Statistical physics Informationstheorie (DE-588)4026927-9 gnd Codierungstheorie (DE-588)4139405-7 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Informatik Coding theory Computer science Statistical physics Informationstheorie Codierungstheorie Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016491985&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mezardmarc informationphysicsandcomputation AT montanariandrea informationphysicsandcomputation |