Information geometry: near randomness and near independence
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | Lecture notes in mathematics
1953 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 253 S. graph. Darst. |
| ISBN: | 9783540693918 9783540693932 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035034260 | ||
| 003 | DE-604 | ||
| 005 | 20170723 | ||
| 007 | t | ||
| 008 | 080902s2008 d||| |||| 00||| eng d | ||
| 020 | |a 9783540693918 |9 978-3-540-69391-8 | ||
| 020 | |a 9783540693932 |9 978-3-540-69393-2 | ||
| 035 | |a (OCoLC)232976381 | ||
| 035 | |a (DE-599)BSZ285356860 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-824 |a DE-19 |a DE-355 |a DE-83 |a DE-29T |a DE-11 |a DE-188 |a DE-20 | ||
| 050 | 0 | |a QA3 | |
| 082 | 0 | |a 519 |2 22 | |
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a SK 110 |0 (DE-625)143215: |2 rvk | ||
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 084 | |a SK 830 |0 (DE-625)143259: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a MAT 605f |2 stub | ||
| 084 | |a DAT 570f |2 stub | ||
| 084 | |a 62B10 |2 msc | ||
| 084 | |a MAT 536f |2 stub | ||
| 100 | 1 | |a Arwini, Khadiga A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Information geometry |b near randomness and near independence |c Khadiga A. Arwini ; Christopher T. J. Dodson |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a X, 253 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1953 | |
| 650 | 4 | |a Géométrie différentielle | |
| 650 | 4 | |a Statistique mathématique | |
| 650 | 4 | |a Théorie de l'information | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Information theory | |
| 650 | 4 | |a Mathematical statistics | |
| 650 | 0 | 7 | |a Informationstheorie |0 (DE-588)4026927-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Informationstheorie |0 (DE-588)4026927-9 |D s |
| 689 | 0 | 1 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | 2 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Dodson, Christopher T. J. |d 1941- |e Verfasser |0 (DE-588)12958472X |4 aut | |
| 830 | 0 | |a Lecture notes in mathematics |v 1953 |w (DE-604)BV000676446 |9 1953 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016703184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016703184 | ||
Datensatz im Suchindex
| _version_ | 1804137966012989440 |
|---|---|
| adam_text | Contents
Preface
........................................................
V
1
Mathematical Statistics and Information Theory
........... 1
1.1
Probability Functions for Discrete Variables
................. 2
1.1.1
Bernoulli Distribution
.............................. 3
1.1.2
Binomial Distribution
.............................. 3
1.1.3
Poisson
Distribution
............................... 4
1.2
Probability Density Functions for Continuous Variables
...... 6
1.2.1
Uniform Distribution
.............................. 8
1.2.2
Exponential Distribution
........................... 8
1.2.3
Gaussian, or Normal Distribution
................... 9
1.3
Joint Probability Density Functions
........................ 9
1.3.1
Bivariate Gaussian Distributions
.................... 10
1.4
Information Theory
...................................... 11
1.4.1
Gamma Distribution
............................... 13
2
Introduction to Riemannian Geometry
.................... 19
2.0.2
Manifolds
........................................ 20
2.0.3
Tangent Spaces
................................... 20
2.0.4
Tensors and Forms
................................ 22
2.0.5
Riemannian Metric
................................ 25
2.0.6
Connections
...................................... 26
2.1
Autoparallel
and Geodesic Curves
......................... 29
2.2
Universal Connections and Curvature
...................... 29
3
Information Geometry
..................................... 31
3.1
Fisher Information Metric
................................ 32
3.2
Exponential Family of Probability Density Functions
......... 33
3.3
Statistical a-Connections
................................. 34
3.4
Affine
Immersions
....................................... 35
3.4.1
Weibull Distributions: Not of Exponential Type
....... 36
VII
VIII Contents
3.5
Gamma 2-Manifold
Q....................................
37
3.5.1
Gamma o-Connection
.............................. 38
3.5.2
Gamma a-Curvatures
.............................. 39
3.5.3
Gamma
Manifold Geodesies ........................
40
3.5.4
Mutually Dual Foliations
........................... 42
3.5.5
Gamma
Affine
Immersion
.......................... 42
3.6
Log-Gamma 2-Manifold
£................................ 42
3.6.1
Log-Gamma Random Walks
........................ 45
3.7
Gaussian 2-Manifold
..................................... 45
3.7.1
Gaussian Natural Coordinates
...................... 47
3.7.2
Gaussian Information Metric
........................ 47
3.7.3
Gaussian Mutually Dual Foliations
.................. 48
3.7.4
Gaussian
Affine
Immersions
......................... 48
3.8
Gaussian
α
-Geometry
....................................
49
3.8.1
Gaussian a-Connection
............................. 49
3.8.2
Gaussian
а
-Curvatures.............................
50
3.9
Gaussian Mutually Dual Foliations
........................ 50
3.10
Gaussian Submanifolds
.................................. 51
3.10.1
Central Mean Submanifold
......................... 51
3.10.2
Unit Variance Submanifold
......................... 52
3.10.3
Unit Coefficient of Variation Submanifold
............ 52
3.11
Gaussian
Affine
Immersions
............................... 52
3.12
Log-Gaussian Manifold
................................... 53
4
Information Geometry of Bivariate Families
............... 55
4.1
McKay Bivariate Gamma 3-Manifold
M
.................... 55
4.2
McKay Manifold Geometry in Natural Coordinates
.......... 58
4.3
McKay Densities Have Exponential Type
................... 59
4.3.1
McKay Information Metric
......................... 59
4.4
McKay
ö-Geometry ..................................... 60
4.4.1
McKay a-Connection
.............................. 60
4.4.2
McKay a-Curvatures
............................... 61
4.5
McKay Mutually Dual Foliations
.......................... 64
4.6
McKay Submanifolds
.................................... 65
4.6.1
Submanifold Mi
.................................. 65
4.6.2
Submanifold M2
.................................. 68
4.6.3
Submanifold M3
..............
^
.................. 69
4.7
McKay Bivariate Log-Gamma Manifold
M
................. 71
4.8
Generalized McKay 5-Manifold
............................ 72
4.8.1
Divariate
3-Parameter Gamma Densities
............. 72
4.8.2
Generalized McKay Information Metric
.............. 73
4.9 Freund
Bivariate Exponential 4-Manifold
T
................. 74
4.9.1 Freund
Fisher Metric
.............................. 75
4.10 Freund
Natural Coordinates
.............................. 76
Contents
IX
4.11 Freund
α
-Geometry
...................................... 77
4.11.1
Ereund
a-Connection
.............................. 77
4.11.2 Freund o-Curvatures............................... 78
4.12 Freund
Foliations
........................................ 80
4.13 Freund Submanifolds .................................... 81
4.13.1
Independence Submanifold
F ....................... 81
4.13.2 Submanifold F2................................... 82
4.13.3 Submanifold F3................................... 83
4.13.4 Submanifold F4................................... 84
4.14 Freund Affine Immersion................................. 87
4.15 Freund
Divariate
Log-Exponential Manifold
................. 87
4.16
Divariate
Gaussian
5-Manifold
λί
.......................... 88
4.17
Bivariate
Gaussian Fisher Information Metric
............... 89
4.18
Bivariate Gaussian Natural Coordinates
.................... 90
4.19
Bivariate Gaussian
α
-Geometry
...........................
91
4.19.1
a-Connection
..................................... 91
4.19.2
«-Curvatures
...................................... 94
4.20
Bivariate Gaussian Foliations
............................. 98
4.21
Bivariate Gaussian Submanifolds
.......................... 99
4.21.1
Independence Submanifold
.Λ/Ί
...................... 99
4.21.2
Identical Marginals Submanifold
N2.................101
4.21.3
Central Mean Submanifold JV3
......................103
4.21.4
Affine
Immersion
..................................105
4.22
Bivariate Log-Gaussian Manifold
..........................106
Neighbourhoods of
Poisson
Randomness, Independence,
and Uniformity
............................................109
5.1
Gamma Manifold
G
and Neighbourhoods
of Randomness
..........................................110
5.2
Log-Gamma Manifold
£
and Neighbourhoods of Uniformity
..
Ill
5.3 Freund
Manifold
Τ
and Neighbourhoods of Independence
.....112
5.3.1 Freund
Submanifold F2
............................113
5.4
Neighbourhoods of Independence for
Gaussiane
..............114
Cosmological Voids and Galactic Clustering
...............119
6.1
Spatial Stochastic Processes
..............................120
6.2
Galactic Cluster Spatial Processes
.........................121
6.3
Cosmological Voids
......................................125
6.4
Modelling Statistics of Cosmological Void Sizes
..............126
6.5
Coupling Galaxy Clustering and Void Sizes
.................130
6.6
Representation of Cosmic Evolution
.......................132
Amino
Acid Clustering
With A.J. Doig
.............................................139
7.1
Spacings of
Amino
Acids
.................................139
7.2
Poisson
Spaced Sequences
................................141
X
Contents
7.3
Non-Poisson
Sequences
as Gamma Processes
................142
7.3.1
Local
Geodesic
Distance Approximations
.............145
7.4
Results
.................................................148
7.5
Why Would
Amino
Acids Cluster?
.........................151
8
Cryptographic Attacks and Signal Clustering
..............153
8.1
Cryptographic Attacks
...................................153
8.2
Information Geometry of the Log-gamma Manifold
..........154
8.3
Distinguishing Nearby Unimodular Distributions
............155
8.4
Difference
Erom
a Uniform Distribution
....................157
8.5
Gamma Distribution Neighbourhoods
of Randomness
..........................................157
9
Stochastic Fibre Networks
With W.W. Sampson
.......................................161
9.1
Random Fibre Networks
..................................161
9.2
Random Networks of Rectangular Fibres
...................164
9.3
Log-Gamma Information Geometry for Fibre Clustering
......168
9.4
Divariate
Gamma Distributions for Anisotropy
..............169
9.5
Independent Polygon Sides
...............................171
9.5.1
Multiplanar Networks
..............................175
9.6
Correlated Polygon Sides
.................................179
9.6.1
McKay
Divariate
Gamma Distribution
...............182
9.6.2
McKay Information Geometry
......................184
9.6.3
McKay Information Entropy
........................188
9.6.4
Simulation Results
................................191
10
Stochastic Porous Media and Hydrology
With J. Scharcanski and S. Pelipussi
.........................195
10.1
Hydrological Modelling
...................................195
10.2
Univariate Gamma Distributions and Randomness
...........196
10.3
Mckay Bivariate Gamma 3-Manifold
.......................196
10.4
Distance Approximations in the McKay Manifold
............198
10.5
Modelling Stochastic Porous Media
........................200
10.5.1
Adaptive
Tomographie
Image Segmentation
..........201
10.5.2
Mathematical Morphology Concepts
.................203
10.5.3
Adaptive Image Segmentation and Representation
.....209
10.5.4
Soil
Tomographie Data.............................214
11
Quantum Chaology
........................................223
11.1
Introduction
............................................223
11.2
Eigenvalues of Random Matrices
..........................226
11.3
Deviations
..............................................229
References
.....................................................235
Index
..........................................................247
|
| adam_txt |
Contents
Preface
.
V
1
Mathematical Statistics and Information Theory
. 1
1.1
Probability Functions for Discrete Variables
. 2
1.1.1
Bernoulli Distribution
. 3
1.1.2
Binomial Distribution
. 3
1.1.3
Poisson
Distribution
. 4
1.2
Probability Density Functions for Continuous Variables
. 6
1.2.1
Uniform Distribution
. 8
1.2.2
Exponential Distribution
. 8
1.2.3
Gaussian, or Normal Distribution
. 9
1.3
Joint Probability Density Functions
. 9
1.3.1
Bivariate Gaussian Distributions
. 10
1.4
Information Theory
. 11
1.4.1
Gamma Distribution
. 13
2
Introduction to Riemannian Geometry
. 19
2.0.2
Manifolds
. 20
2.0.3
Tangent Spaces
. 20
2.0.4
Tensors and Forms
. 22
2.0.5
Riemannian Metric
. 25
2.0.6
Connections
. 26
2.1
Autoparallel
and Geodesic Curves
. 29
2.2
Universal Connections and Curvature
. 29
3
Information Geometry
. 31
3.1
Fisher Information Metric
. 32
3.2
Exponential Family of Probability Density Functions
. 33
3.3
Statistical a-Connections
. 34
3.4
Affine
Immersions
. 35
3.4.1
Weibull Distributions: Not of Exponential Type
. 36
VII
VIII Contents
3.5
Gamma 2-Manifold
Q.
37
3.5.1
Gamma o-Connection
. 38
3.5.2
Gamma a-Curvatures
. 39
3.5.3
Gamma
Manifold Geodesies .
40
3.5.4
Mutually Dual Foliations
. 42
3.5.5
Gamma
Affine
Immersion
. 42
3.6
Log-Gamma 2-Manifold
£. 42
3.6.1
Log-Gamma Random Walks
. 45
3.7
Gaussian 2-Manifold
. 45
3.7.1
Gaussian Natural Coordinates
. 47
3.7.2
Gaussian Information Metric
. 47
3.7.3
Gaussian Mutually Dual Foliations
. 48
3.7.4
Gaussian
Affine
Immersions
. 48
3.8
Gaussian
α
-Geometry
.
49
3.8.1
Gaussian a-Connection
. 49
3.8.2
Gaussian
а
-Curvatures.
50
3.9
Gaussian Mutually Dual Foliations
. 50
3.10
Gaussian Submanifolds
. 51
3.10.1
Central Mean Submanifold
. 51
3.10.2
Unit Variance Submanifold
. 52
3.10.3
Unit Coefficient of Variation Submanifold
. 52
3.11
Gaussian
Affine
Immersions
. 52
3.12
Log-Gaussian Manifold
. 53
4
Information Geometry of Bivariate Families
. 55
4.1
McKay Bivariate Gamma 3-Manifold
M
. 55
4.2
McKay Manifold Geometry in Natural Coordinates
. 58
4.3
McKay Densities Have Exponential Type
. 59
4.3.1
McKay Information Metric
. 59
4.4
McKay
ö-Geometry . 60
4.4.1
McKay a-Connection
. 60
4.4.2
McKay a-Curvatures
. 61
4.5
McKay Mutually Dual Foliations
. 64
4.6
McKay Submanifolds
. 65
4.6.1
Submanifold Mi
. 65
4.6.2
Submanifold M2
. 68
4.6.3
Submanifold M3
.
^
. 69
4.7
McKay Bivariate Log-Gamma Manifold
M
. 71
4.8
Generalized McKay 5-Manifold
. 72
4.8.1
Divariate
3-Parameter Gamma Densities
. 72
4.8.2
Generalized McKay Information Metric
. 73
4.9 Freund
Bivariate Exponential 4-Manifold
T
. 74
4.9.1 Freund
Fisher Metric
. 75
4.10 Freund
Natural Coordinates
. 76
Contents
IX
4.11 Freund
α
-Geometry
. 77
4.11.1
Ereund
a-Connection
. 77
4.11.2 Freund o-Curvatures. 78
4.12 Freund
Foliations
. 80
4.13 Freund Submanifolds . 81
4.13.1
Independence Submanifold
F\. 81
4.13.2 Submanifold F2. 82
4.13.3 Submanifold F3. 83
4.13.4 Submanifold F4. 84
4.14 Freund Affine Immersion. 87
4.15 Freund
Divariate
Log-Exponential Manifold
. 87
4.16
Divariate
Gaussian
5-Manifold
λί
. 88
4.17
Bivariate
Gaussian Fisher Information Metric
. 89
4.18
Bivariate Gaussian Natural Coordinates
. 90
4.19
Bivariate Gaussian
α
-Geometry
.
91
4.19.1
a-Connection
. 91
4.19.2
«-Curvatures
. 94
4.20
Bivariate Gaussian Foliations
. 98
4.21
Bivariate Gaussian Submanifolds
. 99
4.21.1
Independence Submanifold
.Λ/Ί
. 99
4.21.2
Identical Marginals Submanifold
N2.101
4.21.3
Central Mean Submanifold JV3
.103
4.21.4
Affine
Immersion
.105
4.22
Bivariate Log-Gaussian Manifold
.106
Neighbourhoods of
Poisson
Randomness, Independence,
and Uniformity
.109
5.1
Gamma Manifold
G
and Neighbourhoods
of Randomness
.110
5.2
Log-Gamma Manifold
£
and Neighbourhoods of Uniformity
.
Ill
5.3 Freund
Manifold
Τ
and Neighbourhoods of Independence
.112
5.3.1 Freund
Submanifold F2
.113
5.4
Neighbourhoods of Independence for
Gaussiane
.114
Cosmological Voids and Galactic Clustering
.119
6.1
Spatial Stochastic Processes
.120
6.2
Galactic Cluster Spatial Processes
.121
6.3
Cosmological Voids
.125
6.4
Modelling Statistics of Cosmological Void Sizes
.126
6.5
Coupling Galaxy Clustering and Void Sizes
.130
6.6
Representation of Cosmic Evolution
.132
Amino
Acid Clustering
With A.J. Doig
.139
7.1
Spacings of
Amino
Acids
.139
7.2
Poisson
Spaced Sequences
.141
X
Contents
7.3
Non-Poisson
Sequences
as Gamma Processes
.142
7.3.1
Local
Geodesic
Distance Approximations
.145
7.4
Results
.148
7.5
Why Would
Amino
Acids Cluster?
.151
8
Cryptographic Attacks and Signal Clustering
.153
8.1
Cryptographic Attacks
.153
8.2
Information Geometry of the Log-gamma Manifold
.154
8.3
Distinguishing Nearby Unimodular Distributions
.155
8.4
Difference
Erom
a Uniform Distribution
.157
8.5
Gamma Distribution Neighbourhoods
of Randomness
.157
9
Stochastic Fibre Networks
With W.W. Sampson
.161
9.1
Random Fibre Networks
.161
9.2
Random Networks of Rectangular Fibres
.164
9.3
Log-Gamma Information Geometry for Fibre Clustering
.168
9.4
Divariate
Gamma Distributions for Anisotropy
.169
9.5
Independent Polygon Sides
.171
9.5.1
Multiplanar Networks
.175
9.6
Correlated Polygon Sides
.179
9.6.1
McKay
Divariate
Gamma Distribution
.182
9.6.2
McKay Information Geometry
.184
9.6.3
McKay Information Entropy
.188
9.6.4
Simulation Results
.191
10
Stochastic Porous Media and Hydrology
With J. Scharcanski and S. Pelipussi
.195
10.1
Hydrological Modelling
.195
10.2
Univariate Gamma Distributions and Randomness
.196
10.3
Mckay Bivariate Gamma 3-Manifold
.196
10.4
Distance Approximations in the McKay Manifold
.198
10.5
Modelling Stochastic Porous Media
.200
10.5.1
Adaptive
Tomographie
Image Segmentation
.201
10.5.2
Mathematical Morphology Concepts
.203
10.5.3
Adaptive Image Segmentation and Representation
.209
10.5.4
Soil
Tomographie Data.214
11
Quantum Chaology
.223
11.1
Introduction
.223
11.2
Eigenvalues of Random Matrices
.226
11.3
Deviations
.229
References
.235
Index
.247 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Arwini, Khadiga A. Dodson, Christopher T. J. 1941- |
| author_GND | (DE-588)12958472X |
| author_facet | Arwini, Khadiga A. Dodson, Christopher T. J. 1941- |
| author_role | aut aut |
| author_sort | Arwini, Khadiga A. |
| author_variant | k a a ka kaa c t j d ctj ctjd |
| building | Verbundindex |
| bvnumber | BV035034260 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 SK 110 SK 370 SK 830 SK 950 |
| classification_tum | MAT 605f DAT 570f MAT 536f |
| ctrlnum | (OCoLC)232976381 (DE-599)BSZ285356860 |
| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02399nam a2200601 cb4500</leader><controlfield tag="001">BV035034260</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20170723 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080902s2008 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783540693918</subfield><subfield code="9">978-3-540-69391-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783540693932</subfield><subfield code="9">978-3-540-69393-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)232976381</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BSZ285356860</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA3</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 110</subfield><subfield code="0">(DE-625)143215:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 370</subfield><subfield code="0">(DE-625)143234:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 830</subfield><subfield code="0">(DE-625)143259:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 605f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">DAT 570f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">62B10</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 536f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Arwini, Khadiga A.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Information geometry</subfield><subfield code="b">near randomness and near independence</subfield><subfield code="c">Khadiga A. Arwini ; Christopher T. J. Dodson</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 253 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1953</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Géométrie différentielle</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Statistique mathématique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Théorie de l'information</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Differential</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Information theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical statistics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Informationstheorie</subfield><subfield code="0">(DE-588)4026927-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Wahrscheinlichkeitsverteilung</subfield><subfield code="0">(DE-588)4121894-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Informationstheorie</subfield><subfield code="0">(DE-588)4026927-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Wahrscheinlichkeitsverteilung</subfield><subfield code="0">(DE-588)4121894-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Dodson, Christopher T. J.</subfield><subfield code="d">1941-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)12958472X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1953</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">1953</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016703184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016703184</subfield></datafield></record></collection> |
| id | DE-604.BV035034260 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:50:58Z |
| indexdate | 2024-07-09T21:20:41Z |
| institution | BVB |
| isbn | 9783540693918 9783540693932 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016703184 |
| oclc_num | 232976381 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-824 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-83 DE-29T DE-11 DE-188 DE-20 |
| owner_facet | DE-91G DE-BY-TUM DE-824 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-83 DE-29T DE-11 DE-188 DE-20 |
| physical | X, 253 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Arwini, Khadiga A. Verfasser aut Information geometry near randomness and near independence Khadiga A. Arwini ; Christopher T. J. Dodson Berlin [u.a.] Springer 2008 X, 253 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1953 Géométrie différentielle Statistique mathématique Théorie de l'information Geometry, Differential Information theory Mathematical statistics Informationstheorie (DE-588)4026927-9 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Informationstheorie (DE-588)4026927-9 s Differentialgeometrie (DE-588)4012248-7 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s DE-604 Dodson, Christopher T. J. 1941- Verfasser (DE-588)12958472X aut Lecture notes in mathematics 1953 (DE-604)BV000676446 1953 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016703184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arwini, Khadiga A. Dodson, Christopher T. J. 1941- Information geometry near randomness and near independence Lecture notes in mathematics Géométrie différentielle Statistique mathématique Théorie de l'information Geometry, Differential Information theory Mathematical statistics Informationstheorie (DE-588)4026927-9 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4026927-9 (DE-588)4121894-2 (DE-588)4012248-7 |
| title | Information geometry near randomness and near independence |
| title_auth | Information geometry near randomness and near independence |
| title_exact_search | Information geometry near randomness and near independence |
| title_exact_search_txtP | Information geometry near randomness and near independence |
| title_full | Information geometry near randomness and near independence Khadiga A. Arwini ; Christopher T. J. Dodson |
| title_fullStr | Information geometry near randomness and near independence Khadiga A. Arwini ; Christopher T. J. Dodson |
| title_full_unstemmed | Information geometry near randomness and near independence Khadiga A. Arwini ; Christopher T. J. Dodson |
| title_short | Information geometry |
| title_sort | information geometry near randomness and near independence |
| title_sub | near randomness and near independence |
| topic | Géométrie différentielle Statistique mathématique Théorie de l'information Geometry, Differential Information theory Mathematical statistics Informationstheorie (DE-588)4026927-9 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Géométrie différentielle Statistique mathématique Théorie de l'information Geometry, Differential Information theory Mathematical statistics Informationstheorie Wahrscheinlichkeitsverteilung Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016703184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT arwinikhadigaa informationgeometrynearrandomnessandnearindependence AT dodsonchristophertj informationgeometrynearrandomnessandnearindependence |