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Arwini K. — Information Geometry: Near Randomness and Near Independence
Arwini K. — Information Geometry: Near Randomness and Near Independence



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Название: Information Geometry: Near Randomness and Near Independence

Автор: Arwini K.

Аннотация:

This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 259

Добавлена в каталог: 31.01.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$m$-form      23
Affine fundamental form      36
Affine immersion      35 48
Affine shape operator      36
Alpha-helix      151
Amino acid      139
Amino acid sequences      140
Anisotropic networks      180
Approximation to discrete      139
Arc length      26 146
Arc length element      26
Arc length function      38 40
Aspect ratio      121
Asymtotic independence      38 75
Atlas      20
Autoparallel      29
Basis fields      24
Bernoulli distribution      3
Bernoulli trials      3
Bessel function      173
Between cell variance      121
Bhattacharyya distance      199 216 219
binary images      205
Binary representation      201
Binomial distribution      3 141
Binomial process      141
Bivariate exponential mixture distribution      74
Bivariate families      55
Bivariate Gaussian      10 55 88 114
Bivariate Gaussian $\alpha$ - Ricci tensor      95
Bivariate Gaussian $\alpha$-connection      92
Bivariate Gaussian $\alpha$-curvature      94
Bivariate Gaussian $\alpha$-geometry      91
Bivariate Gaussian $\alpha$-scalar curvature      96
Bivariate Gaussian affine immersion      105
Bivariate Gaussian correlation coefficient      89
Bivariate Gaussian foliations      98
Bivariate Gaussian geodesic coordinates      98
Bivariate Gaussian information metric      89
Bivariate Gaussian marginals      89
Bivariate Gaussian mean curvatures      97
Bivariate Gaussian metric      89
Bivariate Gaussian natural coordinates      90
Bivariate Gaussian potential      90
Bivariate Gaussian sectional curvatures      96
Bivariate Gaussian submanifold      99
Bivariate log - Gaussian      106
Bivariate log-gamma distribution      71
Block and Basu ACBED      84
Boundaries      214
Bundle splitting      27
Canonical parameters      33
Carbon fibre network      161
Cauchy - Schwartz inequality      10
CDF      7
Cell culture scaffolds      161
Censored Poisson      14
Central limit theorem      9 116 166
Central mean submanifold      103
Change of random variables      10
Change of variable      7
Chaos      11
Chaotic structure      128
Chart      20
Chi-square distribution      14
Christoffel symbols      27
Clumped      175
Clumping      168
Clustered structure      128
Clustering      148 168
Clusters of galaxies      121
Coefficient of variation      2 7
Coefficient of variation of counts      132
Coefficient of variation of counts in cells      127
Coiled-coils      151
Commutator      25
Complete sampling      121
Connected components      205
Connection flat      28
Connection symmetric      28
Connection torsion-free      28
Constant scalar curvature      96
Constant total fibre length      182 184
Constraints      5
Contrast criterion      208
Contrast parameter      208
Convolution of exponential distribution      14
Correlated polygon sides      179 182
Correlation      210
Correlation analysis      210
Correlation coefficient      10 216
Correlation functions      125
Cosmic evolution      132
Cosmological filaments      119
Cosmological sheets      119
Cosmological voids      119 125
Count density      126
Counts in cells      120
Coupled process      55
Covariance      9 56
Covariance zero      10
Covariant derivative      27 28
Coverage      164 178
Cross-section      201
Cross-sectional area      214
Cumulative distribution function      7
Curvature      28
Curvature zero      70
Curve      21
Decision operator      212
Decoding      153
Decryption key      153
Deepest valley      213
Departure from random      110
Departure from randomness      131
Departures from Poisson      126
Departures from random      167
Dependence      10
Derivation      24
Deviations from random      5
Diffeomorphic      22
Diffeomorphism      22
Differentiable      21 22
Differential Power Analysis      153
Digamma function      186
Dilation      204
Direct product      99
Discriminate      209
Discrimination      154
Diseases      151
Disorderly      15
Disperse      175
Dispersed structure      128
Distance functions      216
Distribution of galaxies      120
DPA      153
Dual operation      204
Eccentricity      181
Eigenvalues      39 102
Eigenvectors      39
Eighbourhood of independence      114
Eighbourhoods of uniformity      109
Einstein space      101
Elementary geodesic dilations      205
Encoding      153
Encryption key      153
Energy      26
Energy of curve      26
Energy-distance      186
entropy      11 12 47
Entropy difference      154
Entropy for gamma density      15
Entropy gradient field      15
Entropy maximum      15
Equiaffine      36
Equivalent elliptical voids      192
Equivalent pore      174
Equivalent pore radius      181
Equivalent radius      174
Erosion of a set      204
Euler gamma constant      187
Evolution      151
Expectation      6
Expected value      2
Experimental data      140
Exponential      14
Exponential connection      35
Exponential distribution      110 142 144 146
Exponential family      33 47
Exponential marginal      184 188
Exponential PDF      8
Exponential type      33
exponentiation      153
Extended maxima      209
Extended minima      209
Exterior derivative      25
Exterior differentiation      23
Extremal property      29
Fibre aspect ratio      164
Fibre intersections      178
Fibre length $\lambda$      164
Fibre orientation      170 179
Fibre width $\omega$      164
Fibres of finite width      164
Filter      208
Finite width fibres      164
Fisher information metric      31
Fisher metric      33 37
Flat connection      28
Flocculation      168
Freund $\alpha$ - Ricci eigenvectors      79
Freund $\alpha$ - Ricci tensor      79
Freund $\alpha$-connection      77
Freund $\alpha$-curvature      78
Freund $\alpha$-geometry      77
Freund $\alpha$-mean curvature      80
Freund $\alpha$-sectional curvature      80
Freund affine immersion      87
Freund correlation coefficient      75
Freund covariance      75
Freund distribution      74
Freund exponential family      76
Freund foliations      80
Freund geodesic coordinates      81
Freund includes ACBED      81
Freund independence submanifold      81
Freund information metric      75 76
Freund log-exponential      87
Freund marginal      74
Freund natural coordinates      76 77
Freund neighbourhood of independence      112
Freund potential      76
Freund scalar curvature      79
Freund submanifold      81 113
Galactic wall filament      121
Galaxies      119
Galaxies, 40% in filaments      124
Galaxy clusters and voids      130
Galaxy counts in cells      130
Gamma $\alpha$ - Ricci tensor      39
Gamma $\alpha$-curvature      39
Gamma $\alpha$-scalar curvature      40
Gamma affine immersion      110
Gamma alpha connection      38
Gamma distribution      12 13 128 143 173 174
Gamma distribution characterized      14
Gamma distribution discrete version      126
Gamma entropy      133
Gamma exponential family      37
Gamma geodesic sprays      135
Gamma geodesics      135
Gamma manifold      37
Gamma natural coordinates      37
Gamma potential function      37
Gamma probability density function      13
Gamma uniqueness property      14
gaps      171
Gaussian      9
Gaussian curvature      65
Gaussian entropy      47
Gaussian Fisher metric      47
Gaussian manifold      47
Gaussian orthogonal foliations      48
Gaussian truncated      43
Gaussian univariate      45
Gaussians neighbourhood of independence      114
Generalized gamma distribution      225
Generalized McKay      72
Generalized Poisson      14
Genome      139
Geodesic      66
Geodesic curve      29
Geodesic dilation      204 205
Geodesic distance      204
Geodesic distance approximations      145
Geodesic foliation      146
Geodesic mesh      146
Geodesic spray      41
Geodesic sprays      133
Glass fibre network      161
Glass spheres      213
Grains      201
Graph immersion      36
Greyscale      205
Greyscale reconstruction      207
Ground state correlation      180 181
H-extrema      208
H-maxima      208
H-maxima transform      208
H-minima      208
H-minima transform      208
hessian      37 47 60
Horizontal gamma geodesic      136
Horizontal lift      27
Horizontal subbundle      27
Horizontal subspace      27
Hydrology      195
Hydrophobicity      151
Idempotence      205
Identical marginals      85 101
Image analysis      201 216
Image histogram      209
Image segmentation      209
Increased contrast      175
Independence submanifold      99
Independent      10
Independent polygon sides      171
Induced connection      36
Inductive probes      154
Information energy      186
Information length      145
Information metric      31 33 219
Information source      11
Information theory      11
Inner product      25
Inscribed circles      164 173
Inter-crossing intervals      171
Inter-event distance      9
Inter-event distances      12
Inter-event spacing      5
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