Quantum Bio-Informatics: From Quantum Information to Bio-informatics: Tokyo University of Science, Japan, 14-17 March 2007 (Quantum Probability and White Noise Analysis)

CONTENTS......Page 8
Preface......Page 6
1. Introduction......Page 12
2. Graphs......Page 14
3. Bundles on graphs......Page 15
4. Definition of QMF......Page 16
5. 1-dimensional weak Markov states......Page 18
6. Entangled Markov fields on trees......Page 21
7. Maximally Entangled Markov fields on general graphs......Page 26
7.1. Interpretation......Page 29
References......Page 30
2. Classical and Quantum mathematical models in Bio-Sciences......Page 31
3. Towards new stage of Quantum Information and Life Science......Page 34
1. Introduction......Page 37
2.1. Definition and examples......Page 38
2.2. Time-Energy Uncertainty Relation......Page 41
3. Strong Time Operators......Page 42
5 . Strong Time Operators on Direct Sum Hilbert Spaces......Page 44
6.1. A class of perturbed Aharonov-Bohm time operators......Page 45
References......Page 46
1. Introduction......Page 47
1.1. Entropic Chaos Degree......Page 48
2. Algorithm Computing Entropic Chaos Degree......Page 49
3. Rotations Map and its Entropic Chaos Degree......Page 51
4. Log-linear Dynamics and Chaos Degree......Page 53
4.1. Function of Gr......Page 55
4.2. Relation of (A, G) and ( M , L M )......Page 58
4.3. Entropic Chaos Degree of Log-linear Dynamics......Page 59
4.4. Two Viewpoints to Log-linear Dynamics......Page 62
References......Page 63
1. Introduction......Page 64
2. Master equation......Page 66
3. General Formalism......Page 67
3.1. The equations......Page 68
3.3. A variational principle......Page 69
4. A one-qubit example......Page 70
5 . Summary......Page 72
ACKNOWLEDGEMENTS......Page 73
References......Page 74
On a Quantum Model of the Recognition Process K.-H. Fichtner, L. Fichtner, W. Freudenberg and M. Ohya......Page 75
1. Introduction......Page 76
2.1. The Boson Fock Space......Page 78
2.2. Exponential Vectors - Coherent States......Page 82
2.3. The Space of Elementary Signals......Page 84
3.1. Jntroduction......Page 88
3.2. A Model for Recognition of a Signal by Projections......Page 89
3.3. Properties of the Symmetric Beam Splitter......Page 91
3.4. Approximation of by a Splitting Procedure......Page 92
References......Page 93
1. Introduction......Page 96
2.1. Chern-Simons models......Page 97
2.2. Torus gauge fixing applied to Chern-Simons models......Page 98
3. Finding a rigorous realization of the r.h.s. of Eq. (12)......Page 101
References......Page 106
Introduction......Page 108
1. Finite-dimensional systems......Page 109
2. Quantum lattice systems......Page 111
3. Free energy density in perturbation of Gibbs states......Page 113
4. Free pressure in free probability theory......Page 117
References......Page 120
1. Prologue......Page 122
2. Generalized white noise functional......Page 124
3. Differential calculus......Page 127
4. Infinite dimensional rotation group......Page 129
5.1. 1 ) Finite dimensional approximations.......Page 131
5.2. 2) Continuously many dimensional measures.......Page 132
6. Duality in stochastic analysis......Page 133
References......Page 136
2. Quantum Algorithm......Page 137
3. OMV SAT algorithm......Page 139
3.1. OM algorithm......Page 140
3.2. OV algorithm......Page 142
4.1. Generalized Quantum Turing Machine......Page 143
4.3. Language classes defined by GQTM......Page 146
4.4. GQTM for OV algorithm......Page 147
4.5. Computational complexity of the SAT algorithm......Page 148
5. GQTM for partial recursive function......Page 149
References......Page 151
1. Introduction......Page 153
2. Observability of Classical Stochastic Systems......Page 155
3. Minimalization of the Number of Measurements......Page 163
4. Unconditional Observability......Page 165
5. Observability of Generalized Birth-and-Death Processes......Page 167
6. Final Remarks......Page 170
References......Page 171
1. Introduction......Page 172
2. Reduced dynamics in the Heisenberg picture......Page 174
3. The Friedrichs approximation......Page 176
References......Page 179
1. Introduction......Page 181
2.1. Pure state......Page 182
2.2. Classification of quantum compound states via entangling operator......Page 184
3. Relation between PPT condition and q-entanglement......Page 188
References......Page 191
1. Introduction......Page 192
1.2. Schematic Expression of Understanding......Page 194
2.1. Description of chaos......Page 195
2.2. Chameleon dynamics......Page 196
2.3. Quantum SAT algorithm......Page 197
2.4. Summary......Page 198
3. Adaptive Dynamics Describing Chaos......Page 199
3.1. Information Dynamics......Page 200
3.1.1. State change and complexities......Page 201
3.2. Entropic Chaos Degree......Page 204
3.3. Algorithm computing Entropic Chaos Degree......Page 205
3.3.1. ECD with memory......Page 208
3.4. Adaptive Chaos Degree......Page 210
3.4.1. Chaos degree with adaptivity......Page 213
4.1. SAT problem......Page 214
4.2. Quantum Algorithm......Page 216
4.2.1. Channel expression of conventional unitary algorithm......Page 217
4.3. Quantum Algorithm of SAT......Page 218
4.4. Quantum chaos algorithm......Page 220
4.5. Stochastic limit and adaptive SAT problem......Page 222
References......Page 225
1. Sectors as Quantum-Classical Boundary......Page 228
2. Instruments for Intra-sectorial Searches......Page 229
3. Amplification in Intra-sectorial Measurements......Page 233
4. From Amplification to Emergence of Macro......Page 235
References......Page 238
1. Introduction......Page 240
2. Two-potential formulation......Page 243
3.1. Basic theory......Page 245
3.2. Numerical method......Page 248
4. Difficulty of the Coulomb renormalization approach in the three-body problem......Page 250
5. Conclusion and discussion......Page 253
Acknowledgements......Page 256
References......Page 257
1. Introduction......Page 258
2. An estimation scheme for k-level systems......Page 259
3. Estimation schemes for 2-level systems......Page 261
3.1. Non-complementary observables......Page 263
3.2. Diflerent measurement numbers......Page 264
3.3. Adaptive measurement schemes......Page 265
References......Page 267
1. Introduction......Page 269
3. Results and Discussion......Page 270
References......Page 275
1. Introduction......Page 277
2. Unitary representations of a symmetric group S ( n )......Page 278
3. Projective limit of S ( n ) and quadratic Hida distributions......Page 279
References......Page 283
1. Basic ideas......Page 284
2. Entropy change and quantum analysis......Page 286
3. Generalized linear response theory......Page 289
4. Simple application to classical stochastic resonance......Page 292
5 . Simple application to quantum spin systems......Page 294
6. Discussion......Page 296
References......Page 297
1. Introduction......Page 299
3. Parametric Control of the Qubit......Page 300
4. Vacuum Rabi Oscillations in a Macroscopic Superconducting Qubit LC Oscillator System......Page 302
References......Page 304
The Analysis of Gene Expression and Cis-Regulatory Elements in Large Microarray Expression Datasets D. Wanke, J. Kilian, J . Supper, K . W . Berendzen, A. Zell and K. Harter......Page 305
1. Introduction......Page 306
2.1. Arabidopsis thaliana Gene Expression Data......Page 308
2.4. Two-step Clustering......Page 309
2.7. Comparative Analysis of Gene Expression......Page 310
3. Results......Page 311
4. Conclusions......Page 323
References......Page 324
1. Introduction......Page 326
2. Quantum Channels......Page 327
3. Ohya Mutual Entropy and Capacity......Page 328
4.1. Attenuation channel......Page 329
5. Quantum Mutual Type Entropies......Page 330
6. Numerical Calculation of Quantum Mutual Type Measures......Page 331
References......Page 334
1.1. Statistical Models......Page 336
1.2. Regular and Singular Statistical Models......Page 337
2.1. Standard Form of Singular Likelihood......Page 339
3. Maximum Likelihood and Maximum A Posteriori......Page 341
4.1. Theoretical Results......Page 343
4.2. Mean Fie Id Approximation......Page 344
References......Page 345
1. Introduction......Page 348
2.1. Models of symmetry......Page 349
2.2. Models of asymmetry......Page 350
2.3. Models of symmetry and asymmetry based o n cumulative probabilities......Page 351
3. Test......Page 352
4.2. Analysis of Table 2......Page 353
4.4. Analysis of Table 4......Page 354
5 . Concluding remarks......Page 355
References......Page 356
1. Introduction......Page 361
3. The important role of two kinds of multiplets......Page 362
4. An extended two-story house model (The K-S model)......Page 364
5. Mechanism of high temperature superconductivity......Page 366
References:......Page 368
1. Introduction......Page 370
2.1. Helical geometry......Page 372
2.2. Helical restraint potential......Page 374
3. Simulation Stability with Restraint Potentials......Page 375
4. Applications......Page 376
4.1. Helix-helix association of pVNVV......Page 377
4.2. Helical tilting of WALPIS......Page 378
5 . Concluding discussion......Page 379
References......Page 380
1.2. Base composition of the upstream regions......Page 382
1.3. Search for cis element-like sequence of the upstream region......Page 383
2. Analysis of correlation between the diversity of &-elements sequences and the DNA binding domain structures of transcription factors.......Page 384
2.1. The acquisition of data......Page 385
2.4. Hierarchical clustering of cis-elements......Page 386
2.5. Results and Discussion......Page 388
3.2. Verification of training data set......Page 389
3.3. Quantification and identzjkation of functional site......Page 390
References......Page 391
1. Introduction......Page 392
2. Large Scale mRNA Expression Analysis of Phytohormone Signaling......Page 393
3. Utilization of Coexpressed Gene Data for Identification of Regulatory Factor of Phytohormone Signaling......Page 395
References......Page 398
2. Multiple Alignment by Quantum Algorithm......Page 400
2.1. Quantum Algorithm......Page 402
2.2. Quantum Algorithm of Multiple Alignment......Page 403
3.1. How to encode genes......Page 404
3.2. Entropy Evolution Rate......Page 406
3.3. HIV-1 gene analysis by coding theory......Page 407
4.1. The Complexity of Information dynamics and Chaos degree......Page 411
4.2. Analysis of the disease course of HIV-1 by Entropic Chaos Degree......Page 412
References......Page 414
1. Introduction......Page 416
2. Theoretical Approach......Page 419
3. Present Status and Future Plans......Page 420
4. Conclusion......Page 421
References......Page 422
1. Introduction......Page 423
2. Origin and Evolution of MHC-B and MHC-C......Page 425
3. Origin and Evolution of MICA and MICB......Page 428
4. Divergence Time of Rhesus Monkey......Page 429
5. Discussion......Page 431
References......Page 435
1. Introduction......Page 438
2. The discrete case......Page 441
3. The continuous case......Page 445
4. The non-commutative case......Page 448
References......Page 450
1. Introduction......Page 451
1.1. Structure prediction......Page 452
1.3. Free energy calculation of binding affinity (Function prediction- quantitative)......Page 453
2. Brownian dynamics simulation for structure prediction (15-171......Page 454
2.1. Brownian dynamics simulation [IS]......Page 455
2.2. BDin membrane environment......Page 456
2.3. Development of a volunteer computing project, “TANPAKU” (Fig. 5)......Page 457
2.4. Conclusions and perspectives......Page 458
3.1. Algorithm of FCANAL (Fig. 6)......Page 459
3.2. An example (Application of FCANAL to carbonic dehydratase)......Page 461
4. Free energy calculation......Page 462
5. Systems biology......Page 463
Acknowledgements......Page 464
References......Page 465